Remote sensing of cirrus cloud parameters using advanced ...people.atmos.ucla.edu/liou/Group_Papers/Ou_AO_32_1993.pdf · Remote sensing of cirrus cloud parameters using advanced very-high-resolution

Remote sensing of cirrus cloud parameters usingadvanced very-high-resolution radiometer 3.7- and1 O.9-pum channels

S. C. Ou, K. N. Liou, W. M. Gooch, and Y. Takano

We develop a retrieval scheme by using advanced very-high-resolution radiometer (AVHRR) 3.7- and

10.9-pum data to compute simultaneously the temperature, optical depth, and mean effective ice-crystalsize for cirrus clouds. The methodology involves the numerical solution of a set of nonlinear algebraic

equations derived from the theory of radiative transfer. The solution requires the correlation ofemissivities of two channels in terms of the effective extinction ratio. The dependence of this ratio onice-crystal size distribution is examined by using an adding-doubling radiative transfer program. Inves-tigation of the effects of cirrus parameters on upwelling radiances reveals that the brightness-temperature difference between the two channels becomes larger for colder cirrus and smaller ice-crystalsizes. We apply the current retrieval scheme to satellite data collected at 0930 UTC, 28 October 1986,

over the region of the First International Satellite Cloud Climatology Project Regional Experiment CirrusIntensive Field Observation. We select the data over an area (- 440 N, 92° W) near Fort McCoy,Wisconsin, for analysis. The retrieved cirrus heights compare reasonably well with lidar measurementstaken at Fort McCoy 2 h after a satellite overpass at the target region. The retrieved mean effectivecrystal size is close to that derived from in situ aircraft measurements over Madison, Wisconsin, six hours

after a satellite overpass.

1. Introduction

Cirrus clouds are global in nature and occur primarilyin the upper troposphere and lower stratosphere.These clouds are composed almost entirely of icecrystals. Information on cirrus cloud parameters iscritically important to the development of cirruscloud forecast models, the upgrading of real-timeglobal cloud analysis, and the investigation of cloudfeedbacks in global climate change.'

In recent years, data from multichannel imagerysources, particularly the advanced very-high-resolu-tion radiometer (AVHRR) on board National Oceanicand Atmospheric Administration (NOAA) operationalsatellites, have been available for the retrieval ofcloud parameters. Verification of the retrieved re-sults has also become possible because we now haveaccess to measurements by instruments on board

S. C. Ou and W. M. Gooch are with Liou and Associates, SaltLake City, Utah 84124; K. N. Liou and Y. Takano are with theCenter for Atmospheric and Remote Sounding Studies/Departmentof Meteorology, University of Utah, Salt Lake City, Utah 84112.

Received 27 December 1991.0003-6935/93/122171-10$05.00/0.c 1993 Optical Society of America.

aircraft, ground-based lidar, and rawinsonde thatwere used during the First International SatelliteCloud Climatology Project Regional Experiment(FIRE) Cirrus Intensive Field Observation (IFO) overWisconsin during October-November 1986.

Numerous methods have been proposed to infercirrus cloud parameters by using satellite infrared(IR) imaging channels. Liou2 proposed a methodbased on four spectral bands in the 10-pim windowregion to determine the cloud thickness and emissiv-ity. Szejwach3 developed a technique based on theEuropean Meterological Satellite channels in the6.5-[um H20 band and the 10-pim window band todetermine cirrus temperature and emissivity. In asimilar approach, Pollinger and Wendling4 used the6.3- and 11.0-jim spectral bands to infer the height ofoptically thin ice clouds. Huang and Liou5 describeda dual-channel and dual-scanning angle technique fordetermining cirrus optical depth and temperature byusing the 3.7- and 10.9-jim spectral channels of anAVHRR. A general retrieval program for cloud pa-rameters by using AVHRR channels has also beendiscussed by Arking and Childs.6 More recently,Liou et al.7 developed a physical retrieval method toinfer the temperature and optical depth of tropicalcirrus anvils by using the data of the dual-channel

20 April 1993 / Vol. 32, No. 12 / APPLIED OPTICS 2171

(6.5- and 10.5-jim), downward-viewing, narrow-field-of-view radiometers on board NASA ER-2. In thatwork, an iterative numerical scheme was developed tosolve the resultant nonlinear algebraic equations.In addition, the effects of scattering by nonsphericalice crystals on cirrus emissivities have been takeninto account in radiative transfer calculations. Theeffects of nonspherical particles on the radiances overcirrus clouds have also been examined by Ackermanand Smith8 and Kinne et al.9

Another approach to inferring cirrus parametersutilizes the properties of the brightness-temperaturedifference (BTD) between AVHRR IR channels. In-oue'o showed that the cirrus cloud top temperatureand the IR effective emissivity may be inferred fromBTD values between AVHRR channel (Ch.) 4, 10.9jim, and Ch. 5, 12 jim. He also showed that positiveBTD values for these two channels are always associ-ated with semitransparent cirrus clouds and that theBTD is sensitive to cirrus radiative and microphysicalproperties. Wu" investigated the dependence of theBTD between AVHRR 10.9- and 12-jim channels onthe cirrus particle size and temperature. d'Entrem-ont et al.12 derived optical depths and altitudes ofcirrus clouds over the FIRE-IFO region in the earlymorning of 28 October 1986 by using AVHRR Chs. 3,4, and 5 BTD's and comparing these with calculatedand observed values for clear areas. Stone et al.13examined the BTD between the Geostationary Opera-tional Environmental Satellite 3.9- and 12.7-jim chan-nels as a function of optical depth and microphysicsand showed that the 3.9-jim radiances are sensitive tocirrus microphysical properties. However, they de-veloped a retrieval method to compute the cirrusoptical depth by using only the AVHRR 10.8-jimchannel data. This method requires the estimate ofboth cloud base radiance and cloud emission by usingradiosonde and lidar data. Cloud temperature andice-crystal size are not determined from the retrieval.In all the preceding investigations that used the BTDmethod, the absorption and the scattering propertiesof nonspherical ice crystals have not been accountedfor in the retrieval program.

In this paper we have developed a physical retrievalscheme to infer cirrus cloud parameters from thetheory of radiative transfer and by using the AVHRR3.7- and 10.9-jim channels. Analysis has been fo-cused on the sensitivity of channel radiances to theheight and mean effective crystal size of cirrus clouds.Moreover we illustrate that the BTD is a good indica-tor for the presence of cirrus clouds, and we apply theretrieval scheme to the AVHRR satellite data col-lected at 0930 UTC, 28 October 1986, over theFIRE-IFO region. Section 2 describes the retrievalalgorithm. Section 3 presents the results of sensitiv-ity studies and discusses the implications of using theBTD to identify the presence of cirrus clouds. InSection 4 we demonstrate the applicability of theretrieval algorithm to real satellite data. Finally,conclusions are given in Section 5.

2. Retrieval of Cirrus Cloud Parameters

The retrieval program for deriving cirrus tempera-ture, mean effective crystal size, and optical depthfrom upwelling radiances of AVHRR cloud detectionchannels follows the principles of the dual-IR-channel technique presented in Liou et al.7 TheAVHRR 3.7-jim (Ch. 3) and 10.9-jm (Ch. 4) radianceshave been selected for the development. A majoradvantage of using these two channels for cirrusretrieval is that the radiances of these spectral re-gions are affected relatively little by the presence ofwater vapor. However, the Ch. 3 radiances for localdaytime contain solar radiation that is reflected bythe Earth-atmosphere system. Thus the algorithmdescribed in this section is applicable to cirrus re-trieval for local nighttime conditions. It may beused for daytime cirrus retrieval if the solar contami-nation in the Ch. 3 radiance is removed by anadequate method.

From the theory of radiative transfer, we mayexpress the upwelling radiances at the top of theatmosphere for Ch. 3 and Ch. 4 over a cirrus cloudyatmosphere in terms of the cirrus mean temperatureT, and emissivities E3,4 , as follows:

R3 _ Ra3 (l - e3) + 3B3(T),

R4 Ra4(l - 4) + E4B4(T),

(la)

(lb)

where Ra3 and Ra4 denote the upwelling radiancesreaching the cloud base for the two spectral bandsand B3(T,) and B4 (T,) are the respective Planckintensities at T The first terms on the right-handside of expressions (la) and (lb) represent the contri-bution of the transmitted radiance from below thecloud. The second terms denote the emission contri-bution from the cloud itself. The emission by watervapor above the cirrus cloud has been neglected.The effects of cloud reflectivity, which are generallyless than 3% of the incident radiance based on exactradiative transfer calculations, have also been ne-glected.

In order to solve expressions (1) for T and e34numerically, we need to relate 3 and 4 and B3(T,) andB4(T,). The clear radiances Ra3,4 must also be known.First we compute the Planck intensities B3(T,) andB4(T,), taking into account the filter functions of bothchannels. A look-up table for both B3(T,) and B4 (T,)in 1-K intervals is constructed by using a range of TCfrom 150 to 300 K. Values in the look-up table arethen fitted to a third-degree polynomial based on aleast-squares regression method:

B3(T,) = 2 a[B4(Tc)]- = f(B4 )-n=O

(2)

The resulting coefficients are a = 2.6327 x 10-4,a, = -1.063 x 10-4, a2 = 8.2976 x 10-6, and a3 =3.7311 x 10-7. Errors in the fitted polynomial areless than 1%.

Second, we investigate the relationship betweenthe emissivities for the two channels. From radia-

2172 APPLIED OPTICS / Vol. 32, No. 12 / 20 April 1993

tive transfer calculations and following the approachproposed by Liou et al. 7, we may parameterize cirrusemissivities at the 3.7- and 10.9-jim wavelengths interms of visible optical depths T in the form

E3 = 1 - exp(-k 3 T), (3a)

E4= 1 - exp(-k 4 7). (3b)

The exponential terms represent the effective trans-missivities. The parameters k3 and k4 account formultiple scattering within cirrus clouds and for thedifference between visible and IR extinction coeffi-cients. Both k3 and k 4 are smaller than 1 becausethe effect of multiple scattering increases transmis-sion. Thus the products k3T and k4T may be consid-ered as effective optical depths, which are the opticaldepths that would yield the same emissivity values fornonscattering conditions at the 3.7- and 10.9-jimwavelengths. By eliminating T from Eqs. (3) weobtain

(1 - E3 )1/k3 = (1 - e)1/k4. (4)

Equation (4) relates 3 with 4 directly. A furthercombination of expressions (1) and Eq. (4) leads to

[R3 - B3(Te) 11/k3 _ [R4 B4(Tc) 11/k4 (5)LRa3 - B3 (Tc)] [Ra4 -B 4(Tc)]

Substitution of Eq. (2) into Eq. (5) results in anonlinear algebraic equation, with B4 (T,) as the onlyunknown:

R4 - B4(T.)Ra4 - B4(Tc)

R3 - f [B4(T)] k4 /k 3

Ra3 - f[B4(Tc)]

We investigate the dependence of these parameterson the optical depth based on radiative transfercalculations by using two cirrus cloud types involvingsmall cirrostratus (Cs) and large cirrus uncinus (Ci)ice crystals. A reasonable range of optical depth forCs and Ci is shown in Table 1. In both cases, thevariations of k 4 and k 3 are less than 2%. As a goodapproximation, we may take k 4 and k 3 as independentof the optical depth. This will eliminate the complex-ity of retrieving the optical depth from satellitemeasurements.

The ratio, k4/k3 in Eq. (6) can be considered to bethe effective extinction ratio, which, as is shownbelow, is primarily dependent on ice-crystal size

Table 1. Values of k4 and k3 as Functions of the Visible Optical Depth r

Cirrostratus (Cs) Cirrus Uncinus (Ci)

k3 k4 T k3 k4

0.05 0.290 0.516 0.2 0.416 0.4970.10 0.292 0.517 0.5 0.419 0.4980.20 0.295 0.518 1.0 0.422 0.4990.50 0.302 0.520 2.0 0.426 0.5021.00 0.308 0.522 5.0 0.428 0.504

distribution. We have analyzed 12 size distributionfunctions of cirrus clouds that were obtained from thedata presented in Heymsfield and Platt,14 Takano andLiou,15 and recently obtained from the FIRE-IFO.We first define a mean effective width (or size) torepresent ice-crystal size distribution in the form

De = D D LDn(L)dL 1 LDn(L)dL, (7)

where D and L denote the width and the maximumdimension of a nonspherical ice crystal, respectively,and n(L) is the size distribution in terms of L. Therationale for defining De to represent ice-crystal sizedistribution is that the scattering of light is related tothe geometric cross section, which is proportional toLD. Light scattering and absorption programs devel-oped by Takano and Liou15 for hexagonal ice crystalsand radiative transfer programs developed by Takanoand Liou16 and Liou et al. 17 have been used tocompute cirrus emissivity as a function of De.

Figure 1 shows the dependence of k4/k 3 on De basedon the 12 measured size distributions mentionedabove. Generally k4/k3 decreases as De increases.For a small De (- 20 jm), k4/k 3 3, which is muchlarger than 1. This is primarily because the single-scattering albedo is larger for the 3.7-jim wavelength( 0.79) than that for the 10.9-jim wavelength( 0.41), which implies that more scattering is associ-ated with the former wavelength. For De > 100 jm,k 4/k 3 approaches 1 for the following reasons. First,the extinction coefficients are approximately the samefor the two wavelengths because of large-size parame-ters in which the geometric optics limit is valid. Sec-ond, the single-scattering albedos are also approxi-mately the same for these wavelengths becausesubstantial absorption occurs within large ice crystalsso that only the diffracted and externally reflectedlight contributes to the scattering processes. Wehave carried out a second-degree polynomial least-

3.00

90

H,

2.50

2.00

0.50

0 50 100 150

De (pm)

Fig. 1. Effective extinction ratio k4 /k 3 as a function of the meaneffective size De. Points are based on a number of measuredice-crystal size distributions and the curve is the best quadratic fit.


Heymsfield S Platt (1984)

o Takano 6 LIou (1989)

x FIRE Measurement (1986)

- Quadratic fit

squares fitting in terms of 1/De in the form

2

k4/k3 = I bnDe, (8)n=o

wherebo= 0.722,bl= 55.08,andb2 = -174.12. Thefitted curve is also shown in the figure. The root-mean-square difference between the computed andleast-squares fitted values of k4/k 3 is 0.045, whichindicates that the polynomial fitting is an excellentparameterization to relate k4/k 3 and De.

We have also carried out calculations of k4 and k 3byusing area-equivalent ice spheres, which would giveapproximately the same extinction cross section asnonspherical ice crystals. If the number density andcloud thickness remain unchanged, then the cloudoptical depth would be approximately the same forspherical and nonspherical ice particles. For the Cscase (De 41.5 m), the k 4/k 3 value is 1.50 for icespheres compared with a value of 1.75 for hexago-nal ice crystals. This difference can produce errorsin the retrievals of cloud temperature by more than

7 K. The difference for the k4/k 3 values betweenspherical and nonspherical ice particles increases(decreases) as the mean effective size De decreases(increases).

A direct determination of De from data of satelliteIR channels that are presently available appears to bedifficult. However, we may relate De to the cloudtemperature through appropriate observations.From a large number of cirrus microphysical datacollected by optical probes during flights over midlati-tudes, Heymsfield and Platt14 have suggested thatice-crystal size distribution can be represented by ageneral power form,

n(L) = {ALbl(IWC),n()=A2L'2(IWC),

L <Lo

L > Lo'

where Lo = (A 2 /A)1/(bl-b2); IWC is the ice-watercontent; and A, 2 and b, 2 are empirical coefficientsdetermined from the measured data. The values ofb, A, and IWC may be parameterized in terms oftemperature in the range of -20° to -60'C.1 8 Usingthis parameterization, we find that n(L) is a functionof temperature. Moreover, based on aircraft andlaboratory measurements, the width D and the lengthL are related (see, e.g., Auer and Veal'9) in such a waythat a parameterization relation can be developed forthe two. Thus, with the functional form of n(L)determined, the mean effective size De can be ob-tained from Eq. (7). Subsequently we perform aleast-squares polynomial fitting to relate De to T, inthe form

De = Cn(T - 273)n,n=O

(10)

where c = 326.3, c = 12.42, c2 = 0.197, and C3 =

0.0012.Finally, in order to solve Eq. (6) for B4(Tc), the

upwelling radiances reaching the cloud base, Ra3,4,must be given. We may approximate these radi-ances by radiances measured from satellites in clearconditions because little water vapor is present abovecirrus clouds. In the case of AVHRR data, each scanline spans 2500 km. Because of the high resolu-tion of the AVHRR data points, it is most likely that,over a large area scanned by the radiometer, some ofthe data points correspond to clear conditions. Itfollows that if we can identify the clear data points,Ra3 ,4 may be determined by a statistical method. Wemay select a scene and use the data within this sceneto construct a two-dimensional histogram in thedomain of R 3 and R 4. The area of the scene shouldbe large enough to contain a statistically significantamount of data points, but, at the same time, thisarea should also be sufficiently small to guarantee thehomogeneity of the surface temperature and water-vapor distributions within the scene. Usually, a 10by 1 scene is adequate for the analysis. The radi-ances corresponding to the peak of the frequencydistribution are assigned as the mean clear radiances.Details for the determination of clear radiances areillustrated in Section 4.

3. Sensitivity Studies

In order to apply the above algorithm for the infer-ence of cloud parameters, we must first determinewhether cirrus clouds are present within the field ofview of the radiometers. We have investigated theinformation content of the BTD between Ch. 3 andCh. 4 radiances. The brightness temperature isdefined as the equivalent blackbody temperature thatcorresponds to the measured radiance and is deter-mined through the Planck function. First we carryout an analysis concerning the sensitivity of BTDvalues to various cloudy conditions. For opticallythick clouds, the upwelling radiances for the twochannels are approximately equal to the Planck inten-sities; a result that can be obtained from expressions(1) for 3 4 = 1.0. The plot of the Planck intensitiesby Eq. (2) over the range of cloud temperature T isshown in Fig. 2 as the solid curve. This curve is thelimiting case, which corresponds to perfect blackbody

0.70

0.60

*0

I0

0.0

0.40 -

0.30 -

0.20 -

0.10

0.00

3TD - OK . / /BTD -2K . / /

--- DOTO-5K- - - BTO-1OK / /

BTD-20K /

e //

:S~~~ //0 10 20 30 40 50 60 70

ch. 4 radlance (mW/m/r/c-r)80 90 100 110 120

Fig. 2. Constant BTD lines for BTD = 0, 2, 6,10, and 20 K in thedomain of Ch. 3 and Ch. 4 radiances.


I

_

w.ww

emission. The radiances can be converted to thebrightness temperatures through the Planck func-tion along the curve BTD = 0.0. For nonblack cirrusclouds, e < 1.0, the brightness temperature of Ch. 3 islarger than that of Ch. 4. The reason for thisbehavior is as follows. First, E(3.7 jim) is usually lessthan E(10.9 jim). As a result, the 3.7-jim transmit-tance is larger than the 10.9-jim transmittance,which implies a larger transmission of below-cloudradiance for the former wavelength. Second, thetemperature dependence of the Planck function at 3.7jim is approximately three times larger than that at10.9 jim. Thus, in the retrieval analysis, we maydetermine cirrus pixels by filtering out those pixelswith a BTD that is less than a threshold value. Inthe case in which the cloud optical properties aresimilar (e.g., at large De, k4 _ k3), differential bright-ness temperatures for E < 1.0 are produced by thePlanck function at two different wavelengths; thedegree of the differences depends on the cloud posi-tion and cloud composition. Figure 2 also shows thecontours for BTD = 2,5,10, and 20 K. These curvesare obtained from the look-up table described inSection 2. From simulation results that are dis-cussed below, we find that data points correspondingto cirrus conditions generally have a BTD larger than2 K. As shown in Section 4, the BTD's from themeasured satellite radiances over cirrus clouds arealso larger than 2 K.

Next we investigate the sensitivity of upwellingradiances to cloud base height. We have selected themidlatitude summer profile20 for the study. Thebases of cirrus clouds are prescribed at 7, 9, and 11km. For each cirrus height, we use 11 visible opticaldepths, ranging between 0.4 and 9, and compute theircorresponding emissivity values according to Eqs. (3).Upwelling radiances from cirrus atmospheres arecomputed from expressions (1). The ratio k4/k 3 isfixed as 1.07, which corresponds to De 200 jim.Figure 3 shows the distributions of Ch. 3 and Ch. 4radiances, along with the Planck intensity curve [Eq.

0.60

0.50

t 0.40

* 0.30

9 0.20

0.10

0.00

ch. 4 radiance (mW/m/sr/cm')

Fig. 3. Distributions of the computed Ch. 3 and Ch. 4 radiancesthat are based on expressions (1) along with the Planck intensitycurve. The clear radiances are obtained from the midlatitudesummer profile. Cloud bases are set at 7, 9, and 11 km. The

ratio k 4 /k3 is fixed at a value of 1.07.

(2)]. The simulated cloud-base radiances are 0.45and 100 mW/m 2 /sr/cm-1 for Chs. 3 and 4, respec-tively. The Planck intensities of surface tempera-ture (294 K) are 0.48 and 102.4 mW/m 2 /sr/cm-1,respectively. The simulated clear radiances are closeto, but not exactly the same as, the correspondingsurface Planck intensities, because of the effects ofsmall water-vapor absorption. From Eq. (5) we findthat radiances for the same cirrus base height form acurve that is nearly linear because k4/k 3 is close to 1.As the cloud base height increases, both radiances forthe same optical depth decrease. The radiance curvefor the same height intercepts the Planck intensitycurve at lower radiance values. The radiances at theintercept (E -> 1) correspond to the Planck intensitiesof cirrus temperature according to expressions (1).Similar patterns also occur in the study that usestropical atmospheric profile.20

Moreover we study the effects of k 4/k 3 on the cloudtemperature retrieval. Figure 4 shows the curves ofR3 versus R4 for three different values of k4/k 3 thatare based on Eq. (5). The cirrus height is fixed at 9km. As shown in this diagram, the Ch. 3 radiancesare sensitive to the value of k4/k3. A variation ink4/k 3 from 1 to 3 leads to the maximum change in Ch.3 radiances of 0.2 mW/m 2 /sr/cm-1. The Ch. 4radiances are nearly independent of k4/k 3 because k4changes little over the range of De considered here.An incorrect value of k4/k 3 can produce significanterrors in the retrieved cloud temperature and opticaldepth. As an example, let Ch. 3 and Ch. 4 radiancesbe 0.26 and 70 mW/m 2 /sr/cm-1, respectively. If weprescribe k4/k 3 with a value of 1, the retrieved cloudtemperature and optical depth will be 240 K and1.3, respectively. However, if we set k4/k 3 to a valueof 3, then the cloud temperature and optical depthwill differ by 30 K and 4.2, respectively. Thedifferences represent an extreme case. Neverthelessthis example does point out the importance of incorpo-rating the dependency of k4/k 3 on De in the retrievalanalysis. By comparing Fig. 2 with Figs. 3 and 4, weclearly see that BTD values are the observed quanti-

0.70

0.60

E'0I

0.50

0.40

0.30

0.20

0.10

0.00

0 10 20 30 40 50 60 70 80

.h. 4 radIance (mW/m'/srcnr')

90 100 110 120

Fig. 4. Distributions of the computed Ch. 3 and Ch. 4 radiancesthat are based on Eq. (6) for three values of k 4 /k3. The cloudheight is 9 km. Also shown is the Planck intensity curve.


ties that can be used to identify the presence of cirrusclouds.

Once the cirrus pixels are identified and clearcolumn radiances are determined, iterative proce-dures are established to solve for T, E34, and Desimultaneously. Figure 5 shows a schematic descrip-tion of the sequence of iterations. Equation (6) issolved by using a modified Newton's iteration scheme,which is efficient for the solution of nonlinear alge-braic equations.

Finally, we examine the potential instrument noisesfor Chs. 3 and 4 on the above retrieval method. Ac-cording to Dudhia,21 the noises in terms of thebrightness temperature are of the order of 0.4 and0.03 K for Ch. 3 and Ch. 4, respectively. Thesevalues have been obtained from measurements fromAVHRR IR channels on NOAA-9 and NOAA-10 satel-lites. The noise for Ch. 3 exceeds the design specifi-cation of 0.12 K. Random numbers within the uncer-tainty range are generated and added to the brightnesstemperatures associated with Rai and Ri, which arethen converted to radiances. Subsequently we per-form retrievals by using perturbed radiances. Theresults indicate that the errors of retrieved tempera-tures increase with the cirrus cloud height, butdecrease with increasing emissivity. The largestmaximum errors are less than 2 K. Errors incloud temperature are largely independent of thetemperature profile. In general, for e > 0.5, theerror is less than 0.5 K. The errors in the retrievedemissivities are less than 0.1%.

Obtain e,, from expressions (1) I

Fig. 5. Schematic description of the iterative procedures for thesimultaneous solution of cloud temperature, cloud emissivities,and mean effective size.

4. Application to FIRE-IFO DataFor the purpose of testing the retrieval scheme, wehave acquired the AVHRR GAC (global area cover-age) data collected at 0930 UTC (local nighttime), 28October 1986, over the FIRE-IFO region (42°-47° N;87°-92° W). The resolution near the satellite nadiris 1 km x 4 km, and all IR channel data have beenconverted to brightness temperatures. Figures 6(a),6(b), and 6(c) show the halftone display for thebrightness temperatures of Ch. 3 and Ch. 4, and theassociated BTD map, respectively. Several pocketsof cold brightness temperature are shown in theupper-left quadrant. These areas are cloudy. How-ever, it is not clear from the displays presented inFigs. 6(a) and 6(b) whether the clouds are cirrus orwater clouds. Figure 6(c) shows that the BTD's overthese cloudy areas largely exceed 4 K. According tothe discussion in Section 3, these cloudy pockets mustbe cirrus clouds.

To test the present retrieval algorithm, we focus ona region west of Fort McCoy (43.9° N; 90.8 W;marked as x in Figs. 6). We select the data for a zonefrom 43.5° to 44.5° N and from 910 to 92°W (highlight-ed in Fig. 6) that consists of a total of 668 satellitedata points. Within this zone, a band of cirrusextends from the northwest to the southeast. Thisregion was selected because the air mass over thisregion drifted over Fort McCoy approximately twohours later (see below for further discussion), whensurface lidar observations became available. Also,the distinctive feature of the cirrus cloud band andthe well-defined clear area made it suitable for testingthe current retrieval scheme.

Figure 7 shows a three-dimensional display of thefrequency distribution of the radiance pair R 3, R4 ,which is based on the AVHRR data set. The maxi-mum frequency radiance values are R = 0.21 andR4 = 78 mW/m 2 /sr/cm-1, which correspond to clearconditions. These values are asssigned as the meanclear radiances. The spread of clear radiances ispresumably due to the nonhomogeneity of the landsurface temperature or the surface emissivity of Ch.3.We have investigated the effects of area selection onthe determination of clear radiances by reducing thearea of interest to a zone from 44.0 to 44.5° N andfrom 91.50 to 92.0 W. This reduced area contains amajor part of the cirrus band. All the pixels thatcontain cirrus data are largely preserved. The vari-ability in clear radiances is much reduced. However,the mean clear radiances remain unchanged. Wehave also compared the clear brightness tempera-tures that are converted from radiances with thesurface temperature ( 278 K) reported from thesounding. Differences are less than 1 K. We haveset a clear BTD threshold value of 2 K to differenti-ate between clear and cloudy conditions. A total of580 clear pixels are identified, as described in Section3. The remaining 88 data points are classified ascirrus clouds.

To estimate the range of cloud parameters beforecarrying out retrieval, we show a two-dimensional


A0c Hi cs..( i I ikli" c ch. 4

; ; a; t:;e~i ts reiep. ji,. 4

display of R3 versus R4 for data points that have beenidentified as cirrus clouds (Fig. 8). This analysis ishelpful in prescribing the initial cloud parameters fornumerical iteration and for checking the reliability ofthe retrieved values. The cross symbol depicted atthe upper right denotes the mean clear radiancesdetermined from satellite data. Superimposed onthese data points are the three theoretical curves fork4/k3 = 1.8, 1.4, and 1.1, according to Eq. (5), inwhich three cloud temperatures of 220, 235, and 250K are used in the calculations. The correspondingvalues for De from Eq. (10) are 45, 70, and 150 jim.These three curves show the combined effects ofice-crystal size and cloud height. For lower cirrusclouds and larger ice crystals, the theoretical curve iscloser to the Planck intensity curve. It is evidentthat a major portion of data points lies between the

Fig. 6. Halftone displays of the brightness temperature map for(a) Ch. 3, and (b) Ch. 4, and (c) the associated BTD map over theFIRE-IFO region.

curves correspondingto k4/k 3 of 1.4 and 1.1. Accord-ingly, for these data points, the cloud temperature T,should be between 235 and 250 K, while the meaneffective size De should be between 70 and 150 jim.In addition, when expressions (1) and Eq. (5) are used,the 10.9-jim emissivity should range between 0.2 and0.7. From the temperature sounding report of FortMcCoy at 0900 UTC, we estimate that the range ofcirrus heights (z, is between 6 and 9 km.

The retrieval program is applied to each satellitedata point that has been identified as cirrus. Toguarantee the numerical stability in the retrieval, werejected 18 pairs of R3, R4 involving a 10% differencebetween either R3 and Ra3 or between R4 and Ra4.7

This is because uncertainities that are due to thespread of clear radiances can result in unrealisticvalues for the retrieved cirrus parameters. The


40

Fig. 7. Three-dimensional display of the frequency of occurrenceof the radiance pair R3, R4 based on the AVHRR data used in thiswork.

results of cloud temperature, mean effective crystalsize, and optical depth are presented in terms ofcontour maps in Figs. 9. In Fig. 9(a), we note thatthe areas of lower T (<240 K) are located in thecenter part of cloudy regions and that they occupyonly a small fraction of the total cloudy areas. Theregions of lower T also correspond to lower De [Fig.9(b)]. The contour map for De represents valuableinformation concerning the horizontal distribution ofthe mean ice-crystal size. In Fig. 9(c), the retrievedoptical depth is between 1 and 2 for most of thecirrus region. However, there is a small area ofoptically thick cirrus ( > 2) near the northwestcorner. Table 2 lists the mean values and ranges (inparentheses) of the retrieved parameters. It shouldbe noted that these values correspond to the meanproperties of the cloud. Determination of the verti-cal temperature gradient and the ice-crystal sizedistributions from satellite radiance observations

0.35

0.3 . AVHRR cirrus dta points( 43.5-44.5N. 91.0-92.0W. 0930 UTC. 10-26-86

T. k/k, D.

0.2 - - - - - 220K 1.8 A5

- * - 235K i.4 70

r:0.2 -- 250K 1.1 10

:50.10 7,

LI 0.1

0.05

0 10 20 30 40 50 60 70 6o 90

CH. 4 RADIANCE (W/m'ar/cm-')

Fig. 8. Two-dimensional display of AVHRR Ch. 3 and Ch. 4radiances for data points that have been identified as cirrus. Thecross symbol denotes the mean clear radiances determined fromsatellite data. Superimposed on these data points are the theoret-ical curves for k 4 /k 3 = 1.8, 1.4, and 1.1, according to Eq. (5).

would require an advanced sounding system alongwith an innovative retrieval technique.

Since the collocated ground and the in situ aircraftmeasurements for cloud parameters are not avail-able, a direct verification of the retrieved resultscannot be made. However, we may carry out anindirect comparison by using the surface and theaircraft data that are available in the surroundingareas. The Langley Research Center lidar systemslocated at Fort McCoy were continuously collectingdata from 0800-2400 UTC, 28 October. However,significant responses that were due to the presence ofcirrus were detected only after 1100 UTC.22 This isconsistent with satellite observations because therewas no cirrus over Fort McCoy at the time of satelliteoverpass (0930 UTC). The cirrus band was thenapproximately 50 to 100 km west of Fort McCoy.According to the synoptic analysis, northwesterlies ata speed of 15 m/s were prevalent over the areaaround Fort McCoy during the lidar observationperiod.23 It is estimated that this band of cirrusdrifted over Fort McCoy two hours after the satelliteoverpass. Lidar measurements collected between1100 and 1500 UTC show cirrus heights that aremostly between 6 and 8 km. Higher and thickercirrus clouds were observed after 1500 UTC. Therange of height derived from the retrieved T, and thesounding at Fort McCoy (0900 UTC) is between 6 and9km.

We have acquired microphysical measurementscollected by the National Center for AtmosphericResearch King Air turboprop on 28 October, between1525 and 1729 UTC, near Madison, Wisconsin.24

Madison is approximately 250 km southeast of FortMcCoy. From the satellite cloud pictures, we ob-served that the cirrus that the aircraft observed overMadison drifted from the cloud band located west ofFort McCoy. We estimate that the air mass west ofFort McCoy, driven by the prevalent northwesterlies,would take approximately six hours to reach theMadison area. In addition, lidar observations atFort McCoy (1100 UTC) and at Madison (1500 UTC)both recorded cirrus cloud heights of between 6 and 9km. The aircraft was equipped with two ParticleMeasuring systems two-dimensional (2D) probes forthe detection of ice particles. The 2D C probe mea-sures the size of ice crystals from 25 jim to 1 mm in25-jLm increments. The two-dimensional P probemeasures ice crystals with dimensions ranging be-tween 100 ji.m and 2 mm in 100-jLm increments.Samplings were taken every 5 s. A composite sizedistribution was derived for each sampling from thecombined 2D probe data by using a scheme thatemphasized the best measurement range of eachinstrument. We used the average composite sizedistributions of all samplings taken during the 2-hflight period to derive a mean De of 107 jim, basedon Eq. (10). This value is close to the mean De(- 104 jim) retrieved from satellite data. The aver-age composite size distribution for this particularcase exhibits the two-section power form described in


(a) CLOUD TEMP. (K), 43.5-44.5N 92-91W

Fig. 9. Contour displays of (a) the retrieved cloud temperature, (b)the mean effective size, and (c) the optical depth.

Eq. (9), which is common for cirrus clouds withtemperatures greater than 400C. The values forslopes b and b2 are approximately -2.0 and -6.0,respectively, while the coefficients A1 and A2 are 1.403x 108 and 9.36 x 1018, respectively. The values thatwere used to obtain k4/k3 are b = -2.27, b2 = -5.87,

Table 2. Mean Values of the Retrieved Parameters for Cirrus Pixelswithin a 1° x 1' Scene West of Fort McCoy at 0930 UTC, 28 October 1986

Parameter Current Scheme

Tc(K) 244 (233-255)E3 0.36 (0.17-0.70)E4 0.42 (0.20-0.76)

1.08 (0.41-2.77)k4/k3 1.25 (1.07-1.44)

De (>Lm) 104 (68-156)z, (km) 7.5 (6-9)"

aInferred from the Fort McCoy sounding at 0900 UTC.

A = 2.58 x 108, and A2 = -5.58 x 1018; these valuesare based on the results presented by Heymsfield andPlatt.14 The two sets of data for the determinationof ice-crystal size distribution are fairly close.

5. Conclusions

The current retrieval scheme uses radiance data ofAVHRR IR channels to determine cirrus tempera-ture, mean effective size, and optical depth simulta-neously from the theory of radiative transfer. Wehave focused our efforts on the retrieval of cirrusparameters by using AVHRR Ch. 3 (3.7-jim) and Ch.4 (10.9-im) radiances. These channels are affectedrelatively little by the presence of water vapor andare, therefore, ideal for the inference of cirrus cloudparameters.

In order to solve the governing equations, we haveestablished relationships between the emissivities ofthe two channels and have introduced a parameter


(C) OPTICAL DEPTH, 43.5-44.5N 92-91W

k4 /k 3 , which is a function of ice-crystal size distribu-tion. Using a number of typical size distributionfunctions taken from the data presented by a numberof researchers, we have examined the dependence ofk4/k 3 on the mean effective size that defines ice-crystal size distribution. The value k4/k 3 decreasesas the mean effective size increases. We have devel-oped a parameterization of k4/k 3 in terms of meaneffective size.

We have performed sensitivity studies on the ef-fects of cirrus parameters on upwelling radiances.We find that for higher cirrus and smaller cirrusparticle size, the brightness temperature differencebecomes larger, and that nonzero BTD's between thetwo channels are good indicators of the presence ofcirrus clouds. In addition, we show that radiancesfrom cirrus cloudy atmospheres depend significantlyon k4/k 3 and that variations in k4/k 3 must be ac-counted for in the retrieval.

Finally, the current retrieval scheme has beenapplied to satellite data collected over the FIRE-IFOregion. The retrieved cirrus heights are in generalagreement with lidar observations at Fort McCoy twohours after a satellite overpass. The retrieved meaneffective size is close to that derived from in situaircraft microphysical measurements over Madisonsix hours after a satellite overpass.

This work was supported by the Small BusinessInnovation Research Program under contract F19628-90-C-0123, Geophysics Directorate of the PhillipsLaboratory, U.S. Air Force, Bedford, Mass. Thanksare due to P. Minnis of NASA Langley ResearchLaboratory, Langley, Va., for providing the AVHRRGAC data on the FIRE-IFO region and to J. W. Snowand his colleagues at the Satellite Meterology Branchof the Geophysics Directorate for offering helpfulcomments on this paper. Kathy Roberts and Jenni-fer Bangerter typed the manuscript.

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