Weighting Function Project

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Brightness Temperatures and Weighting Functions Obtained from the Advanced

Microwave Sounding Unit

Tracey Dorian

ABSTRACT

Weighting functions can be used to understand the relative contributions of individual layersof the atmosphere to given radiances detected by a satellite. Atmospheric scientists can usesatellite-derived weighting functions to construct plausible temperature proles of the atmosphere,although there are challenges in constructing these estimates. Atmospheric scientists can also startwith known vertical proles of temperature and humidity of an atmosphere and then based on thoseproles estimate certain atmospheric variables which can then be used to solve for the weightingfunctions. For a tropical sounding and a high latitude sounding, starting with frequency-dependentmass absorption coefficients derived from a computer code, we can then nd the optical depths of each layer using known mass paths, and then solve for the transmissivity and emissivity of eachlayer. After solving for those radiative properties of the atmospheric layers for the two soundings,

we can use particular microwave frequencies from the Advanced Microwave Sounding Unit (AMSU)that are near the O 2 and water vapor absorption channels to solve for the total top of atmospheremicrowave brightness temperatures from the sums of the individual layer contributions. Thebrightness temperatures seen by the satellite at the top of the atmosphere change depending on howclose the frequency of interest is to the center of the oxygen and water vapor absorption lines. Thebrightness temperatures also change for experiments where we alter the surface emissivity, assumingthe satellite can see down to the surface, and also where we alter the nadir viewing angles.

1. Introduction

Every day, atmospheric scientists and the general pub-lic see satellite images that are a result of satellite-derivedradiances obtained at the top of the atmosphere. An in-strument on a satellite called a spectrometer can measurethe emitted radiance, which depends on the wavelength (orfrequency) of radiation, the distribution of the atmosphericconstituent of interest, and the vertical temperature andhumidity structure. For this research, we focused on mi-crowave wavelengths between 1 mm and 10 cm, correspond-ing to frequencies of 300 GHz (Gigahertz = 109 Hertz) and3 GHz, respectively. The microwave band is a very impor-tant band used by scientists today for studying the atmo-sphere and surface using remote sensing techniques. Thebenets of using the microwave band as opposed to thevisible and infrared bands are that the EM waves are notattenuated by clouds and therefore the microwave wave-lengths can penetrate through the clouds. Because of this,microwave wavelengths can be used in any type of cloudcover regime, with the exception of clouds that are precip-itating since heavy rainfall tends to contaminate the satel-lite retrievals. The disadvantages of using microwave wave-lengths include the fact that microwave surface emissivitiesvary signicantly between different surfaces, which makesit more challenging to estimate surface temperatures accu-

rately. The emissivities vary signicantly with soil type,soil wetness, and vegetation density (Petty (2006)). An-other disadvantage of using the microwave band is that thespatial resolution of passive microwave is very low around

30-50km.In this experiment, we used 7 of the 15 different chan-nels from the Advanced Microwave Sounding Unit (AMSU)on the edge of a strong O 2 absorption band near 60 GHz(AMSU-A) and all 5 channels near a strong H 2 O absorp-tion band near 183 GHz (AMSU-B). Using properties of the atmospheric layers obtained from information from thesoundings, we can through a series of calculations computethe total brightness temperature for each channel. Bright-ness temperatures for each wavelength are a function notonly of the vertical distributions of O 2 and H 2 0, but alsoa function of the temperature of the atmospheric layersnear the weighting function peak, and therefore on the

vertical temperature prole of the atmosphere. The closerthe wavelength is to the absorption line center, the higherthe weighting function will peak in the atmosphere (Petty(2006)). By putting channels closer and closer to the centerof the absorption band, we can get information from dif-ferent layers of the atmosphere. Because the emission (andthus absorption) observed from the satellite for each wave-length does not originate from a single level, the observa-

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tions are not independent and the weighting functions willbe broad and will overlap with height. Another contribu-tion to the brightness temperatures is the surface emissionthat could be detected by the satellite and also emissionthat originated from the bottom of the atmospheric layersthat then reected off the surface and transmitted throughthe atmosphere to space. After computing the brightness

temperatures for just the AMSU-A and AMSU-B frequen-cies and the contributions of each layer to the observedbrightness temperatures, we then computed the brightnesstemperatures for both a high latitude and a tropical sound-ing for the entire spectra of microwave frequencies between.1 GHz and 300 GHz. Finally, we changed the surface emis-sivity to determine the effects this had on the observedbrightness temperatures for the both the tropical and highlatitude soundings. Additionally, we changed the viewingangles of the satellite to determine the effects this had onthe brightness temperatures for just the tropical sounding.

2. Methods

We focused on two soundings associated with differentregions of the world, one in the high latitudes and onein the deep tropics. The tropical sounding, seen in Figure1, was taken from the University of Wyoming Atmospheric Sounding website and was chosen to be Boa Vista, Brazilon 12Z March 1, 2012. The high latitude sounding, seen inFigure 2, was chosen to be Churchill, Canada on 12Z March1, 2012. We then used python code to read in the text for-mats of these atmospheric soundings and then interpolatedboth soundings to ner levels. After this, we implementedradiative transfer code to calculate the brightness temper-atures and the emission weighting functions for the mi-crowave frequencies associated with the AMSU channels.The AMSU-A channels, listed in Table 1, include 7 chan-nels near 60 GHz, which is a frequency that correspondsto the center of an absorption band for oxygen, which isa well-mixed gas. The AMSU-B channels, listed in Table2, include 5 channels centered around 184 GHz, which is afrequency that corresponds to the center of an absorptionband for water vapor, which is a highly variable gas. Forthe initial experiments, we assume a non-scattering, plane-parallel horizontally innite and homogeneous atmosphere.We assume the surface is a specular reector and that thesurface temperature corresponds to the temperature in thelowest atmospheric layer of the particular sounding. Lastly,

we assume the surface emissivity to be 1, meaning thatthere is perfect absorption and emission and thus no re-ection, and we assumed that the satellite viewed the ra-diances from a nadir angle of Θ = 0 ◦ .

Then through a series of calculations within the code,we computed and plotted the weighting functions associ-ated with the individual soundings and for the AMSU-Aand AMSU-B frequency bands. The code also included

Fig. 1. Tropical Sounding: Boa Vista, Brazil radiosondesounding for 12Z March 1, 2012

Fig. 2. High Latitude Sounding: Churchill, Canada ra-diosonde sounding for 12Z March 1, 2012

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computations for the brightness temperatures seen by thesatellite microwave radiometer for the entire spectrum of microwave frequencies for every .1 GHz between 0 GHzand 300 GHz. In order to solve for the weighting func-tions of the layers of the atmosphere and the brightnesstemperatures seen by the satellite, we had to compute cer-tain radiative properties of the layers, assuming that each

layer was an isothermal slab. We started with the massabsorption coefficients calculated in a python code, thenfrom the mass absorption coefficients we computed the op-tical depths of each layer, then the transmittance of eachlayer, then the emissivity of each layer, then nally the to-tal brightness temperatures seen by the satellite at someparticular frequency. The total brightness temperature ateach frequency was calculated by taking the sum of the up-ward contribution of radiance from each individual layer,the downward radiance emitted from the layers that re-ected back up towards the satellite (when surface emissiv-ity is not equal to 1), and the surface emission contributionassuming that the atmosphere was not opaque and that

the satellite could see down to the surface. The non-dimensional weight of each layer was then calculated bytaking the ratio of the total brightness temperature to theaverage temperature of each layer. Therefore, the weightwas the value of everything that was multiplied to the meantemperature of the layer. Because the thicker layers willhave larger contributions to the brightness temperaturesthan the thinner layers will with all other factors beingequal, we chose to normalize the weight by dividing eachlayer weight by the corresponding layer thickness. The -nal result was the emission weighting function in units of inverse length (km − 1 ).

Table 1. AMSU-A channels near center of a strong ab-sorption band for O 2 (60 GHz)

Channel F requency (GHz )3 50.30004 52.80005 53.71106 54.40007 54.94008 55.50009 57.2900

10 57.5070

Table 2. AMSU-B channels around center of a strongabsorption band for H 2 0 (183 GHz)

Channel F requency (GHz )16 89.0017 150.018 184.3119 186.3120 190.31

3. Results

Weighting Functions

For the weighting function plots, we assume that thesurface temperature corresponds to the lowest atmospherictemperature within the particular sounding of interest. We

also took the surface emissivity to be equal to 1, suggest-ing no reection off of the surface. Lastly, we assumednadir viewing (Θ = 0 ◦ ) from the satellite. The weight-ing functions associated with the AMSU-A channels forthe 12Z March 1, 2012 Boa Vista, Brazil and Churchill,Canada soundings are depicted in Figure 3. The weight-ing functions for the Brazil sounding (solid lines) showthat the maximum height for a weighting is around 23 kmand is associated with the 57.5070 GHz frequency. Since57.5070 GHz is the closest to the center of the O 2 absorp-tion band, and because oxygen is well-mixed throughoutthe atmosphere, then we expect the maximum absorptionof oxygen to occur at that frequency. Maximum absorp-tion means that the sounder will not be able to see too farinto the atmosphere because the maximum absorption andthus emission will occur in the higher altitudes due to theincreased sensitivity of the sounder. The lowest weight-ing function peak for the Brazil sounding is at the surfacefor the 50.3000 GHz channel. As we can see, the weights,or the relative contributions of each altitude for each of the frequencies, are generally equally distributed through-out the atmosphere. Almost all atmospheric layers haveweights between .07 km − 1 and .10 km − 1 , with the excep-tion of the 57.2900 GHz weighting function peak at around20 km with a weight of about .12 km − 1 . This means thatat the 57.2900 GHz frequency, the contribution of emissioncomes dominantly from about the 20 km level. Therefore,the 20 km level has the most inuence on the calculatedbrightness temperature associated with that particular fre-quency.

We see a very similar situation with the Canada sound-ing (dashed lines) weighting functions. The atmosphericlayers are generally weighted equally for all the AMSU-Achannels, and the highest weighting function is associated

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Fig. 3. Weighting functions for AMSU-A channels forBrazil and Canada Soundings. Solid lines represent weight-ing functions for the tropical sounding, dashed lines repre-sent weighting functions for the high latitude sounding.

with the frequency closest to the strongest absorption fre-quency for oxygen. It appears that the weighting functionpeaks for the high latitude sounding case are slightly be-low the weighting function peaks for the tropical soundingcase, but that in general the weighting function peaks forthe frequencies are located near the same altitudes for bothsoundings. This suggest that oxygen is evenly distributedacross the globe and through vertical depth, which makessense for a well-mixed gas.

The weighting functions associated with the AMSU-Bchannels for the Brazil and Canada soundings are illus-

trated in Figure 4. In this case, the weighting functionpeaks differ quite substantially between the tropical sound-ing and the high latitude sounding. The three tropicalweighting functions (solid lines) are much higher in the at-mosphere, between about 5 km and 12 km, with the high-est peak at 12 km being associated with the 184.31 GHzfrequency. This makes sense to see the highest peak associ-ated with the frequency within the AMSU-B channels thatis closest to the strongest absorption frequency for watervapor. The satellite is unable to detect radiance on thefar side near the surface because the satellite is extremelysensitive at 183 GHz to any water vapor amount, and there-fore detects emission from the upper troposphere and lowerstratosphere. So even though there are lesser amounts of water vapor in the upper layers of the tropical atmosphere,even those smaller amounts of water vapor are detectedwhen the sounder is measuring emission in the 183 GHzfrequency. The relative weights (in km − 1 ) of the differentlayers where the weighting functions peak are between .2km − 1 and .3 km − 1 . Even the channel farthest from the 183GHz channel of 190.31 GHz still has a weighting function

peak at about 5 km for the Brazil sounding. This suggeststo me that even though the atmosphere is more transpar-ent in that frequency, the emission still comes from prettyhigh in the atmosphere because of the abundant moisturewithin the tropical atmosphere.

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Fig. 4. Weighting functions for AMSU-B channels forBrazil and Canada Soundings. Solid lines represent weight-ing functions for the tropical sounding, dashed lines repre-sent weighting functions for the high latitude sounding.

The weighting functions for the high latitude sounding(dashed lines) peak much lower in the atmosphere, with the184.31 GHz frequency weighting function peaking around3 km, and the 186.31 GHz frequency weighting functionpeaking around 2.5 km, and the 190.31 GHz frequencyweighting function peaking around 2 km. The weightingfunctions overlap signicantly for the polar sounding, im-plying that emission seen by the satellite for the three fre-quencies is coming from the same general levels within thelowest 5 km in Churchill. The lower layers also have largercontributions, illustrated by the magnitude of the weightson the x-axis, for the radiances observed from the satellitefor the different channels than the contributions that wesaw for the tropical case. Also worth noting is that theweighting functions for both soundings are not as smoothand that the peaks are not as well-dened for the AMSU-B channels as they are for the AMSU-A channels. Theshapes of the weighting functions associated with the highlatitude sounding are especially unsmooth in the AMSU-B channels. This difference in smoothness is likely dueto the fact that oxygen is well-mixed throughout both thetropical and high latitude atmospheres, whereas water va-por is highly variable both spatially and temporally, andboth horizontally and vertically (Petty (2006)). Overall thelargest differences seen in the weighting functions for thetwo soundings in the AMSU-B channels are the altitudes of the weighting function peaks. Warm, humid environments

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are capable of holding much more moisture, and those en-vironments typically have deep moist atmospheres. Tropi-cal environments also have a higher and colder tropopausethan polar environments have. Based on the soundings, theheight of the tropopause over Churchill, Canada is around9 km and over Boa Vista, Brazil is around 15 km.

a. Brightness Temperatures

The microwave brightness temperatures for the com-plete spectra for the two soundings are shown in Figure 5.For this case, we again assumed sfc = 1 and nadir view-ing angle Θ = 0 ◦ . The brightness temperatures are muchwarmer for the deep tropics sounding for certain frequen-cies for which the atmosphere is relatively transparent. Inother words, for frequencies far enough away from the mi-crowave absorption bands associated with O 2 and H 2 0, thesatellite is essentially seeing down to the surface. Follow-ing this logic, it is evident that the surface temperaturein Boa Vista is about 297 K since we assumed the surfaceto be a blackbody. From our calculations of brightnesstemperature, we also nd a surface temperature of 297 K.The surface temperature in Churchill is about 255 K. Forthe frequencies approaching 22 GHz, a weak water vaporabsorption band, we see a signal of colder brightness tem-peratures for the tropical atmosphere but no inkling of adip in the high latitude sounding. This is probably be-cause the high latitude atmosphere is so dry that there isnot enough water vapor to produce an absorption signalat the weak 22 GHz frequency. We do, however, see asignal for the tropical sounding likely because the copiousamounts of water vapor in the atmosphere are enough toproduce a signal even within the weak 22 GHz water vaporabsorption band.

Right around 60 GHz there is an extremely strong ab-sorption signal due to O 2 for both atmospheres that cor-responds with colder brightness temperatures around 205K for Brazil and about 215 K for Canada. Because ourcode calculated the brightness temperatures for every .1GHz frequency, we have very high resolution results withmany individual absorption lines in the vicinity of 60 GHz.Based on the plot of the weighting functions for the AMSU-A channels, we see that the weighting functions for both

soundings peaked at about the same height (as should beexpected since O 2 is well-mixed everywhere) for the 57.5070GHz band at around 22 km high. Why then are the bright-ness temperatures around 60 GHz colder for the tropicalatmosphere than the high latitude atmosphere? The reasonfor this is because for the tropical atmosphere we only justentered into the stratosphere where temperature begins toincrease with height. In the polar region, the transitionto the region of increasing temperatures happens earlier,

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B r i g h t n e s s T e m p e r a t u r e s f o r C o m p l e t e S p e c t r a f o r T w o D i f f e r e n t S o u n d i n g s

D e e p T r o p i c s

H i g h L a t i t u d e

Fig. 5. Complete spectra of microwave brightness temper-atures for Brazil and Canada soundings. Dashed red linesrepresent brightness temperatures for the tropical sound-ing, solid blue lines represent brightness temperatures forthe high latitude sounding.

around 10 km, and so this is why the polar brightness tem-peratures appear warmer than the tropical brightness tem-peratures even though both signals came from the samegeneral altitude. Moving through the spectrum, we seeanother signal due to the narrower O 2 absorption bandaround 118 GHz with the same general differences in thebrightness temperatures between the soundings. In thiscase, the absorption appears to occur just at that one fre-quency, which differs from the 60 GHz case in which theabsorption occurs for ± 10 GHz centered around 60 GHz.

Therefore, one can deduce that the sounder may be moresensitive to absorption due to O 2 for the 60 GHz frequencyas compared to the 118 GHz since there is absorption oc-curring in the bands around the frequency. Because of thestrong O 2 absorption band around 60 GHz, this band is of-ten used for satellite retrievals of atmospheric temperatureproles (Petty (2006)).

The next indication of absorption correlating with lowerbrightness temperatures occurs around 183 GHz, which isassociated with a very strong water vapor absorption band.Based on the weighting functions plot for the AMSU-Bchannels, the altitude of maximum absorption due to wa-ter vapor at 183 GHz occurs at two very different altitudesfor both soundings. The altitude of maximum absorptionoccurs around 10 km for the tropical sounding and around3 km for the high latitude sounding. This difference isagain due to the signicant differences in water vapor con-centration between the two environments. The emissioncoming from the upper atmospheric layers for the tropi-cal environment indicates deep humidity and the emissioncoming from lower layers for the high latitude environment

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indicates a drier atmosphere. For the 183 GHz frequency,there appears to be just one absorption line instead of mul-tiple absorptions lines surrounding the center at nearby fre-quencies. Nevertheless, due to the very strong absorptionby water vapor in this band, the 183 GHz band is often usedin microwave retrievals of humidity proles (Petty (2006)).

Experiments

Changing surface emissivity

Changing the emissivity of the surface changes the in-tensity of emission that would be detected by the satel-lite assuming that the atmosphere is not opaque abovethe surface. Since brightness temperature is equal to theproduct of emissivity and physical temperature accord-ing to the Rayleigh-Jeans Approximation (T B = T) forsmaller microwave frequencies, the brightness temperaturewill change with a change in emissivity for the same sur-face temperature. Figure 6 depicts the resulting brightnesstemperatures for the Brazil atmosphere for all of the AMSUchannels between .1 and 300 GHz, again for every .1 GHz,for surface emissivity equal to 1 (solid line) and for sur-face emissivity equal to .5 (dashed line). When emissivityequals 1, the brightness temperature seen in atmosphericwindows is generally an accurate representation of the ac-tual physical temperature of the surface, since the surfaceis both absorbing and emitting the maximum amount of radiation back to space for the satellite to detect. Whensurface emissivity is .5, on the other hand, this means thatthe satellite will only see about 50% of the maximum emis-sion that the surface could potentially emit. Therefore, thebrightness temperatures will be lower because of less emis-sion but will not accurately represent the real temperaturesof the surface, since brightness temperature assumes thatthe surface is a blackbody (and so the brightness tempera-ture will underestimate the true temperature). The oceanis an example of a surface that has an emissivity of .5 inthe microwave band, and so the ocean absorbs more thanit emits.

Based on Figure 6, for the frequencies where the atmo-sphere is transparent, we can see an enormous difference in

surface brightness temperatures between sfc = 1 and sfc= .5. Focusing on sfc = .5, as we approach the 22 GHz fre-quency where water vapor absorbs, the brightness temper-atures for the frequencies surrounding 22 GHz are actuallycolder than the brightness temperatures at 22 GHz! Thismakes sense because in the wavelengths far enough awayfrom the weak water vapor absorption band at 22 GHz,there is virtually no absorption by water vapor and so thesatellite sees closer to the surface, which appears very cold

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T r o p i c a l S o u n d i n g : B r i g h t n e s s T e m p s f o r C o m p l e t e S p e c t r a - - C h a n g i n g E m i s s i v i t y

E m i s s i v i t y = 1

E m i s s i v i t y = . 5

Fig. 6. Complete spectra of microwave brightness temper-atures for Brazil sounding with changing surface emissivity.Solid line represents the brightness temperatures for when

sfc = 1, dashed line represents the brightness tempera-tures for when sfc = .5.

because of the assumed low emissivity. The brightness tem-peratures leading up to 22 GHz are rather unphysical, withtemperatures of about 150 K, which would correspond toabout -190 ◦ F! This is why it is difficult to retrieve accu-rate sea surface temperatures from microwave sounders onsatellites – because the brightness temperatures severelyunderestimate the actual sea surface temperatures. Soright at 22 GHz for surface emissivity of .5, the tropicalatmosphere appears warmer than surrounding frequenciesbecause the atmospheric layers perhaps have higher emis-

sivities than the underlying surface. Thus, even thoughthe weighting function at 22 GHz peaks higher up wherewe would expect colder temperatures, the emission mayactually be greater because the layers are closer to beingblackbodies than the surface is.

Still focusing on the sfc = .5 line, leading up to thevery strong oxygen absorbing frequency at 60 GHz, thebrightness temperatures again appear warmer because of absorption is occurring in atmospheric layers (with higheremissivities than the surface) around the 60 GHz frequency.When the atmosphere is opaque at a particular wavelengthor frequency, the brightness temperature gives a reasonableestimate of the physical temperature at the level wherethe weighting function peaks (Petty (2006)). Therefore,for these frequencies where there is maximum absorption(corresponding to the peak of the weighting function), thebrightness temperatures we nd at the level of the maxi-mum absorption should be fairly close to the actual tem-perature at that level. For the narrower oxygen absorp-tion band at 118 GHz, we again see brightness temper-atures increasing towards the 118 GHz due to increasing

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absorption by atmospheric layers until the brightness tem-peratures drops suddenly right at 118 GHz because we aremuch higher in the atmosphere. As we approach the 183GHz frequency where a very strong water vapor absorptioncauses the atmosphere to be opaque, the satellite cannotsee down to the surface and instead sees the atmospherictemperature corresponding to the level of maximum ab-

sorption due to water vapor. The brightness temperaturestherefore increased slowly as we got away from the coldsurface emission and got closer to the warmer layer thatis closer to a blackbody. For frequencies after 183 GHz,the brightness temperatures do not change when the sur-face emissivity changes from 1 to .5. This may be due towhat is known as the continuum absorption by water va-por, which causes the atmosphere to become more opaqueas frequency increases (Petty (2006)). This increase in ab-sorption with increasing frequencies even within spectralwindows may also explain the slight downward trend inthe brightness temperatures for the tropical sounding inFigure 6 for sfc = 1. The spectral windows in the mi-

crowave band include the 0-40 GHz frequencies and alsothe 80-100 GHz frequencies, but these spectral windowsmay not be 100% transparent because there may still beslight absorption due to water vapor in what is known asspectral dirty windows . These effects are most impor-tant for very humid atmospheres.

Taking a look at the brightness temperatures with chang-ing emissivity for the high latitude sounding in Figure 7,we see similar changes. For sfc = .5, we now see more of a signal at 22 GHz by the small amounts of water vaporin the Canada sounding than what we see for the sfc =1 line since the emission by water vapor is now easier todetect with the cold surface background. Another way

of thinking about this is that in this case, the atmosphericlayers with low amounts of water vapor near the surface arecloser to being blackbodies than the surface is with surfaceemissivity equal to .5. Therefore, slightly more emissionis occurring due to the water vapor above the surface atexactly 22 GHz than the underlying surface. Passive mi-crowave instruments can detect atmospheric contributionswhen radiometrically cool surfaces lie underneath. Thisis why we see more of a signal from atmospheric contribu-tions for sfc = .5 than we see for sf c = 1. For the 60 GHz,118 GHz, and 183 GHz bands we see a similar increase inemission before reaching the center of the absorption bandand then a sudden decrease in brightness temperature rightat the centers. The brightness temperatures for sfc = .5do appear to have an upward trend as the frequencies in-crease, even for the non-absorbing frequencies, and so thepolar brightness temperatures are more affected by the con-tinuum absorption by water vapor. We do not see any signof increasing brightness temperatures within the spectralwindows for the sfc = 1 case. This may due to the factthat the dirty windows are more easily detected in the

case of very low surface emissivity versus the case whenthe surface emissivity is higher. Overall, there is a generalupward trend in brightness temperatures for sfc = .5 forboth the tropical and high latitude gures, likely due to thefact that at higher microwave frequencies the atmospherebecomes more opaque and the microwave sounder becomesmore sensitive to atmospheric properties.

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P o l a r S o u n d i n g : B r i g h t n e s s T e m p s f o r C o m p l e t e S p e c t r a - - C h a n g i n g E m i s s i v i t y

E m i s s i v i t y = 1

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Fig. 7. Complete spectra of microwave brightness temper-atures for Canada sounding with changing surface emissiv-ity. Solid line represents the brightness temperatures forwhen sfc = 1, dashed line represents the brightness tem-peratures for when sfc = .5.

Changing nadir angles

Our nal experiment deals with the effects of changingthe satellite viewing angle through the atmosphere, focus-ing only on the tropical atmosphere. Figure 8 comparesa case in which the satellite is viewing straight down, orwhere Θ = 0 ◦ and µ = cos(0 ◦ )= 1, with a case in whichthe satellite views the atmosphere at an angle of Θ = 55 ◦

and thus µ = cos(55 ◦ ). The effect of changing the nadirangle was to decrease the brightness temperatures acrossthe entire spectra, which implies faster absorption in the at-mosphere and thus higher weighting function peaks. These

changes in brightness temperatures make sense because thepath length increases when the satellite views radiationthrough the atmosphere at an angle, and so the satellite is

seeing through more atmosphere. When the path lengthincreases, the optical depth increases, which then increasesabsorption and decreases the transmissivity. This same ef-fect can also be seen when viewing brightness temperatureson the wings of the satellite swath view. The optical pathlength increases on the wings of the satellite swatch and

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thus absorption happens faster and we see higher peaksand colder brightness temperatures on the wings.

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T r o p i c a l S o u n d i n g : B r i g h t n e s s T e m p s f o r C o m p l e t e S p e c t r a - - C h a n g i n gµ = C o s i n e ( Θ )

µ = C o s i n e ( 0 )

µ = C o s i n e ( 5 5 )

Fig. 8. Complete spectra of microwave brightness temper-atures for Brazil sounding with changing nadir angle. Solidline represents the brightness temperatures for when Θ =0◦ , dashed line represents the brightness temperatures forwhen Θ = 55 ◦ .

4. Conclusions

Satellite microwave sounders provide very useful infor-mation about the different atmospheric constituents thatabsorb and emit radiation at certain microwave frequen-cies. When there are no constituents that absorb in aparticular wavelength range, the emission from the atmo-sphere below comes mainly from radiation emitted fromthe surface. In these atmospheric windows, the microwavesounder can be used to nd out information about thesurface if surface emissivity is close to 1, even in cloudyconditions. Although within these atmopsheric windowsfor humid environments, absorption may still occur forlarger frequencies due to water vapor in the so-called dirtywindows . Using microwave wavelengths also allows us toconsider scattering in the atmosphere negligible. However,some complications do arise when using microwave wave-

lengths. Complications include poor spatial resolution,contamination by rainfall, different surface emissivities de-pending on surface types and how wet the surface is, andalso the unusually low emissivity of water in the microwavebands. Ocean emissivities, which depend on wavelengthand wind speed, are much lower than the emissivities forland and ice in the microwave frequencies. Atmosphericscientists can sometimes use these low ocean emissivitiesto their advantage by viewing water vapor amounts above

the radionmetrically cold sea surface emissions.Where the atmosphere is not transparent to microwave

frequencies, the microwave sounder can be used to learnabout atmospheric properties. Microwave sounders can beused to interpret the vertical distribution of atmosphericconstituents based on the emission weighting functions andthe brightness temperatures. The emission weighting func-

tion describes the contributions of the atmospheric layersto the observed radiances. The weighting function peaksoverlap one another since emission seen by the satellite fora given frequency does not originate from a single level.The observed brightness temperatures seen by the satel-lite are dependent on the vertical distribution of a con-stituent and on the temperature structure of the atmo-sphere (Petty (2006)). We found that the deep tropicstend to have colder brightness temperatures because of thedeep moist layer compared to the brightness temperaturesof drier atmospheres associated with the higher latitudes.We also found that for both Brazil and Canada, the bright-ness temperatures decreased considerably with lower sur-

face emissivites in atmospheric windows at the lower fre-quencies for Brazil and at all frequencies for Canada. Wealso found that brightness temperatures decreased in theatmospheric windows for the Brazil case when the satelliteviewed the atmosphere at an angle as opposed to viewingstraight down.

Using the AMSU-A and AMSU-B frequencies, we foundweighting functions from interpolating known temperatureand humidity proles to ner levels. The weighting func-tions for AMSU are typical for most current temperaturesounders in infrared and microwave bands (Petty (2006)).The AMSU instrument can also be used to retrieve temper-ature proles from satellite observations, but it is more dif-

cult since there are many temperature proles that couldbe consistent with given atmospheric emission measure-ments. In other words, there are many other factors thatmay affect the temperature structure that satellites simplydo not retrieve. Meteorologists get around this by makinginitial guesses of the temperature proles and associatedintensities and then comparing those intensities with thesatellite observed intensities (Petty (2006)). Nevertheless,satellite-derived temperature retrievals are representativeof the current state of the atmosphere and are imported to-day into numerical weather prediction models. Althoughsatellite observations are far from perfect, without themthe accurate long-range and short-range forecasts that wehave today would not be possible.

REFERENCES

Petty, G., 2006: A rst course in atmospheric radiation .Sundog Pub., URL http://books.google.com/books?id=Q5sRAQAAIAAJ.

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Weighting Function Project