Changes between Version 6 and Version 7 of doc/tec/biomet/uv_implementation

Timestamp:

Jul 25, 2019 2:06:41 PM (5 years ago)

Author:

Schrempf

Comment:

--

doc/tec/biomet/uv_implementation

@@ -7 +7 @@
 
 
-[[Image(integration_equation.png, 900px)]] 
-\\\\
-
 {{{#!td style="vertical-align:top; text-align:left"
 == Code realization of exposure model ==
 To calculate the human exposure the 3 main exposure model parameters (biologically weighted radiance, human geometry and obstructions) and an array of integration factors are used. The latter one is important for the integration over all solid angles e.g. over all directions of the upper hemisphere. This spatial integration can then easily be done by summation of all final weighted radiance values.
 
-The calculation can be illustrated by using the polar plots of the exposure model parameters (see sections basic model and obstacles) and arrange them as an exploded view (see Fig. 2.4). The process of weighting the radiance of each solid angle with the human geometry and the existing obstructions can be easily envisioned by multiplying each value of the top polar plot with the corresponding values below. This is indicated in Figure 2.4 by the red asterisks and the black arrows.
+The calculation can be illustrated by using the polar plots of the exposure model parameters (see sections basic model and obstacles) and arrange them as an exploded view (see Figure on the right). The process of weighting the radiance of each solid angle with the human geometry and the existing obstructions can be easily envisioned by multiplying each value of the top polar plot with the corresponding values below. This is indicated in the Figure by the red asterisks and the black arrows.
 
-Visualization of the exposure model parameters and the calculation of the final weighted radiance. The red asterisks mark values of exemplary directions and the black arrows indicate the multiplication of these values. The polar plots are shown as function of azimuth and incident angle 
 }}}
 {{{#!td style="text-align:left;style=width: 50px" 
@@ -23 +19 @@
 \\\\
 
+
+For the calculation of the exposure Ex,,weighted,,, the weighted radiances (see framed polar plot in the Figure above) are integrated over all solid angles (directions). For this, the area of each solid angle d''Ω'' on a unit sphere must be calculated. These dimensionless areas have the unit [sr] and can be understood as weighting factors since not all considered solid angles from the different directions have the same size (see also schematic diagram below).
+
+By multiplying the areas of the solid angles with the weighted radiances of each corresponding direction, the final integral can be carried out by summation of the products. The equation can be expressed as:
+
+
+{{{
+#!Latex
+\begin{equation*}
+Ex_{\text{weighted}} \quad=\quad \int_{\Omega} L_{\text{weighted}}(\varepsilon,\varphi)\;\; \text{d}\Omega \quad=\quad \sum_{\Omega}\Big(\:\Omega(\varepsilon,\varphi) \cdot L_{\text{weighted}}(\varepsilon,\varphi)\:\Big) \;.
+\end{equation*}
+}}}
+\\\\
+
+
 {{{#!td style="vertical-align:top; text-align:left"
 == Integration factors ==
-
-For the calculation of the exposure, the weighted radiances (see polar plot in Figure ??) are integrated over all solid angles (directions). For this, the area of each solid angle d on a unit sphere must be calculated. These dimensionless areas have the unit [sr] and can be understood as weighting factors since not all considered solid angles from the different directions have the same size (see also Fig. 2.5).
-
-The summation of the radiances, multiplied with the areas of the solid angles of the corresponding directions, yields the final integral. 
-
-Figure 2.5: Schematic diagram of an exemplary segmented upper hemisphere, that visualizes the different segments. The numbers and proportions of the segments in the schematic diagram are for demonstration purposes only and do not exactly match the solid
+\\\\
+\\\\
+The Figure on the right shows a schematic diagram of an exemplary segmented upper hemisphere, that visualizes the different segments. The numbers and proportions of the segments in the schematic diagram are for demonstration purposes only and do not exactly match the solid
 angles used in the exposure model.
 }}}
@@ -37 +45 @@
 }}}
 \\\\
+
+== Storage of obstruction information ==
+To calculate the exposure of a human in an urban (obstructed) environment, information about the present obstructions must be derived. This is described in [https://palm.muk.uni-hannover.de/trac/wiki/wiki/doc/tec/uvem/obstacles '''obstacles'''].
+If the obstruction information is derived for an city area, it is stored in a 3-dimesional array. The first two dimensions represent the x and y grid points of the model domain and the third dimension contains the obstruction information of the analyzed directions. Since the obstruction information needs quite a lot of disk space, the size of the obstruction information input file is reduced by using the FORTRAN bit function ''ibset''. This function can set/modify each of the eight values of a Byte (1 Byte = 8 Bit) to 0 or 1 or in other words to true or false. Since the obstruction information only contains true or false information (i.e. is the sky visible or not) this bit function enables the storage of 8 different directions in one byte. The analyzed obstruction information with a resolution of 10° corresponds to 360 directions (36 azimuth directions * 10 zenith directions) and can be stored with the bit function in an array with the z dimension being 45.
+
+In the exposure model the obstruction information are then restored from this array and converted back to integer numbers (zero for obstructed directions and 1 for directions from which radiation can reach the human).
+
+
 == References: ==
 * [=#Seckmeyer2013] '''Seckmeyer, G., Schrempf, M.Wieczorek, A., Riechelmann, S., Graw, K., Seckmeyer, S., and Zankl, M.''' 2013. A Novel Method to Calculate Solar UV Exposure Relevant to Vitamin D Production in Humans, Photochem. Photobiol., 89(4), 974-983, DOI: 10.1111/php.12074.