Remote Sensing of Environment 113 (2009) 745–754

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Remote Sensing of Environment

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Estimation of high-spatial resolution clear-sky longwave downward and net radiationover land surfaces from MODIS data

Wenhui Wang ⁎, Shunlin Liang 1

Department of Geography, University of Maryland, Department of Geography, 2181 LeFrak Hall, University of Maryland, College Park MD 20742, United States

⁎ Corresponding author. Tel.: +1 301 405 4538.E-mail addresses: whwang1@umd.edu (W. Wang), sl

1 Tel.: +1 301 405 4556.

0034-4257/$ – see front matter © 2008 Elsevier Inc. Aldoi:10.1016/j.rse.2008.12.004

a b s t r a c t

a r t i c l e i n f o

Article history:

Surface downwelling longw Received 29 February 2008Received in revised form 4 December 2008Accepted 6 December 2008

Keywords:Remote sensingSurface radiation budgetSurface downwelling longwave radiationSurface net longwave radiationMODIS

ave radiation (LWDN) and surface net longwave radiation (LWNT) are twocomponents in the surface radiation budget. In this study, we developed new linear and nonlinear modelsusing a hybrid method to derive instantaneous clear-sky LWDN over land from the Moderate ResolutionImaging Spectroradiometer (MODIS) TOA radiance at 1 km spatial resolution. The hybrid method is based onextensive radiative transfer simulation (physical) and statistical analysis (statistical). Linear and nonlinearmodels were derived at 5 sensor view zenith angles (0°, 15°, 30°, 45°, and 60°) to estimated LWDN usingchannels 27–29 and 31–34. Separate models were developed for daytime and nighttime observations.Surface pressure effect was considered by incorporating elevation in the models. The linear LWDN modelsaccount for more than 92% of variations of the simulated data sets, with standard errors less than 16.27 W/m2

for all sensor view zenith angles. The nonlinear LWDN models explain more than 93% of variations, withstandard errors less than 15.20 W/m2. The linear and nonlinear LWDNmodels were applied to both Terra andAqua TOA radiance and validated using ground data from six SURFRAD sites. The nonlinear modelsoutperform the linear models at five sites. The averaged root mean squared errors (RMSE) of the nonlinearmodels are 17.60 W/m2 (Terra) and 16.17 W/m2 (Aqua), with averaged RMSE ~2.5 W/m2 smaller than that ofthe linear models. LWNT was estimated using the nonlinear LWDN models and the artificial neural network(ANN) model method that predicts surface upwelling longwave radiation. LWNT was also validated using thesame six SURFRAD sites. The averaged RMSEs are 17.72 (Terra) and 16.88 (Aqua) W/m2; the averaged biasesare −2.08 (Terra) and 1.99 (Aqua) W/m2. The LWNT RMSEs are less than 20 W/m2 for both Terra and Aquaobservations at all sites.

© 2008 Elsevier Inc. All rights reserved.

1. Introduction

The Earth's Surface Radiation Budget (SRB) plays an important rolein determining the thermal conditions of the atmosphere, oceans, andland. It is valuable in addressing a variety of scientific and applicationissues related to climate trends, land surface modeling, and agricul-ture. Three longwave (4–100 μm) components of SRB are: surfacedownwelling longwave radiation (LWDN), surface upwelling long-wave radiation (LWUP), and surface net longwave radiation (LWNT).LWNT is one of two components in surface net radiation (the otherbeing surface net shortwave radiation), which is the key driving forcefor evapotranspiration. The meteorological, hydrological, and agricul-tural research communities require an accuracy of 5–10 W/m2 for themonthly-averaged satellite-derived surface longwave radiation bud-get (CEOS &WMO, 2000). To achieve this goal, the acceptable accuracyfor instantaneous surface longwave radiation is 20W/m2 (Gupta et al.,2004; Suttles & Ohring, 1986).

iang@geog.umd.edu (S. Liang).

l rights reserved.

The regional and global surface longwave radiation budget canonly be estimated from satellite data, which provides sufficient spatialand temporal sampling at a low cost. Clear-sky LWUP can be derivedfrom satellite-derived surface skin temperature and emissivityproducts or estimated directly from satellite top of atmosphere(TOA) spectral radiance (Meerkoetter & Grassl, 1984; Smith & Wolfe,1983; Wang et al., 2005; Wang et al., 2009). Two kinds of methodshave been developed for estimating clear-sky LWDN during the pastthree decades: physical and hybrid methods. The physical methodcalculates LWDNusing radiative transfer model and satellite-retrievedatmospheric profiles. In the hybrid method, LWDN and TOA spectralradiance for a particular sensor are first simulated using a radiativetransfer model and a large number of atmospheric profiles. Empiricalrelationships between LWDN and TOA radiance or brightness tem-perature are then established using statistical analysis. The physics isembedded in the radiative transfer simulation process. Many studieshave been conducted to estimate LWDN from satellite data (Darnellet al., 1983; Francis, 1997; Frouin et al., 1988; Gupta et al., 1997; Gupta& Wilber, 1992; Inamdar & Ramanathan, 1997; Lee & Ellingson, 2002;Meerkoetter & Grassl, 1984; Morcrette & Deschamps, 1986; Smith &Wolfe, 1983; Tang & Li, 2008; Zhou et al., 2007). Comprehensive

Table 2MODIS products used in this study

MODISproduct

Short name Version Spatialresolution

Temporalcoverage

Parameters used

Atmosphereproduct

MOD07_L2(Terra)

5 5 km 2001 Atmospheric profile,surface skintemperature, columnwater vapor, surfacepressure, and elevation

2004

Land coverproduct

MOD11C3(Terra)

5 5 km 2001 Plant function type2004

Cloudproduct

MOD06_L2(Terra)

5 1 km 2005 Cloud mask

MYD06_L2(Aqua)

2006

TOA radianceproduct

MOD021KM(Terra)

5 1 km 2005 TIR channel radiance

MYD021KM(Aqua)

2006

Geolocationproduct

MOD03(Terra)

5 1 km 2005 Geolocation sensor andviewing zenith angle

MYD03(Aqua)

2006

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reviews are available from the literature (Diak et al., 2004; Ellingson,1995; Niemela et al., 2001; Schmetz, 1989). The accuracy of availabledatasets is about 21.00–33.60 W/m2 at a monthly timescale, which isinadequate.

High resolution (down to 1 km) numerical weather predictionmodels and land surfacemodels have beenwidely studied and appliedin short range forecasting, natural hazards warning, and mesoscaleland surface and atmospheric modeling in recent years (Christensen &Christensen, 1998; Guan et al., 2000; Soci & Fischer, 2006). Surfacelongwave radiation budget components are important diagnosticparameters for these models. While multiple satellite surface skintemperature and emissivity products are routinely available at 1 kmspatial resolution (Dash et al., 2002; Prata, 2002;Wan,1999), availableLWDN datasets (20–40 km) are all designed for large scale models.

The Moderate Resolution Imaging Spectroradiometer (MODIS)onboard the NASATerra andAqua Earth Observation System satellitesprovides the opportunity to estimate the surface longwave radiationbudget at 1 km spatial resolution. The MODIS sensor has 16 thermalinfrared (TIR) channels ranging from3.660 to 14.385 μm(Barnes et al.,1998) (see Table 1). The twoMODIS sensors can potentially provide atleast four daily observations over most locations on the Earth'ssurface with more observations available at high latitudes. TheMODIS local overpass times are 10:30 am and 10:30 pm (Terra) versus1:30 pm and 1:30 am (Aqua). The higher spatial resolution of theMODIS data may enable more accurate derivation of surface long-wave radiation because it provides more detailed information aboutthe atmosphere and land surface than the sensors with a coarserspatial resolution.

This paper presents new linear and nonlinear models for es-timating high-spatial resolution instantaneous clear-sky LWDN overthe North American continent. Moreover, clear-sky LWNT was alsoderived: LWDN component was estimated using the nonlinearmodelsdeveloped in this study; LWUPwas estimated using an artificial neuralnetwork (ANN) model method (Wang et al., 2009). Tang and Li(2008) developed linear models for estimating LWDN using MODISTOA radiance. Our study used MODIS-retrieved atmospheric profilesand derived new linear and nonlinear models. The models derived inthis paper were applied to both MODIS Terra and Aqua data andextensively validated using two years' ground data. Moreover, ourstudy used a different approach to estimate LWNT.

2. Data

2.1. MODIS products

Both physical and hybrid methods require atmospheric profiles.The MODIS science team provides an atmospheric profile product

Table 1MODIS thermal infrared channels

Channel Bandwidth(um) Primary use

20 3.660–3.840 Surface temperature21 3.929–3.98922 3.929–3.98923 4.020–4.08024 4.433–4.498 Temperature profile25 4.482–4.54927 6.535–6.895 Moisture profile28 7.175–7.47529 8.400–8.70030 9.580–9.880 Ozone31 10.780–11.280 Surface temperature32 11.770–12.27033 13.185–13.485 Temperature profile34 13.485–13.78535 13.785–14.08536 14.085–14.385

routinely (Menzel et al., 2002; Seemann et al., 2003). Temperature,moisture, pressure, and geopotential height profiles are given at 20fixed pressure levels (1000, 950, 920, 850, 800, 700, 620, 500, 400,300, 250, 200, 150, 100, 70, 50, 30, 20, 10, and 5 hPa) in the prod-uct. Validation studies indicated that MODIS retrievals are similarto ground observations for the atmosphere with fairly monotonic,smooth temperature and moisture distributions (Seemann et al.,2003). Beside atmospheric profiles, the product also provides surfaceskin temperature (Tskin), surface pressure, column water vapor, andelevation corresponding to each profile. Other MODIS products,including land cover (Strahler et al., 1999), cloud mask (Ackerman etal., 2002; Ackerman et al., 1998), TOA radiance (Toller et al., 2006), andgeolocation, were also used for method development and/or valida-tion. Table 2 summarizes product version, spatial resolution, temporalcoverage, and parameters used from each product. The details abouthow each parameter was utilized were given in Sections 3 and 4.

2.2. Ground measurements

Two years (2005 and 2006) of ground data from the SurfaceRadiation Budget Network (SURFRAD) (Augustine et al., 2000) wereused for method evaluation. Widely used for satellite-derived landsurface and atmospheric products validation (Fang et al., 2007; Guptaet al., 2004; Zhou et al., 2007), SURFRAD data have been acquired forgrassland, cropland, and desert land cover types. SURFRAD groundmeasurements, including LWDN, LWUP, and surface air temperature(Tair), are three-minute averaged values. Table 3 summarizes thelatitude, longitude, land cover type, and elevation of the six SURFRADsites.

LWDN and LWUP were measured using the Precision InfraredRadiometer (model PIR, Eppley Laboratories) in the spectral range from3–50 μm (The Eppley Laboratory, 2007). The PIRs are elevated ~8 m

Table 3SURFRAD validation sites

Site Name Lat & Lon (Deg) Land cover Elevation(m)

Bondville, IL 40.05, −88.37 Cropland 213Sioux Falls, SD 43.73, −96.62 Grassland 473Penn State, PA 40.72, −77.93 Cropland 376Desert Rock, NV 36.63, −116.02 Desert 1007Fort Peck, MT 48.31, −105.10 Grassland 634Boulder, CO 40.13, −105.24 Grassland 1689

Fig. 1. Comparing clear-sky LWDN calculated using physical method and the SURFRAD ground-measured LWDN at Penn State (376 m, 2005 & 2006) and Boulder (1689 m, 2005)sites (unit W/m2).

Fig. 2. Flowchart of the hybrid method.

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above the surface and the maximum signal comes from 45°. SURFRADhas three standard PIRs that are calibrated annually at the WorldRadiation Center's Physikalisch-Meteorologisches Observatorium inDavos (PMOD), Switzerland. The PMOD blackbody infrared radiationcalibration unit was chosen because it performed well in a round-robintest that involved a blind comparison of several comparable devices(Philipona et al., 1998). After the SURFRAD standard PIRs are calibratedin the blackbody, their calibrations are fine tuned by running themoutdoors against PMOD's World Pyrgeometer Standard Group. Fieldinstruments are calibrated in operation next to the three standard PIRs,using the simultaneous data to transfer the mean calibration of thethree standard PIRs to each field instrument. During the daytime, ashade ball shades the PIR dome to minimize errors associated withinward infrared emission from the dome to the thermopile. Albrechtand Cox's method (Albrecht & Cox, 1977) is used to correct for domeemission and compute the longwave irradiance. The overall accuracyof ground data is about ±9 W/m2 (Augustine et al., 2000).

3. Developing LWDN models using hybrid method

It is straight forward to calculate LWDN using atmospheric profilesand a radiative transfer model.We conducted a pilot study to calculateLWDN using MODIS-retrieved atmospheric profiles and the ModerateResolution Transmittance Code Version 4 (MODTRAN4) (Berk et al.,1999). The calculated LWDN were compared to SURFRAD groundmeasurements. Fig. 1 shows the calculated and ground-measuredLWDN over two SURFRAD sites: Penn State (376 m, 2005 and 2006)and Boulder (1689 m, 2005). The root mean squared errors (RMSE) atboth sites are larger than 20 W/m2; the RMSE at the Boulder site is aslarge as 37.26 W/m2. The results indicated that LWDN cannot beestimated with acceptable accuracy using the physical method,especially over high elevation surfaces.

The large errors maymainly be caused by the errors in the MODIS-retrieved atmospheric profiles. Previous study indicated the accuracyof the MODTRAN4 radiative transfer model is ~2 W/m2 for calculatingLWDN (Philipona et al., 2001). The physical method is sensitive to theerrors in the individual atmospheric profiles. LWDN is dominated bythe radiation from a shallow layer that is close to the surface of theEarth. The contribution from the atmosphere above 500 m from thesurface only accounts for 16–20% of total LWDN (Schmetz, 1989). Thevertical resolution of the MODIS-retrieved atmospheric profiles iscoarse. Only 5 layers are available between 1000 and 800 hPa pressure

levels and the detailed structures of the atmosphere cannot becaptured (Seemann et al., 2003). The hybrid method, which is lesssensitive to the errors in atmospheric profiles, is a better alternative.Fig. 2 illustrates the hybrid method used in this study.

3.1. Radiative transfer simulation

The MODIS Terra atmosphere product was used to establish theatmospheric profiles database needed in radiative transfer simulationof TIR TOA radiance and LWDN to derive statistical relationships. Thedatabase consists of more than 8000 representative profiles extractedover the North American Continent in 2001 and 2004. Tskin, surfacepressure, columnwater vapor, surface elevation, and Tair correspond-ing to each profile were also included in the database to facilitatemethod development. Tair was linearly interpolated or extrapolatedfrom MODIS-retrieved temperature profile and surface pressure.

Our study aims to estimate LWDN over land surfaces. The plantfunction type for each profile was determined using co-locatedMODISland cover product. The Johns Hopkins University (JHU) emissivityspectra in the ASTER Spectral Library (ASTER, 1999) were used toapproximate spectral emissivity for each plant function type.

MODTRAN4 radiative transfer model was used in radiative transfersimulation. LWDN, spectral LWDN, thermal path radiance, and surface-

Fig. 3. The relationships between Tair (ground-measured) and Tskin (MODIS-retrieved) during daytime and nighttime at Sioux Fall (473 m) and Boulder (1689 m) sites.

Table 4Linear and nonlinear LWDN models fitting results (Standard error unit W/m2)

Θ Linear Nonlinear

Daytime Nighttime Daytime Nighttime

R2 Std. Err. R2 Std. Err. R2 Std. Err. R2 Std. Err.

0° 0.923 16.19 0.930 15.50 0.939 14.44 0.943 13.9815° 0.923 16.17 0.930 15.52 0.938 14.47 0.942 14.0130° 0.923 16.13 0.929 15.58 0.938 14.55 0.943 14.1045° 0.923 16.10 0.928 15.72 0.936 14.74 0.940 14.3260° 0.923 16.27 0.924 16.11 0.932 15.20 0.936 14.79

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TOA transmittance were simulated for each atmospheric profile.Thermal path radiance and transmittance were calculated at 0°, 15°,30°, 45°, and 60° sensor view zenith angles. Surface temperature wasassigned using Tskin from the MODIS atmosphere product. Lambertiansurfacewas assumed in the simulation. Spectral surface emissions werecalculated using Planck's function and emissivity spectra. MODIS TOAradiance was synthesized using spectral LWDN, emissivity spectra,thermal path radiance, surface-TOA transmittance, and theMODIS Terraspectral response function.

3.2. Deriving linear and nonlinear LWDN models

Previous studies indicated LWDN can be modeled using a linearcombination of TIR TOA radiance (Morcrette & Deschamps, 1986;Smith&Wolfe,1983). Stepwise regressionwas used to identify the bestchannel combinations, based on standard errors (standard deviationof the difference between predicted LWDN and simulated LWDN) andR-squared values of each combination. The results indicated thatMODIS channels 27–29 and 31–34 are most valuable for predictingLWDN. This is consistent to the physics that governs LWDN: 27, 28 and29 are water vapor channels; 33 and 34 are near surface air tem-perature profile channels; 29, 31, and 32 are used for retrieving Tskin.

Tair is one of the dominant factors for clear-sky LWDN. Tskinchannels are important for estimating LWDN because it is closelycorrelated to Tair. However, the daytime and nighttime relationshipsbetween Tair and Tskin differ. Fig. 3 shows the relationships betweendaytime and nighttime Tair and Tskin using two years' (2005 and2006) ground-measured Tair and MODIS retrieved Tskin at the SiouxFalls and Boulder sites. The R-squared values were 0.82 or more in allcases. Therefore, separate models were developed to predict LWDNduring daytime and nighttime.

Surface pressure is also an important factor in estimating LWDNbecause of the effect of the pressure broadening of the spectral lines(Lee and Ellingson, 2002). Surface pressure has not been included inthe LWDN models in previous studies. In this study, we use elevation(H, unit km) as a surrogate to surface pressure to account for thesurface pressure effect. Eq. (1) shows the linear models developed:

LWDN = a0 +∑aiLi + bH i = 27;28;29;31;32;33;34ð Þ ð1Þ

where a0, ai, and b are regression coefficients; Li are MODIS TOAradiance (unit W/m2/μm/sr). A total of ten linear models, correspond-ing to five view zenith angles (0°, 15°, 30°, 45°, and 60°) and twoobservation times (daytime and nighttime) were developed. The

linearmodels account formore than 92% of variations in the simulateddata sets, with biases of zero and standard errors less than 16.11(nighttime) and 16.27 (daytime) W/m2.

Residuals analysis indicated LWDN tends to be underestimatedunder high temperature/moisture conditions and overestimated underlow temperature conditions. Nonlinear LWDN models were developedto account for the nonlinear effect. The same set of predictor variables asthe linear models was used in the nonlinear models:

LWDN= LTair a0 + a1L27 + a2L29 + a3L33 + a4L34 + b1L32L31

+ b2L33L32

+ b3L28L31

+ c1H� �

ð2Þ

where LTair represent Tair (it equals to L31 in the nighttime models andequals to L32 in the daytime models); ai, bi, and c1 are regressioncoefficients. Table 4 compares the linear and nonlinear model fittingresults. The regression coefficients of the nonlinear models are given inTable 5. The three ratio terms represent of the effect of water vapor onLWDN. The signs of bi values are consistent to the physics because L32

L31and L28

L31are negatively correlated to columnwater vapor; L33

L32is positively

correlated to column water vapor. The negative c1 values are alsoconsistent with the surface pressure effect. The nonlinear modelsaccount for more than 93% of the variation, with biases of zero andstandard errors less than 14.79 (nighttime) and 15.20 (daytime) W/m2.

4. Evaluation and discussion

4.1. Using MODIS Terra TOA radiance

The linear and nonlinear LWDN models were first evaluated usingtwo years' (2005 and 2006) MODIS Terra clear-sky TOA radiance andco-located SURFRAD ground measurements. For observations with

Table 5Nonlinear LDWN models regression coefficients

Daytime Nighttime

0° 15° 30° 45° 60° 0° 15° 30° 45° 60°

a0 150.204 153.149 162.142 180.911 214.228 84.143 87.069 95.437 112.646 142.438a1 4.453 4.344 3.909 3.119 2.129 5.365 5.274 4.899 4.184 3.049a2 −1.740 −1.800 −1.989 −2.411 −3.279 −1.782 −1.833 −1.993 −2.374 −3.199a3 −21.030 −20.367 −18.460 −14.022 −3.723 −15.508 −14.870 −13.069 −8.880 0.426a4 32.217 31.676 30.226 26.553 16.927 27.077 26.520 25.066 21.511 13.061b1 −150.869 −154.969 −167.043 −192.689 −239.237 −106.529 −110.082 −119.872 −140.713 −177.342b2 33.176 34.007 35.638 40.589 53.681 62.673 63.050 63.200 64.904 69.793b3 −26.812 −25.894 −22.376 −16.065 −6.780 −40.546 −39.727 −36.611 −30.986 −21.948c1 −1.911 −1.907 −1.902 −1.914 −1.987 −1.984 −1.977 −1.966 −1.962 −2.001

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view zenith angle (θ) less than 60°, LWDN values were first calculatedat the two angles (among 0, 15, 30, 45, and 60) that are closest to θ.Then, LWDN at θ was linear interpolated from the two LWDNs. Forobservations with θ larger than 60°, LWDN at 60° were simply used(our study indicated the error caused by this approximation is small).Clear-sky observations were identified using MODIS cloud product.We also examined all data points manually to exclude obvious cloud-contaminated pixels with unreasonably low TOA radiance values inMODIS channel 31.

The statistics of validation results using Terra data are summarizedin Table 6. Figs. 4 and 5 show the validation plots for six sites. The non-linear model outperforms the linear model at five out of six sites, withRMSEs from 14.35 to 20.35W/m2 and biases from −6.88 to 9.72W/m2.The RMSEs of linear models are from 15.58 to 25.29 W/m2 and biasesfrom −12.18 to 8.79 W/m2.

We calculated mean RMSEs for different conditions. The daytimemean RMSEs are 20.75 (spring/summer) and 19.06 (fall/winter) W/m2; the nighttime mean RMSEs are 14.76 (spring/summer) and 15.03(fallwinter) W/m2. The daytime mean RMSEs are ~5W/m2 larger thanthat of nighttime during all seasons. The spatial mismatch betweenthe MODIS footprint (1 km at nadir) and the ground PIR footprint(~200 m) may be a potential cause of the larger scatter and RMSEsduring daytime in the nonlinear model validation results. The Earth'ssurface behaves almost as an isothermal and homogeneous surface atnight. During daytime, Tskin under shadows is lower than that insunshine areas and the temperature differences can be as large as20 °C (Wan & Dozier, 1996).

Using channel 32 radiance to represent Tair may cause larger errorsduring daytime when Tskin can exceed Tair by more than 20°. The Lairterm in Eq. (2) represents Tair. Both channels 31 and 32 are Tskinchannels and can be potentially used to approximate Lair becauseTskin is closely correlated to Tair (see Fig. 3). Our study indicatedchannel 32 represents Tair better than Tair during daytime. However,using channel 32 to represent Tair still causes errors when the dif-ference between Tskin and Tair is large (over bare ground and highelevation surfaces).

Since surface pressure does not vary significantly during the dayand at night, the nighttime results at the two high elevation sites

Table 6LWDN models validation results using MODIS Terra TOA radiances

Sites #Obs. MODIS Terra (W/m2)

Linear Nonlinear

Bias RMSE Bias RMSE

Bondville 298 −5.60 25.29 −2.20 19.41Sioux Falls 350 −6.26 20.44 −2.65 16.87PennState 290 −5.30 19.89 −0.52 16.73DesertRock 667 −12.18 20.85 −6.88 17.91FortPeck 153 −0.84 15.58 0.15 14.35Boulder 383 8.79 18.66 9.72 20.35Mean – −3.57 20.12 −0.40 17.60

(Desert Rock and Boulder, see Figs. 4 and 5) indicated that the modelscan account for surface pressure effects reasonably well. However,large errors exist at the Boulder site during daytime. Statistics showthe current profile database has limited high temperature/moistureand high elevation profiles because high elevation surface only con-sists a small portion of North America continent. The errors at theBoulder site may be reduced after more such profiles are used inradiative transfer simulation in the future.

Cloud contamination may be a significant source of error in thisstudy. The MODIS cloud product cannot mask clouds in all cases,especially for cirrus clouds. Some pixels used in the study may becontaminated by clouds even after manual screening. The TOA ra-diance of these pixels are mixtures of surface and cloud top con-tributions and will be lower than true clear-sky values (Wan, 2008;Wang et al., 2007). The negative biases at some sites may be caused bycloud contamination. This is especially true at the Desert Rock site. Airtraffic out of Los Angeles produces a considerable amount of cirrusover this site. The Lambertian assumption in radiative transfer simu-lationmay also cause errors. Additional research is required to identifythe sources of errors and further refine the models.

4.2. Using MODIS Aqua TOA radiance

Although the LWDN models were developed using MODIS Terraretrieved atmospheric profiles and spectral response functions, themodels were also applied (without modification) to two years ofMODIS Aqua TOA radiance (2005 and 2006) because the two sensorshave similar designs. Table 7 summarizes the validation results usingAqua data. The linear models' biases range from −13.99 to 6.88 W/m2

and RMSEs range from 16.27 to 24.54 W/m2. The nonlinear models'biases range from −10.03 to 5.40W/m2 and RMSEs range from13.82 to18.89 W/m2.

Terra and Aqua have different satellite overpass times: 10:30 amand 10:30 pm versus 1:30 pm and 1:30 am (local time), and as aconsequence, the atmosphere and land surface conditions are dif-ferent for the two sensors. However, the nonlinear model biases andRMSEs are generally smaller for Aqua. Liu et al. (2006) show that theAqua MODIS has smaller systematic sensor errors than Terra inthermal channels, which may contribute to the small errors in Aqua-derived LWDN. The Aqua validation results indicated that the LWDNmodels developed in this study are general enough to be applied forboth Terra and Aqua observations. Fig. 6 shows the nonlinear modelsvalidation result using two years (2005 and 2006) of Terra and Aquaclear-sky observations from all six SURFRAD sites, with bias of −1.54and RMSE of 17.52 W/m2.

4.3. Comparing with previous studies

The nonlinear models predicted LWDN were compared with twoprevious studies. The nonlinear model-derived LWDN has slightlylarge errors than the CERES-derived instantaneous clear-sky LWDN(Charlock, 2006) over low elevation surfaces, with the RMSEs of

Fig. 4. Linear LWDN models validation results using MODIS Terra data (black—fallwinter/day; cyan—fallwinter/night; magenta—springsummer/day; green—springsummer/night). (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

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Fig. 5.Nonlinear LWDNmodels validation results using MODIS Terra data (black—fallwinter/day; cyan—fallwinter/night; magenta—springsummer/day; green—springsummer/night). (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.) 751

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Table 8LWNT validation results (unit W/m2)

Sites Terra Aqua

Bias RMSE Bias RMSE

Bondville 3.97 19.12 7.67 19.74Sioux Falls −2.43 17.08 −1.00 15.60PennState 1.37 18.92 6.19 18.87DesertRock −3.88 18.40 −0.09 16.90FortPeck −1.79 13.44 4.70 14.44Boulder −9.69 19.38 −5.51 15.75Mean −2.08 17.72 1.99 16.88

Table 7LWDN models validation results using MODIS Aqua TOA radiances

Sites #Obs. MODIS Aqua (W/m2)

Linear Nonlinear

Bias RMSE Bias RMSE

Bondville 228 −4.33 24.54 −2.90 18.89Sioux Falls 254 −7.19 22.60 −4.30 15.86PennState 205 −8.86 20.00 −2.55 14.25DesertRock 681 −13.99 21.47 −10.03 17.86FortPeck 296 −3.32 17.27 −2.75 13.82Boulder 341 6.88 16.27 5.4 16.35Mean – −5.14 20.36 −2.86 16.17

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CERES-derived LWDN ~5–6 W/m2 smaller than MODIS. However, theRMSEs of MODIS-derived LWDN are ~7–12 W/m2 smaller than CERESat higher elevation sites. The RMSEs of our nonlinear models are ~6–19W/m2 smaller than that of Tang and Li's linear models (2008) at thefive common SURFRAD validation sites.

Random noises tend to cancel each other after LWDN is integratedspatially and/or temporally. Our analysis of the preliminary spatialscaling shows that RMSEs were further reduced by 2 W/m2 after thenonlinear model-predicted LWDN was aggregated to 5 km and be-yond. The accuracy of existing LWDN products are 21–33W/m2 at 20–40 km spatial resolution and monthly temporal scale (ASDC, 2006;Francis & Secora, 2004; Wielicki et al., 1996). Our nonlinear modelvalidation results indicated the LWDN estimated in this study has abetter accuracy than existing products. However, cloudy-sky LWDNare required to compare our results with existing products in the samespatial and temporal scale. Thorough comparison will be performedafter cloud-sky MODIS LWDN method is developed in the next step.

5. Estimating LWNT

Clear-sky LWNT was calculated by subtracting LWDN from LWUP.LWDNwas estimated using the nonlinear LWDNmodels developed inSection 3. LWUP was estimated using an ANN model method (Wanget al., 2009). The ANN model method predicts LWUP directlyfrom MODIS channels 29, 31, and 32 TOA radiance. It was also basedon extensive radiative transfer simulation and statistical analysis(hybrid method). There are three major differences compared to thehybrid method for developing LWDN models. First, the University of

Fig. 6. MODIS LWDN nonlinear models validation results using two years (2005 and2006) of Terra and Aqua clear-sky observations from all six SURFRAD sites.

California Santa Barbara (UCSB) emissivity library (Wan, 1999) wasused in the radiative transfer simulation for developing LWUPmodels.LWUP is more sensitive to land surface emissivity variations thanLWDN. The UCSB emissivity library, containing 150 emissivity spectrarepresenting a variety of natural and manmade materials, can betterrepresent land surface emissivity properties than the JHU emissivitylibrary. Second, LWUP is not affected by surface pressure or elevation.Therefore elevation is not a predictor variable in the LWUP models.Third, LWUP was modeled using a single hidden layer neural net-work provided by the S-Plus 7 statistical software package (Insightful,2005).

LWUP predicted using the ANN model method had been validatedusing the same six SURFRAD sites. The averaged RMSEs of the ANNmodel method are 15.89 W/m2 (Terra) and 14.57 W/m2 (Aqua). Ourstudy indicated that the ANN model method systematically under-estimated LWUP over all surfaces. In this study, a bias of 8.00 W/m2

was adjusted to the derived LWUP.MODIS-derived LWNTwere validated used the same SURFACE sites

as LWDN. Table 8 summarizes LWNT validation results. The averagedRMSEs were 17.72W/m2 (Terra) and 16.88W/m2 (Aqua); the averagedbiases are −2.08 W/m2 (Terra) and 1.99 W/m2 (Aqua). The RMSEs areless than the acceptable error (20W/m2) for the instantaneous surfacelongwave radiation budget in all cases. Fig. 7 illustrates validationresults at individual sites using Terra data. Larger scatter exists fordaytime observations during spring and summer (high temperature/moisture conditions), similar to the error patterns in LWDN. Aquavalidation results are similar to that of Terra, with averaged RMSE~1 W/m2 smaller than that of Terra. The RMSEs of LWNT estimated inthis study using Terra data are ~1–13W/m2 smaller than Tang and Li'sstudy (2008) at the 5 common validation sites.

6. Summary

This study presents new linear and nonlinear models for estimat-ing high spatial resolution clear-sky land LWDN from 1 km MODISTOA radiance. The models were developed based on extensive ra-diative transfer simulations and statistical analysis. The linear modelsexplain more than 92% of variations of the simulated data sets, withstandard errors less than 16.27W/m2 for all sensor view zenith angles.The nonlinear models explain more than 93% of variations, withstandard errors less than 15.20W/m2. We validated the LWDNmodelsusing two years of ground measurements at six SURFRAD sites. Thenonlinear models outperform the linear models, with mean RMSE of17.60 (Terra) and 16.17 (Aqua) W/m2. The mean RMSE of the nonlinearmodels is ~2.5 W/m2 smaller than that of the linear models. Thevalidation results indicate that the models developed in this study canbe applied to both Terra and Aqua observations. LWDN can be esti-mated usingMODIS TOA radiance and nonlinear models with a higheraccuracy than the existing LWDN datasets. LWNTwas estimated usingthe nonlinear LWDN models and the ANN model method for esti-mating clear-sky LWUP. Validation results indicate that LWNT can beestimated with accuracy within 20W/m2 using both MODIS Terra andAqua TOA radiance.

Fig. 7.MODIS Terra-derived LWNT validation results (black—fallwinter/day; cyan—fallwinter/night; magenta—springsummer/day; green—springsummer/night). (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.) 753

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754 W. Wang, S. Liang / Remote Sensing of Environment 113 (2009) 745–754

The method presented in this paper is designed to estimate in-stantaneous clear-sky LWDN and LWNT. Future research will con-centrate on developingmethods to estimate instantaneous cloudy-skysurface longwave radiation budget components fromMODIS data andestimating daily and monthly averaged surface longwave radiationbudget components using instantaneous estimations. The MODIS-derived 1 km surface longwave radiation budget dataset is valuable inevaluating high resolution numerical weather prediction models andland surface models. It can also be used to evaluate surface longwaveradiation budget datasets derived from sensors with coarser spatialresolutions.

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