Angular Distribution Models for Top of A

3. CERES ADM scene identification

One of the major advances in CERES–TRMM is the availability of coincident high-spatial-and-spectral-res- olution VIRS measurements. Previous studies (e.g., Loeb et al. 2000; Manalo-Smith and Loeb 2001) have demonstrated that changes in the physical and optical properties of a scene have a strong influence on the anisotropy of the radiation at the TOA. Ignoring these effects results in large TOA-flux errors (Chang et al. 2000). The following sections provide a brief overview of the CERES cloud mask, aerosol, and cloud property retrieval algorithms and the cloud layering and aerosol/ cloud property convolution procedures used to provide scene identification for CERES footprints.

a. CERES cloud mask To determine the cloud cover over a CERES footprint,

the CERES cloud mask (Trepte et al. 1999; Minnis et

al. 1999) is applied to all VIRS pixels that lie within a CERES footprint. The cloud mask consists of a series of threshold tests applied to all five VIRS spectral chan- nels during the daytime (u o , 788, where u o is the solar zenith angle at the VIRS pixel), and three channels (3.78, 10.8, and 12.0 mm) at night. If the observed ra- diances deviate significantly from expected clear-sky radiances in at least one of the available channels, a pixel is classified as cloudy. A cloudy pixel can be clas- sified as either glint, ‘‘weak’’ cloud, or ‘‘strong’’ cloud, depending on how much its radiances deviate from the predicted clear-sky radiances. A clear pixel is classified as weak, strong, or aerosol, where ‘‘aerosol’’ can be smoke, dust, ash, oceanic haze, or ‘‘other’’ (e.g., when

a combination of aerosols is detected or when algorithms cannot distinguish between two or more aerosol types). Expected clear-sky radiances are determined on a 109 latitude–longitude grid. Clear-sky albedo maps (Sun- Mack et al. 1999), directional reflectance models, and bidirectional reflectance functions are used to predict expected clear-sky radiances in the 0.63-, 1.6-, and 3.75- mm channels (Minnis et al. 1999). Top-of-atmosphere brightness temperatures at 3.75, 10.8, and 12 mm are determined using surface skin temperatures and atmo- spheric profiles from numerical weather analyses and empirical spectral surface emissivities (Chen et al. 1999). Surface elevation, vegetation type, and up-to- date snow-coverage maps are also used to determine the expected clear-sky radiances.

The daytime cloud mask involves a three-step anal- ysis of each pixel. The first step is a simple IR test that flags the pixels that are so cold they must be a cloud. Over ocean, this condition occurs if the VIRS 10.8-mm- channel brightness temperature is more than 208C below the ocean surface skin temperature. For most land sur- faces, a pixel is flagged as cloudy if its 10.8-mm-channel brightness temperature is smaller than the temperature at 500 hPa. A temperature corresponding to a lower pressure is used for surface pressures of less than 600 hPa. The second step involves a series of three tests that compare the pixel to a known background or clear-sky value for 0.63-mm reflectance, 10.8-mm brightness tem- perature, and 3.75–10.8-mm brightness temperature dif- ference. If all three tests unanimously determine the pixel to be clear (cloudy), this pixel is labeled strong clear (cloudy). If one or two tests fail, a series of ad- ditional tests that involve the ratio of 1.6-mm to 0.63- mm reflectances and/or the difference between 11-mm and 12-mm brightness temperatures are applied to de- termine whether a pixel is weak or strong clear/cloud.

The first step in the nighttime cloud mask is identical to the initial daytime brightness temperature test. The next step consists of tests that compare a pixel’s bright- ness temperature and brightness temperature difference (3.75–11 mm) to predetermined clear-sky values. If ei- ther test fails to identify the pixel as clear, then a set of additional tests with a different set of thresholds is used

243 to determine whether a pixel is weak clear or is weak/

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strong cloud (Trepte et al. 1999). Over very hot land and desert, the VIRS thermal channels may saturate. To avoid misclassifying clear CERES footprints because of saturated VIRS data, the CERES WN filtered radiance is tested for the possibility that the scene may be clear. This test is used when the VIRS thermal radiance in a CERES footprint is flagged as ‘‘bad’’ and the VIRS 0.63-mm channel contains a good radiance. If the CERES WN filtered radiance ex- ceeds a predetermined threshold, the footprint is re- classified as ‘‘clear’’ and a flux is determined from CE- RES. Otherwise, the scene type is assumed to be ‘‘un- known.’’ The predetermined CERES WN filtered ra-

F IG . 1. Schematic of a CERES footprint showing two cloud layers

diance is derived from radiative transfer model and a clear region. Two distinct cloud layers are defined only if their mean effective cloud pressures (denoted by dashed lines) are statis- simulations in 58 viewing zenith angle increments over tically different and exceed at least 50 hPa.

a hot desert scene with a dry tropical atmosphere and

a surface temperature of 314 K (D. Kratz 2001, personal communication). Between 358S and 358N, saturation oc-

In cases in which the cloud algorithm cannot deter- curs in less than 0.5% of the observations. Most of these mine a solution for the observed radiances, a second occurrences are for daytime scenes over desert during cloud mask based on Welch et al. (1992) is used to the summer months.

reassess whether the pixel is really cloudy. The pixel is reclassified as clear if this second cloud mask determines it to be clear. Otherwise, the pixel is labeled as ‘‘cloudy

b. Aerosol and cloud property retrieval algorithm no retrieval.’’ The no-retrieval classification is used for Aerosol optical depths from VIRS pixels identified approximately 4% of all cloudy cases. as clear are inferred from 0.63-mm VIRS radiances based on the retrieval algorithm of Ignatov and Stowe (2002). The algorithm uses a single-channel lookup ta-

c. CERES PSF convolution and cloud layering ble approach based on radiances computed from the

Accurate relationships among aerosol, cloud, and ra- ‘‘second simulation of the satellite signal in the solar diative fluxes require accurate spatial and temporal spectrum’’ (6S) radiative transfer model (Vermote et al. matching of imager-derived aerosol and cloud properties 1997). Aerosols are assumed to be nonabsorbing and with CERES broadband radiation data. When CERES are represented by a lognormal particle size distribution is in cross-track mode, VIRS and CERES observe a with a modal radius of 0.1 mm and a standard deviation scene simultaneously. However, scenes observed by CE- in the logarithm of particle radius of 2.03 mm. These RES in the along-track direction at oblique viewing ze- particle size distribution parameters were determined by nith angles are observed by VIRS within ø2 min of fitting Mie calculations for a monomodal lognormal size CERES. To achieve the closest spatial match between distribution to an empirically derived phase function CERES and VIRS, the distribution of energy received (Ignatov 1997).

at the CERES broadband detectors must be taken into Radiances from VIRS pixels identified as cloudy are account when averaging imager-derived properties over analyzed to estimate parameters that characterize the the CERES footprint. This distribution of energy is de- optical and physical properties of the cloud. These pa- scribed by the CERES point spread function (Smith rameters include cloud visible optical depth, infrared 1994). The PSF accounts for the effects of detector re- emissivity, phase, liquid or ice water path, cloud-top sponse, optical FOV, and electronic filters. To determine pressure, and particle effective size. The algorithm con- appropriately weighted and matched aerosol and cloud sists of an iterative inversion scheme to determine the properties within CERES FOVs, pixel-level imager-de- cloud properties that, when input to a plane-parallel ra- rived aerosol and cloud properties are convolved with diative transfer model, yield the best match to observed the CERES PSF. radiances at a particular satellite viewing geometry. A

Within a CERES footprint, the properties of every detailed description of the retrieval algorithm and initial cloudy imager pixel are assigned to a cloud layer. If results is provided in Minnis et al. (1995, 1998, 1999). there is a significant difference in cloud phase or ef- Cloud-top height and pressure are determined from the fective pressure within a CERES FOV, up to two non- retrieved cloud-top temperature using the nearest ver- overlapping cloud layers are defined. In general, a single tical temperature and pressure profiles from numerical footprint may contain any combination of clear area and weather analyses. Liquid and ice water paths are derived one or two distinct cloud areas (Fig. 1). from retrievals of cloud optical depth and particle ef-

To determine whether two distinct cloud layers are fective size.

present, the imager pixels are initially binned by phase

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into either water or ice categories. Two distinct cloud retrievals are available is assumed to provide the mean layers are present if (i) the mean and standard deviation cloud properties over the CERES footprint. That is, we of effective cloud pressure from the two populations are assume that the cloud mean properties over the region significantly different based on a Student’s t test (at the of no retrievals are the same as over the region for which 95% confidence interval) and (ii) the mean cloud ef- retrievals are available. fective pressure differs by more than 50 hPa. If both

Because CERES relies on the imager to identify the conditions are met, a threshold effective pressure is de- scene within a footprint, a minimum amount of imager fined at the midpoint between the effective pressures of coverage and cloud property information is needed to the lowest and highest cloud layers. The imager pixels construct ADMs. The total fraction A unk of unknown are then recategorized using the threshold effective pres- cloud properties over the footprint is determined by com- sure before the PSF weighted-average cloud properties bining the imager coverage A im and the fraction A ncl of are determined for each layer.

the cloudy area lacking cloud properties as follows: If this method fails to identify two distinct cloud lay-

A unk ers, a second approach is considered. The pixel-level 5 (1 2 A ) 1 A (1 2 A )A , im im clr ncl (2) cloud effective pressures are sorted from lowest to high- where the first term provides the fraction of the footprint

est. The largest gap in this series (exceeding 50 hPa) is with no imager coverage, and the second term is the used to separate pixels into two cloud layers. The Stu- fraction of the footprint from the cloudy area with un- dent’s t test is then performed on the mean and standard known cloud properties. In general, only footprints with

deviation of the cloud effective pressures for these two A unk # 0.35are used to construct CERES ADMs. For populations. If they are statistically different, they are cloudy scenes over ocean observed at glint angles g of convolved over the footprint as two separate layers. If less than 408, only footprints with A im $ 0.5 are con- the pixels fail to meet these minimum requirements, they sidered. Here g is the angle between the reflected ray are assigned to one layer. When present, multilayer im- and the specular ray for a flat ocean given by ager pixels (e.g., thin cirrus over low cloud) are iden- tified with an overlapped cloud detection algorithm

cosg 5 mm 1 o Ï(1 2 m) Ï(1 2 m ) cosf, (3) 2 o 2

(Baum et al. 1999), but cloud properties are retrieved where m and m o are the cosine of the viewing and solar and convolved as if only one layer were present. The zenith angles, respectively, and f is the relative azimuth overlapped cloud detection algorithm only identifies angle. Over all surfaces except snow, cloudy footprints multilayer clouds when a well-defined thin upper-level must have a valid cloud optical depth in the lower layer cloud layer lies above a well-defined lower-level cloud to be considered. Although footprints with insufficient (Baum et al. 1999).

imager coverage or cloud property information are not considered when constructing the ADMs, a flux estimate

d. Cloud effective parameters over CERES footprints is nonetheless provided for these footprints when the ADMs are applied to determine TOA fluxes. The strat-

The cloud fraction over a CERES footprint is deter- egy for estimating fluxes from footprints with insuffi- mined from 1 2 A clr , where A clr is the imager clear-area cient imager or cloud property information is described fractional coverage. A cloud fraction is determined only in section 5c. over the part of a CERES footprint that has imager coverage. Footprints near the edge of the VIRS swath have only partial coverage by VIRS. Partial imager cov-

4. CERES ADM development

erage can also be due to bad imager data or because a TOA flux is the radiant energy emitted or scattered pixel cannot be determined as clear or cloudy by the by the Earth–atmosphere per unit area. Flux is related CERES cloud mask. All full and partial Earth-view CE- to radiance I as follows: RES FOVs that contain at least one imager pixel are

EE 0 0

recorded in the SSF product. The effective mean of a p/2

2p

I(u , u, f ) cosu sinu du df, (4) parameter x over a CERES footprint is derived from the

F(u ) 5

PSF-weighted layer mean values as follows: where u o is the solar zenith angle, u is the observer

Ax1Ax

x5 1 1 2 2 ,

(1) viewing zenith angle, and f is the relative azimuth angle A1A 1 2 defining the azimuth angle position of the observer rel-

where A 1 and A 2 are the fractional coverage of layers 1 ative to the solar plane (Fig. 2). An ADM is a function and 2, respectively, over a CERES footprint.

R that provides anisotropic factors for determining the Under some conditions, a pixel can be identified as TOA flux from an observed radiance as follows: cloudy but the cloud algorithm may fail to determine

pI(u , u, f) o cloud properties from the observed radiances. These

. (5) cases, referred to as no retrievals, can occur alongside

F(u ) 5 o

R(u , u, f ) o

pixels for which the cloud algorithm does provide cloud Because CERES measures the upwelling radiation properties. When this pattern occurs, the region in which from a scene at any given time from one or more di-

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F IG . 3. The u and f angular bin discretization of the CERES– TRMM ADMs.

F IG . 2. Schematic of Sun–Earth–satellite viewing geometry.

bins one-half of the size of the CERES–TRMM ADM angular bins. In the SW, this means that up to eight

rections, F (or R) cannot be measured instantaneously. subresolution angular bin average radiances (two solar Instead, R is obtained from a set of predetermined em- zenith angle bins 3 two viewing zenith angle bins 3 pirical ADMs defined for several scene types with dis- two relative azimuth angle bins) can be used to deter-

tinct anisotropic characteristics. Each ADM is con- mine I for every CERES angular bin. In the LW and structed from a large ensemble of radiance measure-

WN regions, two subresolution angular bins are avail- ments that are sorted into discrete angular bins and pa- able given that the LW and WN ADMs are a function

rameters that define an ADM scene type. The ADM of viewing zenith angle only. A CERES angular bin is anisotropic factors for a given scene type j are given by assumed to have sufficient sampling in the SW only if

at least five of the eight subresolution angular bins have R (u , u , f ) 5 j oi k l

pI (u , u , f ) j oi k l

(6) been observed by CERES. In the LW and WN regions,

oi F (u )

both subresolution viewing zenith angle bins must have where I j is the average radiance (corrected for Earth– measurements. An ADM is defined only when at least Sun distance in the SW) in angular bin (u oi ,u k ,f l ), and 75% of the viewing zenith angle and relative azimuth

F j is the upwelling flux in solar zenith angle bin u oi . angle bins for a given solar zenith angle bin have suf- The set of angles (u oi ,u k ,f l ) corresponds to the mid- ficient sampling. A total of 269 CERES–TRMM days point of a discrete angular bin defined by [u oi 6 (Du o )/ are used to determine SW mean radiances, whereas only

77 RAP and along-track days are used to determine represent the angular bin resolution (Fig. 3). Relative mean LW and WN radiances. azimuth angles range from 08 to 1808 because the mod-

2, u k 6 (Du)/2, f l 6 (Df)/2], where Du o , Du, and Df

For CERES–TRMM, Earth’s surface covers the entire els are assumed to be azimuthally symmetric about the instrument FOV (i.e., ‘‘full-Earth’’ view) for u between principal plane. Angular bins for u o are defined over the

08 and 808 when u is defined at the surface reference same intervals as for u. In the SW, R j is a function of level. In this range, radiances are generally available in all three angles; in the LW and WN regions, R j is defined the SSF product. However, because at least part of a as a function of viewing zenith angle only. Although CERES footprint must lie within the VIRS imager swath the dependence of LW and WN anisotropy on solar to be included in the SSF, the number of footprints from zenith angle and relative azimuth angle is neglible in oblique CERES viewing zenith angles is limited. For u most conditions, Minnis and Khaiyer (2000) showed between 808 and 908, the footprint centroid intersects that for clear land regions, especially those consisting Earth, but the leading edge of the footprint in the along- of rough terrain, LW anisotropy depends systematically scan direction lies beyond the Earth tangent point (i.e., on relative azimuth angle. This occurs because warm, ‘‘partial-Earth’’ view). Because imager pixels are un- solar-illuminated surfaces are observed in the back- available beyond Earth’s tangent point, only the part of scattering direction, whereas cooler, shadowed surfaces the CERES FOV covered by Earth has imager coverage. are observed in the forward scattering direction. Thus, As a consequence, scene identification for CERES foot- in certain viewing configurations, errors in LW TOA prints with viewing zenith angles of greater than 808 is

fluxes of up to 7 W m 22 can occur in clear mountainous unreliable, and these footprints are not used to determine regions (D. Doelling 2002, personal communication). scene-type-dependent ADMs. Similar azimuthal dependencies may also occur in bro-

To calculate the upwelling flux for a given scene type, ken or thin cloud conditions.

average radiances in all angular bins are needed. This To determine I j in Eq. (6), instantaneous radiances is unfortunately not always feasible from satellite mea- for each scene type are first averaged daily in angular surements. Average radiances for angular bins with

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missing data are estimated by using either directional reciprocity or radiative transfer theory. Directional rec- iprocity is used only for SW ADM types that are cloud free (Di Girolomo et al. 1998). The procedure for filling in angular bins using directional reciprocity is described in Suttles et al. (1988). For missing angular bins for which directional reciprocity is not used, the average radiance is estimated from a combination of observed radiances in angular bins for which data are available and theoretical radiances as follows:

oi I (u , u , f ) p q

OO j oi I (u , u , f ) k l k51 l51 th

[ I (u , u , f ) oi k l ]

where I ˆ j (u oi ,u p ,f q ) corresponds to the estimated ra-

diance for an angular bin, I j (u oi ,u k ,f l )corresponds to

an observed mean radiance, and I th is a theoretically derived radiance. The summation limits, m and n, cor-

respond to the number of angular bins for which I j (u oi ,

u k ,f l ) is available. The theoretical radiances are se- lected from a database of plane-parallel, horizontally homogeneous radiative transfer simulations for Earth scenes under a wide range of conditions. For a given surface type and cloud category (clear ocean, cloud over land, etc.), the specific theoretical radiances in Eq. (7) are determined from the model simulation that mini- mizes the root-mean-square difference in radiance be-

F IG . 4. Schematic of observer viewing geometry at reference level

tween theory and observations in the angular bins for

h. Region I corresponds to Earth views; region II corresponds to

which data are available. In the SW, the radiative trans- viewing zenith angles between Earth’s tangent point and the tangent

point of a cloud; region III corresponds to viewing zenith angles that

fer calculations are based on the discrete-ordinate-meth- view the atmosphere above the cloud. od radiative transfer code (DISORT; Stamnes et al. 1988); in the LW, radiances are based on a code by Gupta et al. (1985). The appendix describes the cases troid intersects Earth’s surface for angles u (h 100 ) be- that compose the theoretical radiance database.

tween 08 and 79.98 (region I in Fig. 4), where u (h 100 ) To determine F j , the usual approach is to integrate denotes viewing zenith angles defined at the 100-km

I j explicitly, using a discrete form of Eq. (4). However, FOV reference level. For this range of angles, I j is de- as pointed out by Loeb et al. (2002), radiance contri- termined from the measurements, as described above. butions from the entire Earth disk and overlying at- For u (h 100 ) of greater than 79.98, the CERES footprint mosphere must be taken into account, including radi- centroid lies beyond the Earth tangent point, and the ances that emerge from the atmosphere along slant at- number of CERES footprints in the SSF at these angles mospheric paths beyond Earth’s horizon (i.e., above is limited because of the narrow VIRS swath. For clear Earth’s tangent point). Ignoring these radiance contri- scenes, as u (h 100 ) increases beyond 79.98, the radiance

butions can cause 1–2 W m 22 underestimation in TOA decreases rapidly and eventually approaches zero as CE- flux. To account for these contributions, Loeb et al. RES begins to observe cold space. To estimate radiances (2002) showed that the FOV reference level must be for u (h 100 ) . 79.98, moderate-resolution transmittance defined at least at 100 km above Earth’s surface. To model and code (MODTRAN) (Kneizys et al. 1996) convert the viewing zenith angle from a surface FOV simulations for a molecular atmosphere are used. If the reference level to a 100-km FOV reference level, the scene type is cloudy, however, the MODTRAN molec- following transformation is used:

ular atmosphere approximation is only used at observer viewing zenith angles for which the FOV centroid lies

above the cloud top (region III in Fig. 4). The cloud- sinu(h 100 )5

r1h e sfc

1 r1h e 100 2 height of all footprints in the ADM class. For most

sinu(h ), sfc

(8) top height is given by the average effective cloud-top

where u (h sfc ) is the viewing zenith angle at the surface clouds, the observer viewing zenith angle corresponding reference level, and r e is the mean radius of Earth (which to the cloud top is close to that for the Earth tangent is set to 6371 km).

point [i.e., u (h 100 ) 5 79.98]. For example, for a cloud At a 100-km FOV reference level, the CERES cen- at 5 km, u (h 100 ) 5 80.178, and, for a cloud at 15 km,

247 u(h 100 ) 5 80.78. In the narrow range of angles between

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5. Instantaneous TOA flux estimation

the Earth tangent point and cloud top (region II in Fig. 4), radiances are extrapolated from radiances at u (h )

a. Interpolation bias correction

, 79.98. To estimate a flux from a radiance measurement, the The reflected shortwave and emitted longwave ADM appropriate ADM scene type must first be determined

fluxes are determined as follows: from the imager retrievals. Next, Eq. (5) is applied using

F SW j (u ; h oi 100 ) an estimate of the anisotropic factor. However, because the anisotropy of Earth scenes generally varies with view-

5 OO w l wI k j (u , u , f ; h oi k l 100 ) cosu k (9) uous manner, whereas the CERES ADMs [Eqs. (11) and

N l N k SW

[ k51 ] (12)] are defined for discrete angular bins and scene

ing geometry and cloud/clear-sky properties in a contin-

l51

and types, an adjustment to the CERES anisotropic factors is

k51 O

needed to avoid introducing large instantaneous flux er-

k LW

LW

rors or sharp flux discontinuities between angular bins

F j (h 100 )5

wI k j (u ; h k 100 ) cosu , k

or scene types. One way of reducing angular bin dis- cretization errors is to obtain anisotropic factors by lin-

where w k and w l are Gaussian quadrature weights for early interpolating bin-average ADM radiances [e.g., integration over viewing zenith angles from 08 to 908

and relative azimuth angles from 08 to 1808, respec- l ;h sfc )] and fluxes [e.g., F SW j (u oi ;h sfc )] to

I SW

(u oi ,u k ,f

tively. The number of Gaussian quadrature points (i.e., o , u, f) and evaluating aniso-

each observation angle (u

tropic factors from Eq. (6) using the interpolated quan- N k and N l ) used to evaluate Eqs. (9) and (10) is 200. tities. In addition, interpolation over other parameters that

Radiances at the Gaussian points are determined by lin- influence anisotropy (e.g., cloud optical depth) can also early interpolating the mean radiances defined over the

be used. In some cases it may even be advantageous to CERES angular bins. combine empirical and theoretical ADMs to estimate the Because the viewing geometry and footprint geolo- anisotropic factor at a particular angle (e.g., clear ocean

cation in the SSF product are provided at the surface SW ADMs in section 6a). reference level, the CERES ADMs are defined so that

When linear interpolation is used, the instantaneous they also correspond to the surface reference level. The TOA flux is given by

SW and LW ADMs at the surface reference level are given by

pI(u , u, f; h ) o sfc

, (14) R SW j (u , u , f ; h ) oi k l sfc

F(u , u, f; h ) 5 o sfc ˜

R (u , u, f; h ) j o sfc

pI (u , u , f ; h ) where R (u , u, f; h ) represents an anisotropic factor

SW

1 r1h e 100 2 polated ADM radiances [I˜ j (u o , u, f; h sfc )] and fluxes

at the surface reference level determined from inter-

j SW

F (u ; h oi 100 )

and [F ˜ j (u o ;h sfc )]. Although instantaneous flux errors are

2 likely reduced with this approach, there is no guarantee

pI j (u ; h ) k sfc r e that ensemble averages of the instantaneous fluxes will R j (u ; h ) 5 k sfc

LW

(h 100 ) 1 r1h e 100 2 remain unbiased. A bias in the mean flux will occur if linear interpolation is used when the actual radiance

Because I j in Eq. (6) is inferred from daily mean varies nonlinearly within an angular bin. It also occurs radiances, an estimate of the variability in the SW when theoretical models are used to supplement em- ADMs can be inferred from the standard deviation in pirical ADMs. The bias for a specific scene type j in daily mean radiances as follows:

angular bin (u oi ,u k ,f l ) is determined from the differ-

ence between the estimated mean flux and the ADM « (u , u , u ) 5 t R j oi k l p,n

s (u , u , u ) I j oi k l

oi F (u ) [ ÏN (u , u , u ) I j oi k l ] es) as follows:

, (13) mean flux (determined by direct integration of radianc-

where t p,n is the 100 (1 2 p)th percentile of the Student’s

DF (u , u , f ; h ) j oi k l sfc

t distribution with n degrees of freedom, and s , and I j

N , are the standard deviation and number of daily mean I j

pI(u , u, f; h )

7 R (u , u, f; h ) j o sfc 8 ikl

sfc

radiances in an angular bin, respectively. For the 95%

2 F (u ; h ), j oi sfc (15)

confidence interval, p 5 0.025 and n 5 (N 2 1). A I j

similar expression can also be used to estimate the var- where the first term on the right-hand side is the average iability in LW ADMs. Note that Eq. (13) is only an of all instantaneous flux estimates from Eq. (14) falling estimate of the ADM variability—the actual ADM var- in angular bin [u oi 6 (Du o )/2, u k 6 (Du k )/2, f l 6 (Du l )/ iability would require knowledge of the standard de- 2] for scene type j, and F j (u oi ;h sfc ) is the corresponding viation in daily mean anisotropic factors rather than the ADM flux. To remove the bias, a correction term is mean radiances.

added to instantaneous TOA fluxes:

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F IG . 5. Clear-sky ADM anisotropic factors for u o 5 308–408 for individual IGBP types with moderate-to-high tree/shrub coverage.

Positive u corresponds to forward scattering directions, whereas negative u corresponds to backscattering.

that only reflects and absorbs radiation. The TOA flux F9(u , u, f; h ) 5 o sfc

pI(u , u, f; h ) o sfc

R (u , u, f; h ) ˜ j o sfc

at the 20-km reference level h 20 is determined from the flux at the surface reference level as follows:

1 dF (u , u, f; h ), j o sfc (16)

where r e F9(u , u, f; h ) 5 F9(u , u, f; h ) ˆ o 20 ˆ o sfc . (18)

1 r1h e dF (u , u, f; h ) 20 2

jo sfc

On the CERES SSF product, instantaneous TOA fluxes I(u , u, f; h ) o sfc DF (u , u , f ; h ) j oi k l sfc

52 . (17) are provided only for CERES radiances with u (h sfc )# ˜I (u , u, f; h ) j o sfc I(u , u, f; h ) o sfc

708 and u o 7 # 86.58.

˜ j o I (u , u, f; h ) sfc 8 ikl

c. Footprints with insufficient imager information When the ensemble average of instantaneous TOA fluxes

from Eq. (16) is determined, the mean flux is unbiased As noted in section 3d, CERES footprints sometimes because dF j (u oi ,u k ,f l ;h sfc ) 5 DF j (u oi ,u k ,f l ;h sfc ). This lack sufficient imager information to define an ADM scene procedure is used in all SW TOA flux estimates (except type because part of the footprint may lie outside the VIRS over snow). In the LW and WN channels, dF j (u) is close imager swath, because the imager data are flagged as bad, to zero and is therefore not explicitly accounted for.

or because the cloud algorithm fails to determine cloud properties from the observed radiances (no retrievals). If the total fraction of unknown cloud properties [defined in

b. TOA flux reference level Eq. (2)] exceeds a threshold, the footprint is not used in

Based on theoretical radiative transfer calculations ADM development. It is tempting also to reject such foot- using a model that accounts for spherical Earth geom- prints when applying the ADMs in determining instan- etry, Loeb et al. (2002) recently showed that the optimal taneous TOA fluxes, but this rejection could introduce reference level for defining TOA fluxes in Earth radi- systematic biases in the mean TOA flux if the no-retrievals ation budget studies is approximately 20 km. This ref- assignments are correlated with cloud type (e.g., thin ice erence level corresponds to the effective radiative ‘‘top- clouds). To avoid introducing potential biases in regional of-atmosphere’’ because the radiation budget equation TOA flux estimates caused by systematic rejection of is equivalent to that for a solid body of a fixed diameter clouds whose optical properties fall outside the expected

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F IG . 6. Same as in Fig. 5 but for low-to-moderate tree/shrub-coverage ADM class.

F IG . 7. ADM anisotropic factors at u o 5 308–408 for open shrub and barren desert IGBP types.

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range of the retrieval model (resulting in no-retrievals as- signments), instantaneous TOA fluxes are estimated re- gardless of what the total fraction of unknown cloud prop- erties is over the footprint. TOA flux estimates for these footprints likely have greater instantaneous errors than those derived with complete imager information, but bi- ases in the overall means will be avoided if the errors are random.

To determine a TOA flux for a footprint that lacks suf- ficient imager information to define an ADM scene type, SW ADM radiances [e.g., I j (u oi ,u k ,f l ;h sfc )] are interpolated to the EOV viewing geometry and are compared with the measured radiance. The anisotropic factor used to convert the measured radiance to flux is evaluated from the ADM whose interpolated radiance most closely matches the mea- sured radiance. To constrain the result, only ADMs having the same underlying surface type as the measurement are

F IG . 8. Reflectance relative frequency distribution for open shrub

considered as possible candidates. From the 9-month CE- and barren desert IGBP types for angular bin u o 5 408–508, u 5 08– RES–TRMM dataset, footprints with insufficient imager 108, and f 5 708–908. coverage to determine an ADM scene type occur approx- imately 7% of the time.

pends on aerosol optical depth, this dependence should also be accounted for when estimating SW fluxes over

d. Mixed scenes clear ocean. The SSF product provides aerosol optical depth retrievals (Ignatov and Stowe 2002), but only in

When a CERES footprint contains a mixture of sur- viewing conditions for which the glint angle exceeds 408. face types (e.g., ocean and land, land and desert), in- It is consequently not possible to construct empirical stantaneous TOA fluxes are determined using the ADM ADMs stratified by the Ignatov and Stowe (2002) aerosol that corresponds to the surface type with the highest optical depth retrievals because no information on how percent coverage over the footprint. For example, near CERES radiances vary with aerosol optical depth in the coastlines, if most of the footprint PSF-weighted area glint region is available. As an alternative, instantaneous is over ocean, an ocean ADM is used to convert the TOA fluxes are first inferred in any viewing geometry radiance to flux. In converse, if most of the footprint from wind speed–dependent empirical ADMs. Next, these area is over land, one of the land ADMs is used. An TOA flux estimates are adjusted as follows: exception occurs when SW TOA fluxes are estimated from mixed land–ocean footprints in the sunlight region.

F9(u , u, f; h ) 5 ˆ o sfc

pI(u , u, f; h ) o sfc

In that case, if the glint angle [Eq. (3)] is #408 and the ˜ th R (w , I ) j footprint is covered by more than 5% ocean, the foot-

[ R (w , I ) th j ]

R(w ; u , u, f; h ) j o sfc ˜ print bidirectional reflectance is assumed to be closer

to that for ocean, and one of the ocean ADMs is used.

1 dF(w ; u , u, f, h ) j o sfc (19) where R ˜ (w j ,u o , u, f; h sfc ) is determined from the wind

6. SW ADM scene types

speed–dependent ADMs, and R th (w j , I) and R th (w j , I˜) are

a. Clear ocean anisotropic factors inferred from the measured CERES radiance I(u o , u, f; h sfc ) and the interpolated ADM radiance

Clear footprints are defined as footprints with $99.9% I˜(u o , u, f; h sfc ), respectively. To determine R th (w j , I) and of VIRS imager pixels identified as cloud free. Separate R th (w j , I˜), CERES radiances I(u o , u, f; h sfc ) and I˜(u o , u, clear ocean ADMs are defined for four intervals of wind f; h sfc ) are compared with lookup tables of theoretical SW speed corresponding to the 0–25th, 25th–50th, 50th–75th, radiances stratified by aerosol optical depth. Here, R th (w j , and 75th–100th percentiles of the wind speed probability

I) and R th (w j , I˜) correspond to the aerosol optical depth density distribution. These correspond to wind speed in- for which the theoretical radiances match the CERES ra- tervals of approximately ,3.5, 3.5–5.5, 5.5–7.5, and .7.5 diances. The radiative transfer calculations are based on

ms 21 . The wind speeds, which correspond to the 10-m the DISORT model (Stamnes et al. 1988) and assume level, are based on Special Sensor Microwave Imager maritime tropical aerosols based on Hess et al. (1998) (SSM/I) retrievals (Goodberlet et al. 1990) that have been evaluated at 24 optical depths. The ocean surface in the ingested into the ECMWF data assimilation analysis. For calculations accounts for the bidirectional reflectance of

a given wind speed interval w j , the ADM is defined fol- the ocean at the five wind speeds that correspond to the lowing the procedure outlined in section 4.

midpoints of the CERES ADM wind speed intervals using

Because the anisotropy of clear ocean scenes also de- the ocean surface bidirectional reflectance ‘‘OCEABRDF’’

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F IG . 9. The SW flux difference over (a) dark and (b) bright desert, and rms SW flux difference over (c) dark and (d) bright desert attributable to differences between CERES, ScaRaB, and ERBE desert ADMs against solar zenith-angle bin midpoint. Solar zenith angle bins are based on the ERBE definition given by: 08–25.88, 25.88–36.98, 36.98–45.68, 45.68–53.18, 53.18–60.08, 60.08–66.48, 66.48–72.58, 72.58–78.58, and 78.58–84.38.

subroutine from the 6S radiative transfer code (Vermote the overall regional mean. To avoid this bias, fluxes in et al. 1997). This routine accounts for specular reflection cloud-free sunlight are given by the clear ocean wind

(Cox and Munk 1954), wind speed–dependent whitecaps speed–dependent ADM flux ( F SW j ) interpolated at the (Koepke 1984), and below–water surface reflectance (Mo- solar zenith angle of the observation. rel 1988).

To determine whether a footprint is too close to the Equation (19) can be used to estimate TOA flux in specular reflection direction to provide a reliable flux any viewing geometry. However, as the satellite viewing retrieval, the derivatives of clear ocean ADM aniso- geometry moves towards the ocean specular reflection tropic factors with respect to illumination and viewing direction, the radiance increase for a change in angle as geometries (]R j /]u o , ]R j /]u, and ]R j /]f) are evaluated small as 18 can be very large. Because such changes in each CERES angular bin. If an observation falls in are unresolved by the relatively coarse angular bins used an angular bin for which one of the derivatives exceeds to define CERES ADMs, instantaneous TOA flux es-

a threshold value, a radiance-to-flux conversion is not timates are generally unreliable for footprints near the performed. In this study, a threshold of 0.075 per degree

specular reflection direction. As a consequence, the ra- is used as the cutoff, which corresponds approximately diance-to-flux conversion is not performed in these re- to a 408 glint angle threshold. gions. However, ignoring these samples (e.g., by not providing a TOA flux estimate) can introduce biases in

b. Clear land and desert

regional mean fluxes because fluxes over cloudy por- The anisotropy of surface-leaving radiances over land tions of a region will contribute disproportionately to and desert regions depends on several factors, including

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F IG . 10. Anisotropic factors for u 5 08–158 ERBE angular bin against solar zenith angle for CERES, ScaRaB, and ERBE SW ADMs for relative azimuth angle bins (a) 08–98, (b) 98–308, (c) 308–608, (d) 608–908, (e) 908–1208, (f ) 1208–1508, (g) 1508–1718, and (h) 1718–1808.

vegetation coverage, surface type, and surface hetero- erage (i.e., IGBP types 1–6 and 8) account for 13%. It geneity (Roujean et al. 1992). The intervening atmo- is unfortunate that there are not enough data over the sphere modifies the surface anisotropy, particularly at Tropics to construct ADMs for deciduous needleleaf shorter wavelengths (Zhou et al. 2001) and for large forests (3), permanent wetlands (11), and urban (13) aerosol optical depth (Li et al. 2000). The observed IGBP types. anisotropy of TOA-leaving radiances also depends on

Figures 5 and 6 show clear-sky ADM anisotropic instrument resolution, because clear land scenes become factors for u o 5 308–408 for individual IGBP types more inhomogeneous when observed at larger spatial (colored lines) together with ADMs determined by scales.

grouping all IGBP types falling in the moderate-to- The inclined orbit of the TRMM satellite provides a high and low-to-moderate tree/shrub coverage classes, unique opportunity for determining ADMs under all so- respectively (solid circles). Of interest is that ADM lar zenith angle conditions. To account for climatolog- anisotropic factors for individual IGBP scene types ical differences between surface types, ADMs are first show a remarkable similarity to one another and to the constructed for each of the International Geosphere Bio- combined low-to-moderate and moderate-to-high tree/ sphere Programme (IGBP) Global Land Cover types shrub coverage classes. In Fig. 5, deviations in aniso- (Loveland and Belward 1997) for which there are suf- tropic factors for individual IGBP types from the mod- ficient data in the Tropics. CERES uses a 109 latitude erate-to-high tree/shrub ADM class occur primarily in by 109 longitude map of IGBP types that covers the angular bins that are poorly sampled. This result is globe (D. A. Rutan and T. P. Charlock 2001, personal particularly evident for the closed shrubs (6) and mixed communication). The IGBP classification scheme is pro- forest (5) IGBP types. The most persistent differences vided in Table 1, along with the fraction of cloud-free between anisotropic factors from the individual IGBP CERES footprints for each IGBP surface-type category types and the combined low-to-moderate tree/shrub over the entire 9 months of daytime CERES–TRMM coverage class occur close to nadir: grassland (10) an- observations (last column). Over land and desert, barren isotropic factors are generally larger by up to 4% (rel- desert (16) and open shrubs (7) account for 53% of the ative difference), whereas anisotropic factors for crops clear footprints, IGBP types with low-to-moderate tree/ (12) are generally lower by up to 3%. Differences also shrub coverage (i.e., IGBP types 9–14) account for 34%, increase at larger viewing zenith angles, at which the and IGBP types with moderate-to-high tree/shrub cov- data sampling is reduced (note that because the CERES

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T ABLE 1. IGBP-type classification scheme. Coverage refers to the fractional coverage of a surface type over 1 3 1 km 2 area. Height refers to the height of the vegetation. Fraction refers to the cloud-free CERES footprints in each IGBP type over the entire 9 months of daytime CERES–TRMM observations.

Coverage Height Fraction IGBP type

(%) (m) (%) 1. Evergreen needleleaf forests

Surface type

.60 .2 0.60 2. Evergreen broadleaf forests

Trees

.60 .2 1.71 3. Deciduous needleleaf forests

Trees

.60 .2 0.00 4. Deciduous broadleaf forests

Trees

.60 .2 0.55 5. Mixed forests

Trees

.60 .2 0.43 6. Closed shrublands

Trees

.60 ,2 0.49 7. Open shrubs

Woody vegetation

10–60 ,2 10.14 8. Woody savannahs

Woody vegetation

30–60 .2 2.73 9. Savannahs

Herbaceous and other understory systems

10–30 .2 4.45 10. Grasslands

Herbaceous and other understory systems

,10 3.97 11. Permanent wetlands

Herbaceous

.60 0.02 12. Croplands

Water and herbaceous/woody

— 4.32 13. Urban

Temporary crops followed by bare soil

— 0.02 14. Cropland/natural vegetation mosaics

Anthropogenic structures (e.g., buildings, roads)

— 3.57 15. Snow and ice

Mosaic of croplands, forests, shrublands, and grasslands

0.00 16. Barren desert

Snow and ice

,10 15.55 17. Water bodies

Exposed soil, sand, rocks, or snow

50.22 18. Tundra

Oceans, seas, lakes, reservoirs, and rivers

0.01 19. Fresh snow

Tundra

1.21 20. Sea ice

Fresh snow

Sea ice

SSF only retains footprints within the VIRS swath,

r(u , u, f; h ) o sfc

oblique viewing zenith angles are only sampled when CERES is in RAP or along-track mode, which only 2 pI(u , u, f; h ) d

12 d o

5 sfc

occurs every third day of data acquisition).

mE o o

To reduce errors in flux attributable to poorly sampled ADM angular bins, the CERES ADMs are constructed where m o 5 cosu o ,E o is the incident solar irradiance using the low-to-moderate and moderate-to-high tree/ (51365 W m 22 ), d corresponds to the Earth–Sun dis- shrub coverage classes to determine fluxes over land. tance at the time of observation, and d o is the mean For these cases, the variability in the anisotropic factors Earth–Sun distance. is estimated to be less than 0.04 at the 95% confidence

Figure 8 shows results for angular bin u o 5 408–508, level for most solar zenith and viewing zenith angle u 5 08–108, and f 5 708–908. The two desert types

bins. The variability in anisotropic factors is estimated have a well-defined primary peak at reflectances near from the variability in daily mean radiances for each 15% (open shrubs) and 30% (barren desert), there is a angular bin [Eq. (13)].

secondary peak in the barren desert distribution near

ADM anisotropic factors for u o 5 308–408 for two 15%, and there is a hint of a secondary peak in the open IGBP types characteristic of desert regions are presented shrubs distribution at reflectances near 25%. The reason for the multiple peaks in the two reflectance distribu-

in Fig. 7. Open shrubs (7) are prevalent over west and central Australia, the southwest parts of North America, tions may be because the fixed IGBP map cannot ac- South America, and Africa, and in central Asia. Barren count for annual or seasonal changes in vegetation type

and cover. To provide a better separation between the deserts (16) are associated primarily with the Saharan, two desert types, all CERES footprints in 109 desert

Arabian, Thar, and Gobi deserts. As shown in Fig. 7, regions are reclassified as either ‘‘dark’’ or ‘‘bright’’ ADMs are different for these two IGBP types. The desert. Regions with CERES SW reflectances closer to ADMs over barren desert regions are more isotropic, the primary peak of the open shrubs reflectance distri- presumably because of the lower vegetation coverage bution are classified as dark desert, whereas regions with there. Capderou (1998) showed similar differences CERES SW reflectances closer to the primary peak of based on ScaRaB measurements from the Meteor-3-07 the barren desert reflectance distribution are classified satellite.

as bright desert.

To examine how well the IGBP classification sepa- The largest difference in ADM characteristics be- rates the two classes of desert, relative frequency dis- tween the reclassified desert ADMs (dark and bright

tributions of SW reflectance were determined in each desert) from the original IGBP classes (open shrubs and angular bin. Shortwave reflectance is inferred from a barren deserts) occurs for the bright desert class. In that measured SW radiance as follows:

case, the bright desert ADMs are more isotropic than

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F IG . 11. Frequency of occurrence of (a) liquid water and (b) ice cloud ADM classes by cloud fraction and cloud optical depth.

the barren desert ADMs, particularly in the forward bin (u . 758 excluded) as though the radiances were scattering direction, for which differences in anisotropic instantaneous values. Figure 9 shows the resulting SW factors can reach 6%. In addition, for both desert types, flux differences and root-mean-square (rms) differences the ADM variability estimate [Eq. (13)] is much smaller as a function of solar zenith angle inferred from all for the new dark and bright desert classes. For these angular bins. Also provided are results comparing fluxes cases, the variability in the anisotropic factors is esti- based on ERBE (Suttles et al. 1988) and CERES desert mated to be less than 0.03 at the 95% confidence level ADMs. For solar zenith angle bins ,608, the ScaRaB for most solar zenith and viewing zenith angle bins.

and ERBE fluxes are generally within 3 W m 22 of the Capderou (1998) recently constructed clear desert CERES fluxes for both the dark and bright desert mod-

ADMs using measurements from the ScaRaB instru- els. At larger solar zenith angles, both the ScaRaB and ment on board the Meteor-3-07 satellite. Using scene ERBE fluxes are lower than the CERES fluxes by up

identification based on the ERBE maximum likelihood to 7 W m 22 .

estimation (MLE) technique (Wielicki and Green 1989) The cause for the increase in flux difference with solar to identify clear scenes over the Saharan, Arabian, Na- mib–Kalahari, and Australian deserts, Capderou (1998) zenith angle is unclear. Further examination of the

derived ADMs for dark and bright desert conditions. To ScaRaB and ERBE ADMs reveals some large jumps in compare the ScaRaB and CERES ADMs, the CERES the nadir anisotropic factors at solar zenith angles .608. ADMs are adjusted to the midpoint of the ScaRaB ADM Figures 10a–h show the CERES, ScaRaB, and ERBE angular bins (ScaRaB uses the same angular bin defi- ADM anisotropic factors for the u 5 08–158 ERBE an- nition as ERBE) by interpolating CERES ADM mean gular bin against solar zenith angle in each of the ERBE

radiances ( I j SW )and fluxes ( F j SW ) to the angular bin mid- relative azimuth angle bins. Whereas the CERES an- points and inferring the anisotropic factors from the ra- isotropic factors show a smooth dependence on solar tio. The ScaRaB–CERES ADM differences are con- zenith angle, the ScaRaB and ERBE models are much verted to equivalent SW flux differences by inferring noisier, in particular at the larger solar zenith angles.

fluxes from the CERES ADM mean radiances ( I SW j ) us- The cause for the large variability in the ScaRaB and ing both sets of ADMs in each ScaRaB ADM angular ERBE models may be poor sampling or possibly a solar

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F IG . 12. Overcast ice cloud ADMs with cloud optical depths between (a) 1.0 and 2.5 and (b) 20 and 25 for u o 5 508–608. (c), (d) Differences in anisotropic factors between liquid water and ice clouds (liquid 2 ice) for the same cloud optical depth intervals as (a) and (b).