Special Topics EAS 8803
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Date Created: 11/02/15
ENERGETICS This article treats a technical aspect of climate and weather studies some of it is intended for readers at an advanced level Atmospheric energetics the study of the distribution and transformation of energy in the atmosphere has long been a subject of fascination for meteorologists None theless it may be argued that energetics serves more as an afterthefact bookkeeping check than as a practical tool for developing a predictive understanding of weather and climate A brief discussion of the ambiguous role of energetics in atmospheric science serves as our introduc tion to the topic The remainder of this article is struc tured in three parts First definitions of potential kinetic and available potential energy are presented along with a more advanced and mathematical discussion of how these are linked to internal energy enthalpy and entropy We then examine transformations between various forms of energy considering the atmosphere as a thermody namic heatengine Finally we consider the observed energy transports focusing on meridional transport in the atmosphere and ocean Energy is one of the basic physical quantities for which we can write a local conservation lawan accounting that says that the change of a quantity inside a volume equals the net ux ow of that quantity through the walls of the volume See Conservation Laws This con servation law allows us to make powerful claims about the largescale distribution and transport of energy with out knowing the details of smallscale dynamics For example knowing that the energy of polar regions is approximately constant allows us to infer the oceanic energy transport into those regions from the difference between the poleward atmospheric transport and net energy radiated to space Energy is the common currency that allows us to balance the books between uxes of radi ation moisture heat and mechanical energy In many areas of physics an understanding of ener getics provides an efficient route to understanding and predicting a system s dynamics In the atmosphere the winds which themselves contain only about 004 percent of the system s total energy transport large uxes of heat and moisture and thus strongly in uence the distribution of energy Although the maintenance of the winds them selves may be studied as a problem of energetics consid eration of other propertiessuch as momentum or potential vorticitymay provide a more powerful route to understanding the winds and so to understanding the distribution of heat and moisture See Potential Vorticity Comparing energy uxes in the solardriven planetary heat engine which are of order 200 watts per square meter with the uxes typical of various biogeochemical cycles illustrates the limitations to the degree of insight that can be gained from energetic considerations Nuclear decay in the planet s interior provides an upward ux of about 007 watts per square meter This ux drives volcanoes and continental drift which in uence climate through emission of gases and reconfiguration of oceans and land with an importance that overwhelms the trivial direct impact of the geothermal heat ux Photo synthesis converts solar radiation to chemical energy with peak uxes of about 1 watt per square meter as with geophysical energy uxes the relevant climatic impact of biology is not on energetics but rather on the chemical composition of the atmosphere which indirectly regulates much larger energy uxes The energy uxes associated with our fossilfueled civilization amount to only a few tens of watts per square meter over large urban areas and only 002 watts per square meter on a global average yet the indirect effects of our modification of atmospheric gas and aerosol concentrations may have already changed global energy uxes by a few watts per square meter See Global Warming Paleoclimates Definitions Gravitational potential energy is the energy that mass has by virtue of its position in a gravi tational field It is the stored work that was done against the force of gravity in lifting an object from a reference surface It does not depend on the composition of the bodyonly on its mass and position In general only changes in potential energy have significance the actual magnitudes depend on the definition of the reference sur face and have no physical meaning However when the planetary surface is used as a reference the absolute value of the potential energy of an atmosphere in hydrostatic equilibrium is meaningful because of the partition between internal and potential energy see the more detailed discussion below In atmospheric physics we assume that the gravita tional field is constant with height so that potential energy is a linear function of height as well as mass We usually consider an effective gravitational field which is the sum of the gravitational field and the vertical com ponent of the outward force due to the earth s rotation the centrifugal force The resulting acceleration denoted g varies by only about 03 percent between the equator and the poles The potential energy of a mass m is mgz where z is the height and the potential energy per unit volume is pgz where p is the density Kinetic energy the energy of motion is the total work done on an object in accelerating it from rest It is linearly proportional to an object s mass and to the square of its velocity In the atmosphere we write the kinetic energy I densitythe amount per unit volume as pill2 where p is the density and v is the speed Kinetic energy is gen erated when a parcel of air is accelerated by gravitational or pressuregradient forces the energy supplied by the force comes from the conversion of potential energy in the former case or internal energy in the latter Kinetic energy can be destroyed by conversion back to internal or potential energy which occurs when the correspond ing gravitational or pressuregradient forces act to decel erate the parcel Alternatively kinetic energy can be dis sipated by viscous frictional forces which always act to remove velocity gradients and convert kinetic energy into heat See Friction Before discussing available potential energy we need to mention the connection between internal and potential energy and to review the definition of adiabatic and dia batic processes In addition we will write the continuity equation for energy in the atmosphere although it is not necessary for understanding the rest of this article Internal and potential energy are closely coupled When air in a hydrostatic atmosphere is heated it expands doing work against the local pressure by lifting the air above it and converting some of the heat into potential energy Raising the temperature of a parcel by BT requires Cw 39f39 of internal energy and R8T of work where C1 is the specific heat at constant volume and R is the ideal gas constant The sum C1 R 6T CPST is called the enthalpy where CI is the specific heat at con stant pressure The ratio R Ci of potential to internal energy is constant in a column of air in hydrostatic equi librium and it is thus to a good approximation a con stant ratio in the atmosphere as a whole See Enthalpy When we add heat to a parcel of airdiabatic heating we increase both its entropy and its enthalpy A parcel that moves without exchanging heat maintains its entropy and is said to move adiabatically Temperature change of a parcel due to adiabatic compression is called adiabatic heating Dry air that moves adiabatically in a hydrostatic atmosphere conserves the sum of its enthalpy and potential energythe dry static energy CPT gz which corresponds to its potential temperature See Adi abatic Processes Diabatic Processes Entropy If air is ascending or descending while maintaining a constant temperature then diabatic and adiabatic tem perature tendencies are balanced For example in the tropics ascending air is confined to small regions of active convection while most of the upper tropical troposphere experiences gradual descent Where the air is descending adiabatic heating is matched by radiative cooling In the convective systems adiabatic cooling is mainly balanced by latent heating We can now write the local conservation law for energy in the atmosphere Ignoring moisture the energy density is the sum of internal potential and kinetic energies pCqT g2 t1 However the quantity which is conserved by a parcel moving in a hydrostatic atmosphere includes the enthalpy rather than the internal energy it is called the dry static energy The energy ux is the product of the dry static energy and the velocity vector pCPT gz v2 1 The conservation law for atmospheric energy density says that the rate of change of energy in a volume plus the flux out of the volume equals the diabatic heating rate iMCQT gz 112 V pCpTgzv2vpQ Moisture can be included in this accounting by adding a latent heat term La to the expressions for energy density and flux and subtracting the diabatic heating due to con densation from the righthand side Only a small fraction of the atmosphere s total internal and potential energy can be converted to kinetic energy This fraction is called the available potentialenergy it may be defined as the maximum energy that can be extracted from an atmosphere at rest by adiabatic processes Avail able potential energy is computed by considering a hypo thetical atmosphere called the reference state which is in the minimum energy state that may be produced from the real state by adiabatic rearrangement of mass The difference between the potential plus internal energy of the atmosphere and that of the reference state is the avail able potential energy In a hydrostatic atmosphere the available potential energy is proportional to the variance of temperature on pressure surfaces Unlike internal potential or kinetic energywhich may be defined for individual parcels of airthe available potential energy depends on the con guration of the atmosphere on a larger scale Although it is sometimes convenient to discuss the available potential energy per unit mass or area one must remember that it is not a local property and cannot be incorporated into a local conservation law A few examples may help to clarify the role of available potential energy Consider an isothermal uniformtem perature atmosphere which is at rest and in hydrostatic equilibriumthat is in which the pressure gradient force is balanced by gravity This idealized atmosphere has zero available potential energy Each parcel of air which we may imagine as a small balloon could do work either by expanding against the pressure that confines it thereby converting internal to mechanical energy or by being lowered in the gravitational field thereby liberating potential energy However no net energy can be extracted from the system by such methods because more work must be done on other parcels of air in com pressing or lifting them to make room for the first parcel than can be gained by its expansion or lowering This is both a necessary and a suf cient condition for hydro static equilibrium Now consider an atmosphere divided into two regions with the same surface pressure each at rest and in hydro static equilibrium which have uniform but different potential temperatures Note that constant potential tem perature implies a temperature that decreases linearly with height and note that potential temperature rather than temperature is constant for a parcel of air moving in a hydrostatic atmosphere Now imagine that the bar rier between the two regions is removed At a given alti tude the pressure is smaller on the side with the higher temperatures These pressure differences produce a net I force which accelerates the gas converting available potential and internal energy to kinetic energy In order to compute the total amount of available potential energy we must determine the minimum energy reference state which in this case is the state where the high potential temperature air lies atop the low in a situation of uniform horizontal stratification See Potential Temperature Atmospheric Thermodynamics The sunlight absorbed by the Earth oceans and atmosphere deposits energy which must be returned to space as infrared radi ation in order for the planet to maintain a roughly con stant temperature Although solar absorption and infra red radiation must be approximately balanced globally they are not in balance locally Solar absorption is con centrated at the surface and in the tropics most of the infrared radiation to space however originates in the middle troposphere and it is more evenly distributed between equatorial and polar regions than is solar absorption In order to maintain the timeaverage tem perature distribution the system must transport heat from regions where solar heating dominates infrared cooling to regions where radiative cooling dominates Thus the atmosphere transports heat from the ground to the upper troposphere and the atmosphere and ocean together transport heat poleward from the tropics Figure 1 illustrates the various processes considered under atmospheric thermodynamics See Thermodynamics The difference between solar heating and infrared cooling called the net radiative heating may be regarded as the driving force for atmospheric thermodynamics Solar radiation reaches the top of the atmosphere with a ux of 1370 i 10 watts per square meter about 30 per cent of which the planetary albedo is re ected back to space The remainder is absorbed with a ux of 250 watts per square meter when averaged over the Earth s area which is four times larger than the disk it presents to the sun About 70 percent of the solar absorption happens Solar radiation reflected by clouds dust and Earth s surface At Solar radiation com1ng in to space by Earth s surface Infrared radiation lost Infrared radiation 50 absorbed by atmosphere 14 v 7 Infrared radiation lost to space by atmosphere 64 Generation kinetic energy Internal 0395 Kinetic Potential Dissipation of kinetic Energy i Energy 39 energy by friction Heat released by 8 H C 24 condensation 8 8 of water vapor 3 g L t t g 5 Q 21 en 0 b gt 6 Heat 0002 m g a a a a if 2 4 Flux of latent heat B sensl 6 eg due to evaporation ENERGETICS Figure l Atmospheric thermodynamics a schematic diagram of energy ows in the climate system Adapted from Peixoto and Oort 1992 at the surface and about 40 percent of that leaves the surface as net infrared radiation leaving a net surface radiative heating of 150 watts per square meter On a global and annual average the net radiative heating of the surface is equal to the net radiative cooling of the atmosphere because of the balance between absorbed solar and outgoing infrared at the top of the atmosphere See Albedo Radiation Over the oceans or moist ground most of the net radi ative heating of the surface is used to evaporate water which removes energy from the surface as latent heat When the vapor condenses it deposits almost all of its latent heat in the air rather than in the condensed water which returns to the surface as precipitation The net result is to transport heat from the surface to the air where condensation occurs On a global average about 70 per cent of the net radiative heating of the surface is removed by latent heat ux The remaining 30 percent leaves the surface by conduction of sensible heat to the overlying air See Latent Heat Sensible Heat In summary the atmosphere experiences diabatic heating or cooling from four processes latent heating sensible heating at the surface solar absorption and infrared heating or cooling There is additional heating due to the dissipation of kinetic energy which is usually ignored The component of diabatic heating that is une venly distributed horizontally produces available poten tial energy at a globally averaged rate of about 2 watts per square meteronly about 1 percent of the solar heat ing Available potential energy is then transformed into kinetic energy which is ultimately dissipated to produce heat A deeper insight into the process of dissipation may be gained by considering the spatial scale at which various energy transformations occur First a few general words about the definition of spatial scale are in order The dis tribution of a quantity with respect to scale is defined by its spatial power spectrum which is usually computed as a Fourier transform We say that a quantity varies at a certain scale when most of its total spatial variancethe power in its power spectrumis concentrated at that scale Physical laws that are linear such as Newton s F 2 ma force equals mass times acceleration preserve the distribution of variance with respect to scale that is if F varies at a certain scale then so will a Nonlinear laws allow energy to be transferred between scales generally from a larger to smaller scale The generation of available potential energy by dia batic heating and its subsequent conversion to kinetic energy are concentrated at the spatial scale that Charac terizes the heating s variancein the horizontal plane this is a few thousand kilometers and larger Kinetic energy is dissipated when work is done against viscosity Viscous forces depend on velocity gradients which are larger in smaller eddies The rate of dissipation in eddies is there fore a strong function of their scale it is in fact inversely proportional to the square of an eddy s size Thus kinetic energy generated at large scales is transferred to smaller and smaller scales as allowed by the nonlinearity of the equations of uid motion until it reaches a scale where frictional dissipation balances the ow of energy from larger scales In both the atmosphere and the ocean this dissipation scale called the Kolmogorov length is about 1 millimeter Although the net flow of energy is from available potential energy to kinetic energy and from larger to smaller scales reverse ows also occur Some energy is transformed from small to large scales and at larger scales some kinetic energy is transformed back to avail able potential energy The net result is always to balance the generation of available potential energy by the dissi pation of kinetic energy It is interesting to view atmospheric energetics from the standpoint of thermodynamicsthat is to analyze the atmosphere as a heat engine operating between regions of net radiative heating and cooling A heat engine trans forms heat into work by taking heat energy from a hot reservoir transforming a fraction of it into work and dumping the remainder into a cold reservoir The maX imum work that can be produced is limited by the requirement that entropy not decrease The fraction of the thermal energy input which can be converted to workthe maXimum thermodynamic efficiencyis given by the temperature difference between the two res ervoirs divided by the temperature of the hot reservoir Because of the continuous nature of the atmospheric temperature distribution we cannot precisely define hot and cold reservoirs as a rough approximation a pole to equator differential of 30 K and a hot temperature of 300 K limits the thennodynamic efficiency to about 10 per cent The generation of kinetic energy is thus more strongly constrained by limited production of available potential energy which amounts to only about 1 percent of the solar heating Energy Transport As discussed above the most important global energy ows are vertical and meridio nal upward from the surface and poleward from the tropics There is a huge westtoeast zonal energy ow associated with the midlatitude jet streams but only the convergence or divergence of this closed loop of ow can alter local energy budgets and so this is a small contri bution to annual averages See Jet Stream Although its annual average contribution is small zonal transport plays an important role in reducing the seasonal variation of midlatitude continental climates by coupling the large oceanic heat reservoir to the much smaller terrestrial one It is instructive to divide the zonally averaged meridi onal transport into contributions from transient eddies zonal mean ow and zonally stationary eddies Figure 2 Each component is caused by a different physical mechanism The transient eddies are due to the covari ance of energy density and meridional wind A positive transienteddy heat ux re ects the tendency of positive deviations from the mean wind to be correlated with pos 6 4 2k g 0 2 n 4 a 6 I I IIII I I I 4r I Latent o N I 2 4 A CT v 6 IIII1 IIIII Total Transient lll I I l I l I I I I J I I 1 LI 90 N 60 30 0 30 60 90 S c Latitude ENERGETICS Figure 2 Meridional energy transport a Annual average energy transported by the atmosphere thin line ocean broken line and atmosphere and ocean combined thick line b Transport of latent heat on an annual average thick line transports during DecemberJanuaryFebruary thin line and transport during JuneJulyAugust broken line c Energy transport by transient eddies on an annual average thick line DecemberJanuaryFebruary thin line and JuneJulyAugust broken line From Keith 1995 Input documentation for SBDAR39I39 summer 2002 release This file documents input parameters for SBDART Santa Barbara DISORT Atmospheric Radiative Transfer SBDART is a software tool that computes plane parallel radiative transfer in clear and cloudy conditions within the Earth39s atmosphere and at the surface For a general description and review of the program please refer to Ricchiazzi et al 1998 Bulletin of the American Meteorological Society October 1998 SBDART39s main input file is called INPUT This file contains a single NAMELIST input block also named INPUT A significant advantage of NAMELIST input is that not all elements of an input block need be specified by t e user Since most of the code inputs have been initialized with reasonable default values new users can start by specifying just a few interesting input parameters The default state of input parameters may be determined by removing INPUT from the current working directory When SBDART detects the absence of file INPUT it will print the default settings of all input parameters This output may be redirected to a file for editing The default configuration of INPUT is as follows ampINPUT idatm 4 amix 00 isat 0 wlinf 0550 wlsup 0550 wlinc 00 sza 00 csza 10 solfac 1 0 nf 2 iday 0 time 160 alat 647670 alon 640670 zpres 10 pbar 10 sclh20 10 uw 1 0 uo3 10 o3trp 10 ztrp 0 0 xrsc 10 xn2 10 x02 1 0 xcoZ 10 xch4 10 xn20 1 0 xco 10 xnoZ 10 xsoZ 1 0 xnh3 10 xno 10 xhno3 1 0 x04 10 isalb 0 albcon 00 sc 10300 zcloud 500 tcloud 500 lwp 500 nre 580 rhcld 10 krhclr 0 jaer 50 zaer 500 taerst 500 iaer 0 vis 230 rhaer 10 wlbaer 4700 tbaer 4700 abaer 10 wbaer 470950 gbaer 47070 pmaer 94000 zbaer 50 10 dbaer 50 10 nothrm 1 nosct 0 kdist 3 zgrid1 00 zgrid2 300 ngrid 50 zout 001000 iout 10 deltam t lamber t ibcnd 0 saza 1800 prnt 7f ipth 1 fisot 00 temis 00 nstr 4 nzen 0 uzen 20 10 vzen 2090 nphi 0 phi 20 10 imomc 3 imoma 3 ttemp 10 btemp 10 spowder f idb 200 NOTE Unfortunately many fortran compilers produce rather cryptic error messages in response to improper NAMELIST input files Here are three common NAMELIST error messages and their meaning I ERROR MESSAGE invalid reference to variable in NAMELIST input MEANING you misspelled one of the NAMELIST variable names 2 ERROR MESSAGE too many values for NAMELIST variable MEANING you specified too many values for a variable most likely because you separated variables by more than one comma 2 ERROR MESSAGE end of file during read or namelist block INPUT not found MEANING There are two possibilities A you didn39t include a NAMELIST block specifier INPUT DINPUT or END or you misspelled it or B You used the wrong character to signify a namelist block name EORTRAN9O expects the namelist blocks to start with ampltnamegt and end with but most EORTRAN77 compilers used the ltnamegt SEND convention Other input files are sometimes required by SBDART atmsdat atmospheric profile see input quantity IDATM aerosoldat aerosol information see input quantity IAER albedodat spectral surface albedo see input quantity ISALB filterdat sensor filter function see input quantity ISAT solardat solar spectrum see input quantity NE usrclddat cloud vertical profile see input quantity TCLOUD SBDART usually lists computational results directly to the standard output device ie the terminal if run interactively However some warning messages are written to files named SBDART7WARNING where the question marks indicate a warning message number When running SBDART iteratively over many inputs the SBDART7WARNING files will only be created once on the first iteration that generated the warning condition The warning files contain a warning message and a copy of the input file that triggered the warning General options NAMELIST ampINPUT WAVELENGTH LIMITS FILTER FUNCTION SPECIFICATION NF SOLAR SPECTRUM SELECTOR 2 use TOA solar irradiance read from CKTAU file when kdist l NF 2 is not a valid input when kdistne l l read from file solardat user supplied data file quotsolardatquot is read from the current working directory This ASCII file is read with the following free format read statements readl3end100 wlsunisuniil5000 100 continue where wlsun wavelength sample points microns sun direct normal solar irradiance at the top of the atmosphere Wm2micron The number of wavelength sample points read from solardat should be less than or equal to 5000 Old versions of SBDART used a different format for spectral input files albedodat filterdat and solardat A perl script 39newform39 is available from ftpzftpicessucsbedupubesrgsbdart to convert old data files to the new format 0 spectrally uniform l 5s solar spectrum 0005 micron resolution 25 to 4 micron 2 LOWTRAN77 solar spectrum default 20 cm l resolution 0 to 28780 cm l 10 cm l resolution 28780 to 57490 cm l 3 MODTRAN73 solar spectrum 20 cm l resolution 100 49960 cm l ISAT FILTER FUNCTION TYPES 4 Guassian filter WLINF 2WLSUP to WLINF2WLSUP 3 Trianglar filter WLINF WLSUP to WLINFWLSUP 2 Flat filter WLINF5WLSUP to WLINF5WLSUP l USER DEFINED read from filterdat H H H H ugtm H o w m 4 m w m N H NNNNNNHHHHl H m m N H O m m 4 m m 26 WLINF TO WLSUP WITH FILTER FUNCTION l default then the values of effect if they default values Otherwise the as specified in NOTE if ISATO and KDISTl WLINF and WLSUP only have an have been changed from their such that WLINF ne WLSUP wavelength sample points are the CKTAU file GTR lOO 410nm channel GTR lOO 936nm channel 415nm channel 500nm channel 610nm channel 665nm channel 862nm channel 940nm channel nominal nominal nominal Biological action spectra for DNA damage by UVB radiation AIRSl 380 460nm AIRSZ 520 700nm AIRS3 670 975nm AIRS4 415 lllOnm NOTE If ISAT l a user supplied filter data file quotfilterdatquot is read from the current working directory This ASCII file is read with the following free format read numbers may be separated by spaces commas or carriage returns readl3endlOO wlfiltifiltiilhugeOH lOO continue where wlfilt wavelength sample points microns filt filter response value unitless The number of wavelength sample points read from filterdat should be less than or equal to 1000 WLINF WLSUP WLINC This file format is new Previous versions of SBDART used a different format for spectral input files albedodat filterdat and solardat A perl script 39newform39 is available from ftpzftpicessucsbedupubesrgsbdart to convert old data files to the new format lower wavelength limit when TSAT0 WLTNF gt 250 microns central wavelength when TSAT 2 3 4 upper wavelength limit when TSAT0 equivalent width when TSAT 2 3 4 WLSUP lt 1000 microns NOTE If TSAT eq 2 a rectangular filter constant with wavelength is used with central wavelength at WLTNF and an equivalent width of WLSUP full width WLSUP If TSAT eq 3 a triangular filter function is used with the central wavelength at WLTNF and an equivalent width of WLSUP full width 2WLSUP filter function is zero at end points and one at WLTNF If TSAT eq 4 a gaussian filter function is used with the central wavelength at WLTNF and an equivalent width of WLSUP full width 4WLSUP If output is desired at a single wavelength set WLTNFWLSUP and TSAT0 In this case SBDART will set WLTNCl the user specified value of WLTNC is ignored and the output will be in units of WmZum for irradiance and WmZumsr for radiance This parameter specifies the spectral resolution of the SBDART run Though the spectral limits of the calculation are always input in terms of wavelength the spectral step size can be specified in terms of constant increments of wavelength logwavelength same as constant increment of logwavenumber or wavenumber Which one to choose depends on where in the spectral bandpass you want to place the most resolution Since SBDART is based on LOWTRAN7 band models which have a spectral resolution of 20 cm l it would be extreme overkill to allow spectral step size less than 1 cm l On the other hand a spectral resolution coarser than 1 um is also pretty useless Therefore the way WLTNC is interpreted depends on whether it is less than zero between zero and one or greater than 1 WLTNC 0 the default gt wavelength increment is equal to 0005 um or 110 the wavelength range which CSZA SAZA IDAY ever is smaller If the WLINFWLSUP then WLINC001 WLINC lt 0 gt wavelength increment is a constant fraction of the current wavelength WLINC is interpreted as a specified value of deltalambdalambda and the wavelength steps are adjusted so that wavelength step is approximately the product of the current wavelength and WLINC Specifying the wavelength increment as a fractional step size is useful when the wavelength range extends over more than an decade of wavelength For example if the wavelength range is 05 to 200 specifying a constant wavelength increment of 01 microns tends to under resolve the low wavelengths and over resolve the long wavelengths Setting WLINC Ol causes the code to use a wavelength increment of about 005 microns in the visible and about 2 micron in the thermal infrared which is a better compromise of resolution and computer time 1 gt WLINC gt 0 gt WLINC is the wavelength step size um if WLINC gt 1 then WLINC is the step size in inverse centimeters If maximum fidelity is required and gaseous absorption is the primary influence on the output then WLINC should be set to 20 which is the wavenumber resolution of the LOWTRAN7 band models The total number of wavelength steps nwl is given by nwl llnwlsupwlinfwlinc wlinc lt 0 nwl lwlsup wlinfwlinc l gt wlinc gt 0 nwl 110000lwlinf lwlsupwlinc wlinc gt 1 SOLAR GEOMETRY solar zenith angle degrees default OJ Solar input may be turned off by setting szagt90 SZA is ignored if CSZA is non negative or IDAY is non zero Cosine of solar zenith angle If CSZA gt 0 solar zenith angle is set to acosCSZA default l solar azimuth angle degrees default OJ SAZA is ignored if IDAY is non zero Setting SAZA180 will cause the forward scattering peak to appear near phi0 see below If IDAY gt 0 the solar illumination angles SZA SAZA are computed from the specified time and geographic SOLFAC NOSCT ISALB coordinates using an internal solar ephemeris algorithm see subroutine zensun TDAY is the number of days into a standard quotyearquot with TDAYl and the lst of January and TDAY365 on the 31st of December if TDAY gt 365 TDAY is replaced internally by modTDAY l365l If TDAY lt O the code writes the values of absidaytime alatalonszaazm and solfac to standard output and exits UTC time Grenwich in decimal hours latitude of point on earth39s surface east longitude of point on earth39s surface NOTE TIME ALAT and ALON are ignored if TDAY eq 0 solar distance factor Use this factor to account for seasonal variations of the earth sun distance If R is the earth sun distance in Astronomical Units then SOLFAClR2 SOLFAC is set internally when the solar geometry is set through TDAY TIME ALAT and ALON In this case SOLFAC is set to SOLFAC l epscos2piTDAY perh365 where eps orbital eccentricity 001673 and perh day of perihelion 2 jan 2 NOTE seasonal variations in earth sun distance produce a 34 perturbation in the TOA solar flux This factor should be included when making detailed comparisons to surface measurements aerosol scattering mode used for boundary layer aerosols 0 normal scattering and absorption treatment 1 reduce optical depth by l ssaasym set ssaO 2 set ssaO 3 reduce optical depth by l ssa set ssaO where ssasingle scattering albedo and asymasymmetry factor nosct does not affect the stratospheric aerosol models or the iaer5 boundary layer model SURFACE REFLECTANCE PROPERTIES SURFACE ALBEDO FEATURE l spectral surface albedo read from quotalbedodatquot 0 user specified spectrally uniform albedo set with ALBCON l snow 2 clear water 3 lake water 4 sea water 5 sand data range 04 23um 6 vegetation data range 04 26um 7 ocean water brdf includes bio pigments foam and sunglint additional input parameters provided in SC 8 Hapke analytic brdf model additional input parameters provided in SC 9 Ross thick Li sparse brdf model additional input parameters in SC NOTE isalb 7 8 9 causes sbdart to use a non Lambertian surface reflectance Since the reflectance BRDF must first be expanded in terms of orthogonal functions this mode of operation is somewhat more time consuming than the normal Lambertian reflectance models In some cases flux calculations may be accurately computed in Lambertian mode by using directional albedo computed from the brdf assuming all the incomming radiation is along the solar beam direction Of course this approach will probably fail in cases where the solar direct beam doesn39t dominate the downwelling radiation eg in the infrared or under clouds SBDART may be run with directional albedos by setting isalb to 7 8 or 9 10 combination of snow seawater sand and vegetation partition factors set by input quantity SC NOTE If ISALB l a user supplied spectral reflectance file quotalbedodatquot is read from the current working directory This ASCII file is read with the following free format read numbers may be separated by spaces commas or carriage returns readl3end100 wlalbialbiilhuge0 100 continue where wlalb wavelength sample points microns alb spectral albedo unitless The number of wavelength sample points read from albedodat should be less than or equal to 1000 The user specified reflectance may cover any wavelength range and have arbitrarily high resolution This contrasts with the standard reflectance models sand vegetation lake water and sea water which are only specified in in the range 25 to 4 um at 5nm resolution Prior to version 20 SBDART used a different format for spectral input files albedodat filterdat and solardat A perl script 39newform39 is available from ftpftpicessucsbedupubesrgsbdart to convert old data files to the new format NOTE A large collection of spectral reflectance data is available from the JPL Spectral library httpspeclibjplnasagov The jpl spectral files may be used by sbdart after processing with this one line perl command perl lane 39print quotF0 quotFl100 if A 0 939 lt jplfile gt albedodat where jplfile is the name of the spectral library file ALBCON TSALB0 a spectrally uniform surface albedo SC surface albedo specification parameters used for isalb7 8 and 10 SC specifies ocean reflection model parameters SCl Oceanic pigment concentration in mgm3 Pigment is assumed to consist of Chlorophyll a Pheophytin a Pigment concentration affects the ocean brdf in the wavelength range from 04 07um Default 001 Turn off the subsurface contribution by setting SCl0 Note that subsurface contribution is set to a non zero constant for lt pigmenticoncentration lt 00001 Te the subsurface contribution does not approach zero continuously as scl goes to zeroJ SC2 Wind speed over ocean in ms Wind speed affects the sunglint and foam contributions to the ocean brdf Default5 ms SC3 Oceanic salinity in parts per thousand Salinity affects the Fresnel reflectivity of the ocean surface Default343 NOTE The oceanic brdf model is nearly the same as the one used in the 6s radiative transfer model The only difference is that the brdf in SBDART does not depend on the wind direction The brdf dependence on wind direction was eliminated by averaging the 6s reflectance model over 360 degrees of wind azimuth Note The 6s model does not include any provisions for wave facet shading so results for shallow illumination or viewing directions may be incorrect Additional information is available from quotSecond Simulation of the Satellite Signal in the Solar Spectrum 6S user39s guidequot by Vermote E D Tanre JL Deuze M Herman and JJ Morcrette 1995 SC specifies Hapke analytic brdf model parameters Single scattering albedo of surface particle Asymmetry factor of scattering by surface particles Magnitude of hot spot opposition effect Width of hot spot This model is based on Hapke 1981 also see P Pinet A Cord S Chevrel and Y Daydou 2003 39Experimental determination of the Hapke parameters for planetary regolith surface analogs39 Generic vegetation actually clover may be described with sc0101 0263 0589 0046 From Pinty and Verstraete 1991 Snow may be described with sc099 06 00 0995 From Domingue et al 1997 and Verbiscer and Veverka 1990 SC specifies the Ross thick Li sparse brdf model parameters 1isotropic coefficient 2volumetric coefficient SC3geometric shadowing coefficient 4hot spot magnitude 5hot spot width 1981 Li and Strahler Ross 1992 isalb10 SC specifies mixing ratios snow ocean sand and vegetation Composite albedo fractions fraction of snow fraction of ocean fraction of sand fraction of vegetation applies only when ISALB10 SC1SC2SC3SC4 need not sum to 1 Thus it is possible to use the SC factor to boost the overall reflectance of a given surface type For example SC0020 yields 10 IDATM AMIX results for a surface with spectral reflectivity twice that of sand Beware total reflectance greater than one will produce unphysical results MODEL ATMOSPHERES default ozoneatm cm ATMOSPHERIC PROFILE water vapor gcm2 total belowilOkm User Specified 0 l TROPICAL 4117 0253 0216 2 MIDLATITUDE SUMMER 2924 0324 0325 3 MIDLATITUDE WINTER 0854 0403 0336 4 SUBARCTIC SUMMER 2085 0350 0346 5 SUBARCTIC WINTER 0418 0486 0340 6 1418 0349 0252 n List to standard out If IDATM 0 a user supplied atmospheric profile quotatmsdatquot is read from the current working directory This ASCII file is read with the following free format read statements input values may be separated by spaces commas or carriage returns readl3 nn do 10 ilnn readl3 ZipitiWhiWOi 10 continue where nn is the number atmospheric layers nn should be less or equal to than MXLY a parameter used in SBDART see paramsf to set the maximum number of levels in the vertical grids z is the layer altitude in km 2 must be monotonically decreasing p is the pressure in millibars t is the temperature is Kelvin wh water vapor density gm3 wo ozone density gm3 If IDATM is set to a negative number in the range I to 6 SBDART prints the atmospheric model corresponding to absidatm to standard out and then quits The output atmospheric profile will reflect any modifications caused by input parameters UW UO3 O3TRP PBAR ZPRES RHCLD and KRHCLR weighting factor when positive this factor controls how much of the atmsdat atmospheric profile to mix in with one of the standard internal profiles selected by IDATM For example IDATMl and AMIX7 specifies a 70 weighting of atmsdat and a 30 weighting of profile TROPIC No default D 11 UW O3TRP ZTRP NOTE NOTE for zltZTRP integrated water vapor amount GCM2 integrated ozone concentration ATM CM above the level ZTRP The default value of ZTRP0 so U03 usally specifies the total ozone column If U03 is negative the original ozone density is used default 1 1 atm cm 1000 Dobson Units Use UW or U03 to set the integrated amounts of water vapor or ozone in the model atmosphere Aside from multiplicative factors the vertical profile will be that of the original model atmosphere set by TDATM The original unmodified density profile is used when UW or U03 is negative integrated ozone concentration ATM CM in troposphere The original tropospheric density set with TDATM is used when 03TRP is negative default 1J and The altitude of the tropopause The parameters U03 03TRP sets the total column ozone in the stratosphere and troposphere value of ZTRP is zero respectively Note since the default U03 normally sets the integrated ozone amount of the entire atmosphere default0 volume mixing ratio of N2 PPM default 78100000 volume mixing ratio of 02 PPM default 20900000 volume mixing ratio of 002 PPM default 36000 volume mixing ratio of CH4 PPM default 174 volume mixing ratio of N20 PPM default 032 volume mixing ratio of 00 PPM default 015 volume mixing ratio of NH3 PPM default 50e 4 volume mixing ratio of 02 PPM default 30e 4 volume mixing ratio of N0 PPM default 30e 4 volume mixing ratio of HN03 PPM default 50e 5 volume mixing ratio of N02 PPM default 23e 5 NOTE atmospheric component to retain its nominal mixing ratio defined in the U362 atmosphere as listed above The volume mixing ratio VMR Setting any of these factors to 1 causes that of a given species is adjusted by specifying the surface value of its VMR in PPM VMR and the nominal surface VMR There are no further re normalizations of the VMR Thus greater or less than 1006 the total of all the VMRs may be By the way the 12 The entire altitude profile is multiplied by the ratio of the user specified XRSC PBAR ZPRES SCLHZO default set of VMRs do not add up to lOAG because of the exclusion of the noble gases which do not have any radiative effects sensitivity factor for Rayleigh scattering defaultl This factor varies the strength of Rayleigh scattering for sensitivity studies sensitivity factor to adjust strength of absorption by oxygen collisional complexes defaultl see comments in subroutine o4cont surface pressure in millibars PBAR gt 0 causes each pressure to be multiplied by the factor PEARPO where PO is the surface pressure of the original atmosphere The absorption due to mixed gases is affected but absorption by ozone and water vapor is not they are separately controlled by UW and U03 The Rayleigh scattering optical depth is proportional to the PEARPO factor PBAR O disables Rayleigh scattering and all atmospheric absorption including water vapor and ozone Scattering by aerosols or clouds is not affected PBAR lt 0 causes the original pressure profile to be used this is the default NOTE PBAR has no effect of the CKTAU optical depths Surface altitude in kilometers This parameter is just an alternate way of setting the surface pressure and should not be set when PBAR is specified When ZPRES is set PBAR is obtained by logarithmic interpolation on the current model39s atmosphere pressure and altitude arrays Changing ZPRES does not alter other parameters in the atmospheric model in any way Note that setting a large value of ZPRES may push the tropopause where dTdzO to an unrealistically high altitude Water vapor scale height in km If SCLHZO gt 0 then water vapor is vertically distributed as expZSCLH20 If SCLHZO le 0 then the original vertical profile is used Changing SCLHZO has no effect on the total water vapor amount ZCLOUD CLOUD PARAMETERS Altitude of cloud layers km up to 5 values Cloud layers may be specified in two ways To specify separate cloud layers set ZCLOUD to a sequence of monotonically increasing altitudes A cloud layer with optical depth TCLOUDj will start at the highest computation level for which zileZCLOUDjOOl and will extend to the next higher level zil To specify a range of altitudes which will be filled by cloud tag the second element of the range with a minus sign In this case the element of TCLOUD that corresponds to the negative element of ZCLOUD specifies the gradient of the optical depth Setting this element of TCLOUD to 1 causes a uniform opacity between the lower and upper limits of the cloud layer See description of TCLOUD input Consider zcloudl 3lO 15 tcloud4 l 8 l nre 6 6 10 20 In this example two continuous cloud layers are defined the lower one extends from 1 to 3 km and has a total optical depth of 4 and an effective radius of 6um The upper cloud layer extends from 10 to 15 km has a total optical thickness of 8 and a sliding value of effective radius which starts lOum at the bottom of the cloud and ramps up to 20um at 15km The ramping function is logarithmic ie nre12kmlO201012 1015 10 Note that the actual location of the cloud layers is determined by the resolution and placement of vertical grid points in SBDART as explained below SBDART puts the i39th cloud layer at the highest vertical grid point k such that zk le absZCLOUDiOOl NOTE A cloud with a nominal altitude equal to that of one of the computational layer altitudes ZK actually extends from Zk to the next higher grid oint For example a cloud layer at Zk will not affect the direct beam flux at Zkl one layer above but will strongly affect it at Zk You can check this out your self by setting TOUTlO and ZCLOUDl and messing around with ZOUT to get outputs just above or below the cloud Suppose the bottom of your computational grid looks like k zk 6 25 TCLOUD LAgtJgtUquot OOHHN OLFOLFO Consider this input ZCLOUD10 TCLOUD50q NRE 8 60 40 90 10 10 10 8 20 20 Here two overlapping cloud decks are specified one extending from 1 to 6 km with a total optical thickness of 50 and the other from 4 to 9 km with a total thickness of 10 Since the total cloud optical thickness is spread over the total altitude range we would have 10 optical depths per km for the lower cloud deck and 2 optical depths per km for the second The code adds the effects of both cloud decks in the region of overlap Scattering parameters eg single scattering albedo in the overlap region are given by the weighted averages of the values computed from the mie scattering database using effective radius appropriate to each cloud deck and weighting according to the opacity contributed by each cloud deck cloud opacity scattering optical km 1 parameters depth 6 9 km 6 2 mie20 4 6 km 24 12 mie1010mie20212 1 4 km 30 10 mie10 total 60 If you have any doubt about where the code is putting the cloud set IDB51 see below to get a diagnostic print out of cloud optical depth NOTE do not try to put an ice cloud NRE lt 0 in a cloud layer range which includes water cloud 2 le NRE le 128 In other words this specification won39t work ZCLOUD 1 4 TCLOUD 1 1 NRE 8 1 Optical thickness of cloud layer up to 5 values TCLOUD specifies the cloud optical depth at a wavelength of 055um The cloud optical depth at other wavelengths is computed using the relation tau TCLOUDQwlQ055um where Q is the extinction efficiency which is a function of effective radius and wavelength see discussion of LWP for a definition of Q The code contains a look up table of Q that covers effective radii in the range 2 to 128um for water clouds and for a single effective radius of lOGum for ice clouds The wavelengths range is 029 to 33333 um for water clouds and 29 to 20 um for ice clouds When specifying an optical depth for a range of grid levels the second TCLOUD entry corresponding to the cloud top altitude is usually set to one This produces a uniform distribution of opacity over the altitude range For example ZCLOUD l 5 TCLOUD 10 1 NRE 1020 uniformly distributed opacity for a cloud of extent 4 km 25 optical depths per km effective radius ramps from 10 to 20 between 1 and 5km ititititit A linearly varying opacity distribution can be obtained by setting the second TCLOUD entry to a factor which represents the ratio of the opacity in the highest layer to that in the lowest layer For example tautotallO tau4 5kmtaul 2km4 ZCLOUD l 5000 linearly distributed opacity TCLOUD lO 4000 for a cloud of extent 4 km between taul 2kml between tau2 3km2 between tau3 4km3 between tau4 5km4 NOTE if r is the ratio of the top to bottom and t is the average opacity per level then tautop7levelt2rlr taubot7levelt2lr NOTE a linear increase in opacity starting from zero at the cloud bottom is obtained by setting rl 2zdiffdz where dz is the grid spacing and zdiff is the total altitude range over which the cloud extends This formula assumes constant grid spacing over the cloud altitude range Thus if dzl then ZCLOUD l 5 and TCLOUD 107 yeilds a linear 16 increase from zero Cloud drop effective radius microns up to 5 values Default value of NRE8 The absolute value of NRE should be a floating point number in the range 20 to 1280 NRE lt O selects mie scattering parameters for ice particles NRE gt O selects mie scattering parameters for water droplets The drop size distribution is assumed to follow a gamma distribution pl rRo Nr C rRo e where C is a normalization constant ClRogammap p7 and RoNREp2 The factor p2 relating R0 to NRE follows from the defining equation of NRE 3 2 NRE lt r Nr gt lt r Nr gt where the angle brackets indicate integration over all drop radii Another frequently used parameter to describe the size distribution is the mode radius Rm which is defined as the radius at which Nr is maximized For our drop size distribution Rmp lRo Using the relation between R0 and NRE we find that Rmp lNREp2 NOTE If the first element of NRE is zero values of TCLOUD ZCLOUD LWP and NRE are ignored and cloud specification records are read from file usrclddat The first record in this file corresponds to the lowest layer in the atmosphere that is between the surface and the lowest cell boundary altitude Each following record sets values for the next higher atmospheric layer in the model atmosphere usrclddat is read with the following fortran statements do ilnz l readl3endlOO lwpireiprireiicldfraci enddo continue where lwp liquid water path in layer i gm2 defaultO re effective radius of liquid water um in layer i default8um IMOMC pr frozen water path in layer i gm2 if pr lt 0 then scattering parameters are obtained from ccm3 cirrus model see subroutine icepar if pr gt 0 then scattering parameters are obtained from an internal mie scattering database covering ice spheres with effective radii between 2 and 128 um defaultO rei effective radius of frozen water um in layer i only active when pr is non zero if prltO and reileO then effective radius of ice is taken from ccm3 cirrus model see subroutine icepar default l cldfrac cloud fraction in layer this parameter reduces cloud optical depth by factor cldfracl5 defaultl It is not necessary to provide input records for layers above the highest cloud In addition a forward slash terminates interpretation of data values in a record For example the following records in usrclddat specify a cloud that extends from 2 to 4 km assuming idatmgtO and no regridding no cloud between 0 1 km no cloud between 1 2 m 30 lwp30 relO between 2 3 km 60 20 5 3O 2 lwp60 re20 pr5 reice3O cldfrac2 between 3 4 km ititititit Any input quantities that are left unspecified will retain their default values of lwpO reff8 prO reice l and cldfracl The radiative properties of ice are computed from a CCM3 model see subroutine TCEPAR Controls the phase function model used in cloud layers isotropic scattering rayleigh scattering phase function henyey greenstein a function of asymmetry factor gre haze Lias specified by garciasiewert cloud cl as specified by garciasiewert L JgtLAl default3 The liquid water path or frozen water path if nreleO of a cloud is specified in units of gm2 This is another way to specify cloud optical depth A linearly varying opacity distribution can be obtained by setting the second LWP entry to a factor which represents the ratio of the opacity in the highest layer to that in the lowest layer 18 RHCLD KRHCLR For more details see the discussion of TCLOUD NOTE a 1 mm column of liquid water 1000 gm2 NOTE LWP and TCLOUD cannot be used at the same time NOTE The cloud optical depth is related to LWP by 4 RHO NRE where Q is the scattering efficiency and RHO is the density of liquid water 1 gcm3 The value of O that applies to a distribution of cloud droplets can be expressed in terms of the extinction cross section at a given wavelength and liquid drop radius Let sigma extinction cross section at a given wavelength and drop radius q sigmapirA2 dimensionless where pirA2 is the geometrical cross section of the cloud drop then Q is a weighted average over drop radius given y 2 2 Q lt r q Nr gt lt r Nr gt for visible light Q is typically about 2 dimensionless For example NRE lOum and LWP 200gm2 02mm gt tau 30 The relative humidity within a cloud layer a floating point value between 00 and 10 RHCLDlt0 disables the adjustment of relative humidity in which case the relative humidity in the cloud layer is unchanged it varies with the temperature and water vapor density of the initial model atmosphere This parameter has no effect when KDTSTlt0 If zero water vapor mixing ratio in clear layers is RHCLD is negative or TCLOUD is zero if KRHCLRl the relative humidity in clear layers is unchanged default0 NOTE if KRHCLRl and clouds are present the actual water vapor path will differ from that specified by WH On the other hand if KRHCLR0 the normalization procedure 19 JAER ZAER TAERST IAER may drive the water vapor in clear layers to zero and still be unable produce a given WVP This parameter has no effect when KDISTltO STRATOSPHERIC AEROSOLS LOWTRAN 7 model 5 element array of stratospheric aerosol types O no aerosol l background stratospheric 2 aged volcanic 3 fresh volcanic 4 meteor dust altitudes above the surface of stratospheric aerosol layers km Up to 5 layer altitudes may be specified NOTE even though these models are for stratospheric aerosols the scattering layer may be placed anywhere within the numerical grid See ZCLOUD for a discussion of how aerosol cloud layers are positioned within SBDART39s computational grid optical depth at 055 microns of each stratospheric aerosol layer Up to 5 layer optical depths may be specified BOUNDARY LAYER AEROSOLS BLA Boundary layer aerosol type selector l read aerosol optical depth and scattering parameters from aerosoldat See subroutine AEREAD the file format is readable by the following Fortran code readll nn moma do klhugeO readllendlOO wlk do inz nnlnz readll dtauikwaerikpmomlmomaiM enddo enddo lOO continue where nn is the number of atmospheric levels for which aerosol information is specified moma number of phase function moments wlk is the wavelength wlk lt wlkl 20 RHAER dtauik is the optical depth increment within level i at wavelength k information is specified in top down order waerik is the single scattering albedo pmommik are legendre moments of the phase function Note that zeroeth moment is not read it is assumed to be NOTE Layers are read from top to bottom starting from layer nz nnl ie the lowest nn levels in the atmosphere A single forward slash may be used to indicate levels with zero aerosol optical depth O no boundary layer aerosols all BLA parameters ignored l rural 2 urban 3 oceanic 4 tropospheric S user defined spectral dependence of BLA The wavelength dependence of the aerosol scattering parameters are replaced by those read in from input parameters wlbaer tbaer wbaer and gbaer Between 1 and 47 spectral values may be specified NOTE the spectral dependence of the boundary layer aerosol models TAERl234 vary with relative humidi See subroutine AEROSOL for details NOTE Don39t be mislead by the term quotboundary layer aerosolquot The BLA models TAERl234 were originally developed to describe aerosols in the lower atmosphere However in SBDART the default vertical density of BLA falls off exponentially and affects regions above the normal extent of the boundary layer The vertical influence of t ese aerosols may be confined to a specified boundary layer altitude with the optional parameters ZBAER and DBAER The spectral dependence of the boundary layer aerosol scattering parameters are sensitive to relative humidity Use input parameter RHAER to set the relative humidity used in the boundary layer aerosol model Set RHAER l the default value to use the ambient surface relative humidity computed from the temperature and water vapor density of the current model atmosphere RHAER has no 21 ZBAER DBAER effect when TAER 5 Horizontal Path Visibility km at 055 microns due to boundary layer aerosols This parameter does not set the optical depth for the user defined aerosol model TAER5 but does affect that model through the vertical structure see below NOTE unlike the stratospheric aerosols the boundary layer aerosols have predefined vertical density distributions These vertical structure models vary with visibility see discussion of ZBAER and DBAER NOTE The boundary layer aerosol optical depth absorption scattering at 055 microns is given by tauaero055um 3912 integral nZn0 dz VTS where nz is the vertical profile of aerosol density For the 5 and 23 km visibility models the indicated integral is 105 and 151 km respectively So tauaero055um 39l2l05wl5ll wvis where w is a weighting factor between the two extremes and is given b lvis l23 W 5 lt vis lt 23 15 123 W 1 vis lt 5 W O vis gt 23 NOTE Visibility is defined as the horizontal distance in km at which a beam of light at 055um is attenuated by a factor of 002 n0sigmaVTS ln02 or VTS 3912n0sigma where sigma is the aerosol absorptionscattering cross section at 055 microns See Glossary of Meteorology American Meteorology Society 1959 Altitude grid for custom aerosol vertical profile km Up to MRLY altitude points may be specified ZBAER is active for all positive values of TAER Aerosol density at ZBAER altitude grid points active for 22 TBAER QBAER all positive values of TAER Up to MRLY density values may be specified The number of density values must match the number of ZBAER The units used to specify aerosol density is arbitrary since the overall profile is scaled by the user specified total vertical optical depth The aerosol density at all computational grid points is found through logarithmic interpolation on the ZBAER and DBAER values The normal vertical profile from 5s is used when DBAER is unset For example ZBAER0l100 DBAER10005001 specifies a aerosol density profile that drops by a factor 2 exponential fall off between 0 and lkm altitude and then by a factor of 500 between 1 and 100 km If DBAER is set but ZBAER is not set then the elements of DBAER are used to set the aerosol density for each computational layer starting from the bottom layer For example DBAER10010 puts aerosol in the first and third layer If neither ZBAER or DBAER are set the boundary layer aerosols are assumed to follow a pre defined vertical distribution which drops off exponentially with a scale height between 105 and 151 km depending visibility see VTS Thus even if visibility is not used to set the vertical optical depth it can affect the result through the vertical profile Note that ZBAER and DBAER do not affect the total vertical optical depth of aerosols See discussion for VTS Vertical optical depth of boundary layer aerosols nominally at 055 um TBAER input is significant for all values of TAER When TAERl234 the specified value of TBAER supersedes the aerosol optical depth derived from input parameter VTS but VTS still controls vertical structure model unless DBAER and ZBAER are set QBAER is the extinction efficiency QBAER is only active when TAER5 When TBAER is set QBAER sets the spectral dependence of the extinction optical depth as tau tbaer Qextwave7lengthQext055 where Qextwave7length QBAER interpolated to waveilength and wlireference is 055 um unless modified by WLBAER If TBAER is not set then the values of QBAER are interpreted 23 WLBAER WBAER GBAER PMAER as extinction optical depths at each wavelength WLBAER For example the Multi Filter Rotating Shadowband Radiometer MFRSR installed at the Southern Great Plains ARM site is able to retrieve aerosol optical depth in 6 SW spectral channels This information may be supplied to SBDART by setting wlbaer 414 499 609 665 860 938 0109 0083 0062 0053 0044 0041 gbaer608 This spectral information is iterpolated or extrapolated to all wavelengths using logarithmic fitting on QBAER and linear fitting on WBAER and GBAER Many aerosol types display a power law dependence of extinction efficiency on wavelength The logarithmic interpolationextrapolation on QBAER will reproduce this behavior if it exists in the input data QBAER need not be specified when aerosol information is provided at a single wavelength Wavelengths points um for user defined aerosol spectral dependence Only used when TAER5 WLBAER and QBAER need not be specified if a single spectral point is set In this case the aerosol optical depth is extrapolated to other wavelengths using a power law see ABAER If only one value of WLBAER is set and TAER5 that value is used as the reference wavelength at which the value TBAER WBAER and GBAER or PMAER applies If WLBAER is not set then the reference wavelength defaults to 055um Single scattering albedo used with TAER5 AER represents the single scattering albedo of boundary layer aerosols at wavelengths WLBAER Asymmetry factor used with TAER5 GBAER represents the asymmetry factor of boundary layer aerosols at wavelengths WLBAER Number of values must match the number of WLBAER GBAER is ignored when parameter PMAER is set or when TM MA ne Legendre moments of the scattering phase function of boundary layer aerosols only active for TAER5 The Legendre moments of the phase function are defined as the following integral over the scattering phase function f pmaeri fmu Pimu d mu fmu d mu 24 ABAER IMOMA SPOWDER where Pimu is the Legendre polynomial mu is the cosine of the scattering angle and the range of the integrals are from l to l The Legendre moment for iO is always one Hence the zero39th moment is assumed by SBDART and should not be specified Unlike the previous boundary layer aerosol parameters you need to specify at least NSTR values for each wavelength point for a total of NSTRNAER values where NAER is the number of wavelength points supplied The order of specification should be such that wavelength variation is most rapid For example here is a case with 4 wavelengths and 6 streams nstr6 wlbaer4005006007OO wbaer 8808909l092 pmaer 80070060050 64049036025 51034022012 410240l3006 33017008003 26012005002 Wavelength Angstrom model exponent used to extrapolate BLA extinction efficiency to wavelengths outside the range of WLBAER Qext lambdaA abaer This parameter is only operative when TAER5 defaultO Controls phase function used for boundary layer aerosol The value of TMOMA is ignored when TAER5 and PMAER is specified Note that an asymmetry factor must be specified when TMOMA3 default3 isotropic scattering rayleigh scattering henyeyigreensteingre haze L as specified by garciasiewert cloud cl as specified by garciasiewert lt default L JgtLAl Setting SPOWDER to true causes an extra sub surface layer extending between l and 0 km to be added to the bottom of the atmospheric grid This layer may be used to model the effects of surface reflection and thermal emission caused by a granular surface material eg snow or sand The scattering properties of the surface layer may be specified either with the cloud or aerosol inputs For example a thin water cloud over a snow surface composed of lOOum snow grains may be modeled with the following input file ampINPUT sza30 idatm4 spowdert wlinf3 wlsup2 ioutl tcloud lOOOO lO zcloud l 2 25 NOTHRM KDIST nre lOO 10 Similarly the scattering properties of the surface and atmosphere may be read from aerosoldat with TAER l To model a semi infinite granular surface layer the optical depth of the bottom layer should be made very large eg 10000 as indicated in the example However a smaller optical depth may also be specified in conjuntion with a given value of sub surface albedo selected with TSALB Thus in the previous example the effect of a thin snow layer covering a grass field may be modeled by setting tcloudlOOlO and isalb6 NOTE When SPOWDER is set BTEMP no longer sets surface skin temperature Rather it sets the temperature of the sub surface level below the granular material At present there is no way to set the surface temperature above the graunual layer to something other than the atmospheric temperature of the bottom level nothrm l gt Thermal emission turned on only for wavelengths greater than 20 um default Note During daylight hours solar radiation is a factor of about le5 greater than thermal radiation at 20um nothrmO gt Thermal emission turned on for all wavelengths nothrml gt No thermal emission NOTE If thermal emission is desired be sure that the temperature steps in the atmospheric model are small enough to resolve changes in the Planck function The original version of the DTSORT radiative transfer module issued a warning message if the temperature difference between successive levels in the atmosphere exceeded 20 K All the standard atmospheres violate this condition for at least 1 stratospheric layer This warning message has been disabled to avoid clutter in SBDART39s standard output If near TR thermal emission from the stratosphere is important to your application you should supply SBDART with a new model atmosphere with higher resolution in the stratosphere see ZGRTDl ZGRTDZ an NGRTD KDTST l causes correlated k optical depths and weighting factors to be read from files CKATM and CKTAU The format used to read these files is documented in subroutines gasinit and readk both in file taugasf 26 ZGRlDl ZGRIDZ NGRID If WLTNF eq WLSUP all wavenumbers in the CKTAU file are processed otherwise only those wavenumbers in the range lOOOOWLSUP to lOOOOWLTNF are used NOTE KDTST l disables the effect of all input parameters that control aspects of the gaseous atmospheric profile Thus KDTST l disables input parameters WLTNC AMTX SCLHZO UW U03 O3TRP ZTRP XN2 x02 x002 XCH4 XNZO xco XNOZ x302 XNH3 XNO XHNO3 x04 RHCLD KRHCLR NGRTD ZGRTDl ZGRTDZ PBAR and ZPRES KDTSTO causes the optical depth due to molecular absorption to be set to the negative log of the LOWTRAN transmission function This approximation is not appropriate for cases in which multiple scattering is important but is not very wrong when the molecular absorption is weak or the scattering optical depth is small KDTSTl causes SBDART to use the LOWTRAN7 k distribution model of absorption by atmospheric gases Since a three term exponential fit is used SBDART execution times are up to 3 times longer with KDTST gt 0 compared to KDTSTO KDTST2 causes the k fit transmissions to exactly match the LOWTRAN transmission along the solar beam direction This option may be useful when computing surface irradiance under clouds of optical thickness less than about 10 This is because in this thin cloud case much of the radiation which reaches the surface propagates along the direct beam direction KDTST3 causes the k fit transmissions to exactly match the LOWTRAN transmission along the solar beam direction for parts of the atmosphere above a scattering layer As the scattering optical depth increases above 1 the k fit factors are ramped back to there original LOWTRAN values The effect of the slant path correction is ramped down to zero for wavelengths greater than 4um where solar energy input is less important KDTST3 is the default These three parameters can be used to change the grid resolution of the model atmosphere ZGRTDl controls the resolution near t e ottom of the grid while ZGRTD2 sets the maximum permissible step size at the top of the grid NGRTD sets the number of grid points For example ZGRTDl5 ZGRTD230 NGRTD45 specifies a 45 element grid with a resolution of 5 km throughout the lower part of the grid and a largest step of 30 km The regridding is performed after the call to subroutine ATMS This allows regridding of the standard internal atmospheres as well as user 27 specified atmospheres read with TDATMO No matter how many grid points were used to specify the original atmosphere the new regridded atmosphere will contain NGRTD vertical array elements The default value of ZGRTDl and ZGRTD2 are set to l and 30km respectively The default value of NGRTDO causes the initial un modified atmsopheric model to be used The internal parameter MRLY sets the maximum number of levels allowed Setting NGRTDgtMRLY causes NGRTD to be set to MXLY If NGRTD is negative SBDART terminates execution after printing out the regridded values of ZPTWHWO to standard out This option can be used to preview the effect of a given set of ZGRTDlZGRTD2 and absNGRTD values Note that the regridded atmosphere listed with negative NGRTD will contain the effects of non default values of UW U03 O3TRP PBAR ZPRES RHCLD and KRHCLR OUTPUT OPTIONS DIAGNOSTIC OUTPUT SELECTOR integer array The TDB print flag is used to select print diagnostics for a variety of computational parameters Setting TDBnm where m is any non zero integer will cause the diagnostics associated with array index n to be listed For some values of n increasing the value of m e g TDB82 will produce more detailed diagnostics defaultO idbl print an explanation of quantities in TOUT output group idb2 prints relative humidity and water vapor density idb3 atmospheric profile used in gas absorption diagnostic prints zpt and correlated k parameters idb4 if iday neO prints idaytimealatalon prints szasolfac zpth20o3 idb5 cloud parameters print wlzidtaucissaipmomiln where zi is altitude the cloud layer extends from zi to zil dtauci is the cloud optical depth contributed by layer i ssai is the single scattering albedo of cloud layer i and pmomiln are the first n moments of the scattering phase function of cloud If idb5l sbdart stops after printing this information for the first wavelength encountered If idb52 the code produces output for all wavelengths specified by WLINF WLSUP and WLINC idb6 aerosol single scattering albedo assymetry factor optical depth increments of total taua and boundary 28 idb7 idb8 idb9 layer aerosols tauab The total optical depth is displayed on the final line of output When kdist ge O idb7l for the surface layer only print wl taui 20 tau7h207c tauio3 tau c20 tau o3 tau n20 tau co tauch4 tau02n2 tauitraceT tauitotals idb72 same as idb7l but for all layers idb73 same as idb72 and add print out of 3 term k distribution terms When kdist lt O idb7l lists wniwtransiw idb72 lists wniwsolbandiw idb73 lists the gwtiwik and dtaukiwikim where iw is the wavenumber index ik is the k distribution index iz is the layer index wl is the wavelength wn is the wavenumber tau7 logtransmission of constituent h20 water vapor h207c water vapor continuum o3 ozone lines and continuum n20 nitrous oxide ch4 methane 02n2 oxygen and nitrogen lines and continua trace no s02 n02 nh3 solband is the toa solar irradiance in the band gwt is k distribution weight dtauk is the k distribution optical depth Note to save time the normal radiative transfer quantities are not computed when idb7 is set surface brdf diagnostics for isalb789 of 7 8 9 idb8l the surface brdf function is integrated over solid angle to obtain the surface albedo albedo is essentially the ratio of botupbotdn with thermal emission turned off for the given solar zenith angle if isalb is positive 789 and idb82 the brdf function is output in the same format used to list the iout20 radiance output The output slots ordinarily filled by botup are filled with the directional albedo assuming incomming radiation is parallel to the solar beam direction Optical depth due to Rayleigh aerosols cloud molecular continuum and line single scattering albedo and asymmetry factor Additional printouts for each 29 ZOUT term in the k fit are produced if KDTSTl 2 element array specifying BOT and TOP altitude points km for TOUT output For example ZOUT050 specifies output information for 0 and 50 km The surface is always set at zero Note that the actual layers for which output is generated is determined by finding the atmospheric layers nearest the chosen value of ZOUTl and ZOUT2 default 0100 This parameter can be used to determine the amount of radiation absorbed in a particular atmospheric layer For example zout23 tcloud10 zcloud2 iout10 will produce flux output just below and above the cloud layer from which the cloud absorption may be computed as topdn topup botdnbotup STANDARD OUTPUT SELECTOR no standard output is produced DTSORT subroutine is not called but diagnostics selected by idb in gas absorption or aerosol subroutines are active one output record for each wavelength output quantities are WL FFV TOPDN TOPUP TOPDTR BOTDN BOTUP BOTDTR WL wavelength microns FFV filter function value TOPDN total downward flux at ZOUT2 km wm2micron TOPUP total upward flux at ZOUT2 km wm2micron TOPDTR direct downward flux at ZOUT2 km wm2micron BOTDN total downward flux at ZOUTl km wm2micron BOTUP total upward flux at ZOUTl km wm2micron BOTDTR direct downward flux at ZOUTl km wm2micron NOTE The filter function value FFV should be used to perform integrations over wavelength intervals For example if WLTNC is set positive wavelength increment is constant the total power wm2 at the surface in the interval from WLTNF to WLSUP would be the sum WLTNC SUM FFViBOTDNi nzen3 records for each wavelength Output format write 39quottbf39 Block id used in postprocessors do mlnw write amp wlffvtopdntopuptopdirbotdnbotupbotdir 30 nphinzen phijjlnphi uzenjjlnzen write write write do inzenl l write uursikklnphi enddo enddo where WL wavelength microns FFV filter function value TOPDN total downward flux at ZOUT2 km wm2micron TOPUP total upward flux at ZOUT2 km wm2micron TOPDIR direct downward flux at ZOUT2 km wm2micron BOTDN total downward flux at ZOUTl km wm2micron BOTUP total upward flux at ZOUTl km wm2micron BOTDIR direct downward flux at ZOUTl km wm2micron NPHI number of user azimuth angles NZEN number of user zenith angles PHI user specified azimuth angles degrees UZEN user specified zenith angles degrees VZEN user specified nadir angles degrees UURS radiance at user angles at wm2umstr altitude ZOUT2 top NOTE The radiance output from SBDART represents scattered radiation It does not include the solar direct beam Also keep in mind that UURS represents the radiance at the user specified sample directions Hence computing the irradiance by an angular integration of UURS will not yield BOTDN because of the neglect of the direct beam and it will probably not yield BOTDN BOTDIR because of under sampling NOTE if IDAY is set then PHI is the actual compass direction in which the radiation in propagating same as IOUT5 except radiance is for ZOUTl altitude bottom radiative flux at each layer for each wavelength This output option can produce a huge amount of output if many wavelength sample points are use write 39quotfzw39 block id used in postprocessors write nz number of z levels write nw number of wavelengths do jlnw write wl write ZiinZ1 1 fdirdi ilnz altitude downward direct flux km wm2um 31 ll 20 amp fdifdiilnz downward diffuse flux wm2um amp flxdniilnz total downward flux amp flxupiilnz total upward flux enddo one output record per run integrated over wavelength output quantities are integrations by trapezoid rule WLINF WLSUP FFEW TOPDN TOPUP TOPDIR BOTDN BOTUP BOTDIR WLINF lower wavelength limit microns WLSUP upper wavelength limit microns FFEW filter function equivalent width microns TOPDN total downward flux at ZOUT2 km wm2 TOPUP total upward flux at ZOUT2 km wm2 TOPDIR direct downward flux at ZOUT2 km wm2 BOTDN total downward flux at ZOUTl km wm2 BOTUP total upward flux at ZOUTl km wm2 BOTDIR direct downward flux at ZOUTl km wm2 NOTE To get the spectral flux density wm2micron divide any of these quantities by FFEW radiant fluxes at each atmospheric layer integrated over wavelength Output format write nzphidw do ilnz write zzppfxdnifxupifxdiridfdzheat enddo where nz number of atmospheric layers phidw filter function equivalent widthum zz level altitudes km level pressure mb fxdn downward flux directdiffuse Wm2 fxup upward flux m2 fxdir downward flux direct beam only Wm2 dfdz radiant energy flux divergence mWm3 heat heating rate Kday NOTE dfdzi and heati are defined at the layer centers ie halfway between level i l and level i radiance output at ZOUT2 km Output format write wlinfwlsupffewtopdntopuptopdir botdnbotupbotdir nphinzen phiiilnphi uzenjjlnzen rijilnphijlnzen The first record of output is the same as format IOUTlO 32 wm2um wm2um 21 22 23 WLINEWLSUP EEEW TOPDN TOPUP TOPDIR BOTDN BOTUP BOTDIR addition records contain NPHI number of user azimuth angles NZEN number of user zenith angles PHI user relative azimuth angles nphi values UZEN user zenith angles nzen values R radiance array nphinzen WmZsr NOTE if IDAY is set then PHI is the actual compass direction in which the radiation in propagating same as IOUT20 except radiance output at ZOUTl km radiance and flux at each atmospheric layer integrated over wavelength Output format write nphinzennzffew write phiiilnphi write uzenjjlnzen write zkknzl l write fxdnkklnz write fxupkklnz write fxdirkklnz write uurlijkilnphijlnzenklnz where nphi number of user specified azimuth angles nzen number of user specified zenith angles nz number of atmospheric levels ffew filter function equivalent width um phi user specified anizmuth angles degreem uzen user specified zenith angles degrees z altitudes of atmospheric layers km fxdn downward flux directdiffuse Wm2 fxup upward flux Wm2 fxdir downward flux direct beam only Wm2 uurl radiance at each layer WmZstr NOTE if IDAY is set then PHI is the actual compass direction in which the radiation in propagating same as IOUT20 except lower hemisphere radiance output corresponds to ZOUTl upper hemisphere radiance output corresponds to ZOUT2 Use this output format to determine radiance above and and below a scattering layer For example if ZCLOUDI and TCLOUDlO you can get the scattered radiation field above and below the cloud with IOUT23 ZOUTl2 NOTE if IDAY is set then PHI is the actual compass direction in which the radiation in propagating 33 DELTAM NSTR CORINT DTSORT options if set to true use delta m method see Wiscombe 1977 This method is essentially a delta Eddington approximation applied to multiple radiation streams In general for a given number of streams intensities and fluxes will be more accurate for phase functions with a large forward peak if 39DELTAM39 is set TRUE Intensities within 10 degrees or so of the forward scattering direction will often be less accurate however so when primary interest centers in this so called 39aureole region39 DELTAM should be set FALSEdefaulttrue number of computational zenith angles used NSTR must be divisible by 2 Using NSTR4 reduces the time required for flux calculations by about a factor of 5 compared to NSTRl6 with very little penalty in accuracy about 05 difference when DELTAM is set true More streams should be used with radiance calculations The default of NSTR depends on the value of TOUT The default for flux computations TOUTl7lOll is NSTR4 The default for radiance computations TOUT5620212223 is NSTR20 When set TRUE intensities are correct for delta M scaling effects see Nakajima and Tanaka 1988 When FALSE intensities are not corrected In general CORTNT should be set true when a beam source is present EBEAM is not zero DELTAM is TRUE and the problem includes scattering However CORINTEALSE runs faster and produces fairly accurate intensities outside the aureole If CORINTTRUE and phase function moments are specified with PMAER TAER5 or in aerosoldat TAER l it is important to specify a sufficient number of phase function moments to adequately model single scattered radiation in the forward direction Otherwise if too few moments are provided the intensities might actually be more accurate with CORINTEALSE Default value CORINTfalse The input value of CORTNT is ignored for l in irradiance mode ie iout ne 56202122 2 there is no beam source EBEAM00 or 3 there is no scattering SSALB00 for all layers Radiance output 34 NZEN UZEN VZEN NPHI Number of user zenith angles If this parameter is specified SBDART will output radiance values at NZEN zenith angles evenly spaced between the first two values of input array UZEN For example nzen9 uzenO80 will cause output at zenith angles OlO20304050607080 User zenith angles If NZEN is specified then UZEN is interpreted as the limits of the zenith angle range and only the first two elements are required If NZEN is not specified then up to NSTR values of UZEN may be specified If neither NZEN nor UZEN is specified and a radiance calculation is requested IOUT5620212223 a default set of zenith angles is used which depends on the value IOUT as follows IOUT5 or 20 NZEN18 UZENO85 IOUT6 or 21 NZEN18 UZEN95180 IOUT22 or 23 NZEN18 UZENO180 NOTE UZEN specifies the zenith angle of at which the radiation is propagating UZEN O gt radiation propagates directly up UZEN lt 90 gt radiation in upper hemisphere UZEN gt 90 gt radiation in lower hemisphere UZEN 180 gt radiation propagates directly down user nadir angles This is just an alternate way to specify the direction of user radiance angles whereby uzenIBO vzen Number of user azimuth angles If this parameter is specified SBDART will output radiance values at NPHI azimuth angles evenly spaced between the first two values of input array PHI For example nphi7 phiOIBO will cause output at zenith angles 0306090120150180 User relative azimuth angles If NPHI is specified then PHI is interpreted as the limits of the azimuth angle range and only the first two elements are required If NPHI is not specified then up to NSTR values of PHI may be specified If neither NPHI nor PHI is specified and a radiance calculation is requested IOUT5620212223 a default set of azimuth angles is used equivalent to the case NPHIl9 PHIO180 NOTE If SAZA is set then PHIO represents radiation propagating in the Northern direction PHI increases clockwise looking down on the Earth39s surface If SAZA is not set then PHI is the relative azimuth angle from the forward scattering direction 35 IBCND FISOT gt forward scattered radiation PHI lt 90 gt backward scattered radiation PHI gt 90 For example f the sun is setting in the West radiation propagating to the South East has a relative azimuth of 45 degrees SBDART is currently configured to model radiation with at most 40 computational zenith angles and 40 azimuthal modes While these limits may be expanded be aware that running SBDART with a much larger number will significantly increase running time and memory requirements In tests performed on a DEC Alpha the execution time scaled roughly with NSTRAZ for NSTR less than 40 The code39s memory usage also scales roughly as NSTRAZ NOTE The default value of the solar azimuth angle SAZA180 This value of SAZA will cause forward scattered solar radiation to appear near PHI NOTE radiation boundary conditions general case boundary conditions any combination of beam illumination from the top see EBEAM k isotropic illumination from the top see ETSOT thermal emission from the top see TEMTSTTEMP internal thermal emission sources see TEMPER reflection at the bottom see LAMBERALBEDOHL thermal emission from the bottom see BTEMP in order to get isotropic illumination from top and bottom ALBEDO and transmissivity of the entire medium vs incident beam angle The only input variables considered in this case NLYR DTAUC SSALB PMOM NSTR USRANG NUMU UMUALBEDO DELTAM PRNTHEADER and the array dimensions NOPLNKLAMBER are assumed TRUE the bottom boundary can have any ALBEDO the sole output is ALBMEDTRNMED UMU is interpreted as the array of beam angles in this case If USRANG TRUE they must be positive and in increasing order and will be returned this way internally however the negatives of the UMU39s are added so MAXUMU must be at least 2NUMU If USRANG quadrature angle cosines FALSE UMU is returned as the NSTR2 positive 39 in increasing order intensity of top boundary isotropic illumination units wsg m if thermal sources active otherwise arbitrary units corresponding incident flux is pi 314159 times 39ETSOT39 36
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