{"id":375,"date":"2023-08-02T15:39:19","date_gmt":"2023-08-02T15:39:19","guid":{"rendered":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/?page_id=375"},"modified":"2023-08-03T17:54:32","modified_gmt":"2023-08-03T17:54:32","slug":"profile-utility-introduction","status":"publish","type":"page","link":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/profile-utility-introduction\/","title":{"rendered":"Profile Utility Introduction"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Units Conversion Module<\/h2>\n\n\n\n<p>The\u00a0Units_Conversion\u00a0module contains a number of functions for converting the units of atmospheric absorber concentrations. This type of conversion information is usually hard to dig up so this module is an attempt to gather as many of the conversions as possible in one place. All of the available conversion routines are shown in the table below. For more details on the available routines, click on the links below or see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/units-conversion\/\" data-type=\"page\" data-id=\"382\">Units_Conversion<\/a>\u00a0module documentation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th colspan=\"2\">Specific amount &lt;-&gt; mixing ratio<\/th><\/tr><tr><td>SA_to_MR<\/td><td>Function to convert gas concentrations from specific amount to mixing ratio.<\/td><\/tr><tr><td>MR_to_SA<\/td><td>Function to convert gas concentrations from mixing ratio to specific amount<\/td><\/tr><tr><th colspan=\"2\">Relative humidity &lt;-&gt; mixing ratio<\/th><\/tr><tr><td>RH_to_MR<\/td><td>Function to convert water vapor amounts from relative humidity to mixing ratio.<\/td><\/tr><tr><td>MR_to_RH<\/td><td>Function to convert water vapor amounts from mixing ratio to relative humidity.<\/td><\/tr><tr><th colspan=\"2\">Mixing ratio &lt;-&gt; ppmv<\/th><\/tr><tr><td>MR_to_PPMV<\/td><td>Function to convert gas concentrations from mixing ratio to parts-per-million by volume.<\/td><\/tr><tr><td>PPMV_to_MR<\/td><td>Function to convert gas concentrations from parts-per-million by volume to mixing ratio.<\/td><\/tr><tr><th colspan=\"2\">Partial pressure &lt;-&gt; ppmv<\/th><\/tr><tr><td>PPMV_to_PP<\/td><td>Function to convert gas concentrations from parts-per-million by volume to partial pressure.<\/td><\/tr><tr><td>PP_to_PPMV<\/td><td>Function to convert gas concentrations from partial pressure to parts-per-million by volume.<\/td><\/tr><tr><th colspan=\"2\">Partial pressure &lt;-&gt; mixing ratio<\/th><\/tr><tr><td>MR_to_PP<\/td><td>Function to convert gas concentrations from mixing ratio to partial pressure in hectoPascals<\/td><\/tr><tr><td>PP_to_MR<\/td><td>Function to convert gas concentrations from partial pressure in hectoPascals to mixing ratio in g\/kg.<\/td><\/tr><tr><th colspan=\"2\">Partial pressure &lt;-&gt; mass density<\/th><\/tr><tr><td>PP_to_MD<\/td><td>Function to convert gas concentrations in pressure units to mass density.<\/td><\/tr><tr><td>MD_to_PP<\/td><td>Function to convert gas concentration mass density to partial pressure.<\/td><\/tr><tr><th colspan=\"2\">Partial pressure &lt;-&gt; number density<\/th><\/tr><tr><td>PP_to_ND<\/td><td>Function to convert gas concentrations from (partial) pressures in hectoPascals to molecules\/m^3.<\/td><\/tr><tr><td>ND_to_PP<\/td><td>Function to convert gas concentrations from number densities in molecules\/m^3 to (partial) pressures in hectoPascals.<\/td><\/tr><tr><th colspan=\"2\">Number density &lt;-&gt; ppmv<\/th><\/tr><tr><td>PPMV_to_ND<\/td><td>Function to convert gas concentrations from parts-per-million by volume to molecules\/m^3.<\/td><\/tr><tr><td>ND_to_PPMV<\/td><td>Function to convert gas concentrations from number densities in molecules\/m^3 to parts-per-million by volume.<\/td><\/tr><tr><th colspan=\"2\">Column density &lt;-&gt; ppmv<\/th><\/tr><tr><td>PPMV_to_KMOL<\/td><td>Function to convert gas concentrations from parts-per- million by volume to kilomoles per cm^2.<\/td><\/tr><tr><td>KMOL_to_PPMV<\/td><td>Function to convert gas concentrations from kilomoles per cm^2 to parts-per-million by volume.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Atmospheric Properties Module<\/h2>\n\n\n\n<p>This module contains a number of routines to compute various properties of the atmosphere.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Molecular weight of air,\u00a0MW_Air<\/h3>\n\n\n\n<p>This function calculates the effective molecular weight of air. To calculate the air density accurately the profile of the effective molecular weight of air (<em>MW<sub>air<\/sub><\/em>) is required. Although&nbsp;<em>MW<sub>air<\/sub><\/em>&nbsp;does not change a great deal with altitude, the variation is significant as the ratios of concentrations of various absorbers change.<\/p>\n\n\n\n<p>The most significant contributor to the change in&nbsp;<em>MW<sub>air<\/sub><\/em>&nbsp;is water vapor, mostly in the lower troposphere. The effect of the other absorbers (O<sub>3<\/sub>, CO<sub>2<\/sub>, etc.) can be considered negligible. To offset the displacement of &#8220;air molecules&#8221; by water vapor, the molecular weight of air is given by,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/MWair.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>MW<sub>DryAir<\/sub><\/em>&nbsp;= effective molecular weight of dry air<\/li>\n\n\n\n<li><em>MW<sub>H2O<\/sub><\/em>&nbsp;= molecular weight of water<\/li>\n\n\n\n<li><em>p<sub>H2O<\/sub><\/em>&nbsp;= partial pressure of water vapor<\/li>\n\n\n\n<li><em>P<\/em>&nbsp;= total atmospheric pressure<\/li>\n<\/ul>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties\u00a0documentation<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Gas density,\u00a0Density<\/h3>\n\n\n\n<p>This function calculates gas density using the ideal gas law,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Density.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>P<\/em>&nbsp;= gas pressure<\/li>\n\n\n\n<li><em>T<\/em>&nbsp;= gas temperature<\/li>\n\n\n\n<li><em>MW<\/em>&nbsp;= molecular weight of the gas in question<\/li>\n\n\n\n<li><em>R<\/em>&nbsp;= universal gas constant<\/li>\n<\/ul>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties\u00a0documentation<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Saturation vapor pressures,\u00a0SVP_Water\u00a0and\u00a0SVP_Ice<\/h3>\n\n\n\n<p>These functions calculate the saturation vapor pressures over water and ice respectively. The pressures are computed using a polynomial fit to measurements as detailed in Flatau,P.J., R.L.Walko, and W.R.Cotton, 1992: &#8220;Polynomial fits to saturation vapor pressure&#8221;,&nbsp;<em>J.Appl.Met.<\/em>,&nbsp;<strong>31<\/strong>, pp1507-1513,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/SVP.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>T<\/em>&nbsp;= temperature<\/li>\n\n\n\n<li><em>c<sub>i<\/sub><\/em>&nbsp;= relative error norm coefficients for water and ice obtained from Flatau&nbsp;<em>et al.<\/em>&nbsp;(1992).<\/li>\n<\/ul>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties\u00a0documentation<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Saturation mixing ratio,\u00a0Saturation_Mixing_Ratio<\/h3>\n\n\n\n<p>This function calculates the saturation mixing ratio for a given pressure and temperature,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/SMR.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>MW<sub>H2O<\/sub><\/em>&nbsp;= molecular weight of water<\/li>\n\n\n\n<li><em>MW<sub>DryAir<\/sub><\/em>&nbsp;= effective molecular weight of dry air<\/li>\n\n\n\n<li><em>p<sub>H2O<\/sub><\/em>&nbsp;= partial pressure of water vapor<\/li>\n\n\n\n<li><em>P<\/em>&nbsp;= total atmospheric pressure<\/li>\n<\/ul>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties documentation<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Virtual Temperature,\u00a0Virtual_Temperature<\/h3>\n\n\n\n<p>This function calculates the virtual temperature, the temperature that dry air must have in order to have the same density as moist air at the same pressure, given the temperature and water vapor mixing ratio,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Virtual_Temperature.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>T<\/em>&nbsp;= temperature<\/li>\n\n\n\n<li><em>w<\/em>&nbsp;= water vapor mixing ratio<\/li>\n\n\n\n<li>\u03b5 = ratio of the molecular weights of water and dry air.<\/li>\n<\/ul>\n\n\n\n<p>There is also an &#8220;inverse&#8221; capability to compute the temperature given the virtual temperature and the water vapor mixing ratio.<\/p>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties\u00a0documentation<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Potential Temperature,\u00a0Potential_Temperature<\/h3>\n\n\n\n<p>This function calculates the potential temperature, the temperature that a parcel of air would have if it were expanded or compressed adiabatically to some reference pressure.<\/p>\n\n\n\n<p>The conversion is given by Poisson&#8217;s equation,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Potential_Temperature.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>T<\/em>&nbsp;= temperature<\/li>\n\n\n\n<li><em>P<\/em>&nbsp;= pressure<\/li>\n\n\n\n<li><em>P<sub>0<\/sub><\/em>&nbsp;= reference pressure<\/li>\n\n\n\n<li><em>R<sub>DryAir<\/sub><\/em>&nbsp;= gas constant for dry air<\/li>\n\n\n\n<li><em>c<sub>p<\/sub><\/em>&nbsp;= specific heat of gas at constant pressure.<\/li>\n<\/ul>\n\n\n\n<p>This routine uses the standard atmosphere as the reference pressure, the gas constant for dry air and the specific heat for an ideal diatomic gas,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Specific_Heat.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>R<\/em>&nbsp;= universal gas constant<\/li>\n\n\n\n<li><em>MW<sub>DryAir<\/sub><\/em>&nbsp;= effective molecular weight of dry air<\/li>\n<\/ul>\n\n\n\n<p>There is also an &#8220;inverse&#8221; capability to compute the temperature given the potential temperature and pressure.<\/p>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/atmospheric-properties-subprograms\/\" data-type=\"page\" data-id=\"385\">Atmospheric Properties\u00a0documentation<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Geopotential Module<\/h2>\n\n\n\n<p>Geopotential heights are computed using the&nbsp;Geopotential_Height&nbsp;function. Atmospheric layer thicknesses can be calculated via the hypsometric equantion,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Hypsometric.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>P<sub>1<\/sub><\/em>,&nbsp;<em>P<sub>2<\/sub><\/em>&nbsp;= layer boundary pressures<\/li>\n\n\n\n<li><em>z<sub>1<\/sub><\/em>,&nbsp;<em>z<sub>2<\/sub><\/em>&nbsp;= layer boundary heights<\/li>\n<\/ul>\n\n\n\n<p>and&nbsp;<em>H<\/em>&nbsp;is the scale height given by,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Scale_Height.gif\" alt=\"\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>R<sub>DryAir<\/sub><\/em>&nbsp;= gas constant for dry air<\/li>\n\n\n\n<li><em>T<sub>v<\/sub><\/em>&nbsp;= average layer virtual temperature<\/li>\n\n\n\n<li><em>R<sub>Air<\/sub><\/em>&nbsp;= average layer gas constant for air<\/li>\n\n\n\n<li><em>T<\/em>&nbsp;= average layer temperature<\/li>\n\n\n\n<li><em>g<\/em>&nbsp;= acceleration due to gravity at layer altitudepressure<\/li>\n<\/ul>\n\n\n\n<p>The latter form is used here since the gas constant for air is given by,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Rair.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>and this will allow for the effect of other gases, such as O<sub>3<\/sub>, eventually to be included in the calcuation of the effective molecular weight of air,&nbsp;<em>MW<sub>Air<\/sub><\/em>.<\/p>\n\n\n\n<p>Layer values for both&nbsp;<em>R<sub>Air<\/sub><\/em>&nbsp;and&nbsp;<em>T<\/em>&nbsp;are determined from a density weighted average of adjacent level values,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Density_Weighted_Average.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>k<\/em>&nbsp;= layer\/level counters<\/li>\n\n\n\n<li><em>X<\/em>&nbsp;=&nbsp;<em>level<\/em>&nbsp;values to be averaged (<em>R<sub>Air<\/sub><\/em>&nbsp;or&nbsp;<em>T<\/em>)<\/li>\n\n\n\n<li><em>\u03c1<\/em>&nbsp;=&nbsp;<em>level<\/em>&nbsp;air densities<\/li>\n\n\n\n<li><em>X<\/em>&nbsp;=&nbsp;<em>layer<\/em>&nbsp;average values (<em>R<sub>Air<\/sub><\/em>&nbsp;or&nbsp;<em>T<\/em>)<\/li>\n<\/ul>\n\n\n\n<p>For the subprogram interface details, see the\u00a0Geopotential\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/geopotential-subprograms\/\" data-type=\"page\" data-id=\"388\">Geopotential_Height<\/a>\u00a0documentation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Level to Layer Conversion Module<\/h2>\n\n\n\n<p>This module contains routines to convert level-based values to layer-based ones.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Effective Temperature and Pressure,\u00a0Effective_Layer_TP<\/h3>\n\n\n\n<p>This function calculates the effective atmospheric layer temperature and pressure by weighting level values with the integrated layer density. The reference for this method is Gallery, W.O., F.X. Kneizys, and S.A. Clough, &#8220;Air mass computer program for atmospheric transmittance\/radiance calculation: FSCATM&#8221;, AFGL-TR-83-0065, 9 March 1983.<\/p>\n\n\n\n<p>Gallery&nbsp;<em>et al<\/em>&nbsp;(1983) indicates that for determining atmospheric absorption line halfwidths, intensities and blackbody emission,&nbsp;<em>effective<\/em>&nbsp;layer pressures and temperatures are used. The definition supplied (one of many) is the density weighted average,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Effective_P_Integral.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>and<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Effective_T_Integral.gif\">&nbsp;where ds = the element of length along a path.<\/p>\n\n\n\n<p>If we assume that the integration is always done over one layer (between two levels,&nbsp;<em>k<\/em>&nbsp;and&nbsp;<em>k<\/em>-1 where&nbsp;<em>z<\/em><sub><em>k<\/em>-1<\/sub>&nbsp;&gt;&nbsp;<em>z<sub>k<\/sub><\/em>) then the above equations become,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Effective_P_Solution.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>and<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Effective_T_Solution.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>The comparison between the average and effective layer pressure is shown in\u00a0figure 1. The same for the average and effective layer temperatures is shown in\u00a0figure 2.<\/p>\n\n\n\n<p>Note that the gas constant used in the effective temperature equation is for air, not dry air. If the gas constant for dry air is used, the difference between effective and average layer temperatures differs considerably when the atmosphere is sufficiently moist &#8212; as is shown in\u00a0figure 3.<\/p>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/level-layer-conversion\/\" data-type=\"page\" data-id=\"393\">Level Layer Conversion\u00a0documentation<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"376\" src=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_P-Effective_P_Difference.png\" alt=\"\" class=\"wp-image-378\" srcset=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_P-Effective_P_Difference.png 470w, https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_P-Effective_P_Difference-300x240.png 300w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/><\/figure>\n\n\n\n<p>Figure 1.\u00a0Effective_TP. Difference between average and effective layer pressure<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"470\" src=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_T-Effective_T_Difference.png\" alt=\"\" class=\"wp-image-377\" srcset=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_T-Effective_T_Difference.png 587w, https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Average_T-Effective_T_Difference-300x240.png 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<p>Figure 2.\u00a0Effective_TP. Difference between average and effective layer temperature<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"470\" src=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Dependence_of_Effective_T_on_Rair.png\" alt=\"\" class=\"wp-image-376\" srcset=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Dependence_of_Effective_T_on_Rair.png 587w, https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Dependence_of_Effective_T_on_Rair-300x240.png 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<p>Figure 3.\u00a0Effective_TP.\u00a0Comparison and difference between the input level and derived average and effective layer temperature where the gas constant for dry air was used in calculating the effective temperature. Note the difference between the average and effective layer temperatures from 300mb-surface &#8212; the moist part of the atmosphere.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Layer Integration,\u00a0Create_Sublevels\u00a0and\u00a0Integrate_Sublevels<\/h3>\n\n\n\n<p>These two routiens are Fortran90\/95 translations of the routines INTLEV and INTEG, part of the KLAYERS code in the AIRS RTA. This text details the steps required to replicate the profile conversion performed by the front end to the AIRS RTA, KLAYERS,in determining average layer pressure, temperature, and absorber amount &#8212; the latter as a column density in units of kmol\/cm<sup>2<\/sup>.<\/p>\n\n\n\n<p>The assumption is made that temperature and absorber amount vary linearly with\u00a0<em>ln<\/em>(<em>P<\/em>). To improve the quadrature in integrating level amounts to a layer value, each input layer,\u00a0<em>k<\/em>, is split into\u00a0<em>N<\/em>(<em>k<\/em>) sublayers equally spaced in\u00a0<em>ln<\/em>(<em>P<\/em>) as shown in\u00a0figure 4<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"395\" src=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Create_Sublevels.png\" alt=\"\" class=\"wp-image-379\" srcset=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Create_Sublevels.png 469w, https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-content\/uploads\/sites\/7\/2023\/08\/Create_Sublevels-300x253.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure>\n\n\n\n<p>Figure 4.\u00a0Create_Sublevels. Definition of sublayering scheme.<\/p>\n\n\n\n<p>where<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Create_Sublevels_Eqn.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>given the pressures,&nbsp;<em>P<sub>0<\/sub><\/em>&nbsp;&#8211;&nbsp;<em>P<sub>K<\/sub><\/em>&nbsp;of the input levels where&nbsp;<em>P<sub>0<\/sub><\/em>&nbsp;corresponds to the highest altitude (lowest pressure) level and&nbsp;<em>P<sub>K<\/sub><\/em>&nbsp;corresponds to the surface pressure. Note that the level count starts at 0 and a layer&nbsp;<em>k<\/em>&nbsp;or sublayer&nbsp;<em>n<\/em>&nbsp;is between levels&nbsp;<em>k<\/em>-1 and&nbsp;<em>k<\/em>, and&nbsp;<em>n<\/em>-1 and&nbsp;<em>n<\/em>&nbsp;respectively. Also, the zeroth sublevel corresponds to the&nbsp;<em>k<\/em>-1 level.<\/p>\n\n\n\n<p>Once the sublevels are defined, the level temperatures and absorber amounts are linearly interpolated at the specific number of sublevels and those interpolates associated with the sublevel pressures.<\/p>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/level-layer-conversion\/\" data-type=\"page\" data-id=\"393\">Level Layer Conversion\u00a0documentation<\/a>.<\/p>\n\n\n\n<p>Once the sublevel arrays have been created using&nbsp;Create_Sublevels, they are passed to the&nbsp;Integrate_Sublevels&nbsp;function. This function determines the average layer&nbsp;<em>k<\/em>&nbsp;temperature from the&nbsp;<em>N<\/em>(<em>k<\/em>) sublayers temperature-density product by simple summation,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Integrate_Sublevels_T.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where \u0394<em>z<sub>n<\/sub><\/em>&nbsp;is the sublayer thickness, and the average sublayer&nbsp;<em>n<\/em>&nbsp;pressures and temperatures are given by,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Sublayer_Pressure.gif\" alt=\"\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Sublayer_Temperature.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>respectively.<\/p>\n\n\n\n<p>Similarly to the layer temperature, the integrated layer absorber column density for molecule&nbsp;<em>j<\/em>&nbsp;is determined by summing the sublayer values,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Integrate_Sublevels_A.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>where&nbsp;<em>c<\/em>&nbsp;is a scaling constant, and the average sublayer&nbsp;<em>n<\/em>&nbsp;absorber volume mixing ratio is a simple sublevel average,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cimss.ssec.wisc.edu\/itwg\/groups\/rtwg\/Profile_Utility\/Equations\/Sublayer_Absorber.gif\" alt=\"\" \/><\/figure>\n\n\n\n<p>An explanation of the conversion of layer volume mixing ratios into column density (in kmol\/cm<sup>2<\/sup>) can be found in the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/units-conversion\/\" data-type=\"page\" data-id=\"382\">Units Conversion\u00a0documentation<\/a>.<\/p>\n\n\n\n<p>For the subprogram interface details, see the\u00a0<a href=\"https:\/\/itwg.ssec.wisc.edu\/rtsp\/level-layer-conversion\/\" data-type=\"page\" data-id=\"393\">Level Layer Conversion\u00a0documentation<\/a>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p>This page maintained by\u00a0Paul van Delst<br>Last updated December 3, 2004<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Units Conversion Module The\u00a0Units_Conversion\u00a0module contains a number of functions for converting the units of atmospheric absorber concentrations. This type of conversion information is usually hard to dig up so this module is an attempt to gather as many of the conversions as possible in one place. All of the available conversion routines are shown in [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-375","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/pages\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":5,"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/pages\/375\/revisions"}],"predecessor-version":[{"id":396,"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/pages\/375\/revisions\/396"}],"wp:attachment":[{"href":"https:\/\/itwg.ssec.wisc.edu\/rtsp\/wp-json\/wp\/v2\/media?parent=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}