Nudging

In order to simulate less idealized flow situations large scale forcing can be used in PALM. Horizontal large scale advection of scalars, large scale subsidence and large scale pressure gradients are then considered and additional tendencies are added to the progonostic equations.

An additional possibility to account for tendencies in the LES model resulting from larger scales than those in the boundary layer is the usage of nudging. Nudging is a (Newtonian) relaxation technique which adjusts the large-eddy simulation to a given, larger scale flow situation (Anthes, 1974; Stauffer and Bao, 1993). It can be used to adjust the simulation to an observed state when cyclic boundary conditions are used. In case that continuous measurement data over a longer time period (weeks to month to years) is available (for example from a meteorological super-site or intensive measurement campaigns), these periods can also be simulated with LES. The LES results could for example be used for the comparison with larger-scale models to test parameterizations. The simulation of longer time periods permits to calculate statistics and to identify situations in which the differences to the larger scale model are significant (Neggers et al., 2012).

Instead of taking nudging data from measurements it is also possible to use data from a larger scale model to drive PALM. Further information about nudging can for example be found in Yamada and Koike, 2011; Schlünzen et al., 2011 or Neggers et al., 2012.

Beginning with revision r1241 it is possible to use nudging. The nudging method in PALM which is based on implementations in the ​DALES and ​UCLA-LES model consists principally of the following steps for the prognostic variables

• Interpolation in time and height of large scale (LS) profiles provided by measurements or a larger scale model
• Calculation of domain-averaged profiles of the prognostic variables in the LES model
• Calculation of a tendency
  TracMath macro processor has detected an error. Please fix the problem before continuing.

  
  The command:

  '/usr/bin/pdflatex -interaction=nonstopmode de3cd9220578b9bcba3b5e70f217c72c8eb33f81.tex'

  failed with the following output:

  "This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)\n restricted \\write18 enabled.\nentering extended mode\n(./de3cd9220578b9bcba3b5e70f217c72c8eb33f81.tex\nLaTeX2e <2011/06/27>\nBabel <3.9h> and hyphenation patterns for 78 languages loaded.\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/article.cls\nDocument Class: article 2007/10/19 v1.4h Standard LaTeX document class\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/size10.clo))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/inputenc.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/utf8.def\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1enc.dfu)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/ot1enc.dfu)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/omsenc.dfu)))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/cmap/cmap.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/cm-super/type1ec.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1cmr.fd))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/fontenc.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1enc.def)<<t1.cmap\n>>) (/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsmath.sty\nFor additional information on amsmath, use the `?' option.\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amstext.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsgen.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsbsy.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsopn.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amscls/amsthm.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/amssymb.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/amsfonts.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/tools/bm.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/preview/preview.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/preview/prtightpage.def)\n) (./de3cd9220578b9bcba3b5e70f217c72c8eb33f81.aux)\nPreview: Fontsize 10pt\nPreview: PDFoutput 1\n<<ot1.cmap>><<oml.cmap>><<oms.cmap>><<omx.cmap>>\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/umsa.fd)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/umsb.fd)\nPreview: Tightpage -32891 -32891 32891 32891\n[1{/localdata/software/texlive/2013/texmf-var/fonts/map/pdftex/updmap/pdftex.ma\np}]\n! I can't find file `de3cd9220578b9bcba3b5e70f217c72c8eb33f81.aux'.\n\\enddocument ...keatletter \\@@input \\jobname .aux \n                                                  \\fi \\@dofilelist \\ifdim \\f...\nl.16 \\end{document}\n                   \n(Press Enter to retry, or Control-D to exit)\nPlease type another input file name\n! Emergency stop.\n\\enddocument ...keatletter \\@@input \\jobname .aux \n                                                  \\fi \\@dofilelist \\ifdim \\f...\nl.16 \\end{document}\n                   \n!  ==> Fatal error occurred, no output PDF file produced!\nTranscript written on de3cd9220578b9bcba3b5e70f217c72c8eb33f81.log.\n"

  at each single grid point where
  TracMath macro processor has detected an error. Please fix the problem before continuing.

  
  The command:

  '/usr/bin/gs -dSAFER -dBATCH -dNOPAUSE -r110 -sDEVICE=pngalpha -dGraphicsAlphaBits=4 -dTextAlphaBits=4 -sOutputFile=3c847026b0e72399deb60aea00e08f6c1f578116.png 3c847026b0e72399deb60aea00e08f6c1f578116.pdf'

  failed with the following output:

  'GPL Ghostscript 9.25 (2018-09-13)\nCopyright (C) 2018 Artifex Software, Inc.  All rights reserved.\nThis software comes with NO WARRANTY: see the file PUBLIC for details.\nError: /undefinedfilename in (3c847026b0e72399deb60aea00e08f6c1f578116.pdf)\nOperand stack:\n\nExecution stack:\n   %interp_exit   .runexec2   --nostringval--   --nostringval--   --nostringval--   2   %stopped_push   --nostringval--   --nostringval--   --nostringval--   false   1   %stopped_push\nDictionary stack:\n   --dict:954/1684(ro)(G)--   --dict:0/20(G)--   --dict:77/200(L)--\nCurrent allocation mode is local\nLast OS error: No such file or directory\n'

  'GPL Ghostscript 9.25: Unrecoverable error, exit code 1\n'

  is the nudging time scale

The strength of the nudging strongly depends on the nudging time scale used. Usually, this time scale should be in the order of several hours. By varying the nudging time scale with height it is possible to apply the nudging not everywhere but for example only above the boundary layer. In case this is wanted, the time scale should be set to a very large number (~10¹⁰) inside the boundary layer. By this way, the nudging tendency approaches zero.

A complete example for a PALM run with nudging is documented here.

References

• Anthes, R. A., 1974: Data assimilation and initialization of hurricane prediction models. J. Atmos. Sci, 31, 702-719.​doi
• Neggers, R. A. J., A. P. Siebesma and T. Heus, 2012: Continous single-column model evaluation at a permanent meteorological supersite. Bull. Amer. Meteor. Soc, 29, 91-115. ​doi
• Schlünzen, K. H., D. Grawe, S. I. Bohnenstengel, I. Schlüter and R. Koppmann, 2011: Joint modelling of obstacel induced and meoscale changes - Current limits and challenges. J. Wind Eng. Ind. Aerodyn., 99, 217-225. ​doi
• Stauffer, D. R. and J.-W. Bao, 1993: Optimal determination of nudging coefficients using adjoint equations. Tellus, 45A, 358-369. ​doi
• Yamada, T., and K. Koike, 2011: Downscaling mesoscale meteorological models for computational wind engineering applications. J. Wind Eng. Ind. Aerodyn., 99, 199-216. ​doi