Changeset 61


Ignore:
Timestamp:
Mar 12, 2007 5:42:06 AM (15 years ago)
Author:
raasch
Message:

further preliminary changes for revision 3.2

Location:
palm/trunk
Files:
9 edited

Legend:

Unmodified
Added
Removed
  • palm/trunk/DOC/app/chapter_3.7.html

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    11<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
    2 <html>
    3 <head>
    4   <meta http-equiv="CONTENT-TYPE"
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    6   <title>PALM chapter 3.7</title>
    7   <meta name="GENERATOR" content="StarOffice 7  (Win32)">
    8   <meta name="AUTHOR" content="Siegfried Raasch">
    9   <meta name="CREATED" content="20040809;13460943">
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    11   <meta name="KEYWORDS" content="parallel LES model">
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    17 </head>
    18 <body dir="ltr" lang="en-US">
    19 <h3 style="line-height: 100%;">3.7 Optional software packages</h3>
    20 <p style="line-height: 100%;">Starting from version 2.1 PALM includes
     2<html><head>
     3<meta http-equiv="CONTENT-TYPE" content="text/html; charset=windows-1252"><title>PALM
     4chapter 3.7</title> <meta name="GENERATOR" content="StarOffice 7 (Win32)"> <meta name="AUTHOR" content="Siegfried Raasch"> <meta name="CREATED" content="20040809;13460943"> <meta name="CHANGED" content="20041112;15085727"> <meta name="KEYWORDS" content="parallel LES model"> <style>
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     8</style></head>
     9
     10<body style="direction: ltr;" lang="en-US"><h3 style="line-height: 100%;">3.7 Optional software packages</h3>
     11<p style="line-height: 100%;">Starting from version 2.1
     12PALM includes
    2113so-called software packages which can be used optionally. These
    2214software packages are part of the model, but they are not compiled with
     
    2719compilation time as well as the memory demand of the model is limited
    2820to the real needs. </p>
    29 <p style="line-height: 100%;">To use software packages in a model run,
    30 they must be requested with <b>mrun</b> option <tt><font
    31  style="font-size: 10pt;" size="2">-p</font>.</tt>
     21<p style="line-height: 100%;">To use software packages in
     22a model run,
     23they must be requested with <b>mrun</b> option <tt><font style="font-size: 10pt;" size="2">-p</font>.</tt>
    3224Then the subroutines belonging to the respective package are
    3325additionally compiled for the run (and the respective restart
    3426runs; the filenames of these subroutines are also displayed on the
    35 terminal after <b>mrun</b> has been called). If one wants to use e.g.
     27terminal after <b>mrun</b> has been called). If one wants
     28to use e.g.
    3629the two packages with the names
    37 <tt>package1</tt> and <tt>package2</tt>, then the <b>mrun</b> call
     30<tt>package1</tt> and <tt>package2</tt>, then
     31the <b>mrun</b> call
    3832has to be: </p>
    39 <ul>
    40   <p style="line-height: 100%;"><tt><font style="font-size: 10pt;"
    41  size="2">mrun ... -p “package1 package2” </font>.</tt></p>
    42 </ul>
    43 <p style="line-height: 100%;">Further package names can be added to
     33<ul> <p style="line-height: 100%;"><tt><font style="font-size: 10pt;" size="2">mrun ... -p
     34&ldquo;package1 package2&rdquo; </font>.</tt></p>
     35</ul><p style="line-height: 100%;">Starting from version 3.2, the particles-package is part of the default model, so it does not have to be switched on using <span style="font-weight: bold;">mrun</span>-option <span style="font-family: Courier New,Courier,monospace;">-p</span>. However, the respective parameters have still to be set by using the NAMELIST group <span style="font-family: Courier New,Courier,monospace;">particles_par</span>.</p><p style="line-height: 100%;">Further package
     36names can be added to
    4437the list, separated by blanks. If the respective packages permit user
    4538steering, the appropriate parameters must be given at the end of
    4639the file <a href="chapter_3.4.html#PARIN">PARIN</a>.
    47 They must be given <b>before</b> possible user-defined parameters!
     40They must be given <b>before</b> possible user-defined
     41parameters!
    4842Each package requires its own NAMELIST group. The respective NAMELIST
    4943group name is given in the table below. For the example above one
    5044would have to add the following lines to PARIN (example): &nbsp; </p>
    51 <ul>
    52   <p style="line-height: 100%;"><tt><font style="font-size: 10pt;"
    53  size="2">&amp;namelist_packagename1 var1 = 1,0, var2 =
    54 “abcd” /</font></tt><font style="font-size: 10pt;" size="2"> </font> </p>
    55   <p style="line-height: 100%;"><tt><font style="font-size: 10pt;"
    56  size="2">&amp;namelist_packagename2 var3 = .TRUE.,
     45<ul> <p style="line-height: 100%;"><tt><font style="font-size: 10pt;" size="2">&amp;namelist_packagename1
     46var1 = 1,0, var2 =
     47&ldquo;abcd&rdquo; /</font></tt><font style="font-size: 10pt;" size="2"> </font> </p>
     48<p style="line-height: 100%;"><tt><font style="font-size: 10pt;" size="2">&amp;namelist_packagename2
     49var3 = .TRUE.,
    5750var4 = 0 /</font></tt></p>
    58 </ul>
    59 <p style="margin-bottom: 0cm; line-height: 100%;">The following
     51</ul><p style="margin-bottom: 0cm; line-height: 100%;">The
     52following
    6053packages are available: <br>
    6154&nbsp; <br>
    6255&nbsp; </p>
    63 <table border="1" cellpadding="2" cellspacing="2" width="100%">
    64   <tbody>
    65     <tr>
    66       <td>
    67       <p><b>Package name:</b></p>
    68       </td>
    69       <td>
    70       <p><b>NAMELIST group name:</b></p>
    71       </td>
    72       <td>
    73       <p><b>Functionality:</b></p>
    74       </td>
    75       <td>
    76       <p><b>Control parameter:</b></p>
    77       </td>
    78     </tr>
    79     <tr valign="top">
    80       <td>
    81       <p>particles</p>
    82       </td>
    83       <td>
    84       <p>particles_par</p>
    85       </td>
    86       <td>
    87       <p>Release and advection of particles. The particle sources can
    88 additionally be defined by the user in subroutine <tt><font
    89  style="font-size: 10pt;" size="2">user_init_particles</font></tt> .</p>
    90       </td>
    91       <td>
    92       <p>see section 4.2</p>
    93       </td>
    94     </tr>
    95     <tr valign="top">
    96       <td>
    97       <p>dvrp_graphics</p>
    98       </td>
    99       <td>
    100       <p>dvrp_graphics_par</p>
    101       </td>
    102       <td>
    103       <p>Graphical output with the dvrp software of the RRZN. This is
     56<table border="1" cellpadding="2" cellspacing="2" width="100%"> <tbody> <tr> <td> <p><b>Package
     57name:</b></p> </td> <td> <p><b>NAMELIST
     58group name:</b></p> </td> <td> <p><b>Functionality:</b></p>
     59</td> <td> <p><b>Control parameter:</b></p>
     60</td> </tr> <tr valign="top"> <td> <p>--- (see above)</p>
     61</td> <td> <p>particles_par</p> </td> <td>
     62<p>Release and advection of particles. The particle sources can
     63additionally be defined by the user in subroutine <tt><font style="font-size: 10pt;" size="2">user_init_particles</font></tt>
     64.</p> </td> <td> <p>see section 4.2</p>
     65</td> </tr> <tr valign="top"> <td> <p>dvrp_graphics</p>
     66</td> <td> <p>dvrp_graphics_par</p> </td>
     67<td> <p>Graphical output with the dvrp software of the
     68RRZN. This is
    10469only available on the IBM Regatta "hanni" of the HLRN. Possible output
    10570are iso-surfaces, cross-sections and particles (if the particle package
    106 is selected). The use of this package is described in section <a
    107  href="chapter_4.5.7.html">4.5.7</a>.</p>
    108       </td>
    109       <td>
    110       <p>see section 4.2</p>
    111       </td>
    112     </tr>
    113     <tr valign="top">
    114       <td>
    115       <p>spectra</p>
    116       </td>
    117       <td>
    118       <p>spectra_par</p>
    119       </td>
    120       <td>
    121       <p>Computation and output of horizontal power spectra of the
    122 prognostic variables. </p>
    123       </td>
    124       <td>
    125       <p>see section <a href="chapter_4.2.html#spectra_package">4.2</a></p>
    126       </td>
    127     </tr>
    128   </tbody>
    129 </table>
    130 <hr>
    131 <p style="line-height: 100%;"><br>
    132 <font color="#000080"><font color="#000080"><a href="chapter_3.6.html"><font
    133  color="#000080"><img src="left.gif" name="Grafik1" align="bottom"
    134  border="2" height="32" width="32"></font></a><a href="index.html"><font
    135  color="#000080"><img src="up.gif" name="Grafik2" align="bottom"
    136  border="2" height="32" width="32"></font></a><a href="chapter_4.0.html"><font
    137  color="#000080"><img src="right.gif" name="Grafik3" align="bottom"
    138  border="2" height="32" width="32"></font></a></font></font></p>
    139 <p style="line-height: 100%;"><i>Last change:&nbsp;</i> 15/04/05 (SR)</p>
    140 </body>
    141 </html>
     71is selected). The use of this package is described in section <a href="chapter_4.5.7.html">4.5.7</a>.</p> </td>
     72<td> <p>see section 4.2</p> </td> </tr>
     73<tr valign="top"> <td> <p>spectra</p> </td>
     74<td> <p>spectra_par</p> </td> <td> <p>Computation
     75and output of horizontal power spectra of the
     76prognostic variables. </p> </td> <td> <p>see
     77section <a href="chapter_4.2.html#spectra_package">4.2</a></p>
     78</td> </tr> </tbody>
     79</table><hr>
     80<p style="line-height: 100%;"><br><font color="#000080"><font color="#000080"><a href="chapter_3.6.html"><font color="#000080"><img src="left.gif" name="Grafik1" align="bottom" border="2" height="32" width="32"></font></a><a href="index.html"><font color="#000080"><img src="up.gif" name="Grafik2" align="bottom" border="2" height="32" width="32"></font></a><a href="chapter_4.0.html"><font color="#000080"><img src="right.gif" name="Grafik3" align="bottom" border="2" height="32" width="32"></font></a></font></font></p>
     81<p style="line-height: 100%;"><i>Last
     82change:&nbsp;</i> $Id$</p>
     83</body></html>
  • palm/trunk/DOC/app/chapter_4.1.html

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    35 <h3><a name="chapter4.1"></a>4.1 Initialization parameters</h3>
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    90       <td style="vertical-align: top;"><font size="4"><b>Parameter name</b></font></td>
    91 
    92 
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    101       <td style="vertical-align: top;"><font size="4"><b>Type</b></font></td>
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    120      
    121      
    122      
    123       <p><b><font size="4">Default</font></b> <br>
    124 
    125 
    126 
    127 
    128 
    129 
    130 
    131 
    132 
    133 
    134       <b><font size="4">value</font></b></p>
    135 
    136 
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    145       </td>
    146 
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    156       <td style="vertical-align: top;"><font size="4"><b>Explanation</b></font></td>
    157 
    158 
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    166 
    167     </tr>
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    189       <td style="vertical-align: top;">
    190      
    191      
    192      
    193      
    194      
    195      
    196      
    197      
    198      
    199      
    200       <p><a name="adjust_mixing_length"></a><b>adjust_mixing_length</b></p>
    201 
    202 
    203 
    204 
    205 
    206 
    207 
    208 
    209 
    210 
    211       </td>
    212 
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    222       <td style="vertical-align: top;">L</td>
    223 
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    232 
    233       <td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td>
    234 
    235 
    236 
    237 
    238 
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    240 
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    242 
    243 
    244       <td style="vertical-align: top;">
    245      
    246      
    247      
    248      
    249      
    250      
    251      
    252      
    253      
    254      
    255       <p style="font-style: normal;">Near-surface adjustment of the
    256 mixing length to the Prandtl-layer law.&nbsp; </p>
    257 
    258 
    259 
    260 
    261 
    262 
    263 
    264 
    265 
    266 
    267      
    268      
    269      
    270      
    271      
    272      
    273      
    274      
    275      
    276      
    277       <p>Usually the mixing length in LES models l<sub>LES</sub>
     3<meta http-equiv="content-type" content="text/html; charset=ISO-8859-1"><title>PALM
     4chapter 4.1</title></head>
     5<body><h3><a name="chapter4.1"></a>4.1
     6Initialization parameters</h3>
     7<br><table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody>
     8<tr> <td style="vertical-align: top;"><font size="4"><b>Parameter name</b></font></td>
     9<td style="vertical-align: top;"><font size="4"><b>Type</b></font></td>
     10<td style="vertical-align: top;"> <p><b><font size="4">Default</font></b> <br> <b><font size="4">value</font></b></p> </td>
     11<td style="vertical-align: top;"><font size="4"><b>Explanation</b></font></td>
     12</tr> <tr> <td style="vertical-align: top;">
     13<p><a name="adjust_mixing_length"></a><b>adjust_mixing_length</b></p>
     14</td> <td style="vertical-align: top;">L</td>
     15<td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td> <td style="vertical-align: top;"> <p style="font-style: normal;">Near-surface adjustment of the
     16mixing length to the Prandtl-layer law.&nbsp; </p> <p>Usually
     17the mixing length in LES models l<sub>LES</sub>
    27818depends (as in PALM) on the grid size and is possibly restricted
    27919further in case of stable stratification and near the lower wall (see
    28020parameter <a href="#wall_adjustment">wall_adjustment</a>).
    28121With <b>adjust_mixing_length</b> = <span style="font-style: italic;">.T.</span>
    282 the Prandtl' mixing length l<sub>PR</sub> = kappa * z/phi is calculated
     22the Prandtl' mixing length l<sub>PR</sub> = kappa * z/phi
     23is calculated
    28324and the mixing length actually used in the model is set l = MIN (l<sub>LES</sub>,
    284 l<sub>PR</sub>). This usually gives a decrease of the mixing length at
     25l<sub>PR</sub>). This usually gives a decrease of the
     26mixing length at
    28527the bottom boundary and considers the fact that eddy sizes
    286 decrease in the vicinity of the wall.&nbsp; </p>
    287 
    288 
    289 
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    301      
    302      
    303      
    304      
    305      
    306      
    307       <p style="font-style: normal;"><b>Warning:</b> So far, there is
     28decrease in the vicinity of the wall.&nbsp; </p> <p style="font-style: normal;"><b>Warning:</b> So
     29far, there is
    30830no good experience with <b>adjust_mixing_length</b> = <span style="font-style: italic;">.T.</span> !&nbsp; </p>
    309 
    310 
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    320      
    321      
    322      
    323      
    324      
    325      
    326      
    327      
    328      
    329       <p>With <b>adjust_mixing_length</b> = <span style="font-style: italic;">.T.</span> and the Prandtl-layer being
    330 switched on (see <a href="#prandtl_layer">prandtl_layer</a>) <span style="font-style: italic;">'(u*)** 2+neumann'</span>
     31<p>With <b>adjust_mixing_length</b> = <span style="font-style: italic;">.T.</span> and the
     32Prandtl-layer being
     33switched on (see <a href="#prandtl_layer">prandtl_layer</a>)
     34<span style="font-style: italic;">'(u*)** 2+neumann'</span>
    33135should always be set as the lower boundary condition for the TKE (see <a href="#bc_e_b">bc_e_b</a>),
    33236otherwise the near-surface value of the TKE is not in agreement with
    33337the Prandtl-layer law (Prandtl-layer law and Prandtl-Kolmogorov-Ansatz
    334 should provide the same value for K<sub>m</sub>). A warning is given,
    335 if this is not the case.</p>
    336 
    337 
    338 
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    341 
    342 
    343 
    344 
    345 
    346       </td>
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    379       <td style="vertical-align: top;">
    380      
    381      
    382      
    383      
    384      
    385      
    386      
    387      
    388      
    389      
    390       <p><a name="alpha_surface"></a><b>alpha_surface</b></p>
    391 
    392 
    393 
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    396 
    397 
    398 
    399 
    400 
    401       </td>
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    412       <td style="vertical-align: top;">R<br>
    413 
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    422 
    423       </td>
    424 
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    434       <td style="vertical-align: top;"><span style="font-style: italic;">0.0</span><br>
    435 
    436 
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    444 
    445       </td>
    446 
    447 
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    456       <td style="vertical-align: top;">
    457      
    458      
    459      
    460      
    461      
    462      
    463      
    464      
    465      
    466      
    467       <p style="font-style: normal;">Inclination of the model domain
    468 with respect to the horizontal (in degrees).&nbsp; </p>
    469 
    470 
    471 
    472 
    473 
    474 
    475 
    476 
    477 
    478 
    479      
    480      
    481      
    482      
    483      
    484      
    485      
    486      
    487      
    488      
    489       <p style="font-style: normal;">By means of <b>alpha_surface</b>
     38should provide the same value for K<sub>m</sub>). A warning
     39is given,
     40if this is not the case.</p> </td> </tr> <tr>
     41<td style="vertical-align: top;"> <p><a name="alpha_surface"></a><b>alpha_surface</b></p>
     42</td> <td style="vertical-align: top;">R<br> </td>
     43<td style="vertical-align: top;"><span style="font-style: italic;">0.0</span><br> </td>
     44<td style="vertical-align: top;"> <p style="font-style: normal;">Inclination of the model domain
     45with respect to the horizontal (in degrees).&nbsp; </p> <p style="font-style: normal;">By means of <b>alpha_surface</b>
    49046the model domain can be inclined in x-direction with respect to the
    49147horizontal. In this way flows over inclined surfaces (e.g. drainage
    492 flows, gravity flows) can be simulated. In case of <b>alpha_surface </b>/=
    493       <span style="font-style: italic;">0</span> the buoyancy term
     48flows, gravity flows) can be simulated. In case of <b>alpha_surface
     49</b>/= <span style="font-style: italic;">0</span>
     50the buoyancy term
    49451appears both in
    49552the equation of motion of the u-component and of the w-component.<br>
    496 
    497 
    498 
    499 
    500 
    501 
    502 
    503 
    504 
    505 
    506       </p>
    507 
    508 
    509 
    510 
    511 
    512 
    513 
    514 
    515 
    516 
    517      
    518      
    519      
    520      
    521      
    522      
    523      
    524      
    525      
    526      
    527       <p style="font-style: normal;">An inclination is only possible in
     53</p> <p style="font-style: normal;">An inclination
     54is only possible in
    52855case of cyclic horizontal boundary conditions along x AND y (see <a href="#bc_lr">bc_lr</a>
    52956and <a href="#bc_ns">bc_ns</a>) and <a href="#topography">topography</a> = <span style="font-style: italic;">'flat'</span>. </p>
    530 
    531 
    532 
    533 
    534 
    535 
    536 
    537 
    538 
    539 
    540      
    541      
    542      
    543      
    544      
    545      
    546      
    547      
    548      
    549      
    550       <p>Runs with inclined surface still require additional
     57<p>Runs with inclined surface still require additional
    55158user-defined code as well as modifications to the default code. Please
    55259ask the <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/PALM_group.html#0">PALM
    553 developer&nbsp; group</a>.</p>
    554 
    555 
    556 
    557 
    558 
    559 
    560 
    561 
    562 
    563 
    564       </td>
    565 
    566 
    567 
    568 
    569 
    570 
    571 
    572 
    573 
    574 
    575     </tr>
    576 
    577 
    578 
    579 
    580 
    581 
    582 
    583 
    584 
    585 
    586     <tr>
    587 
    588 
    589 
    590 
    591 
    592 
    593 
    594 
    595 
    596 
    597       <td style="vertical-align: top;">
    598      
    599      
    600      
    601      
    602      
    603      
    604      
    605      
    606      
    607      
    608       <p><a name="bc_e_b"></a><b>bc_e_b</b></p>
    609 
    610 
    611 
    612 
    613 
    614 
    615 
    616 
    617 
    618 
    619       </td>
    620 
    621 
    622 
    623 
    624 
    625 
    626 
    627 
    628 
    629 
    630       <td style="vertical-align: top;">C * 20</td>
    631 
    632 
    633 
    634 
    635 
    636 
    637 
    638 
    639 
    640 
    641       <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
    642 
    643 
    644 
    645 
    646 
    647 
    648 
    649 
    650 
    651 
    652       <td style="vertical-align: top;">
    653      
    654      
    655      
    656      
    657      
    658      
    659      
    660      
    661      
    662      
    663       <p style="font-style: normal;">Bottom boundary condition of the
    664 TKE.&nbsp; </p>
    665 
    666 
    667 
    668 
    669 
    670 
    671 
    672 
    673 
    674 
    675      
    676      
    677      
    678      
    679      
    680      
    681      
    682      
    683      
    684      
    685       <p><b>bc_e_b</b> may be set to&nbsp;<span style="font-style: italic;">'neumann'</span> or <span style="font-style: italic;">'(u*) ** 2+neumann'</span>. <b>bc_e_b</b>
    686 = <span style="font-style: italic;">'neumann'</span> yields to
     60developer&nbsp; group</a>.</p> </td> </tr>
     61<tr> <td style="vertical-align: top;"> <p><a name="bc_e_b"></a><b>bc_e_b</b></p> </td>
     62<td style="vertical-align: top;">C * 20</td> <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
     63<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     64TKE.&nbsp; </p> <p><b>bc_e_b</b> may be
     65set to&nbsp;<span style="font-style: italic;">'neumann'</span>
     66or <span style="font-style: italic;">'(u*) ** 2+neumann'</span>.
     67<b>bc_e_b</b>
     68= <span style="font-style: italic;">'neumann'</span>
     69yields to
    68770e(k=0)=e(k=1) (Neumann boundary condition), where e(k=1) is calculated
    688 via the prognostic TKE equation. Choice of <span style="font-style: italic;">'(u*)**2+neumann'</span> also yields to
     71via the prognostic TKE equation. Choice of <span style="font-style: italic;">'(u*)**2+neumann'</span>
     72also yields to
    68973e(k=0)=e(k=1), but the TKE at the Prandtl-layer top (k=1) is calculated
    69074diagnostically by e(k=1)=(us/0.1)**2. However, this is only allowed if
    69175a Prandtl-layer is used (<a href="#prandtl_layer">prandtl_layer</a>).
    692 If this is not the case, a warning is given and <b>bc_e_b</b> is reset
    693 to <span style="font-style: italic;">'neumann'</span>.&nbsp; </p>
    694 
    695 
    696 
    697 
    698 
    699 
    700 
    701 
    702 
    703 
    704      
    705      
    706      
    707      
    708      
    709      
    710      
    711      
    712      
    713      
    714       <p style="font-style: normal;">At the top boundary a Neumann
    715 boundary condition is generally used: (e(nz+1) = e(nz)).</p>
    716 
    717 
    718 
    719 
    720 
    721 
    722 
    723 
    724 
    725 
    726       </td>
    727 
    728 
    729 
    730 
    731 
    732 
    733 
    734 
    735 
    736 
    737     </tr>
    738 
    739 
    740 
    741 
    742 
    743 
    744 
    745 
    746 
    747 
    748     <tr>
    749 
    750 
    751 
    752 
    753 
    754 
    755 
    756 
    757 
    758 
    759       <td style="vertical-align: top;">
    760      
    761      
    762      
    763      
    764      
    765      
    766      
    767      
    768      
    769      
    770       <p><a name="bc_lr"></a><b>bc_lr</b></p>
    771 
    772 
    773 
    774 
    775 
    776 
    777 
    778 
    779 
    780 
    781       </td>
    782 
    783 
    784 
    785 
    786 
    787 
    788 
    789 
    790 
    791 
    792       <td style="vertical-align: top;">C * 20</td>
    793 
    794 
    795 
    796 
    797 
    798 
    799 
    800 
    801 
    802 
    803       <td style="vertical-align: top;"><span style="font-style: italic;">'cyclic'</span></td>
    804 
    805 
    806 
    807 
    808 
    809 
    810 
    811 
    812 
    813 
    814       <td style="vertical-align: top;">Boundary
    815 condition along x (for all quantities).<br>
    816 
    817 
    818 
    819 
    820 
    821 
    822 
    823 
    824 
    825 
    826       <br>
    827 
    828 
    829 
    830 
    831 
    832 
    833 
    834 
    835 
    836 
    837 By default, a cyclic boundary condition is used along x.<br>
    838 
    839 
    840 
    841 
    842 
    843 
    844 
    845 
    846 
    847 
    848       <br>
    849 
    850 
    851 
    852 
    853 
    854 
    855 
    856 
    857 
    858 
    859       <span style="font-weight: bold;">bc_lr</span> may also be
     76If this is not the case, a warning is given and <b>bc_e_b</b>
     77is reset
     78to <span style="font-style: italic;">'neumann'</span>.&nbsp;
     79</p> <p style="font-style: normal;">At the top
     80boundary a Neumann
     81boundary condition is generally used: (e(nz+1) = e(nz)).</p> </td>
     82</tr> <tr> <td style="vertical-align: top;">
     83<p><a name="bc_lr"></a><b>bc_lr</b></p>
     84</td> <td style="vertical-align: top;">C * 20</td>
     85<td style="vertical-align: top;"><span style="font-style: italic;">'cyclic'</span></td>
     86<td style="vertical-align: top;">Boundary
     87condition along x (for all quantities).<br> <br>
     88By default, a cyclic boundary condition is used along x.<br> <br>
     89<span style="font-weight: bold;">bc_lr</span> may
     90also be
    86091assigned the values <span style="font-style: italic;">'dirichlet/neumann'</span>
    861 (inflow from left, outflow to the right) or <span style="font-style: italic;">'neumann/dirichlet'</span> (inflow from
     92(inflow from left, outflow to the right) or <span style="font-style: italic;">'neumann/dirichlet'</span>
     93(inflow from
    86294right, outflow to the left). This requires the multi-grid method to be
    86395used for solving the Poisson equation for perturbation pressure (see <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">psolver</a>)
    864 and it also requires cyclic boundary conditions along y (see<br>
    865 
    866 
    867 
    868 
    869 
    870 
    871 
    872 
    873 
    874 
    875       <a href="#bc_ns">bc_ns</a>).<br>
    876 
    877 
    878 
    879 
    880 
    881 
    882 
    883 
    884 
    885 
    886       <br>
    887 
    888 
    889 
    890 
    891 
    892 
    893 
    894 
    895 
    896 
     96and it also requires cyclic boundary conditions along y (see<br> <a href="#bc_ns">bc_ns</a>).<br> <br>
    89797In case of these non-cyclic lateral boundaries, a Dirichlet condition
    89898is used at the inflow for all quantities (initial vertical profiles -
     
    906106free of divergence at the inflow and at the outflow. For perturbation
    907107pressure Neumann (zero gradient) conditions are assumed both at the
    908 inflow and at the outflow.<br>
    909 
    910 
    911 
    912 
    913 
    914 
    915 
    916 
    917 
    918 
    919       <br>
    920 
    921 
    922 
    923 
    924 
    925 
    926 
    927 
    928 
    929 
     108inflow and at the outflow.<br> <br>
    930109When using non-cyclic lateral boundaries, a filter is applied to the
    931110velocity field in the vicinity of the outflow in order to suppress any
    932111reflections of outgoing disturbances (see <a href="#km_damp_max">km_damp_max</a>
    933112and <a href="#outflow_damping_width">outflow_damping_width</a>).<br>
    934 
    935 
    936 
    937 
    938 
    939 
    940 
    941 
    942 
    943 
    944       <br>
    945 
    946 
    947 
    948 
    949 
    950 
    951 
    952 
    953 
    954 
     113<br>
    955114In order to maintain a turbulent state of the flow, it may be
    956115neccessary to continuously impose perturbations on the horizontal
     
    961120and <a href="#inflow_disturbance_end">inflow_disturbance_end</a>.
    962121The vertical range and the perturbation amplitude are given by <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">disturbance_level_b</a>,
    963       <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">disturbance_level_t</a>,
     122<a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">disturbance_level_t</a>,
    964123and <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">disturbance_amplitude</a>.
    965124The time interval at which perturbations are to be imposed is set by <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#dt_disturb">dt_disturb</a>.<br>
    966 
    967 
    968 
    969 
    970 
    971 
    972 
    973 
    974 
    975 
    976       <br>
    977 
    978 
    979 
    980 
    981 
    982 
    983 
    984 
    985 
    986 
     125<br>
    987126In case of non-cyclic horizontal boundaries <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#call_psolver_at_all_substeps">call_psolver
    988 at_all_substeps</a> = .T. should be used.<br>
    989 
    990 
    991 
    992 
    993 
    994 
    995 
    996 
    997 
    998 
    999       <br>
    1000 
    1001 
    1002 
    1003 
    1004 
    1005 
    1006 
    1007 
    1008 
    1009 
    1010       <span style="font-weight: bold;">Note:</span><br>
    1011 
    1012 
    1013 
    1014 
    1015 
    1016 
    1017 
    1018 
    1019 
    1020 
     127at_all_substeps</a> = .T. should be used.<br> <br> <span style="font-weight: bold;">Note:</span><br>
    1021128Using non-cyclic lateral boundaries requires very sensitive adjustments
    1022129of the inflow (vertical profiles) and the bottom boundary conditions,
    1023130e.g. a surface heating should not be applied near the inflow boundary
    1024131because this may significantly disturb the inflow. Please check the
    1025 model results very carefully.</td>
    1026 
    1027 
    1028 
    1029 
    1030 
    1031 
    1032 
    1033 
    1034 
    1035 
    1036     </tr>
    1037 
    1038 
    1039 
    1040 
    1041 
    1042 
    1043 
    1044 
    1045 
    1046 
    1047     <tr>
    1048 
    1049 
    1050 
    1051 
    1052 
    1053 
    1054 
    1055 
    1056 
    1057 
    1058       <td style="vertical-align: top;">
    1059      
    1060      
    1061      
    1062      
    1063      
    1064      
    1065      
    1066      
    1067      
    1068      
    1069       <p><a name="bc_ns"></a><b>bc_ns</b></p>
    1070 
    1071 
    1072 
    1073 
    1074 
    1075 
    1076 
    1077 
    1078 
    1079 
    1080       </td>
    1081 
    1082 
    1083 
    1084 
    1085 
    1086 
    1087 
    1088 
    1089 
    1090 
    1091       <td style="vertical-align: top;">C * 20</td>
    1092 
    1093 
    1094 
    1095 
    1096 
    1097 
    1098 
    1099 
    1100 
    1101 
    1102       <td style="vertical-align: top;"><span style="font-style: italic;">'cyclic'</span></td>
    1103 
    1104 
    1105 
    1106 
    1107 
    1108 
    1109 
    1110 
    1111 
    1112 
    1113       <td style="vertical-align: top;">Boundary
    1114 condition along y (for all quantities).<br>
    1115 
    1116 
    1117 
    1118 
    1119 
    1120 
    1121 
    1122 
    1123 
    1124 
    1125       <br>
    1126 
    1127 
    1128 
    1129 
    1130 
    1131 
    1132 
    1133 
    1134 
    1135 
    1136 By default, a cyclic boundary condition is used along y.<br>
    1137 
    1138 
    1139 
    1140 
    1141 
    1142 
    1143 
    1144 
    1145 
    1146 
    1147       <br>
    1148 
    1149 
    1150 
    1151 
    1152 
    1153 
    1154 
    1155 
    1156 
    1157 
    1158       <span style="font-weight: bold;">bc_ns</span> may also be
     132model results very carefully.</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_ns"></a><b>bc_ns</b></p>
     133</td> <td style="vertical-align: top;">C * 20</td>
     134<td style="vertical-align: top;"><span style="font-style: italic;">'cyclic'</span></td>
     135<td style="vertical-align: top;">Boundary
     136condition along y (for all quantities).<br> <br>
     137By default, a cyclic boundary condition is used along y.<br> <br>
     138<span style="font-weight: bold;">bc_ns</span> may
     139also be
    1159140assigned the values <span style="font-style: italic;">'dirichlet/neumann'</span>
    1160141(inflow from rear ("north"), outflow to the front ("south")) or <span style="font-style: italic;">'neumann/dirichlet'</span>
     
    1163144method to be used for solving the Poisson equation for perturbation
    1164145pressure (see <a href="chapter_4.2.html#psolver">psolver</a>)
    1165 and it also requires cyclic boundary conditions along x (see<br>
    1166 
    1167 
    1168 
    1169 
    1170 
    1171 
    1172 
    1173 
    1174 
    1175 
    1176       <a href="#bc_lr">bc_lr</a>).<br>
    1177 
    1178 
    1179 
    1180 
    1181 
    1182 
    1183 
    1184 
    1185 
    1186 
    1187       <br>
    1188 
    1189 
    1190 
    1191 
    1192 
    1193 
    1194 
    1195 
    1196 
    1197 
     146and it also requires cyclic boundary conditions along x (see<br> <a href="#bc_lr">bc_lr</a>).<br> <br>
    1198147In case of these non-cyclic lateral boundaries, a Dirichlet condition
    1199148is used at the inflow for all quantities (initial vertical profiles -
     
    1207156free of divergence at the inflow and at the outflow. For perturbation
    1208157pressure Neumann (zero gradient) conditions are assumed both at the
    1209 inflow and at the outflow.<br>
    1210 
    1211 
    1212 
    1213 
    1214 
    1215 
    1216 
    1217 
    1218 
    1219 
    1220       <br>
    1221 
    1222 
    1223 
    1224 
    1225 
    1226 
    1227 
    1228 
    1229 
    1230 
     158inflow and at the outflow.<br> <br>
    1231159For further details regarding non-cyclic lateral boundary conditions
    1232 see <a href="#bc_lr">bc_lr</a>.</td>
    1233 
    1234 
    1235 
    1236 
    1237 
    1238 
    1239 
    1240 
    1241 
    1242 
    1243     </tr>
    1244 
    1245 
    1246 
    1247 
    1248 
    1249 
    1250 
    1251 
    1252 
    1253 
    1254     <tr>
    1255 
    1256 
    1257 
    1258 
    1259 
    1260 
    1261 
    1262 
    1263 
    1264 
    1265       <td style="vertical-align: top;">
    1266      
    1267      
    1268      
    1269      
    1270      
    1271      
    1272      
    1273      
    1274      
    1275      
    1276       <p><a name="bc_p_b"></a><b>bc_p_b</b></p>
    1277 
    1278 
    1279 
    1280 
    1281 
    1282 
    1283 
    1284 
    1285 
    1286 
    1287       </td>
    1288 
    1289 
    1290 
    1291 
    1292 
    1293 
    1294 
    1295 
    1296 
    1297 
    1298       <td style="vertical-align: top;">C * 20</td>
    1299 
    1300 
    1301 
    1302 
    1303 
    1304 
    1305 
    1306 
    1307 
    1308 
    1309       <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
    1310 
    1311 
    1312 
    1313 
    1314 
    1315 
    1316 
    1317 
    1318 
    1319 
    1320       <td style="vertical-align: top;">
    1321      
    1322      
    1323      
    1324      
    1325      
    1326      
    1327      
    1328      
    1329      
    1330      
    1331       <p style="font-style: normal;">Bottom boundary condition of the
    1332 perturbation pressure.&nbsp; </p>
    1333 
    1334 
    1335 
    1336 
    1337 
    1338 
    1339 
    1340 
    1341 
    1342 
    1343      
    1344      
    1345      
    1346      
    1347      
    1348      
    1349      
    1350      
    1351      
    1352      
    1353       <p>Allowed values are <span style="font-style: italic;">'dirichlet'</span>,
    1354       <span style="font-style: italic;">'neumann'</span> and <span style="font-style: italic;">'neumann+inhomo'</span>.&nbsp; <span style="font-style: italic;">'dirichlet'</span> sets
     160see <a href="#bc_lr">bc_lr</a>.</td> </tr>
     161<tr> <td style="vertical-align: top;"> <p><a name="bc_p_b"></a><b>bc_p_b</b></p> </td>
     162<td style="vertical-align: top;">C * 20</td> <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
     163<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     164perturbation pressure.&nbsp; </p> <p>Allowed values
     165are <span style="font-style: italic;">'dirichlet'</span>,
     166<span style="font-style: italic;">'neumann'</span>
     167and <span style="font-style: italic;">'neumann+inhomo'</span>.&nbsp;
     168<span style="font-style: italic;">'dirichlet'</span>
     169sets
    1355170p(k=0)=0.0,&nbsp; <span style="font-style: italic;">'neumann'</span>
    1356171sets p(k=0)=p(k=1). <span style="font-style: italic;">'neumann+inhomo'</span>
    1357172corresponds to an extended Neumann boundary condition where heat flux
    1358173or temperature inhomogeneities near the
    1359 surface (pt(k=1))&nbsp; are additionally regarded (see Shen and LeClerc
     174surface (pt(k=1))&nbsp; are additionally regarded (see Shen and
     175LeClerc
    1360176(1995, Q.J.R. Meteorol. Soc.,
    13611771209)). This condition is only permitted with the Prandtl-layer
    1362178switched on (<a href="#prandtl_layer">prandtl_layer</a>),
    1363 otherwise the run is terminated.&nbsp; </p>
    1364 
    1365 
    1366 
    1367 
    1368 
    1369 
    1370 
    1371 
    1372 
    1373 
    1374      
    1375      
    1376      
    1377      
    1378      
    1379      
    1380      
    1381      
    1382      
    1383      
    1384       <p>Since at the bottom boundary of the model the vertical
     179otherwise the run is terminated.&nbsp; </p> <p>Since
     180at the bottom boundary of the model the vertical
    1385181velocity
    1386 disappears (w(k=0) = 0.0), the consistent Neumann condition (<span style="font-style: italic;">'neumann'</span> or <span style="font-style: italic;">'neumann+inhomo'</span>) dp/dz = 0 should
     182disappears (w(k=0) = 0.0), the consistent Neumann condition (<span style="font-style: italic;">'neumann'</span> or <span style="font-style: italic;">'neumann+inhomo'</span>)
     183dp/dz = 0 should
    1387184be used, which leaves the vertical component w unchanged when the
    1388185pressure solver is applied. Simultaneous use of the Neumann boundary
    1389186conditions both at the bottom and at the top boundary (<a href="#bc_p_t">bc_p_t</a>)
    1390187usually yields no consistent solution for the perturbation pressure and
    1391 should be avoided.</p>
    1392 
    1393 
    1394 
    1395 
    1396 
    1397 
    1398 
    1399 
    1400 
    1401 
    1402       </td>
    1403 
    1404 
    1405 
    1406 
    1407 
    1408 
    1409 
    1410 
    1411 
    1412 
    1413     </tr>
    1414 
    1415 
    1416 
    1417 
    1418 
    1419 
    1420 
    1421 
    1422 
    1423 
    1424     <tr>
    1425 
    1426 
    1427 
    1428 
    1429 
    1430 
    1431 
    1432 
    1433 
    1434 
    1435       <td style="vertical-align: top;">
    1436      
    1437      
    1438      
    1439      
    1440      
    1441      
    1442      
    1443      
    1444      
    1445      
    1446       <p><a name="bc_p_t"></a><b>bc_p_t</b></p>
    1447 
    1448 
    1449 
    1450 
    1451 
    1452 
    1453 
    1454 
    1455 
    1456 
    1457       </td>
    1458 
    1459 
    1460 
    1461 
    1462 
    1463 
    1464 
    1465 
    1466 
    1467 
    1468       <td style="vertical-align: top;">C * 20</td>
    1469 
    1470 
    1471 
    1472 
    1473 
    1474 
    1475 
    1476 
    1477 
    1478 
    1479       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    1480 
    1481 
    1482 
    1483 
    1484 
    1485 
    1486 
    1487 
    1488 
    1489 
    1490       <td style="vertical-align: top;">
    1491      
    1492      
    1493      
    1494      
    1495      
    1496      
    1497      
    1498      
    1499      
    1500      
    1501       <p style="font-style: normal;">Top boundary condition of the
    1502 perturbation pressure.&nbsp; </p>
    1503 
    1504 
    1505 
    1506 
    1507 
    1508 
    1509 
    1510 
    1511 
    1512 
    1513      
    1514      
    1515      
    1516      
    1517      
    1518      
    1519      
    1520      
    1521      
    1522      
    1523       <p style="font-style: normal;">Allowed values are <span style="font-style: italic;">'dirichlet'</span> (p(k=nz+1)= 0.0) or <span style="font-style: italic;">'neumann'</span>
    1524 (p(k=nz+1)=p(k=nz)).&nbsp; </p>
    1525 
    1526 
    1527 
    1528 
    1529 
    1530 
    1531 
    1532 
    1533 
    1534 
    1535      
    1536      
    1537      
    1538      
    1539      
    1540      
    1541      
    1542      
    1543      
    1544      
    1545       <p>Simultaneous use of Neumann boundary conditions both at the
     188should be avoided.</p> </td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_p_t"></a><b>bc_p_t</b></p>
     189</td> <td style="vertical-align: top;">C * 20</td>
     190<td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     191<td style="vertical-align: top;"> <p style="font-style: normal;">Top boundary condition of the
     192perturbation pressure.&nbsp; </p> <p style="font-style: normal;">Allowed values are <span style="font-style: italic;">'dirichlet'</span>
     193(p(k=nz+1)= 0.0) or <span style="font-style: italic;">'neumann'</span>
     194(p(k=nz+1)=p(k=nz)).&nbsp; </p> <p>Simultaneous use
     195of Neumann boundary conditions both at the
    1546196top and bottom boundary (<a href="#bc_p_b">bc_p_b</a>)
    1547197usually yields no consistent solution for the perturbation pressure and
    1548198should be avoided. Since at the bottom boundary the Neumann
    1549199condition&nbsp; is a good choice (see <a href="#bc_p_b">bc_p_b</a>),
    1550 a Dirichlet condition should be set at the top boundary.</p>
    1551 
    1552 
    1553 
    1554 
    1555 
    1556 
    1557 
    1558 
    1559 
    1560 
    1561       </td>
    1562 
    1563 
    1564 
    1565 
    1566 
    1567 
    1568 
    1569 
    1570 
    1571 
    1572     </tr>
    1573 
    1574 
    1575 
    1576 
    1577 
    1578 
    1579 
    1580 
    1581 
    1582 
    1583     <tr>
    1584 
    1585 
    1586 
    1587 
    1588 
    1589 
    1590 
    1591 
    1592 
    1593 
    1594       <td style="vertical-align: top;">
    1595      
    1596      
    1597      
    1598      
    1599      
    1600      
    1601      
    1602      
    1603      
    1604      
    1605       <p><a name="bc_pt_b"></a><b>bc_pt_b</b></p>
    1606 
    1607 
    1608 
    1609 
    1610 
    1611 
    1612 
    1613 
    1614 
    1615 
    1616       </td>
    1617 
    1618 
    1619 
    1620 
    1621 
    1622 
    1623 
    1624 
    1625 
    1626 
    1627       <td style="vertical-align: top;">C*20</td>
    1628 
    1629 
    1630 
    1631 
    1632 
    1633 
    1634 
    1635 
    1636 
    1637 
    1638       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    1639 
    1640 
    1641 
    1642 
    1643 
    1644 
    1645 
    1646 
    1647 
    1648 
    1649       <td style="vertical-align: top;">
    1650      
    1651      
    1652      
    1653      
    1654      
    1655      
    1656      
    1657      
    1658      
    1659      
    1660       <p style="font-style: normal;">Bottom boundary condition of the
    1661 potential temperature.&nbsp; </p>
    1662 
    1663 
    1664 
    1665 
    1666 
    1667 
    1668 
    1669 
    1670 
    1671 
    1672      
    1673      
    1674      
    1675      
    1676      
    1677      
    1678      
    1679      
    1680      
    1681      
    1682       <p>Allowed values are <span style="font-style: italic;">'dirichlet'</span>
     200a Dirichlet condition should be set at the top boundary.</p> </td>
     201</tr> <tr> <td style="vertical-align: top;">
     202<p><a name="bc_pt_b"></a><b>bc_pt_b</b></p>
     203</td> <td style="vertical-align: top;">C*20</td>
     204<td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     205<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     206potential temperature.&nbsp; </p> <p>Allowed values
     207are <span style="font-style: italic;">'dirichlet'</span>
    1683208(pt(k=0) = const. = <a href="#pt_surface">pt_surface</a>
    1684209+ <a href="#pt_surface_initial_change">pt_surface_initial_change</a>;
     
    1686211and <span style="font-style: italic;">'neumann'</span>
    1687212(pt(k=0)=pt(k=1)).&nbsp; <br>
    1688 
    1689 
    1690 
    1691 
    1692 
    1693 
    1694 
    1695 
    1696 
    1697 
    1698 When a constant surface sensible heat flux is used (<a href="#surface_heatflux">surface_heatflux</a>), <b>bc_pt_b</b> = <span style="font-style: italic;">'neumann'</span>
     213When a constant surface sensible heat flux is used (<a href="#surface_heatflux">surface_heatflux</a>), <b>bc_pt_b</b>
     214= <span style="font-style: italic;">'neumann'</span>
    1699215must be used, because otherwise the resolved scale may contribute to
    1700216the surface flux so that a constant value cannot be guaranteed.</p>
    1701 
    1702 
    1703 
    1704 
    1705 
    1706 
    1707 
    1708 
    1709 
    1710 
    1711       </td>
    1712 
    1713 
    1714 
    1715 
    1716 
    1717 
    1718 
    1719 
    1720 
    1721 
    1722     </tr>
    1723 
    1724 
    1725 
    1726 
    1727 
    1728 
    1729 
    1730 
    1731 
    1732 
    1733     <tr>
    1734 
    1735 
    1736 
    1737 
    1738 
    1739 
    1740 
    1741 
    1742 
    1743 
    1744       <td style="vertical-align: top;">
    1745      
    1746      
    1747      
    1748      
    1749      
    1750      
    1751      
    1752      
    1753      
    1754      
    1755       <p><a name="pc_pt_t"></a><b>bc_pt_t</b></p>
    1756 
    1757 
    1758 
    1759 
    1760 
    1761 
    1762 
    1763 
    1764 
    1765 
    1766       </td>
    1767 
    1768 
    1769 
    1770 
    1771 
    1772 
    1773 
    1774 
    1775 
    1776 
    1777       <td style="vertical-align: top;">C * 20</td>
    1778 
    1779 
    1780 
    1781 
    1782 
    1783 
    1784 
    1785 
    1786 
    1787 
    1788       <td style="vertical-align: top;"><span style="font-style: italic;">'initial gradient'</span></td>
    1789 
    1790 
    1791 
    1792 
    1793 
    1794 
    1795 
    1796 
    1797 
    1798 
    1799       <td style="vertical-align: top;">
    1800      
    1801      
    1802      
    1803      
    1804      
    1805      
    1806      
    1807      
    1808      
    1809      
    1810       <p style="font-style: normal;">Top boundary condition of the
    1811 potential temperature.&nbsp; </p>
    1812 
    1813 
    1814 
    1815 
    1816 
    1817 
    1818 
    1819 
    1820 
    1821 
    1822      
    1823      
    1824      
    1825      
    1826      
    1827      
    1828      
    1829      
    1830      
    1831      
    1832       <p>Allowed are the values <span style="font-style: italic;">'dirichlet'
    1833       </span>(pt(k=nz+1)
    1834 does not change during the run), <span style="font-style: italic;">'neumann'</span> (pt(k=nz+1)=pt(k=nz)), and <span style="font-style: italic;">'initial_gradient'</span>.
    1835 With the 'initial_gradient'-condition the value of the temperature gradient at the top is
     217</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="pc_pt_t"></a><b>bc_pt_t</b></p>
     218</td> <td style="vertical-align: top;">C * 20</td>
     219<td style="vertical-align: top;"><span style="font-style: italic;">'initial gradient'</span></td>
     220<td style="vertical-align: top;"> <p style="font-style: normal;">Top boundary condition of the
     221potential temperature.&nbsp; </p> <p>Allowed are the
     222values <span style="font-style: italic;">'dirichlet' </span>(pt(k=nz+1)
     223does not change during the run), <span style="font-style: italic;">'neumann'</span>
     224(pt(k=nz+1)=pt(k=nz)), and <span style="font-style: italic;">'initial_gradient'</span>.
     225With the 'initial_gradient'-condition the value of the temperature
     226gradient at the top is
    1836227calculated from the initial
    1837 temperature profile (see <a href="#pt_surface">pt_surface</a>, <a href="#pt_vertical_gradient">pt_vertical_gradient</a>)
     228temperature profile (see <a href="#pt_surface">pt_surface</a>,
     229<a href="#pt_vertical_gradient">pt_vertical_gradient</a>)
    1838230by bc_pt_t_val = (pt_init(k=nz+1) -
    1839231pt_init(k=nz)) / dzu(nz+1).<br>
    1840 
    1841 
    1842 
    1843 
    1844 
    1845 
    1846 
    1847 
    1848 
    1849 
    1850232Using this value (assumed constant during the
    1851233run) the temperature boundary values are calculated as&nbsp; </p>
    1852 
    1853 
    1854 
    1855 
    1856 
    1857 
    1858 
    1859 
    1860 
    1861 
    1862      
    1863      
    1864      
    1865      
    1866      
    1867      
    1868      
    1869      
    1870      
    1871      
    1872      
    1873 
    1874 
    1875 
    1876 
    1877 
    1878 
    1879 
    1880 
    1881 
    1882 
    1883      
    1884      
    1885      
    1886      
    1887      
    1888      
    1889      
    1890      
    1891      
    1892      
    1893      
    1894 
    1895 
    1896 
    1897 
    1898 
    1899 
    1900 
    1901 
    1902 
    1903 
    1904      
    1905      
    1906      
    1907      
    1908      
    1909      
    1910      
    1911      
    1912      
    1913      
    1914       <ul>
    1915 
    1916 
    1917 
    1918 
    1919 
    1920 
    1921 
    1922 
    1923 
    1924 
    1925        
    1926        
    1927        
    1928        
    1929        
    1930        
    1931        
    1932        
    1933        
    1934        
    1935         <p style="font-style: normal;">pt(k=nz+1) = pt(k=nz) +
    1936 bc_pt_t_val * dzu(nz+1)</p>
    1937 
    1938 
    1939 
    1940 
    1941 
    1942 
    1943 
    1944 
    1945 
    1946 
    1947      
    1948      
    1949      
    1950      
    1951      
    1952      
    1953      
    1954      
    1955      
    1956      
    1957       </ul>
    1958 
    1959 
    1960 
    1961 
    1962 
    1963 
    1964 
    1965 
    1966 
    1967 
    1968      
    1969      
    1970      
    1971      
    1972      
    1973      
    1974      
    1975      
    1976      
    1977      
    1978       <p style="font-style: normal;">(up to k=nz the prognostic
     234<ul> <p style="font-style: normal;">pt(k=nz+1) =
     235pt(k=nz) +
     236bc_pt_t_val * dzu(nz+1)</p> </ul> <p style="font-style: normal;">(up to k=nz the prognostic
    1979237equation for the temperature is solved).<br>
    1980 
    1981 
    1982 
    1983 
    1984 
    1985 
    1986 
    1987 
    1988 
    1989 
    1990 When a constant sensible heat flux is used at the top boundary (<a href="chapter_4.1.html#top_heatflux">top_heatflux</a>), <b>bc_pt_t</b> = <span style="font-style: italic;">'neumann'</span>
     238When a constant sensible heat flux is used at the top boundary (<a href="chapter_4.1.html#top_heatflux">top_heatflux</a>),
     239<b>bc_pt_t</b> = <span style="font-style: italic;">'neumann'</span>
    1991240must be used, because otherwise the resolved scale may contribute to
    1992 the top flux so that a constant value cannot be guaranteed.</p>
    1993 
    1994 
    1995 
    1996 
    1997 
    1998 
    1999 
    2000 
    2001 
    2002 
    2003       </td>
    2004 
    2005 
    2006 
    2007 
    2008 
    2009 
    2010 
    2011 
    2012 
    2013 
    2014     </tr>
    2015 
    2016 
    2017 
    2018 
    2019 
    2020 
    2021 
    2022 
    2023 
    2024 
    2025     <tr>
    2026 
    2027 
    2028 
    2029 
    2030 
    2031 
    2032 
    2033 
    2034 
    2035 
    2036       <td style="vertical-align: top;">
    2037      
    2038      
    2039      
    2040      
    2041      
    2042      
    2043      
    2044      
    2045      
    2046      
    2047       <p><a name="bc_q_b"></a><b>bc_q_b</b></p>
    2048 
    2049 
    2050 
    2051 
    2052 
    2053 
    2054 
    2055 
    2056 
    2057 
    2058       </td>
    2059 
    2060 
    2061 
    2062 
    2063 
    2064 
    2065 
    2066 
    2067 
    2068 
    2069       <td style="vertical-align: top;">C * 20</td>
    2070 
    2071 
    2072 
    2073 
    2074 
    2075 
    2076 
    2077 
    2078 
    2079 
    2080       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    2081 
    2082 
    2083 
    2084 
    2085 
    2086 
    2087 
    2088 
    2089 
    2090 
    2091       <td style="vertical-align: top;">
    2092      
    2093      
    2094      
    2095      
    2096      
    2097      
    2098      
    2099      
    2100      
    2101      
    2102       <p style="font-style: normal;">Bottom boundary condition of the
    2103 specific humidity / total water content.&nbsp; </p>
    2104 
    2105 
    2106 
    2107 
    2108 
    2109 
    2110 
    2111 
    2112 
    2113 
    2114      
    2115      
    2116      
    2117      
    2118      
    2119      
    2120      
    2121      
    2122      
    2123      
    2124       <p>Allowed values are <span style="font-style: italic;">'dirichlet'</span>
     241the top flux so that a constant value cannot be guaranteed.</p> </td>
     242</tr> <tr> <td style="vertical-align: top;">
     243<p><a name="bc_q_b"></a><b>bc_q_b</b></p>
     244</td> <td style="vertical-align: top;">C * 20</td>
     245<td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     246<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     247specific humidity / total water content.&nbsp; </p> <p>Allowed
     248values are <span style="font-style: italic;">'dirichlet'</span>
    2125249(q(k=0) = const. = <a href="#q_surface">q_surface</a>
    2126250+ <a href="#q_surface_initial_change">q_surface_initial_change</a>;
     
    2128252and <span style="font-style: italic;">'neumann'</span>
    2129253(q(k=0)=q(k=1)).&nbsp; <br>
    2130 
    2131 
    2132 
    2133 
    2134 
    2135 
    2136 
    2137 
    2138 
    2139 
    2140 When a constant surface latent heat flux is used (<a href="#surface_waterflux">surface_waterflux</a>), <b>bc_q_b</b> = <span style="font-style: italic;">'neumann'</span>
     254When a constant surface latent heat flux is used (<a href="#surface_waterflux">surface_waterflux</a>), <b>bc_q_b</b>
     255= <span style="font-style: italic;">'neumann'</span>
    2141256must be used, because otherwise the resolved scale may contribute to
    2142257the surface flux so that a constant value cannot be guaranteed.</p>
    2143 
    2144 
    2145 
    2146 
    2147 
    2148 
    2149 
    2150 
    2151 
    2152 
    2153       </td>
    2154 
    2155 
    2156 
    2157 
    2158 
    2159 
    2160 
    2161 
    2162 
    2163 
    2164     </tr>
    2165 
    2166 
    2167 
    2168 
    2169 
    2170 
    2171 
    2172 
    2173 
    2174 
    2175     <tr>
    2176 
    2177 
    2178 
    2179 
    2180 
    2181 
    2182 
    2183 
    2184 
    2185 
    2186       <td style="vertical-align: top;">
    2187      
    2188      
    2189      
    2190      
    2191      
    2192      
    2193      
    2194      
    2195      
    2196      
    2197       <p><a name="bc_q_t"></a><b>bc_q_t</b></p>
    2198 
    2199 
    2200 
    2201 
    2202 
    2203 
    2204 
    2205 
    2206 
    2207 
    2208       </td>
    2209 
    2210 
    2211 
    2212 
    2213 
    2214 
    2215 
    2216 
    2217 
    2218 
    2219       <td style="vertical-align: top;"><span style="font-style: italic;">C
    2220 * 20</span></td>
    2221 
    2222 
    2223 
    2224 
    2225 
    2226 
    2227 
    2228 
    2229 
    2230 
    2231       <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
    2232 
    2233 
    2234 
    2235 
    2236 
    2237 
    2238 
    2239 
    2240 
    2241 
    2242       <td style="vertical-align: top;">
    2243      
    2244      
    2245      
    2246      
    2247      
    2248      
    2249      
    2250      
    2251      
    2252      
    2253       <p style="font-style: normal;">Top boundary condition of the
    2254 specific humidity / total water content.&nbsp; </p>
    2255 
    2256 
    2257 
    2258 
    2259 
    2260 
    2261 
    2262 
    2263 
    2264 
    2265      
    2266      
    2267      
    2268      
    2269      
    2270      
    2271      
    2272      
    2273      
    2274      
    2275       <p>Allowed are the values <span style="font-style: italic;">'dirichlet'</span>
     258</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_q_t"></a><b>bc_q_t</b></p>
     259</td> <td style="vertical-align: top;"><span style="font-style: italic;">C
     260* 20</span></td> <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
     261<td style="vertical-align: top;"> <p style="font-style: normal;">Top boundary condition of the
     262specific humidity / total water content.&nbsp; </p> <p>Allowed
     263are the values <span style="font-style: italic;">'dirichlet'</span>
    2276264(q(k=nz) and q(k=nz+1) do
    2277265not change during the run) and <span style="font-style: italic;">'neumann'</span>.
     
    2279267condition the value of the humidity gradient at the top is calculated
    2280268from the
    2281 initial humidity profile (see <a href="#q_surface">q_surface</a>, <a href="#q_vertical_gradient">q_vertical_gradient</a>)
     269initial humidity profile (see <a href="#q_surface">q_surface</a>,
     270<a href="#q_vertical_gradient">q_vertical_gradient</a>)
    2282271by: bc_q_t_val = ( q_init(k=nz) - q_init(k=nz-1)) / dzu(nz).<br>
    2283 
    2284 
    2285 
    2286 
    2287 
    2288 
    2289 
    2290 
    2291 
    2292 
    2293272Using this value (assumed constant during the run) the humidity
    2294273boundary values
    2295 are calculated as&nbsp; </p>
    2296 
    2297 
    2298 
    2299 
    2300 
    2301 
    2302 
    2303 
    2304 
    2305 
    2306      
    2307      
    2308      
    2309      
    2310      
    2311      
    2312      
    2313      
    2314      
    2315      
    2316      
    2317 
    2318 
    2319 
    2320 
    2321 
    2322 
    2323 
    2324 
    2325 
    2326 
    2327      
    2328      
    2329      
    2330      
    2331      
    2332      
    2333      
    2334      
    2335      
    2336      
    2337      
    2338 
    2339 
    2340 
    2341 
    2342 
    2343 
    2344 
    2345 
    2346 
    2347 
    2348      
    2349      
    2350      
    2351      
    2352      
    2353      
    2354      
    2355      
    2356      
    2357      
    2358       <ul>
    2359 
    2360 
    2361 
    2362 
    2363 
    2364 
    2365 
    2366 
    2367 
    2368 
    2369        
    2370        
    2371        
    2372        
    2373        
    2374        
    2375        
    2376        
    2377        
    2378        
    2379         <p style="font-style: normal;">q(k=nz+1) =q(k=nz) +
    2380 bc_q_t_val * dzu(nz+1)</p>
    2381 
    2382 
    2383 
    2384 
    2385 
    2386 
    2387 
    2388 
    2389 
    2390 
    2391      
    2392      
    2393      
    2394      
    2395      
    2396      
    2397      
    2398      
    2399      
    2400      
    2401       </ul>
    2402 
    2403 
    2404 
    2405 
    2406 
    2407 
    2408 
    2409 
    2410 
    2411 
    2412      
    2413      
    2414      
    2415      
    2416      
    2417      
    2418      
    2419      
    2420      
    2421      
    2422       <p style="font-style: normal;">(up tp k=nz the prognostic
    2423 equation for q is solved). </p>
    2424 
    2425 
    2426 
    2427 
    2428 
    2429 
    2430 
    2431 
    2432 
    2433 
    2434       </td>
    2435 
    2436 
    2437 
    2438 
    2439 
    2440 
    2441 
    2442 
    2443 
    2444 
    2445     </tr>
    2446 
    2447 
    2448 
    2449 
    2450 
    2451 
    2452 
    2453 
    2454 
    2455 
    2456     <tr>
    2457 
    2458 
    2459 
    2460 
    2461 
    2462 
    2463 
    2464 
    2465 
    2466 
    2467       <td style="vertical-align: top;">
    2468      
    2469      
    2470      
    2471      
    2472      
    2473      
    2474      
    2475      
    2476      
    2477      
    2478       <p><a name="bc_s_b"></a><b>bc_s_b</b></p>
    2479 
    2480 
    2481 
    2482 
    2483 
    2484 
    2485 
    2486 
    2487 
    2488 
    2489       </td>
    2490 
    2491 
    2492 
    2493 
    2494 
    2495 
    2496 
    2497 
    2498 
    2499 
    2500       <td style="vertical-align: top;">C * 20</td>
    2501 
    2502 
    2503 
    2504 
    2505 
    2506 
    2507 
    2508 
    2509 
    2510 
    2511       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    2512 
    2513 
    2514 
    2515 
    2516 
    2517 
    2518 
    2519 
    2520 
    2521 
    2522       <td style="vertical-align: top;">
    2523      
    2524      
    2525      
    2526      
    2527      
    2528      
    2529      
    2530      
    2531      
    2532      
    2533       <p style="font-style: normal;">Bottom boundary condition of the
    2534 scalar concentration.&nbsp; </p>
    2535 
    2536 
    2537 
    2538 
    2539 
    2540 
    2541 
    2542 
    2543 
    2544 
    2545      
    2546      
    2547      
    2548      
    2549      
    2550      
    2551      
    2552      
    2553      
    2554      
    2555       <p>Allowed values are <span style="font-style: italic;">'dirichlet'</span>
     274are calculated as&nbsp; </p> <ul> <p style="font-style: normal;">q(k=nz+1) =q(k=nz) +
     275bc_q_t_val * dzu(nz+1)</p> </ul> <p style="font-style: normal;">(up tp k=nz the prognostic
     276equation for q is solved). </p> </td> </tr> <tr>
     277<td style="vertical-align: top;"> <p><a name="bc_s_b"></a><b>bc_s_b</b></p> </td>
     278<td style="vertical-align: top;">C * 20</td> <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     279<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     280scalar concentration.&nbsp; </p> <p>Allowed values
     281are <span style="font-style: italic;">'dirichlet'</span>
    2556282(s(k=0) = const. = <a href="#s_surface">s_surface</a>
    2557283+ <a href="#s_surface_initial_change">s_surface_initial_change</a>;
    2558284the user may change this value during the run using user-defined code)
    2559 and <span style="font-style: italic;">'neumann'</span> (s(k=0) =
     285and <span style="font-style: italic;">'neumann'</span>
     286(s(k=0) =
    2560287s(k=1)).&nbsp; <br>
    2561 
    2562 
    2563 
    2564 
    2565 
    2566 
    2567 
    2568 
    2569 
    2570 
    2571 When a constant surface concentration flux is used (<a href="#surface_scalarflux">surface_scalarflux</a>), <b>bc_s_b</b> = <span style="font-style: italic;">'neumann'</span>
     288When a constant surface concentration flux is used (<a href="#surface_scalarflux">surface_scalarflux</a>), <b>bc_s_b</b>
     289= <span style="font-style: italic;">'neumann'</span>
    2572290must be used, because otherwise the resolved scale may contribute to
    2573291the surface flux so that a constant value cannot be guaranteed.</p>
    2574 
    2575 
    2576 
    2577 
    2578 
    2579 
    2580 
    2581 
    2582 
    2583 
    2584       </td>
    2585 
    2586 
    2587 
    2588 
    2589 
    2590 
    2591 
    2592 
    2593 
    2594 
    2595     </tr>
    2596 
    2597 
    2598 
    2599 
    2600 
    2601 
    2602 
    2603 
    2604 
    2605 
    2606     <tr>
    2607 
    2608 
    2609 
    2610 
    2611 
    2612 
    2613 
    2614 
    2615 
    2616 
    2617       <td style="vertical-align: top;">
    2618      
    2619      
    2620      
    2621      
    2622      
    2623      
    2624      
    2625      
    2626      
    2627      
    2628       <p><a name="bc_s_t"></a><b>bc_s_t</b></p>
    2629 
    2630 
    2631 
    2632 
    2633 
    2634 
    2635 
    2636 
    2637 
    2638 
    2639       </td>
    2640 
    2641 
    2642 
    2643 
    2644 
    2645 
    2646 
    2647 
    2648 
    2649 
    2650       <td style="vertical-align: top;">C * 20</td>
    2651 
    2652 
    2653 
    2654 
    2655 
    2656 
    2657 
    2658 
    2659 
    2660 
    2661       <td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
    2662 
    2663 
    2664 
    2665 
    2666 
    2667 
    2668 
    2669 
    2670 
    2671 
    2672       <td style="vertical-align: top;">
    2673      
    2674      
    2675      
    2676      
    2677      
    2678      
    2679      
    2680      
    2681      
    2682      
    2683       <p style="font-style: normal;">Top boundary condition of the
    2684 scalar concentration.&nbsp; </p>
    2685 
    2686 
    2687 
    2688 
    2689 
    2690 
    2691 
    2692 
    2693 
    2694 
    2695      
    2696      
    2697      
    2698      
    2699      
    2700      
    2701      
    2702      
    2703      
    2704      
    2705       <p>Allowed are the values <span style="font-style: italic;">'dirichlet'</span>
     292</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_s_t"></a><b>bc_s_t</b></p>
     293</td> <td style="vertical-align: top;">C * 20</td>
     294<td style="vertical-align: top;"><span style="font-style: italic;">'neumann'</span></td>
     295<td style="vertical-align: top;"> <p style="font-style: normal;">Top boundary condition of the
     296scalar concentration.&nbsp; </p> <p>Allowed are the
     297values <span style="font-style: italic;">'dirichlet'</span>
    2706298(s(k=nz) and s(k=nz+1) do
    2707299not change during the run) and <span style="font-style: italic;">'neumann'</span>.
     
    2709301condition the value of the scalar concentration gradient at the top is
    2710302calculated
    2711 from the initial scalar concentration profile (see <a href="#s_surface">s_surface</a>,
    2712       <a href="#s_vertical_gradient">s_vertical_gradient</a>)
     303from the initial scalar concentration profile (see <a href="#s_surface">s_surface</a>, <a href="#s_vertical_gradient">s_vertical_gradient</a>)
    2713304by: bc_s_t_val = (s_init(k=nz) - s_init(k=nz-1)) / dzu(nz).<br>
    2714 
    2715 
    2716 
    2717 
    2718 
    2719 
    2720 
    2721 
    2722 
    2723 
    2724305Using this value (assumed constant during the run) the concentration
    2725306boundary values
    2726 are calculated as </p>
    2727 
    2728 
    2729 
    2730 
    2731 
    2732 
    2733 
    2734 
    2735 
    2736 
    2737      
    2738      
    2739      
    2740      
    2741      
    2742      
    2743      
    2744      
    2745      
    2746      
    2747      
    2748 
    2749 
    2750 
    2751 
    2752 
    2753 
    2754 
    2755 
    2756 
    2757 
    2758      
    2759      
    2760      
    2761      
    2762      
    2763      
    2764      
    2765      
    2766      
    2767      
    2768      
    2769 
    2770 
    2771 
    2772 
    2773 
    2774 
    2775 
    2776 
    2777 
    2778 
    2779      
    2780      
    2781      
    2782      
    2783      
    2784      
    2785      
    2786      
    2787      
    2788      
    2789       <ul>
    2790 
    2791 
    2792 
    2793 
    2794 
    2795 
    2796 
    2797 
    2798 
    2799 
    2800        
    2801        
    2802        
    2803        
    2804        
    2805        
    2806        
    2807        
    2808        
    2809        
    2810         <p style="font-style: normal;">s(k=nz+1) = s(k=nz) +
    2811 bc_s_t_val * dzu(nz+1)</p>
    2812 
    2813 
    2814 
    2815 
    2816 
    2817 
    2818 
    2819 
    2820 
    2821 
    2822      
    2823      
    2824      
    2825      
    2826      
    2827      
    2828      
    2829      
    2830      
    2831      
    2832       </ul>
    2833 
    2834 
    2835 
    2836 
    2837 
    2838 
    2839 
    2840 
    2841 
    2842 
    2843      
    2844      
    2845      
    2846      
    2847      
    2848      
    2849      
    2850      
    2851      
    2852      
    2853       <p style="font-style: normal;">(up to k=nz the prognostic
     307are calculated as </p> <ul> <p style="font-style: normal;">s(k=nz+1) = s(k=nz) +
     308bc_s_t_val * dzu(nz+1)</p> </ul> <p style="font-style: normal;">(up to k=nz the prognostic
    2854309equation for the scalar concentration is
    2855 solved).</p>
    2856 
    2857 
    2858 
    2859 
    2860 
    2861 
    2862 
    2863 
    2864 
    2865 
    2866       </td>
    2867 
    2868 
    2869 
    2870 
    2871 
    2872 
    2873 
    2874 
    2875 
    2876 
    2877     </tr>
    2878 
    2879 
    2880 
    2881 
    2882 
    2883 
    2884 
    2885 
    2886 
    2887 
    2888     <tr>
    2889 
    2890 
    2891 
    2892 
    2893 
    2894 
    2895 
    2896 
    2897 
    2898 
    2899       <td style="vertical-align: top;">
    2900      
    2901      
    2902      
    2903      
    2904      
    2905      
    2906      
    2907      
    2908      
    2909      
    2910       <p><a name="bc_uv_b"></a><b>bc_uv_b</b></p>
    2911 
    2912 
    2913 
    2914 
    2915 
    2916 
    2917 
    2918 
    2919 
    2920 
    2921       </td>
    2922 
    2923 
    2924 
    2925 
    2926 
    2927 
    2928 
    2929 
    2930 
    2931 
    2932       <td style="vertical-align: top;">C * 20</td>
    2933 
    2934 
    2935 
    2936 
    2937 
    2938 
    2939 
    2940 
    2941 
    2942 
    2943       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    2944 
    2945 
    2946 
    2947 
    2948 
    2949 
    2950 
    2951 
    2952 
    2953 
    2954       <td style="vertical-align: top;">
    2955      
    2956      
    2957      
    2958      
    2959      
    2960      
    2961      
    2962      
    2963      
    2964      
    2965       <p style="font-style: normal;">Bottom boundary condition of the
    2966 horizontal velocity components u and v.&nbsp; </p>
    2967 
    2968 
    2969 
    2970 
    2971 
    2972 
    2973 
    2974 
    2975 
    2976 
    2977      
    2978      
    2979      
    2980      
    2981      
    2982      
    2983      
    2984      
    2985      
    2986      
    2987       <p>Allowed values are <span style="font-style: italic;">'dirichlet'
    2988       </span>and <span style="font-style: italic;">'neumann'</span>. <b>bc_uv_b</b>
    2989 = <span style="font-style: italic;">'dirichlet'</span> yields the
     310solved).</p> </td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_uv_b"></a><b>bc_uv_b</b></p>
     311</td> <td style="vertical-align: top;">C * 20</td>
     312<td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     313<td style="vertical-align: top;"> <p style="font-style: normal;">Bottom boundary condition of the
     314horizontal velocity components u and v.&nbsp; </p> <p>Allowed
     315values are <span style="font-style: italic;">'dirichlet' </span>and
     316<span style="font-style: italic;">'neumann'</span>. <b>bc_uv_b</b>
     317= <span style="font-style: italic;">'dirichlet'</span>
     318yields the
    2990319no-slip condition with u=v=0 at the bottom. Due to the staggered grid
    2991320u(k=0) and v(k=0) are located at z = - 0,5 * <a href="#dz">dz</a>
    2992321(below the bottom), while u(k=1) and v(k=1) are located at z = +0,5 *
    2993322dz. u=v=0 at the bottom is guaranteed using mirror boundary
    2994 condition:&nbsp; </p>
    2995 
    2996 
    2997 
    2998 
    2999 
    3000 
    3001 
    3002 
    3003 
    3004 
    3005      
    3006      
    3007      
    3008      
    3009      
    3010      
    3011      
    3012      
    3013      
    3014      
    3015       <ul>
    3016 
    3017 
    3018 
    3019 
    3020 
    3021 
    3022 
    3023 
    3024 
    3025 
    3026        
    3027        
    3028        
    3029        
    3030        
    3031        
    3032        
    3033        
    3034        
    3035        
    3036         <p style="font-style: normal;">u(k=0) = - u(k=1) and v(k=0) = -
    3037 v(k=1)</p>
    3038 
    3039 
    3040 
    3041 
    3042 
    3043 
    3044 
    3045 
    3046 
    3047 
    3048      
    3049      
    3050      
    3051      
    3052      
    3053      
    3054      
    3055      
    3056      
    3057      
    3058       </ul>
    3059 
    3060 
    3061 
    3062 
    3063 
    3064 
    3065 
    3066 
    3067 
    3068 
    3069      
    3070      
    3071      
    3072      
    3073      
    3074      
    3075      
    3076      
    3077      
    3078      
    3079       <p style="font-style: normal;">The Neumann boundary condition
     323condition:&nbsp; </p> <ul> <p style="font-style: normal;">u(k=0) = - u(k=1) and v(k=0) = -
     324v(k=1)</p> </ul> <p style="font-style: normal;">The
     325Neumann boundary condition
    3080326yields the free-slip condition with u(k=0) = u(k=1) and v(k=0) =
    3081327v(k=1).
    3082328With Prandtl - layer switched on, the free-slip condition is not
    3083329allowed (otherwise the run will be terminated)<font color="#000000">.</font></p>
    3084 
    3085 
    3086 
    3087 
    3088 
    3089 
    3090 
    3091 
    3092 
    3093 
    3094       </td>
    3095 
    3096 
    3097 
    3098 
    3099 
    3100 
    3101 
    3102 
    3103 
    3104 
    3105     </tr>
    3106 
    3107 
    3108 
    3109 
    3110 
    3111 
    3112 
    3113 
    3114 
    3115 
    3116     <tr>
    3117 
    3118 
    3119 
    3120 
    3121 
    3122 
    3123 
    3124 
    3125 
    3126 
    3127       <td style="vertical-align: top;">
    3128      
    3129      
    3130      
    3131      
    3132      
    3133      
    3134      
    3135      
    3136      
    3137      
    3138       <p><a name="bc_uv_t"></a><b>bc_uv_t</b></p>
    3139 
    3140 
    3141 
    3142 
    3143 
    3144 
    3145 
    3146 
    3147 
    3148 
    3149       </td>
    3150 
    3151 
    3152 
    3153 
    3154 
    3155 
    3156 
    3157 
    3158 
    3159 
    3160       <td style="vertical-align: top;">C * 20</td>
    3161 
    3162 
    3163 
    3164 
    3165 
    3166 
    3167 
    3168 
    3169 
    3170 
    3171       <td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
    3172 
    3173 
    3174 
    3175 
    3176 
    3177 
    3178 
    3179 
    3180 
    3181 
    3182       <td style="vertical-align: top;">
    3183      
    3184      
    3185      
    3186      
    3187      
    3188      
    3189      
    3190      
    3191      
    3192      
    3193       <p style="font-style: normal;">Top boundary condition of the
    3194 horizontal velocity components u and v.&nbsp; </p>
    3195 
    3196 
    3197 
    3198 
    3199 
    3200 
    3201 
    3202 
    3203 
    3204 
    3205      
    3206      
    3207      
    3208      
    3209      
    3210      
    3211      
    3212      
    3213      
    3214      
    3215       <p>Allowed values are <span style="font-style: italic;">'dirichlet'</span>
    3216 and <span style="font-style: italic;">'neumann'</span>. The
     330</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="bc_uv_t"></a><b>bc_uv_t</b></p>
     331</td> <td style="vertical-align: top;">C * 20</td>
     332<td style="vertical-align: top;"><span style="font-style: italic;">'dirichlet'</span></td>
     333<td style="vertical-align: top;"> <p style="font-style: normal;">Top boundary condition of the
     334horizontal velocity components u and v.&nbsp; </p> <p>Allowed
     335values are <span style="font-style: italic;">'dirichlet'</span>
     336and <span style="font-style: italic;">'neumann'</span>.
     337The
    3217338Dirichlet condition yields u(k=nz+1) = ug(nz+1) and v(k=nz+1) =
    3218339vg(nz+1),
    3219340Neumann condition yields the free-slip condition with u(k=nz+1) =
    3220341u(k=nz) and v(k=nz+1) = v(k=nz) (up to k=nz the prognostic equations
    3221 for the velocities are solved).</p>
    3222 
    3223 
    3224 
    3225 
    3226 
    3227 
    3228 
    3229 
    3230 
    3231 
    3232       </td>
    3233 
    3234 
    3235 
    3236 
    3237 
    3238 
    3239 
    3240 
    3241 
    3242 
    3243     </tr>
    3244 
    3245 
    3246 
    3247 
    3248 
    3249 
    3250 
    3251 
    3252 
    3253 
    3254     <tr>
    3255 
    3256 
    3257 
    3258 
    3259 
    3260 
    3261       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_height"></a>building_height</span></td>
    3262 
    3263 
    3264 
    3265 
    3266 
    3267 
    3268       <td style="vertical-align: top;">R</td>
    3269 
    3270 
    3271 
    3272 
    3273 
    3274 
    3275       <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td>
    3276 
    3277 
    3278 
    3279 
    3280 
    3281 
    3282       <td>Height of a single building in m.<br>
    3283 
    3284 
    3285 
    3286 
    3287 
    3288 
    3289       <br>
    3290 
    3291 
    3292 
    3293 
    3294 
    3295 
    3296       <span style="font-weight: bold;">building_height</span> must be less than the height of the model domain. This parameter requires the use of&nbsp;<a href="#topography">topography</a> = <span style="font-style: italic;">'single_building'</span>.</td>
    3297 
    3298 
    3299 
    3300 
    3301 
    3302 
    3303     </tr>
    3304 
    3305 
    3306 
    3307 
    3308 
    3309 
    3310     <tr>
    3311 
    3312 
    3313 
    3314 
    3315 
    3316 
    3317       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_length_x"></a>building_length_x</span></td>
    3318 
    3319 
    3320 
    3321 
    3322 
    3323 
    3324       <td style="vertical-align: top;">R</td>
    3325 
    3326 
    3327 
    3328 
    3329 
    3330 
    3331       <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td>
    3332 
    3333 
    3334 
    3335 
    3336 
    3337 
    3338       <td><span style="font-style: italic;"></span>Width of a single building in m.<br>
    3339 
    3340 
    3341 
    3342 
    3343 
    3344 
    3345       <br>
    3346 
    3347 
    3348 
    3349 
    3350 
    3351 
    3352 Currently, <span style="font-weight: bold;">building_length_x</span> must be at least <span style="font-style: italic;">3 *&nbsp;</span><a style="font-style: italic;" href="#dx">dx</a> and no more than <span style="font-style: italic;">(&nbsp;</span><a style="font-style: italic;" href="#nx">nx</a><span style="font-style: italic;"> - 1 ) </span><span style="font-style: italic;"> * <a href="#dx">dx</a> </span><span style="font-style: italic;">- <a href="#building_wall_left">building_wall_left</a><a href="#dx"></a><a href="#dx"></a></span>. This parameter requires the use of&nbsp;<a href="#topography">topography</a> = <span style="font-style: italic;">'single_building'</span>.</td>
    3353 
    3354 
    3355 
    3356 
    3357 
    3358 
    3359     </tr>
    3360 
    3361 
    3362 
    3363 
    3364 
    3365 
    3366     <tr>
    3367 
    3368 
    3369 
    3370 
    3371 
    3372 
    3373       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_length_y"></a>building_length_y</span></td>
    3374 
    3375 
    3376 
    3377 
    3378 
    3379 
    3380       <td style="vertical-align: top;">R</td>
    3381 
    3382 
    3383 
    3384 
    3385 
    3386 
    3387       <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td>
    3388 
    3389 
    3390 
    3391 
    3392 
    3393 
    3394       <td>Depth of a single building in m.<br>
    3395 
    3396 
    3397 
    3398 
    3399 
    3400 
    3401       <br>
    3402 
    3403 
    3404 
    3405 
    3406 
    3407 
    3408 Currently, <span style="font-weight: bold;">building_length_y</span> must be at least <span style="font-style: italic;">3 *&nbsp;</span><a style="font-style: italic;" href="#dy">dy</a> and no more than <span style="font-style: italic;">(&nbsp;</span><a style="font-style: italic;" href="#ny">ny</a><span style="font-style: italic;"> - 1 )&nbsp;</span><span style="font-style: italic;"> * <a href="#dy">dy</a></span><span style="font-style: italic;"> - <a href="#building_wall_south">building_wall_south</a><a href="#dy"></a></span>. This parameter requires the use of&nbsp;<a href="#topography">topography</a> = <span style="font-style: italic;">'single_building'</span>.</td>
    3409 
    3410 
    3411 
    3412 
    3413 
    3414 
    3415     </tr>
    3416 
    3417 
    3418 
    3419 
    3420 
    3421 
    3422     <tr>
    3423 
    3424 
    3425 
    3426 
    3427 
    3428 
    3429       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_wall_left"></a>building_wall_left</span></td>
    3430 
    3431 
    3432 
    3433 
    3434 
    3435 
    3436       <td style="vertical-align: top;">R</td>
    3437 
    3438 
    3439 
    3440 
    3441 
    3442 
    3443       <td style="vertical-align: top;"><span style="font-style: italic;">building centered in x-direction</span></td>
    3444 
    3445 
    3446 
    3447 
    3448 
    3449 
    3450       <td>x-coordinate of the left building wall (distance between the left building wall and the left border of the model domain) in m.<br>
    3451 
    3452 
    3453 
    3454 
    3455 
    3456 
    3457       <br>
    3458 
    3459 
    3460 
    3461 
    3462 
    3463 
    3464 Currently, <span style="font-weight: bold;">building_wall_left</span> must be at least <span style="font-style: italic;">1 *&nbsp;</span><a style="font-style: italic;" href="#dx">dx</a> and less than <span style="font-style: italic;">( <a href="#nx">nx</a>&nbsp; - 1 ) * <a href="#dx">dx</a> -&nbsp; <a href="#building_length_x">building_length_x</a></span>. This parameter requires the use of&nbsp;<a href="#topography">topography</a> = <span style="font-style: italic;">'single_building'</span>.<br>
    3465 
    3466 
    3467 
    3468 
    3469 
    3470 
    3471       <br>
    3472 
    3473 
    3474 
    3475 
    3476 
    3477 
    3478 The default value&nbsp;<span style="font-weight: bold;">building_wall_left</span> = <span style="font-style: italic;">( ( <a href="#nx">nx</a>&nbsp;+ 1 ) * <a href="#dx">dx</a> -&nbsp; <a href="#building_length_x">building_length_x</a> ) / 2</span> centers the building in x-direction. </td>
    3479 
    3480 
    3481 
    3482 
    3483 
    3484 
    3485     </tr>
    3486 
    3487 
    3488 
    3489 
    3490 
    3491 
    3492     <tr>
    3493 
    3494 
    3495 
    3496 
    3497 
    3498 
    3499       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_wall_south"></a>building_wall_south</span></td>
    3500 
    3501 
    3502 
    3503 
    3504 
    3505 
    3506       <td style="vertical-align: top;">R</td>
    3507 
    3508 
    3509 
    3510 
    3511 
    3512 
    3513       <td style="vertical-align: top;"><span style="font-style: italic;"></span><span style="font-style: italic;">building centered in y-direction</span></td>
    3514 
    3515 
    3516 
    3517 
    3518 
    3519 
    3520       <td>y-coordinate of the South building wall (distance between the
     342for the velocities are solved).</p> </td> </tr> <tr>
     343<td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_height"></a>building_height</span></td>
     344<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td> <td>Height
     345of a single building in m.<br> <br> <span style="font-weight: bold;">building_height</span> must
     346be less than the height of the model domain. This parameter requires
     347the use of&nbsp;<a href="#topography">topography</a>
     348= <span style="font-style: italic;">'single_building'</span>.</td>
     349</tr> <tr> <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_length_x"></a>building_length_x</span></td>
     350<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td> <td><span style="font-style: italic;"></span>Width of a single
     351building in m.<br> <br>
     352Currently, <span style="font-weight: bold;">building_length_x</span>
     353must be at least <span style="font-style: italic;">3
     354*&nbsp;</span><a style="font-style: italic;" href="#dx">dx</a> and no more than <span style="font-style: italic;">(&nbsp;</span><a style="font-style: italic;" href="#nx">nx</a><span style="font-style: italic;"> - 1 ) </span><span style="font-style: italic;"> * <a href="#dx">dx</a>
     355</span><span style="font-style: italic;">- <a href="#building_wall_left">building_wall_left</a></span>.
     356This parameter requires the use of&nbsp;<a href="#topography">topography</a>
     357= <span style="font-style: italic;">'single_building'</span>.</td>
     358</tr> <tr> <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_length_y"></a>building_length_y</span></td>
     359<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">50.0</span></td> <td>Depth
     360of a single building in m.<br> <br>
     361Currently, <span style="font-weight: bold;">building_length_y</span>
     362must be at least <span style="font-style: italic;">3
     363*&nbsp;</span><a style="font-style: italic;" href="#dy">dy</a> and no more than <span style="font-style: italic;">(&nbsp;</span><a style="font-style: italic;" href="#ny">ny</a><span style="font-style: italic;"> - 1 )&nbsp;</span><span style="font-style: italic;"> * <a href="#dy">dy</a></span><span style="font-style: italic;"> - <a href="#building_wall_south">building_wall_south</a></span>. This parameter requires
     364the use of&nbsp;<a href="#topography">topography</a>
     365= <span style="font-style: italic;">'single_building'</span>.</td>
     366</tr> <tr> <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_wall_left"></a>building_wall_left</span></td>
     367<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">building centered in x-direction</span></td>
     368<td>x-coordinate of the left building wall (distance between the
     369left building wall and the left border of the model domain) in m.<br>
     370<br>
     371Currently, <span style="font-weight: bold;">building_wall_left</span>
     372must be at least <span style="font-style: italic;">1
     373*&nbsp;</span><a style="font-style: italic;" href="#dx">dx</a> and less than <span style="font-style: italic;">( <a href="#nx">nx</a>&nbsp;
     374- 1 ) * <a href="#dx">dx</a> -&nbsp; <a href="#building_length_x">building_length_x</a></span>.
     375This parameter requires the use of&nbsp;<a href="#topography">topography</a>
     376= <span style="font-style: italic;">'single_building'</span>.<br>
     377<br>
     378The default value&nbsp;<span style="font-weight: bold;">building_wall_left</span>
     379= <span style="font-style: italic;">( ( <a href="#nx">nx</a>&nbsp;+
     3801 ) * <a href="#dx">dx</a> -&nbsp; <a href="#building_length_x">building_length_x</a> ) / 2</span>
     381centers the building in x-direction. </td> </tr> <tr>
     382<td style="vertical-align: top;"><span style="font-weight: bold;"><a name="building_wall_south"></a>building_wall_south</span></td>
     383<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;"></span><span style="font-style: italic;">building centered in y-direction</span></td>
     384<td>y-coordinate of the South building wall (distance between the
    3521385South building wall and the South border of the model domain) in m.<br>
    3522 
    3523 
    3524 
    3525 
    3526 
    3527 
    3528       <br>
    3529 
    3530 
    3531 
    3532 
    3533 
    3534 
    3535 Currently, <span style="font-weight: bold;">building_wall_south</span> must be at least <span style="font-style: italic;">1 *&nbsp;</span><a style="font-style: italic;" href="#dy">dy</a> and less than <span style="font-style: italic;">( <a href="#ny">ny</a>&nbsp; - 1 ) * <a href="#dy">dy</a> -&nbsp; <a href="#building_length_y">building_length_y</a></span>. This parameter requires the use of&nbsp;<a href="#topography">topography</a> = <span style="font-style: italic;">'single_building'</span>.<br>
    3536 
    3537 
    3538 
    3539 
    3540 
    3541 
    3542       <br>
    3543 
    3544 
    3545 
    3546 
    3547 
    3548 
    3549 The default value&nbsp;<span style="font-weight: bold;">building_wall_south</span> = <span style="font-style: italic;">( ( <a href="#ny">ny</a>&nbsp;+ 1 ) * <a href="#dy">dy</a> -&nbsp; <a href="#building_length_y">building_length_y</a> ) / 2</span> centers the building in y-direction. </td>
    3550 
    3551 
    3552 
    3553 
    3554 
    3555 
    3556     </tr>
    3557 
    3558 
    3559 
    3560 
    3561 
    3562 
    3563     <tr>
    3564 
    3565 
    3566 
    3567 
    3568 
    3569 
    3570 
    3571 
    3572 
    3573 
    3574       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="cloud_droplets"></a>cloud_droplets</span><br>
    3575 
    3576 
    3577 
    3578 
    3579 
    3580 
    3581 
    3582 
    3583 
    3584 
    3585       </td>
    3586 
    3587 
    3588 
    3589 
    3590 
    3591 
    3592 
    3593 
    3594 
    3595 
    3596       <td style="vertical-align: top;">L<br>
    3597 
    3598 
    3599 
    3600 
    3601 
    3602 
    3603 
    3604 
    3605 
    3606 
    3607       </td>
    3608 
    3609 
    3610 
    3611 
    3612 
    3613 
    3614 
    3615 
    3616 
    3617 
    3618       <td style="vertical-align: top;"><span style="font-style: italic;">.F.</span><br>
    3619 
    3620 
    3621 
    3622 
    3623 
    3624 
    3625 
    3626 
    3627 
    3628 
    3629       </td>
    3630 
    3631 
    3632 
    3633 
    3634 
    3635 
    3636 
    3637 
    3638 
    3639 
    3640       <td style="vertical-align: top;">Parameter to switch on usage of cloud droplets.<br>
    3641 
    3642 
    3643 
    3644 
    3645 
    3646 
    3647 
    3648 
    3649 
    3650 
    3651       <br>
    3652 
    3653 
    3654 
    3655 
    3656 
    3657 
    3658 
    3659 
    3660 
    3661 
     386<br>
     387Currently, <span style="font-weight: bold;">building_wall_south</span>
     388must be at least <span style="font-style: italic;">1
     389*&nbsp;</span><a style="font-style: italic;" href="#dy">dy</a> and less than <span style="font-style: italic;">( <a href="#ny">ny</a>&nbsp;
     390- 1 ) * <a href="#dy">dy</a> -&nbsp; <a href="#building_length_y">building_length_y</a></span>.
     391This parameter requires the use of&nbsp;<a href="#topography">topography</a>
     392= <span style="font-style: italic;">'single_building'</span>.<br>
     393<br>
     394The default value&nbsp;<span style="font-weight: bold;">building_wall_south</span>
     395= <span style="font-style: italic;">( ( <a href="#ny">ny</a>&nbsp;+
     3961 ) * <a href="#dy">dy</a> -&nbsp; <a href="#building_length_y">building_length_y</a> ) / 2</span>
     397centers the building in y-direction. </td> </tr> <tr>
     398<td style="vertical-align: top;"><span style="font-weight: bold;"><a name="cloud_droplets"></a>cloud_droplets</span><br>
     399</td> <td style="vertical-align: top;">L<br> </td>
     400<td style="vertical-align: top;"><span style="font-style: italic;">.F.</span><br> </td>
     401<td style="vertical-align: top;">Parameter to switch on
     402usage of cloud droplets.<br> <br>
    3662403Cloud droplets require to use the particle package (<span style="font-weight: bold;">mrun</span>-option <span style="font-family: monospace;">-p particles</span>),
    3663404so in this case a particle corresponds to a droplet. The droplet
     
    3666407The real number of initial droplets in a grid cell is equal to the
    3667408initial number of droplets (defined by the particle source parameters <span lang="en-GB"><font face="Thorndale, serif"> </font></span><a href="chapter_4.2.html#pst"><span lang="en-GB"><font face="Thorndale, serif">pst</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#psl"><span lang="en-GB"><font face="Thorndale, serif">psl</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#psr"><span lang="en-GB"><font face="Thorndale, serif">psr</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#pss"><span lang="en-GB"><font face="Thorndale, serif">pss</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#psn"><span lang="en-GB"><font face="Thorndale, serif">psn</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#psb"><span lang="en-GB"><font face="Thorndale, serif">psb</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#pdx"><span lang="en-GB"><font face="Thorndale, serif">pdx</font></span></a><span lang="en-GB"><font face="Thorndale, serif">, </font></span><a href="chapter_4.2.html#pdy"><span lang="en-GB"><font face="Thorndale, serif">pdy</font></span></a>
    3668       <span lang="en-GB"><font face="Thorndale, serif">and </font></span><a href="chapter_4.2.html#pdz"><span lang="en-GB"><font face="Thorndale, serif">pdz</font></span></a><span lang="en-GB"></span><span lang="en-GB"></span>) times the <a href="#initial_weighting_factor">initial_weighting_factor</a>.<br>
    3669 
    3670 
    3671 
    3672 
    3673 
    3674 
    3675 
    3676 
    3677 
    3678 
    3679       <br>
    3680 
    3681 
    3682 
    3683 
    3684 
    3685 
    3686 
    3687 
    3688 
    3689 
    3690 In case of using cloud droplets, the default condensation scheme in PALM cannot be used, i.e. <a href="#cloud_physics">cloud_physics</a> must be set <span style="font-style: italic;">.F.</span>.<br>
    3691 
    3692 
    3693 
    3694 
    3695 
    3696 
    3697 
    3698 
    3699 
    3700 
    3701       </td>
    3702 
    3703 
    3704 
    3705 
    3706 
    3707 
    3708 
    3709 
    3710 
    3711 
    3712     </tr>
    3713 
    3714 
    3715 
    3716 
    3717 
    3718 
    3719 
    3720 
    3721 
    3722 
    3723     <tr>
    3724 
    3725 
    3726 
    3727 
    3728 
    3729 
    3730 
    3731 
    3732 
    3733 
    3734       <td style="vertical-align: top;">
    3735      
    3736      
    3737      
    3738      
    3739      
    3740      
    3741      
    3742      
    3743      
    3744      
    3745       <p><a name="cloud_physics"></a><b>cloud_physics</b></p>
    3746 
    3747 
    3748 
    3749 
    3750 
    3751 
    3752 
    3753 
    3754 
    3755 
    3756       </td>
    3757 
    3758 
    3759 
    3760 
    3761 
    3762 
    3763 
    3764 
    3765 
    3766 
    3767       <td style="vertical-align: top;">L<br>
    3768 
    3769 
    3770 
    3771 
    3772 
    3773 
    3774 
    3775 
    3776 
    3777 
    3778       </td>
    3779 
    3780 
    3781 
    3782 
    3783 
    3784 
    3785 
    3786 
    3787 
    3788 
    3789       <td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td>
    3790 
    3791 
    3792 
    3793 
    3794 
    3795 
    3796 
    3797 
    3798 
    3799 
    3800       <td style="vertical-align: top;">
    3801      
    3802      
    3803      
    3804      
    3805      
    3806      
    3807      
    3808      
    3809      
    3810      
    3811       <p>Parameter to switch on the condensation scheme.&nbsp; </p>
    3812 
    3813 
    3814 
    3815 
    3816 
    3817 
    3818 
    3819 
    3820 
    3821 
    3822 For <b>cloud_physics =</b> <span style="font-style: italic;">.TRUE.</span>, equations for the
     409<span lang="en-GB"><font face="Thorndale, serif">and
     410</font></span><a href="chapter_4.2.html#pdz"><span lang="en-GB"><font face="Thorndale, serif">pdz</font></span></a><span lang="en-GB"></span><span lang="en-GB"></span>)
     411times the <a href="#initial_weighting_factor">initial_weighting_factor</a>.<br>
     412<br>
     413In case of using cloud droplets, the default condensation scheme in
     414PALM cannot be used, i.e. <a href="#cloud_physics">cloud_physics</a>
     415must be set <span style="font-style: italic;">.F.</span>.<br>
     416</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="cloud_physics"></a><b>cloud_physics</b></p>
     417</td> <td style="vertical-align: top;">L<br> </td>
     418<td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td> <td style="vertical-align: top;"> <p>Parameter to switch
     419on the condensation scheme.&nbsp; </p>
     420For <b>cloud_physics =</b> <span style="font-style: italic;">.TRUE.</span>, equations
     421for the
    3823422liquid water&nbsp;
    3824423content and the liquid water potential temperature are solved instead
     
    3828427unsaturated (0%-or-100%-scheme). A simple precipitation scheme can
    3829428additionally be switched on with parameter <a href="#precipitation">precipitation</a>.
    3830 Also cloud-top cooling by longwave radiation can be utilized (see <a href="#radiation">radiation</a>)<br>
    3831 
    3832 
    3833 
    3834 
    3835 
    3836 
    3837 
    3838 
    3839 
    3840 
    3841       <b><br>
    3842 
    3843 
    3844 
    3845 
    3846 
    3847 
    3848 
    3849 
    3850 
    3851 
    3852 cloud_physics =</b> <span style="font-style: italic;">.TRUE. </span>requires <a href="#moisture">moisture</a> =<span style="font-style: italic;"> .TRUE.</span> .<br>
    3853 
    3854 
    3855 
    3856 
    3857 
    3858 
    3859 
    3860 
    3861 
    3862 
     429Also cloud-top cooling by longwave radiation can be utilized (see <a href="#radiation">radiation</a>)<br> <b><br>
     430cloud_physics =</b> <span style="font-style: italic;">.TRUE.
     431</span>requires <a href="#moisture">moisture</a>
     432=<span style="font-style: italic;"> .TRUE.</span> .<br>
    3863433Detailed information about the condensation scheme is given in the
    3864434description of the <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM-1/Dokumentationen/Cloud_physics/wolken.pdf">cloud
    3865 physics module</a> (pdf-file, only in German).<br>
    3866 
    3867 
    3868 
    3869 
    3870 
    3871 
    3872 
    3873 
    3874 
    3875 
    3876       <br>
    3877 
    3878 
    3879 
    3880 
    3881 
    3882 
    3883 
    3884 
    3885 
    3886 
    3887 This condensation scheme is not allowed if cloud droplets are simulated explicitly (see <a href="#cloud_droplets">cloud_droplets</a>).<br>
    3888 
    3889 
    3890 
    3891 
    3892 
    3893 
    3894 
    3895 
    3896 
    3897 
    3898       </td>
    3899 
    3900 
    3901 
    3902 
    3903 
    3904 
    3905 
    3906 
    3907 
    3908 
    3909     </tr>
    3910 
    3911 
    3912 
    3913 
    3914 
    3915 
    3916 
    3917 
    3918 
    3919 
    3920     <tr>
    3921 
    3922 
    3923 
    3924 
    3925 
    3926 
    3927 
    3928       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="conserve_volume_flow"></a>conserve_volume_flow</span></td>
    3929 
    3930 
    3931 
    3932 
    3933 
    3934 
    3935 
    3936       <td style="vertical-align: top;">L</td>
    3937 
    3938 
    3939 
    3940 
    3941 
    3942 
    3943 
    3944       <td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td>
    3945 
    3946 
    3947 
    3948 
    3949 
    3950 
    3951 
    3952       <td>Conservation of volume flow in x- and y-direction.<br>
    3953       <br>
    3954       <span style="font-weight: bold;">conserve_volume_flow</span> = <span style="font-style: italic;">.TRUE.</span>
     435physics module</a> (pdf-file, only in German).<br> <br>
     436This condensation scheme is not allowed if cloud droplets are simulated
     437explicitly (see <a href="#cloud_droplets">cloud_droplets</a>).<br>
     438</td> </tr> <tr> <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="conserve_volume_flow"></a>conserve_volume_flow</span></td>
     439<td style="vertical-align: top;">L</td> <td style="vertical-align: top;"><span style="font-style: italic;">.F.</span></td> <td>Conservation
     440of volume flow in x- and y-direction.<br> <br> <span style="font-weight: bold;">conserve_volume_flow</span>
     441= <span style="font-style: italic;">.TRUE.</span>
    3955442guarantees that the volume flow through the xz- or yz-cross-section of
    3956443the total model domain remains constant (equal to the initial value at
    3957444t=0) throughout the run.<br>
    3958 </td>
    3959 
    3960 
    3961 
    3962 
    3963 
    3964 
    3965 
    3966     </tr>
    3967 
    3968 
    3969 
    3970 
    3971 
    3972 
    3973 
    3974     <tr>
    3975 
    3976 
    3977 
    3978 
    3979 
    3980 
    3981 
    3982 
    3983 
    3984 
    3985       <td style="vertical-align: top;">
    3986      
    3987      
    3988      
    3989      
    3990      
    3991      
    3992      
    3993      
    3994      
    3995      
    3996       <p><a name="cut_spline_overshoot"></a><b>cut_spline_overshoot</b></p>
    3997 
    3998 
    3999 
    4000 
    4001 
    4002 
    4003 
    4004 
    4005 
    4006 
    4007       </td>
    4008 
    4009 
    4010 
    4011 
    4012 
    4013 
    4014 
    4015 
    4016 
    4017 
    4018       <td style="vertical-align: top;">L</td>
    4019 
    4020 
    4021 
    4022 
    4023 
    4024 
    4025 
    4026 
    4027 
    4028 
    4029       <td style="vertical-align: top;"><span style="font-style: italic;">.T.</span></td>
    4030 
    4031 
    4032 
    4033 
    4034 
    4035 
    4036 
    4037 
    4038 
    4039 
    4040       <td style="vertical-align: top;">
    4041      
    4042      
    4043      
    4044      
    4045      
    4046      
    4047      
    4048      
    4049      
    4050      
    4051       <p>Cuts off of so-called overshoots, which can occur with the
    4052 upstream-spline scheme.&nbsp; </p>
    4053 
    4054 
    4055 
    4056 
    4057 
    4058 
    4059 
    4060 
    4061 
    4062 
    4063      
    4064      
    4065      
    4066      
    4067      
    4068      
    4069      
    4070      
    4071      
    4072      
    4073       <p><font color="#000000">The cubic splines tend to overshoot in
     445</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="cut_spline_overshoot"></a><b>cut_spline_overshoot</b></p>
     446</td> <td style="vertical-align: top;">L</td>
     447<td style="vertical-align: top;"><span style="font-style: italic;">.T.</span></td> <td style="vertical-align: top;"> <p>Cuts off of
     448so-called overshoots, which can occur with the
     449upstream-spline scheme.&nbsp; </p> <p><font color="#000000">The cubic splines tend to overshoot in
    4074450case of discontinuous changes of variables between neighbouring grid
    4075451points.</font><font color="#ff0000"> </font><font color="#000000">This
    4076 may lead to errors in calculating the advection tendency.</font> Choice
    4077 of <b>cut_spline_overshoot</b> = <i>.TRUE.</i> (switched on by
     452may lead to errors in calculating the advection tendency.</font>
     453Choice
     454of <b>cut_spline_overshoot</b> = <i>.TRUE.</i>
     455(switched on by
    4078456default)
    4079457allows variable values not to exceed an interval defined by the
    4080458respective adjacent grid points. This interval can be adjusted
    4081459seperately for every prognostic variable (see initialization parameters
    4082       <a href="#overshoot_limit_e">overshoot_limit_e</a>, <a href="#overshoot_limit_pt">overshoot_limit_pt</a>, <a href="#overshoot_limit_u">overshoot_limit_u</a>,
     460<a href="#overshoot_limit_e">overshoot_limit_e</a>, <a href="#overshoot_limit_pt">overshoot_limit_pt</a>, <a href="#overshoot_limit_u">overshoot_limit_u</a>,
    4083461etc.). This might be necessary in case that the
    4084462default interval has a non-tolerable effect on the model
    4085 results.&nbsp; </p>
    4086 
    4087 
    4088 
    4089 
    4090 
    4091 
    4092 
    4093 
    4094 
    4095 
    4096      
    4097      
    4098      
    4099      
    4100      
    4101      
    4102      
    4103      
    4104      
    4105      
    4106       <p>Overshoots may also be removed using the parameters <a href="#ups_limit_e">ups_limit_e</a>, <a href="#ups_limit_pt">ups_limit_pt</a>,
     463results.&nbsp; </p> <p>Overshoots may also be removed
     464using the parameters <a href="#ups_limit_e">ups_limit_e</a>,
     465<a href="#ups_limit_pt">ups_limit_pt</a>,
    4107466etc. as well as by applying a long-filter (see <a href="#long_filter_factor">long_filter_factor</a>).</p>
    4108 
    4109 
    4110 
    4111 
    4112 
    4113 
    4114 
    4115 
    4116 
    4117 
    4118       </td>
    4119 
    4120 
    4121 
    4122 
    4123 
    4124 
    4125 
    4126 
    4127 
    4128 
    4129     </tr>
    4130 
    4131 
    4132 
    4133 
    4134 
    4135 
    4136 
    4137 
    4138 
    4139 
    4140     <tr>
    4141 
    4142 
    4143 
    4144 
    4145 
    4146 
    4147 
    4148 
    4149 
    4150 
    4151       <td style="vertical-align: top;">
    4152      
    4153      
    4154      
    4155      
    4156      
    4157      
    4158      
    4159      
    4160      
    4161      
    4162       <p><a name="damp_level_1d"></a><b>damp_level_1d</b></p>
    4163 
    4164 
    4165 
    4166 
    4167 
    4168 
    4169 
    4170 
    4171 
    4172 
    4173       </td>
    4174 
    4175 
    4176 
    4177 
    4178 
    4179 
    4180 
    4181 
    4182 
    4183 
    4184       <td style="vertical-align: top;">R</td>
    4185 
    4186 
    4187 
    4188 
    4189 
    4190 
    4191 
    4192 
    4193 
    4194 
    4195       <td style="vertical-align: top;"><span style="font-style: italic;">zu(nz+1)</span></td>
    4196 
    4197 
    4198 
    4199 
    4200 
    4201 
    4202 
    4203 
    4204 
    4205 
    4206       <td style="vertical-align: top;">
    4207      
    4208      
    4209      
    4210      
    4211      
    4212      
    4213      
    4214      
    4215      
    4216      
    4217       <p>Height where the damping layer begins in the 1d-model
    4218 (in m).&nbsp; </p>
    4219 
    4220 
    4221 
    4222 
    4223 
    4224 
    4225 
    4226 
    4227 
    4228 
    4229      
    4230      
    4231      
    4232      
    4233      
    4234      
    4235      
    4236      
    4237      
    4238      
    4239       <p>This parameter is used to switch on a damping layer for the
     467</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="damp_level_1d"></a><b>damp_level_1d</b></p>
     468</td> <td style="vertical-align: top;">R</td>
     469<td style="vertical-align: top;"><span style="font-style: italic;">zu(nz+1)</span></td>
     470<td style="vertical-align: top;"> <p>Height where
     471the damping layer begins in the 1d-model
     472(in m).&nbsp; </p> <p>This parameter is used to
     473switch on a damping layer for the
    42404741d-model, which is generally needed for the damping of inertia
    4241475oscillations. Damping is done by gradually increasing the value
    4242476of the eddy diffusivities about 10% per vertical grid level
    4243477(starting with the value at the height given by <b>damp_level_1d</b>,
    4244 or possibly from the next grid pint above), i.e. K<sub>m</sub>(k+1) =
     478or possibly from the next grid pint above), i.e. K<sub>m</sub>(k+1)
     479=
    42454801.1 * K<sub>m</sub>(k).
    4246 The values of K<sub>m</sub> are limited to 10 m**2/s at maximum.&nbsp; <br>
    4247 
    4248 
    4249 
    4250 
    4251 
    4252 
    4253 
    4254 
    4255 
    4256 
     481The values of K<sub>m</sub> are limited to 10 m**2/s at
     482maximum.&nbsp; <br>
    4257483This parameter only comes into effect if the 1d-model is switched on
    4258484for
    4259485the initialization of the 3d-model using <a href="#initializing_actions">initializing_actions</a>
    4260 = <span style="font-style: italic;">'set_1d-model_profiles'</span>. <br>
    4261 
    4262 
    4263 
    4264 
    4265 
    4266 
    4267 
    4268 
    4269 
    4270 
    4271       </p>
    4272 
    4273 
    4274 
    4275 
    4276 
    4277 
    4278 
    4279 
    4280 
    4281 
    4282       </td>
    4283 
    4284 
    4285 
    4286 
    4287 
    4288 
    4289 
    4290 
    4291 
    4292 
    4293     </tr>
    4294 
    4295 
    4296 
    4297 
    4298 
    4299 
    4300 
    4301 
    4302 
    4303 
    4304     <tr>
    4305       <td style="vertical-align: top;"><a name="dissipation_1d"></a><span style="font-weight: bold;">dissipation_1d</span><br>
    4306       </td>
    4307       <td style="vertical-align: top;">C*20<br>
    4308       </td>
    4309       <td style="vertical-align: top;"><span style="font-style: italic;">'as_in_3d_</span><br style="font-style: italic;">
    4310       <span style="font-style: italic;">model'</span><br>
    4311       </td>
    4312       <td style="vertical-align: top;">Calculation method for the energy dissipation term in the TKE equation of the 1d-model.<br>
    4313       <br>
    4314 By default the dissipation is calculated as in the 3d-model using diss = (0.19 + 0.74 * l / l_grid) * e**1.5 / l.<br>
    4315       <br>
    4316 Setting <span style="font-weight: bold;">dissipation_1d</span> = <span style="font-style: italic;">'detering'</span> forces the dissipation to be calculated as diss = 0.064 * e**1.5 / l.<br>
    4317       </td>
    4318     </tr>
    4319 <tr>
    4320 
    4321 
    4322 
    4323 
    4324 
    4325 
    4326 
    4327 
    4328 
    4329 
    4330       <td style="vertical-align: top;">
    4331      
    4332      
    4333      
    4334      
    4335      
    4336      
    4337      
    4338      
    4339      
    4340      
    4341       <p><a name="dt"></a><b>dt</b></p>
    4342 
    4343 
    4344 
    4345 
    4346 
    4347 
    4348 
    4349 
    4350 
    4351 
    4352       </td>
    4353 
    4354 
    4355 
    4356 
    4357 
    4358 
    4359 
    4360 
    4361 
    4362 
    4363       <td style="vertical-align: top;">R</td>
    4364 
    4365 
    4366 
    4367 
    4368 
    4369 
    4370 
    4371 
    4372 
    4373 
    4374       <td style="vertical-align: top;"><span style="font-style: italic;">variable</span></td>
    4375 
    4376 
    4377 
    4378 
    4379 
    4380 
    4381 
    4382 
    4383 
    4384 
    4385       <td style="vertical-align: top;">
    4386      
    4387      
    4388      
    4389      
    4390      
    4391      
    4392      
    4393      
    4394      
    4395      
    4396       <p>Time step for the 3d-model (in s).&nbsp; </p>
    4397 
    4398 
    4399 
    4400 
    4401 
    4402 
    4403 
    4404 
    4405 
    4406 
    4407      
    4408      
    4409      
    4410      
    4411      
    4412      
    4413      
    4414      
    4415      
    4416      
    4417       <p>By default, (i.e. if a Runge-Kutta scheme is used, see <a href="#timestep_scheme">timestep_scheme</a>)
     486= <span style="font-style: italic;">'set_1d-model_profiles'</span>.
     487<br> </p> </td> </tr> <tr> <td style="vertical-align: top;"><a name="dissipation_1d"></a><span style="font-weight: bold;">dissipation_1d</span><br>
     488</td> <td style="vertical-align: top;">C*20<br>
     489</td> <td style="vertical-align: top;"><span style="font-style: italic;">'as_in_3d_</span><br style="font-style: italic;"> <span style="font-style: italic;">model'</span><br> </td>
     490<td style="vertical-align: top;">Calculation method for
     491the energy dissipation term in the TKE equation of the 1d-model.<br>
     492<br>
     493By default the dissipation is calculated as in the 3d-model using diss
     494= (0.19 + 0.74 * l / l_grid) * e**1.5 / l.<br> <br>
     495Setting <span style="font-weight: bold;">dissipation_1d</span>
     496= <span style="font-style: italic;">'detering'</span>
     497forces the dissipation to be calculated as diss = 0.064 * e**1.5 / l.<br>
     498</td> </tr>
     499<tr> <td style="vertical-align: top;"> <p><a name="dt"></a><b>dt</b></p> </td>
     500<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">variable</span></td>
     501<td style="vertical-align: top;"> <p>Time step for
     502the 3d-model (in s).&nbsp; </p> <p>By default, (i.e.
     503if a Runge-Kutta scheme is used, see <a href="#timestep_scheme">timestep_scheme</a>)
    4418504the value of the time step is calculating after each time step
    4419505(following the time step criteria) and
    4420 used for the next step.</p>
    4421 
    4422 
    4423 
    4424 
    4425 
    4426 
    4427 
    4428 
    4429 
    4430 
    4431      
    4432      
    4433      
    4434      
    4435      
    4436      
    4437      
    4438      
    4439      
    4440      
    4441       <p>If the user assigns <b>dt</b> a value, then the time step is
     506used for the next step.</p> <p>If the user assigns <b>dt</b>
     507a value, then the time step is
    4442508fixed to this value throughout the whole run (whether it fulfills the
    4443509time step
    4444510criteria or not). However, changes are allowed for restart runs,
    4445511because <b>dt</b> can also be used as a <a href="chapter_4.2.html#dt_laufparameter">run
    4446 parameter</a>.&nbsp; </p>
    4447 
    4448 
    4449 
    4450 
    4451 
    4452 
    4453 
    4454 
    4455 
    4456 
    4457      
    4458      
    4459      
    4460      
    4461      
    4462      
    4463      
    4464      
    4465      
    4466      
    4467       <p>In case that the calculated time step meets the condition<br>
    4468 
    4469 
    4470 
    4471 
    4472 
    4473 
    4474 
    4475 
    4476 
    4477 
    4478       </p>
    4479 
    4480 
    4481 
    4482 
    4483 
    4484 
    4485 
    4486 
    4487 
    4488 
    4489      
    4490      
    4491      
    4492      
    4493      
    4494      
    4495      
    4496      
    4497      
    4498      
    4499       <ul>
    4500 
    4501 
    4502 
    4503 
    4504 
    4505 
    4506 
    4507 
    4508 
    4509 
    4510        
    4511        
    4512        
    4513        
    4514        
    4515        
    4516        
    4517        
    4518        
    4519        
    4520         <p><b>dt</b> &lt; 0.00001 * dt_max (with dt_max = 20.0)</p>
    4521 
    4522 
    4523 
    4524 
    4525 
    4526 
    4527 
    4528 
    4529 
    4530 
    4531      
    4532      
    4533      
    4534      
    4535      
    4536      
    4537      
    4538      
    4539      
    4540      
    4541       </ul>
    4542 
    4543 
    4544 
    4545 
    4546 
    4547 
    4548 
    4549 
    4550 
    4551 
    4552      
    4553      
    4554      
    4555      
    4556      
    4557      
    4558      
    4559      
    4560      
    4561      
    4562       <p>the simulation will be aborted. Such situations usually arise
     512parameter</a>.&nbsp; </p> <p>In case that the
     513calculated time step meets the condition<br> </p> <ul>
     514<p><b>dt</b> &lt; 0.00001 * <a href="chapter_4.2.html#dt_max">dt_max</a> (with dt_max
     515= 20.0)</p> </ul> <p>the simulation will be
     516aborted. Such situations usually arise
    4563517in case of any numerical problem / instability which causes a
    4564 non-realistic increase of the wind speed.&nbsp; </p>
    4565 
    4566 
    4567 
    4568 
    4569 
    4570 
    4571 
    4572 
    4573 
    4574 
    4575      
    4576      
    4577      
    4578      
    4579      
    4580      
    4581      
    4582      
    4583      
    4584      
    4585       <p>A small time step due to a large mean horizontal windspeed
     518non-realistic increase of the wind speed.&nbsp; </p> <p>A
     519small time step due to a large mean horizontal windspeed
    4586520speed may be enlarged by using a coordinate transformation (see <a href="#galilei_transformation">galilei_transformation</a>),
    4587 in order to spare CPU time.<br>
    4588 
    4589 
    4590 
    4591 
    4592 
    4593 
    4594 
    4595 
    4596 
    4597 
    4598       </p>
    4599 
    4600 
    4601 
    4602 
    4603 
    4604 
    4605 
    4606 
    4607 
    4608 
    4609      
    4610      
    4611      
    4612      
    4613      
    4614      
    4615      
    4616      
    4617      
    4618      
    4619       <p>If the leapfrog timestep scheme is used (see <a href="#timestep_scheme">timestep_scheme</a>)
     521in order to spare CPU time.<br> </p> <p>If the
     522leapfrog timestep scheme is used (see <a href="#timestep_scheme">timestep_scheme</a>)
    4620523a temporary time step value dt_new is calculated first, with dt_new = <a href="chapter_4.2.html#fcl_factor">cfl_factor</a>
    4621524* dt_crit where dt_crit is the maximum timestep allowed by the CFL and
     
    4625528least +5 % / -2%. If it is smaller, <span style="font-weight: bold;">dt</span>
    4626529= dt_new is immediately used for the next timestep. If it is larger,
    4627 then <span style="font-weight: bold;">dt </span>= 1.02 * dt_prev
     530then <span style="font-weight: bold;">dt </span>=
     5311.02 * dt_prev
    4628532(previous timestep) is used as the new timestep, however the time
    4629533step is only increased if the last change of the time step is dated
     
    4633537does not change at all. By doing so, permanent time step changes as
    4634538well as large
    4635 sudden changes (increases) in the time step are avoided.</p>
    4636 
    4637 
    4638 
    4639 
    4640 
    4641 
    4642 
    4643 
    4644 
    4645 
    4646       </td>
    4647 
    4648 
    4649 
    4650 
    4651 
    4652 
    4653 
    4654 
    4655 
    4656 
    4657     </tr>
    4658 
    4659 
    4660 
    4661 
    4662 
    4663 
    4664 
    4665 
    4666 
    4667 
    4668     <tr>
    4669 
    4670 
    4671 
    4672 
    4673 
    4674 
    4675 
    4676 
    4677 
    4678 
    4679       <td style="vertical-align: top;">
    4680      
    4681      
    4682      
    4683      
    4684      
    4685      
    4686      
    4687      
    4688      
    4689      
    4690       <p><a name="dt_pr_1d"></a><b>dt_pr_1d</b></p>
    4691 
    4692 
    4693 
    4694 
    4695 
    4696 
    4697 
    4698 
    4699 
    4700 
    4701       </td>
    4702 
    4703 
    4704 
    4705 
    4706 
    4707 
    4708 
    4709 
    4710 
    4711 
    4712       <td style="vertical-align: top;">R</td>
    4713 
    4714 
    4715 
    4716 
    4717 
    4718 
    4719 
    4720 
    4721 
    4722 
    4723       <td style="vertical-align: top;"><span style="font-style: italic;">9999999.9</span></td>
    4724 
    4725 
    4726 
    4727 
    4728 
    4729 
    4730 
    4731 
    4732 
    4733 
    4734       <td style="vertical-align: top;">
    4735      
    4736      
    4737      
    4738      
    4739      
    4740      
    4741      
    4742      
    4743      
    4744      
    4745       <p>Temporal interval of vertical profile output of the 1D-model
    4746 (in s).&nbsp; </p>
    4747 
    4748 
    4749 
    4750 
    4751 
    4752 
    4753 
    4754 
    4755 
    4756 
    4757      
    4758      
    4759      
    4760      
    4761      
    4762      
    4763      
    4764      
    4765      
    4766      
    4767       <p>Data are written in ASCII format to file <a href="chapter_3.4.html#LIST_PROFIL_1D">LIST_PROFIL_1D</a>.
     539sudden changes (increases) in the time step are avoided.</p> </td>
     540</tr> <tr> <td style="vertical-align: top;">
     541<p><a name="dt_pr_1d"></a><b>dt_pr_1d</b></p>
     542</td> <td style="vertical-align: top;">R</td>
     543<td style="vertical-align: top;"><span style="font-style: italic;">9999999.9</span></td>
     544<td style="vertical-align: top;"> <p>Temporal
     545interval of vertical profile output of the 1D-model
     546(in s).&nbsp; </p> <p>Data are written in ASCII
     547format to file <a href="chapter_3.4.html#LIST_PROFIL_1D">LIST_PROFIL_1D</a>.
    4768548This parameter is only in effect if the 1d-model has been switched on
    4769549for the
    4770550initialization of the 3d-model with <a href="#initializing_actions">initializing_actions</a>
    4771551= <span style="font-style: italic;">'set_1d-model_profiles'</span>.</p>
    4772 
    4773 
    4774 
    4775 
    4776 
    4777 
    4778 
    4779 
    4780 
    4781 
    4782       </td>
    4783 
    4784 
    4785 
    4786 
    4787 
    4788 
    4789 
    4790 
    4791 
    4792 
    4793     </tr>
    4794 
    4795 
    4796 
    4797 
    4798 
    4799 
    4800 
    4801 
    4802 
    4803 
    4804     <tr>
    4805 
    4806 
    4807 
    4808 
    4809 
    4810 
    4811 
    4812 
    4813 
    4814 
    4815       <td style="vertical-align: top;">
    4816      
    4817      
    4818      
    4819      
    4820      
    4821      
    4822      
    4823      
    4824      
    4825      
    4826       <p><a name="dt_run_control_1d"></a><b>dt_run_control_1d</b></p>
    4827 
    4828 
    4829 
    4830 
    4831 
    4832 
    4833 
    4834 
    4835 
    4836 
    4837       </td>
    4838 
    4839 
    4840 
    4841 
    4842 
    4843 
    4844 
    4845 
    4846 
    4847 
    4848       <td style="vertical-align: top;">R</td>
    4849 
    4850 
    4851 
    4852 
    4853 
    4854 
    4855 
    4856 
    4857 
    4858 
    4859       <td style="vertical-align: top;"><span style="font-style: italic;">60.0</span></td>
    4860 
    4861 
    4862 
    4863 
    4864 
    4865 
    4866 
    4867 
    4868 
    4869 
    4870       <td style="vertical-align: top;">
    4871      
    4872      
    4873      
    4874      
    4875      
    4876      
    4877      
    4878      
    4879      
    4880      
    4881       <p>Temporal interval of runtime control output of the 1d-model
    4882 (in s).&nbsp; </p>
    4883 
    4884 
    4885 
    4886 
    4887 
    4888 
    4889 
    4890 
    4891 
    4892 
    4893      
    4894      
    4895      
    4896      
    4897      
    4898      
    4899      
    4900      
    4901      
    4902      
    4903       <p>Data are written in ASCII format to file <a href="chapter_3.4.html#RUN_CONTROL">RUN_CONTROL</a>.
     552</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="dt_run_control_1d"></a><b>dt_run_control_1d</b></p>
     553</td> <td style="vertical-align: top;">R</td>
     554<td style="vertical-align: top;"><span style="font-style: italic;">60.0</span></td> <td style="vertical-align: top;"> <p>Temporal interval of
     555runtime control output of the 1d-model
     556(in s).&nbsp; </p> <p>Data are written in ASCII
     557format to file <a href="chapter_3.4.html#RUN_CONTROL">RUN_CONTROL</a>.
    4904558This parameter is only in effect if the 1d-model is switched on for the
    4905559initialization of the 3d-model with <a href="#initializing_actions">initializing_actions</a>
    4906560= <span style="font-style: italic;">'set_1d-model_profiles'</span>.</p>
    4907 
    4908 
    4909 
    4910 
    4911 
    4912 
    4913 
    4914 
    4915 
    4916 
    4917       </td>
    4918 
    4919 
    4920 
    4921 
    4922 
    4923 
    4924 
    4925 
    4926 
    4927 
    4928     </tr>
    4929 
    4930 
    4931 
    4932 
    4933 
    4934 
    4935 
    4936 
    4937 
    4938 
    4939     <tr>
    4940 
    4941 
    4942 
    4943 
    4944 
    4945 
    4946 
    4947 
    4948 
    4949 
    4950       <td style="vertical-align: top;">
    4951      
    4952      
    4953      
    4954      
    4955      
    4956      
    4957      
    4958      
    4959      
    4960      
    4961       <p><a name="dx"></a><b>dx</b></p>
    4962 
    4963 
    4964 
    4965 
    4966 
    4967 
    4968 
    4969 
    4970 
    4971 
    4972       </td>
    4973 
    4974 
    4975 
    4976 
    4977 
    4978 
    4979 
    4980 
    4981 
    4982 
    4983       <td style="vertical-align: top;">R</td>
    4984 
    4985 
    4986 
    4987 
    4988 
    4989 
    4990 
    4991 
    4992 
    4993 
    4994       <td style="vertical-align: top;"><span style="font-style: italic;">1.0</span></td>
    4995 
    4996 
    4997 
    4998 
    4999 
    5000 
    5001 
    5002 
    5003 
    5004 
    5005       <td style="vertical-align: top;">
    5006      
    5007      
    5008      
    5009      
    5010      
    5011      
    5012      
    5013      
    5014      
    5015      
    5016       <p>Horizontal grid spacing along the x-direction (in m).&nbsp; </p>
    5017 
    5018 
    5019 
    5020 
    5021 
    5022 
    5023 
    5024 
    5025 
    5026 
    5027      
    5028      
    5029      
    5030      
    5031      
    5032      
    5033      
    5034      
    5035      
    5036      
    5037       <p>Along x-direction only a constant grid spacing is allowed.</p>
    5038 
    5039 
    5040 
    5041 
    5042 
    5043 
    5044 
    5045 
    5046 
    5047 
    5048       </td>
    5049 
    5050 
    5051 
    5052 
    5053 
    5054 
    5055 
    5056 
    5057 
    5058 
    5059     </tr>
    5060 
    5061 
    5062 
    5063 
    5064 
    5065 
    5066 
    5067 
    5068 
    5069 
    5070     <tr>
    5071 
    5072 
    5073 
    5074 
    5075 
    5076 
    5077 
    5078 
    5079 
    5080 
    5081       <td style="vertical-align: top;">
    5082      
    5083      
    5084      
    5085      
    5086      
    5087      
    5088      
    5089      
    5090      
    5091      
    5092       <p><a name="dy"></a><b>dy</b></p>
    5093 
    5094 
    5095 
    5096 
    5097 
    5098 
    5099 
    5100 
    5101 
    5102 
    5103       </td>
    5104 
    5105 
    5106 
    5107 
    5108 
    5109 
    5110 
    5111 
    5112 
    5113 
    5114       <td style="vertical-align: top;">R</td>
    5115 
    5116 
    5117 
    5118 
    5119 
    5120 
    5121 
    5122 
    5123 
    5124 
    5125       <td style="vertical-align: top;"><span style="font-style: italic;">1.0</span></td>
    5126 
    5127 
    5128 
    5129 
    5130 
    5131 
    5132 
    5133 
    5134 
    5135 
    5136       <td style="vertical-align: top;">
    5137      
    5138      
    5139      
    5140      
    5141      
    5142      
    5143      
    5144      
    5145      
    5146      
    5147       <p>Horizontal grid spacing along the x-direction (in m).&nbsp; </p>
    5148 
    5149 
    5150 
    5151 
    5152 
    5153 
    5154 
    5155 
    5156 
    5157 
    5158      
    5159      
    5160      
    5161      
    5162      
    5163      
    5164      
    5165      
    5166      
    5167      
    5168       <p>Along x-direction only a constant grid spacing is allowed.</p>
    5169 
    5170 
    5171 
    5172 
    5173 
    5174 
    5175 
    5176 
    5177 
    5178 
    5179       </td>
    5180 
    5181 
    5182 
    5183 
    5184 
    5185 
    5186 
    5187 
    5188 
    5189 
    5190     </tr>
    5191 
    5192 
    5193 
    5194 
    5195 
    5196 
    5197 
    5198 
    5199 
    5200 
    5201     <tr>
    5202 
    5203 
    5204 
    5205 
    5206 
    5207 
    5208 
    5209 
    5210 
    5211 
    5212       <td style="vertical-align: top;">
    5213      
    5214      
    5215      
    5216      
    5217      
    5218      
    5219      
    5220      
    5221      
    5222      
    5223       <p><a name="dz"></a><b>dz</b></p>
    5224 
    5225 
    5226 
    5227 
    5228 
    5229 
    5230 
    5231 
    5232 
    5233 
    5234       </td>
    5235 
    5236 
    5237 
    5238 
    5239 
    5240 
    5241 
    5242 
    5243 
    5244 
    5245       <td style="vertical-align: top;">R</td>
    5246 
    5247 
    5248 
    5249 
    5250 
    5251 
    5252 
    5253 
    5254 
    5255 
    5256       <td style="vertical-align: top;"><br>
    5257 
    5258 
    5259 
    5260 
    5261 
    5262 
    5263 
    5264 
    5265 
    5266 
    5267       </td>
    5268 
    5269 
    5270 
    5271 
    5272 
    5273 
    5274 
    5275 
    5276 
    5277 
    5278       <td style="vertical-align: top;">
    5279      
    5280      
    5281      
    5282      
    5283      
    5284      
    5285      
    5286      
    5287      
    5288      
    5289       <p>Vertical grid spacing (in m).&nbsp; </p>
    5290 
    5291 
    5292 
    5293 
    5294 
    5295 
    5296 
    5297 
    5298 
    5299 
    5300      
    5301      
    5302      
    5303      
    5304      
    5305      
    5306      
    5307      
    5308      
    5309      
    5310       <p>This parameter must be assigned by the user, because no
    5311 default value is given.<br>
    5312 
    5313 
    5314 
    5315 
    5316 
    5317 
    5318 
    5319 
    5320 
    5321 
    5322       </p>
    5323 
    5324 
    5325 
    5326 
    5327 
    5328 
    5329 
    5330 
    5331 
    5332 
    5333      
    5334      
    5335      
    5336      
    5337      
    5338      
    5339      
    5340      
    5341      
    5342      
    5343       <p>By default, the
     561</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="dx"></a><b>dx</b></p>
     562</td> <td style="vertical-align: top;">R</td>
     563<td style="vertical-align: top;"><span style="font-style: italic;">1.0</span></td> <td style="vertical-align: top;"> <p>Horizontal grid
     564spacing along the x-direction (in m).&nbsp; </p> <p>Along
     565x-direction only a constant grid spacing is allowed.</p> </td>
     566</tr> <tr> <td style="vertical-align: top;">
     567<p><a name="dy"></a><b>dy</b></p>
     568</td> <td style="vertical-align: top;">R</td>
     569<td style="vertical-align: top;"><span style="font-style: italic;">1.0</span></td> <td style="vertical-align: top;"> <p>Horizontal grid
     570spacing along the x-direction (in m).&nbsp; </p> <p>Along
     571x-direction only a constant grid spacing is allowed.</p> </td>
     572</tr> <tr> <td style="vertical-align: top;">
     573<p><a name="dz"></a><b>dz</b></p>
     574</td> <td style="vertical-align: top;">R</td>
     575<td style="vertical-align: top;"><br> </td> <td style="vertical-align: top;"> <p>Vertical grid
     576spacing (in m).&nbsp; </p> <p>This parameter must be
     577assigned by the user, because no
     578default value is given.<br> </p> <p>By default, the
    5344579model uses constant grid spacing along z-direction, but it can be
    5345580stretched using the parameters <a href="#dz_stretch_level">dz_stretch_level</a>
    5346 and <a href="#dz_stretch_factor">dz_stretch_factor</a>. In case of stretching, a maximum allowed grid spacing can be given by <a href="#dz_max">dz_max</a>.<br>
    5347 
    5348 
    5349 
    5350 
    5351 
    5352 
    5353 
    5354 
    5355 
    5356 
    5357       </p>
    5358 
    5359 
    5360 
    5361 
    5362 
    5363 
    5364 
    5365 
    5366 
    5367 
    5368      
    5369      
    5370      
    5371      
    5372      
    5373      
    5374      
    5375      
    5376      
    5377      
    5378       <p>Assuming a constant <span style="font-weight: bold;">dz</span>,
     581and <a href="#dz_stretch_factor">dz_stretch_factor</a>.
     582In case of stretching, a maximum allowed grid spacing can be given by <a href="#dz_max">dz_max</a>.<br> </p> <p>Assuming
     583a constant <span style="font-weight: bold;">dz</span>,
    5379584the scalar levels (zu) are calculated directly by:&nbsp; </p>
    5380 
    5381 
    5382 
    5383 
    5384 
    5385 
    5386 
    5387 
    5388 
    5389 
    5390      
    5391      
    5392      
    5393      
    5394      
    5395      
    5396      
    5397      
    5398      
    5399      
    5400       <ul>
    5401 
    5402 
    5403 
    5404 
    5405 
    5406 
    5407 
    5408 
    5409 
    5410 
    5411        
    5412        
    5413        
    5414        
    5415        
    5416        
    5417        
    5418        
    5419        
    5420        
    5421         <p>zu(0) = - dz * 0.5&nbsp; <br>
    5422 
    5423 
    5424 
    5425 
    5426 
    5427 
    5428 
    5429 
    5430 
    5431 
    5432 zu(1) = dz * 0.5</p>
    5433 
    5434 
    5435 
    5436 
    5437 
    5438 
    5439 
    5440 
    5441 
    5442 
    5443      
    5444      
    5445      
    5446      
    5447      
    5448      
    5449      
    5450      
    5451      
    5452      
    5453       </ul>
    5454 
    5455 
    5456 
    5457 
    5458 
    5459 
    5460 
    5461 
    5462 
    5463 
    5464      
    5465      
    5466      
    5467      
    5468      
    5469      
    5470      
    5471      
    5472      
    5473      
    5474       <p>The w-levels lie
    5475 half between them:&nbsp; </p>
    5476 
    5477 
    5478 
    5479 
    5480 
    5481 
    5482 
    5483 
    5484 
    5485 
    5486      
    5487      
    5488      
    5489      
    5490      
    5491      
    5492      
    5493      
    5494      
    5495      
    5496       <ul>
    5497 
    5498 
    5499 
    5500 
    5501 
    5502 
    5503 
    5504 
    5505 
    5506 
    5507        
    5508        
    5509        
    5510        
    5511        
    5512        
    5513        
    5514        
    5515        
    5516        
    5517         <p>zw(k) = ( zu(k) + zu(k+1) ) * 0.5</p>
    5518 
    5519 
    5520 
    5521 
    5522 
    5523 
    5524 
    5525 
    5526 
    5527 
    5528      
    5529      
    5530      
    5531      
    5532      
    5533      
    5534      
    5535      
    5536      
    5537      
    5538       </ul>
    5539 
    5540 
    5541 
    5542 
    5543 
    5544 
    5545 
    5546 
    5547 
    5548 
    5549       </td>
    5550 
    5551 
    5552 
    5553 
    5554 
    5555 
    5556 
    5557 
    5558 
    5559 
    5560     </tr>
    5561 
    5562 
    5563 
    5564 
    5565 
    5566 
    5567 
    5568 
    5569 
    5570 
    5571     <tr><td style="vertical-align: top;"><a name="dz_max"></a><span style="font-weight: bold;">dz_max</span></td><td style="vertical-align: top;">R</td><td style="vertical-align: top;"><span style="font-style: italic;">9999999.9</span></td><td style="vertical-align: top;">Allowed maximum vertical grid spacing (in m).<br><br>If the vertical grid is stretched (see <a href="#dz_stretch_factor">dz_stretch_factor</a> and <a href="#dz_stretch_level">dz_stretch_level</a>), <span style="font-weight: bold;">dz_max</span> can be used to limit the vertical grid spacing.</td></tr><tr>
    5572 
    5573 
    5574 
    5575 
    5576 
    5577 
    5578 
    5579 
    5580 
    5581 
    5582       <td style="vertical-align: top;">
    5583      
    5584      
    5585      
    5586      
    5587      
    5588      
    5589      
    5590      
    5591      
    5592      
    5593       <p><a name="dz_stretch_factor"></a><b>dz_stretch_factor</b></p>
    5594 
    5595 
    5596 
    5597 
    5598 
    5599 
    5600 
    5601 
    5602 
    5603 
    5604       </td>
    5605 
    5606 
    5607 
    5608 
    5609 
    5610 
    5611 
    5612 
    5613 
    5614 
    5615       <td style="vertical-align: top;">R</td>
    5616 
    5617 
    5618 
    5619 
    5620 
    5621 
    5622 
    5623 
    5624 
    5625 
    5626       <td style="vertical-align: top;"><span style="font-style: italic;">1.08</span></td>
    5627 
    5628 
    5629 
    5630 
    5631 
    5632 
    5633 
    5634 
    5635 
    5636 
    5637       <td style="vertical-align: top;">
    5638      
    5639      
    5640      
    5641      
    5642      
    5643      
    5644      
    5645      
    5646      
    5647      
    5648       <p>Stretch factor for a vertically stretched grid (see <a href="#dz_stretch_level">dz_stretch_level</a>).&nbsp; </p>
    5649 
    5650 
    5651 
    5652 
    5653 
    5654 
    5655 
    5656 
    5657 
    5658 
    5659      
    5660      
    5661      
    5662      
    5663      
    5664      
    5665      
    5666      
    5667      
    5668      
    5669       <p>The stretch factor should not exceed a value of approx. 1.10 -
     585<ul> <p>zu(0) = - dz * 0.5&nbsp; <br>
     586zu(1) = dz * 0.5</p> </ul> <p>The w-levels lie
     587half between them:&nbsp; </p> <ul> <p>zw(k) =
     588( zu(k) + zu(k+1) ) * 0.5</p> </ul> </td> </tr>
     589<tr><td style="vertical-align: top;"><a name="dz_max"></a><span style="font-weight: bold;">dz_max</span></td><td style="vertical-align: top;">R</td><td style="vertical-align: top;"><span style="font-style: italic;">9999999.9</span></td><td style="vertical-align: top;">Allowed maximum vertical grid
     590spacing (in m).<br><br>If the vertical grid is stretched
     591(see <a href="#dz_stretch_factor">dz_stretch_factor</a>
     592and <a href="#dz_stretch_level">dz_stretch_level</a>),
     593<span style="font-weight: bold;">dz_max</span> can
     594be used to limit the vertical grid spacing.</td></tr><tr>
     595<td style="vertical-align: top;"> <p><a name="dz_stretch_factor"></a><b>dz_stretch_factor</b></p>
     596</td> <td style="vertical-align: top;">R</td>
     597<td style="vertical-align: top;"><span style="font-style: italic;">1.08</span></td> <td style="vertical-align: top;"> <p>Stretch factor for a
     598vertically stretched grid (see <a href="#dz_stretch_level">dz_stretch_level</a>).&nbsp;
     599</p> <p>The stretch factor should not exceed a value of
     600approx. 1.10 -
    56706011.12, otherwise the discretization errors due to the stretched grid not
    5671 negligible any more. (refer Kalnay de Rivas)</p>
    5672 
    5673 
    5674 
    5675 
    5676 
    5677 
    5678 
    5679 
    5680 
    5681 
    5682       </td>
    5683 
    5684 
    5685 
    5686 
    5687 
    5688 
    5689 
    5690 
    5691 
    5692 
    5693     </tr>
    5694 
    5695 
    5696 
    5697 
    5698 
    5699 
    5700 
    5701 
    5702 
    5703 
    5704     <tr>
    5705 
    5706 
    5707 
    5708 
    5709 
    5710 
    5711 
    5712 
    5713 
    5714 
    5715       <td style="vertical-align: top;">
    5716      
    5717      
    5718      
    5719      
    5720      
    5721      
    5722      
    5723      
    5724      
    5725      
    5726       <p><a name="dz_stretch_level"></a><b>dz_stretch_level</b></p>
    5727 
    5728 
    5729 
    5730 
    5731 
    5732 
    5733 
    5734 
    5735 
    5736 
    5737       </td>
    5738 
    5739 
    5740 
    5741 
    5742 
    5743 
    5744 
    5745 
    5746 
    5747 
    5748       <td style="vertical-align: top;">R</td>
    5749 
    5750 
    5751 
    5752 
    5753 
    5754 
    5755 
    5756 
    5757 
    5758 
    5759       <td style="vertical-align: top;"><span style="font-style: italic;">100000.0</span><br>
    5760 
    5761 
    5762 
    5763 
    5764 
    5765 
    5766 
    5767 
    5768 
    5769 
    5770       </td>
    5771 
    5772 
    5773 
    5774 
    5775 
    5776 
    5777 
    5778 
    5779 
    5780 
    5781       <td style="vertical-align: top;">
    5782      
    5783      
    5784      
    5785      
    5786      
    5787      
    5788      
    5789      
    5790      
    5791      
    5792       <p>Height level above which the grid is to be stretched
    5793 vertically (in m).&nbsp; </p>
    5794 
    5795 
    5796 
    5797 
    5798 
    5799 
    5800 
    5801 
    5802 
    5803 
    5804      
    5805      
    5806      
    5807      
    5808      
    5809      
    5810      
    5811      
    5812      
    5813      
    5814       <p>The vertical grid spacings <a href="#dz">dz</a>
    5815 above this level are calculated as&nbsp; </p>
    5816 
    5817 
    5818 
    5819 
    5820 
    5821 
    5822 
    5823 
    5824 
    5825 
    5826      
    5827      
    5828      
    5829      
    5830      
    5831      
    5832      
    5833      
    5834      
    5835      
    5836       <ul>
    5837 
    5838 
    5839 
    5840 
    5841 
    5842 
    5843 
    5844 
    5845 
    5846 
    5847        
    5848        
    5849        
    5850        
    5851        
    5852        
    5853        
    5854        
    5855        
    5856        
    5857         <p><b>dz</b>(k+1) = <b>dz</b>(k) * <a href="#dz_stretch_factor">dz_stretch_factor</a></p>
    5858 
    5859 
    5860 
    5861 
    5862 
    5863 
    5864 
    5865 
    5866 
    5867 
    5868      
    5869      
    5870      
    5871      
    5872      
    5873      
    5874      
    5875      
    5876      
    5877      
    5878       </ul>
    5879 
    5880 
    5881 
    5882 
    5883 
    5884 
    5885 
    5886 
    5887 
    5888 
    5889      
    5890      
    5891      
    5892      
    5893      
    5894      
    5895      
    5896      
    5897      
    5898      
    5899       <p>and used as spacings for the scalar levels (zu). The
    5900 w-levels are then defined as:&nbsp; </p>
    5901 
    5902 
    5903 
    5904 
    5905 
    5906 
    5907 
    5908 
    5909 
    5910 
    5911      
    5912      
    5913      
    5914      
    5915      
    5916      
    5917      
    5918      
    5919      
    5920      
    5921       <ul>
    5922 
    5923 
    5924 
    5925 
    5926 
    5927 
    5928 
    5929 
    5930 
    5931 
    5932        
    5933        
    5934        
    5935        
    5936        
    5937        
    5938        
    5939        
    5940        
    5941        
    5942         <p>zw(k) = ( zu(k) + zu(k+1) ) * 0.5</p>
    5943 
    5944 
    5945 
    5946 
    5947 
    5948 
    5949 
    5950 
    5951 
    5952 
    5953      
    5954      
    5955      
    5956      
    5957      
    5958      
    5959      
    5960      
    5961      
    5962      
    5963       </ul>
    5964 
    5965 
    5966 
    5967 
    5968 
    5969 
    5970 
    5971 
    5972 
    5973 
    5974       </td>
    5975 
    5976 
    5977 
    5978 
    5979 
    5980 
    5981 
    5982 
    5983 
    5984 
    5985     </tr>
    5986 
    5987 
    5988 
    5989 
    5990 
    5991 
    5992 
    5993 
    5994 
    5995 
    5996     <tr>
    5997 
    5998 
    5999 
    6000 
    6001 
    6002 
    6003 
    6004       <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="e_min"></a>e_min</span></td>
    6005 
    6006 
    6007 
    6008 
    6009 
    6010 
    6011 
    6012       <td style="vertical-align: top;">R</td>
    6013 
    6014 
    6015 
    6016 
    6017 
    6018 
    6019 
    6020       <td style="vertical-align: top;"><span style="font-style: italic;">0.0</span></td>
    6021 
    6022 
    6023 
    6024 
    6025 
    6026 
    6027 
    6028       <td>Minimum subgrid-scale TKE in m<sup>2</sup>s<sup>-2</sup>.<br>
    6029 
    6030 
    6031 
    6032 
    6033 
    6034 
    6035 
    6036       <br>This
    6037 option&nbsp;adds artificial viscosity to the flow by ensuring that the
    6038 subgrid-scale TKE does not fall below the minimum threshold <span style="font-weight: bold;">e_min</span>.</td>
    6039 
    6040 
    6041 
    6042 
    6043 
    6044 
    6045 
    6046     </tr>
    6047 
    6048 
    6049 
    6050 
    6051 
    6052 
    6053 
    6054     <tr>
    6055 
    6056 
    6057 
    6058 
    6059 
    6060 
    6061 
    6062 
    6063 
    6064 
    6065       <td style="vertical-align: top;">
    6066      
    6067      
    6068      
    6069      
    6070      
    6071      
    6072      
    6073      
    6074      
    6075      
    6076       <p><a name="end_time_1d"></a><b>end_time_1d</b></p>
    6077 
    6078 
    6079 
    6080 
    6081 
    6082 
    6083 
    6084 
    6085 
    6086 
    6087       </td>
    6088 
    6089 
    6090 
    6091 
    6092 
    6093 
    6094 
    6095 
    6096 
    6097 
    6098       <td style="vertical-align: top;">R</td>
    6099 
    6100 
    6101 
    6102 
    6103 
    6104 
    6105 
    6106 
    6107 
    6108 
    6109       <td style="vertical-align: top;"><span style="font-style: italic;">864000.0</span><br>
    6110 
    6111 
    6112 
    6113 
    6114 
    6115 
    6116 
    6117 
    6118 
    6119 
    6120       </td>
    6121 
    6122 
    6123 
    6124 
    6125 
    6126 
    6127 
    6128 
    6129 
    6130 
    6131       <td style="vertical-align: top;">
    6132      
    6133      
    6134      
    6135      
    6136      
    6137      
    6138      
    6139      
    6140      
    6141      
    6142       <p>Time to be simulated for the 1d-model (in s).&nbsp; </p>
    6143 
    6144 
    6145 
    6146 
    6147 
    6148 
    6149 
    6150 
    6151 
    6152 
    6153      
    6154      
    6155      
    6156      
    6157      
    6158      
    6159      
    6160      
    6161      
    6162      
    6163       <p>The default value corresponds to a simulated time of 10 days.
     602negligible any more. (refer Kalnay de Rivas)</p> </td> </tr>
     603<tr> <td style="vertical-align: top;"> <p><a name="dz_stretch_level"></a><b>dz_stretch_level</b></p>
     604</td> <td style="vertical-align: top;">R</td>
     605<td style="vertical-align: top;"><span style="font-style: italic;">100000.0</span><br> </td>
     606<td style="vertical-align: top;"> <p>Height level
     607above which the grid is to be stretched
     608vertically (in m).&nbsp; </p> <p>The vertical grid
     609spacings <a href="#dz">dz</a>
     610above this level are calculated as&nbsp; </p> <ul> <p><b>dz</b>(k+1)
     611= <b>dz</b>(k) * <a href="#dz_stretch_factor">dz_stretch_factor</a></p>
     612</ul> <p>and used as spacings for the scalar levels (zu).
     613The
     614w-levels are then defined as:&nbsp; </p> <ul> <p>zw(k)
     615= ( zu(k) + zu(k+1) ) * 0.5</p> </ul> </td> </tr>
     616<tr> <td style="vertical-align: top;"><span style="font-weight: bold;"><a name="e_min"></a>e_min</span></td>
     617<td style="vertical-align: top;">R</td> <td style="vertical-align: top;"><span style="font-style: italic;">0.0</span></td> <td>Minimum
     618subgrid-scale TKE in m<sup>2</sup>s<sup>-2</sup>.<br>
     619<br>This
     620option&nbsp;adds artificial viscosity to the flow by ensuring that
     621the
     622subgrid-scale TKE does not fall below the minimum threshold <span style="font-weight: bold;">e_min</span>.</td> </tr>
     623<tr> <td style="vertical-align: top;"> <p><a name="end_time_1d"></a><b>end_time_1d</b></p>
     624</td> <td style="vertical-align: top;">R</td>
     625<td style="vertical-align: top;"><span style="font-style: italic;">864000.0</span><br> </td>
     626<td style="vertical-align: top;"> <p>Time to be
     627simulated for the 1d-model (in s).&nbsp; </p> <p>The
     628default value corresponds to a simulated time of 10 days.
    6164629Usually, after such a period the inertia oscillations have completely
    6165630decayed and the solution of the 1d-model can be regarded as stationary
     
    6168633initialization of the 3d-model with <a href="#initializing_actions">initializing_actions</a>
    6169634= <span style="font-style: italic;">'set_1d-model_profiles'</span>.</p>
    6170 
    6171 
    6172 
    6173 
    6174 
    6175 
    6176 
    6177 
    6178 
    6179 
    6180       </td>
    6181 
    6182 
    6183 
    6184 
    6185 
    6186 
    6187 
    6188 
    6189 
    6190 
    6191     </tr>
    6192 
    6193 
    6194 
    6195 
    6196 
    6197 
    6198 
    6199 
    6200 
    6201 
    6202     <tr>
    6203 
    6204 
    6205 
    6206 
    6207 
    6208 
    6209 
    6210 
    6211 
    6212 
    6213       <td style="vertical-align: top;">
    6214      
    6215      
    6216      
    6217      
    6218      
    6219      
    6220      
    6221      
    6222      
    6223      
    6224       <p><a name="fft_method"></a><b>fft_method</b></p>
    6225 
    6226 
    6227 
    6228 
    6229 
    6230 
    6231 
    6232 
    6233 
    6234 
    6235       </td>
    6236 
    6237 
    6238 
    6239 
    6240 
    6241 
    6242 
    6243 
    6244 
    6245 
    6246       <td style="vertical-align: top;">C * 20</td>
    6247 
    6248 
    6249 
    6250 
    6251 
    6252 
    6253 
    6254 
    6255 
    6256 
    6257       <td style="vertical-align: top;"><span style="font-style: italic;">'system-</span><br style="font-style: italic;">
    6258 
    6259 
    6260 
    6261 
    6262 
    6263 
    6264 
    6265 
    6266 
    6267 
    6268       <span style="font-style: italic;">specific'</span></td>
    6269 
    6270 
    6271 
    6272 
    6273 
    6274 
    6275 
    6276 
    6277 
    6278 
    6279       <td style="vertical-align: top;">
    6280      
    6281      
    6282      
    6283      
    6284      
    6285      
    6286      
    6287      
    6288      
    6289      
    6290       <p>FFT-method to be used.<br>
    6291 
    6292 
    6293 
    6294 
    6295 
    6296 
    6297 
    6298 
    6299 
    6300 
    6301       </p>
    6302 
    6303 
    6304 
    6305 
    6306 
    6307 
    6308 
    6309 
    6310 
    6311 
    6312      
    6313      
    6314      
    6315      
    6316      
    6317      
    6318      
    6319      
    6320      
    6321      
    6322       <p><br>
    6323 
    6324 
    6325 
    6326 
    6327 
    6328 
    6329 
    6330 
    6331 
    6332 
     635</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="fft_method"></a><b>fft_method</b></p>
     636</td> <td style="vertical-align: top;">C * 20</td>
     637<td style="vertical-align: top;"><span style="font-style: italic;">'system-</span><br style="font-style: italic;"> <span style="font-style: italic;">specific'</span></td>
     638<td style="vertical-align: top;"> <p>FFT-method to
     639be used.<br> </p> <p><br>
    6333640The fast fourier transformation (FFT) is used for solving the
    6334641perturbation pressure equation with a direct method (see <a href="chapter_4.2.html#psolver">psolver</a>)
    6335642and for calculating power spectra (see optional software packages,
    6336643section <a href="chapter_4.2.html#spectra_package">4.2</a>).</p>
    6337 
    6338 
    6339 
    6340 
    6341 
    6342 
    6343 
    6344 
    6345 
    6346 
    6347      
    6348      
    6349      
    6350      
    6351      
    6352      
    6353      
    6354      
    6355      
    6356      
    6357       <p><br>
    6358 
    6359 
    6360 
    6361 
    6362 
    6363 
    6364 
    6365 
    6366 
    6367 
     644<p><br>
    6368645By default, system-specific, optimized routines from external
    6369646vendor libraries are used. However, these are available only on certain
    6370647computers and there are more or less severe restrictions concerning the
    6371 number of gridpoints to be used with them.<br>
    6372 
    6373 
    6374 
    6375 
    6376 
    6377 
    6378 
    6379 
    6380 
    6381 
    6382       </p>
    6383 
    6384 
    6385 
    6386 
    6387 
    6388 
    6389 
    6390 
    6391 
    6392 
    6393      
    6394      
    6395      
    6396      
    6397      
    6398      
    6399      
    6400      
    6401      
    6402      
    6403       <p>There are two other PALM internal methods available on every
     648number of gridpoints to be used with them.<br> </p> <p>There
     649are two other PALM internal methods available on every
    6404650machine (their respective source code is part of the PALM source code):</p>
    6405 
    6406 
    6407 
    6408 
    6409 
    6410 
    6411 
    6412 
    6413 
    6414 
    6415      
    6416      
    6417      
    6418      
    6419      
    6420      
    6421      
    6422      
    6423      
    6424      
    6425       <p>1.: The <span style="font-weight: bold;">Temperton</span>-method
     651<p>1.: The <span style="font-weight: bold;">Temperton</span>-method
    6426652from Clive Temperton (ECWMF) which is computationally very fast and
    6427653switched on with <b>fft_method</b> = <span style="font-style: italic;">'temperton-algorithm'</span>.
    6428654The number of horizontal gridpoints (nx+1, ny+1) to be used with this
    6429 method must be composed of prime factors 2, 3 and 5.<br>
    6430 
    6431 
    6432 
    6433 
    6434 
    6435 
    6436 
    6437 
    6438 
    6439 
    6440       </p>
    6441 
    6442 
    6443 
    6444 
    6445 
    6446 
    6447 
    6448 
    6449 
    6450 
     655method must be composed of prime factors 2, 3 and 5.<br> </p>
    64516562.: The <span style="font-weight: bold;">Singleton</span>-method
    6452657which is very slow but has no restrictions concerning the number of
    6453 gridpoints to be used with, switched on with <b>fft_method</b> = <span style="font-style: italic;">'singleton-algorithm'</span>. </td>
    6454 
    6455 
    6456 
    6457 
    6458 
    6459 
    6460 
    6461 
    6462 
    6463 
    6464     </tr>
    6465 
    6466 
    6467 
    6468 
    6469 
    6470 
    6471 
    6472 
    6473 
    6474 
    6475     <tr>
    6476 
    6477 
    6478 
    6479 
    6480 
    6481 
    6482 
    6483 
    6484 
    6485 
    6486       <td style="vertical-align: top;">
    6487      
    6488      
    6489      
    6490      
    6491      
    6492      
    6493      
    6494      
    6495      
    6496      
    6497       <p><a name="galilei_transformation"></a><b>galilei_transformation</b></p>
    6498 
    6499 
    6500 
    6501 
    6502 
    6503 
    6504 
    6505 
    6506 
    6507 
    6508       </td>
    6509 
    6510 
    6511 
    6512 
    6513 
    6514 
    6515 
    6516 
    6517 
    6518 
    6519       <td style="vertical-align: top;">L</td>
    6520 
    6521 
    6522 
    6523 
    6524 
    6525 
    6526 
    6527 
    6528 
    6529 
    6530       <td style="vertical-align: top;"><i>.F.</i></td>
    6531 
    6532 
    6533 
    6534 
    6535 
    6536 
    6537 
    6538 
    6539 
    6540 
    6541       <td style="vertical-align: top;">Application of a Galilei-transformation to the
     658gridpoints to be used with, switched on with <b>fft_method</b>
     659= <span style="font-style: italic;">'singleton-algorithm'</span>.
     660</td> </tr> <tr> <td style="vertical-align: top;"> <p><a name="galilei_transformation"></a><b>galilei_transformation</b></p>
     661</td> <td style="vertical-align: top;">L</td>
     662<td style="vertical-align: top;"><i>.F.</i></td>
     663<td style="vertical-align: top;">Application of a
     664Galilei-transformation to the
    6542665coordinate
    6543 system of the model.<br><p>With <b>galilei_transformation</b> = <i>.T.,</i> a so-called
     666system of the model.<br><p>With <b>galilei_transformation</b>
     667= <i>.T.,</i> a so-called
    6544668Galilei-transformation is switched on which ensures that the coordinate
    6545669system of the model is moved along with the geostrophical wind.
     
    6556680each case, the distance the coordinate system has been moved is written
    6557681to the file <a href="chapter_3.4.html#RUN_CONTROL">RUN_CONTROL</a>.&nbsp;
    6558       </p>
    6559 
    6560 
    6561 
    6562 
    6563 
    6564 
    6565 
    6566 
    6567 
    6568 
    6569      
    6570      
    6571      
    6572      
    6573      
    6574      
    6575      
    6576      
    6577      
    6578      
    6579       <p>Non-cyclic lateral boundary conditions (see <a href="#bc_lr">bc_lr</a>
    6580 and <a href="#bc_ns">bc_ns</a>), the specification of a gestrophic
     682</p> <p>Non-cyclic lateral boundary conditions (see <a href="#bc_lr">bc_lr</a>
     683and <a href="#bc_ns">bc_ns</a>), the specification
     684of a gestrophic
    6581685wind that is not constant with height
    6582686as well as e.g. stationary inhomogeneities at the bottom boundary do
    6583 not allow the use of this transformation.</p>
    6584 
    6585 
    6586 
    6587 
    6588 
    6589 
    6590 
    6591 
    6592 
    6593 
    6594       </td>
    6595 
    6596 
    6597 
    6598 
    6599 
    6600 
    6601 
    6602 
    6603 
    6604 
    6605     </tr>
    6606 
    6607 
    6608 
    6609 
    6610 
    6611 
    6612 
    6613 
    6614 
    6615 
    6616     <tr>
    6617 
    6618 
    6619 
    6620 
    6621 
    6622 
    6623 
    6624 
    6625 
    6626 
    6627       <td style="vertical-align: top;">
    6628      
    6629      
    6630      
    6631      
    6632      
    6633      
    6634      
    6635      
    6636      
    6637      
    6638       <p><a name="grid_matching"></a><b>grid_matching</b></p>
    6639 
    6640 
    6641 
    6642 
    6643 
    6644 
    6645 
    6646 
    6647 
    6648 
    6649       </td>
    6650 
    6651 
    6652 
    6653 
    6654 
    6655 
    6656 
    6657 
    6658 
    6659 
    6660       <td style="vertical-align: top;">C * 6</td>
    6661 
    6662 
    6663 
    6664 
    6665 
    6666 
    6667 
    6668 
    6669 
    6670 
    6671       <td style="vertical-align: top;"><span style="font-style: italic;">'match'</span></td>
    6672 
    6673 
    6674 
    6675 
    6676 
    6677 
    6678 
    6679 
    6680 
    6681 
    6682       <td style="vertical-align: top;">Variable to adjust the subdomain
    6683 sizes in parallel runs.<br>
    6684 
    6685 
    6686 
    6687 
    6688 
    6689 
    6690 
    6691 
    6692 
    6693 
    6694       <br>
    6695 
    6696 
    6697 
    6698 
    6699 
    6700 
    6701 
    6702 
    6703 
    6704 
     687not allow the use of this transformation.</p> </td> </tr>
     688<tr> <td style="vertical-align: top;"> <p><a name="grid_matching"></a><b>grid_matching</b></p>
     689</td> <td style="vertical-align: top;">C * 6</td>
     690<td style="vertical-align: top;"><span style="font-style: italic;">'match'</span></td> <td style="vertical-align: top;">Variable to adjust the
     691subdomain
     692sizes in parallel runs.<br> <br>
    6705693For <b>grid_matching</b> = <span style="font-style: italic;">'strict'</span>,
    6706694the subdomains are forced to have an identical
     
    6708696respective directions of the virtual processor net must fulfill certain
    6709697divisor conditions concerning the grid point numbers in the three
    6710 directions (see <a href="#nx">nx</a>,
    6711       <a href="#ny">ny</a>
     698directions (see <a href="#nx">nx</a>, <a href="#ny">ny</a>
    6712699and <a href="#nz">nz</a>).
    6713700Advantage of this method is that all PEs bear the same computational
    6714 load.<br>
    6715 
    6716 
    6717 
    6718 
    6719 
    6720 
    6721 
    6722 
    6723 
    6724 
    6725       <br>
    6726 
    6727 
    6728 
    6729 
    6730 
    6731 
    6732 
    6733 
    6734 
    6735 
     701load.<br> <br>
    6736702There is no such restriction by default, because then smaller
    6737703subdomains are allowed on those processors which
     
    6741707the grid point numbers used. Information about the respective settings
    6742708are given in file <a href="file:///home/raasch/public_html/PALM_group/home/raasch/public_html/PALM_group/doc/app/chapter_3.4.html#RUN_CONTROL">RUN_CONTROL</a>.<br>
    6743 
    6744 
    6745 
    6746 
    6747 
    6748 
    6749 
    6750 
    6751 
    6752 
    6753       <br>
    6754 
    6755 
    6756 
    6757 
    6758 
    6759 
    6760 
    6761 
    6762 
    6763 
     709<br>
    6764710When using a multi-grid method for solving the Poisson equation (see <a href="http://www.muk.uni-hannover.de/%7Eraasch/PALM_group/doc/app/chapter_4.2.html#psolver">psolver</a>)
    6765711only <b>grid_matching</b> = <span style="font-style: italic;">'strict'</span>
    6766 is allowed.<br>
    6767 
    6768 
    6769 
    6770 
    6771 
    6772 
    6773 
    6774 
    6775 
    6776 
    6777       <br>
    6778 
    6779 
    6780 
    6781 
    6782 
    6783 
    6784 
    6785 
    6786 
    6787 
    6788       <b>Note:</b><br>
    6789 
    6790 
    6791 
    6792 
    6793 
    6794 
    6795 
    6796 
    6797 
    6798 
     712is allowed.<br> <br> <b>Note:</b><br>
    6799713In some cases for small processor numbers there may be a very bad load
    6800714balancing among the
    6801 processors which may reduce the performance of the code.</td>
    6802 
    6803 
    6804 
    6805 
    6806 
    6807 
    6808 
    6809 
    6810 
    6811 
    6812     </tr>
    6813 
    6814 
    6815 
    6816 
    6817 
    6818 
    6819 
    6820 
    6821 
    6822 
    6823     <tr>
    6824 
    6825 
    6826 
    6827 
    6828 
    6829 
    6830 
    6831 
    6832 
    6833 
    6834       <td style="vertical-align: top;"><a name="inflow_disturbance_begin"></a><b>inflow_disturbance_<br>
    6835 
    6836 
    6837 
    6838 
    6839 
    6840 
    6841 
    6842 
    6843 
    6844 
    6845 begin</b></td>
    6846 
    6847 
    6848 
    6849 
    6850 
    6851 
    6852 
    6853 
    6854 
    6855 
    6856       <td style="vertical-align: top;">I</td>
    6857 
    6858 
    6859 
    6860 
    6861 
    6862 
    6863 
    6864 
    6865 
    6866 
    6867       <td style="vertical-align: top;"><span style="font-style: italic;">MIN(10,</span><br style="font-style: italic;">
    6868 
    6869 
    6870 
    6871 
    6872 
    6873 
    6874 
    6875 
    6876 
    6877 
    6878       <span style="font-style: italic;">nx/2 or ny/2)</span></td>
    6879 
    6880 
    6881 
    6882 
    6883 
    6884 
    6885 
    6886 
    6887 
    6888 
    6889       <td style="vertical-align: top;">Lower
     715processors which may reduce the performance of the code.</td> </tr>
     716<tr> <td style="vertical-align: top;"><a name="inflow_disturbance_begin"></a><b>inflow_disturbance_<br>
     717begin</b></td> <td style="vertical-align: top;">I</td>
     718<td style="vertical-align: top;"><span style="font-style: italic;">MIN(10,</span><br style="font-style: italic;"> <span style="font-style: italic;">nx/2 or ny/2)</span></td>
     719<td style="vertical-align: top;">Lower
    6890720limit of the horizontal range for which random perturbations are to be
    6891 imposed on the horizontal velocity field (gridpoints).<br>
    6892 
    6893 
    6894 
    6895 
    6896 
    6897 
    6898 
    6899 
    6900 
    6901 
    6902       <br>
    6903 
    6904 
    6905 
    6906 
    6907 
    6908 
    6909 
    6910 
    6911 
    6912 
     721imposed on the horizontal velocity field (gridpoints).<br> <br>
    6913722If non-cyclic lateral boundary conditions are used (see <a href="#bc_lr">bc_lr</a>
    6914723or <a href="#bc_ns">bc_ns</a>),
     
    6917726horizontal velocity field. Perturbations must be switched on with
    6918727parameter <a href="chapter_4.2.html#create_disturbances">create_disturbances</a>.</td>
    6919 
    6920 
    6921 
    6922 
    6923 
    6924 
    6925 
    6926 
    6927 
    6928 
    6929     </tr>
    6930 
    6931 
    6932 
    6933 
    6934 
    6935 
    6936 
    6937 
    6938 
    6939 
    6940     <tr>
    6941 
    6942 
    6943 
    6944 
    6945 
    6946 
    6947 
    6948 
    6949 
    6950 
    6951       <td style="vertical-align: top;"><a name="inflow_disturbance_end"></a><b>inflow_disturbance_<br>
    6952 
    6953 
    6954 
    6955 
    6956 
    6957 
    6958 
    6959 
    6960 
    6961 
    6962 end</b></td>
    6963 
    6964 
    6965 
    6966 
    6967 
    6968 
    6969 
    6970 
    6971 
    6972 
    6973       <td style="vertical-align: top;">I</td>
    6974 
    6975 
    6976 
    6977 
    6978 
    6979 
    6980 
    6981 
    6982 
    6983 
    6984       <td style="vertical-align: top;"><span style="font-style: italic;">MIN(100,</span><br style="font-style: italic;">
    6985 
    6986 
    6987 
    6988 
    6989 
    6990 
    6991 
    6992 
    6993 
    6994 
    6995       <span style="font-style: italic;">3/4*nx or</span><br style="font-style: italic;">
    6996 
    6997 
    6998 
    6999 
    7000