Mapping High-Resolution Surface Shortwave Net RadiationFrom Landsat Data

Mapping High-Resolution Surface Shortwave Net Radiation From Landsat DataDongdong Wang,Shunlin Liang,Fellow,IEEE,and Tao HeAbstract—Maps of high-resolution surface shortwave net radia-tion(SSNR)are important for resolving differences in the surface energy budget at the ecosystem level.The maps can also bridge the gap between existing coarse-resolution SSNR products and point-basedfield measurements.This study presents a modified hybrid method to estimate both instantaneous and daily SSNR from Landsat data.SSNR values are directly linked to Land-sat top-of-atmosphere reflectance by extensive radiative transfer simulation.Regression coefficients are pre-calculated and stored in a look-up table(LUT).Atmospheric water vapor is a key parameter affecting SSNR,and three methods of treating water vapor are evaluated in this parison between Landsat retrievals andfield measurements at six AmeriFlux sites shows that the hybrid method with water vapor as a dimension of LUT can estimate SSNR with a root mean square error of77.5W/m2 (instantaneous)and36.1W/m2(daily).The method of water vapor correction produces similar results.However,a generic LUT that covers all levels of water vapor results in much larger errors.Index Terms—Albedo,daily radiation,Enhanced Thematic Mapper Plus(ETM+),hybrid method,Landsat,net radiation, water vapor correction.I.I NTRODUCTIONS HORTW A VE net radiation at Earth’s surface is the differ-ence between incident shortwave radiation at the surface and shortwave radiation reflected back to the atmosphere by the surface.Surface shortwave net radiation(SSNR)is closely related to the surface(all-wave)net radiation during the day-time[1].Surface net radiation plays essential roles in many land processes(e.g.,evapotranspiration[2]and snow melting [3])and boundary layer weather conditions[4].Hence,efforts have been made to estimate surface net radiation from SSNR e.g.,[5].Meanwhile,estimating SSNR has also become an important research topic[6],[7].SSNR varies temporally and spatially due to differences in solar geometry,atmospheric conditions and underlying surface reflectivity.Current SSNR data are typically available at two scales:point-basedfield measurements at local scales[8]and coarse-resolution products at regional or global scales derived from satellites[9]or data assimilation[10].However,SSNR data at intermediate scales,which are important for character-izing heterogeneous terrestrial features,are simply missing. High-resolution SSNR data are important for resolving dif-ferences in the surface energy budget at the ecosystem level.Manuscript received March2,2013;revised April26,2013;accepted May31,2013.Date of publication June28,2013;date of current version November25,2013.The authors are with the Department of Geographical Sciences,University of Maryland,College Park,MD20742USA(e-mail:ddwang@). Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/LGRS.2013.2266317They can also bridge the gap between existing coarse-resolution SSNR products and point-basedfield measurements and be used to validate coarse-resolution data.Gowda et al.pointed out that existing coarse-resolution data are insufficient for the man-agement of irrigation in agriculture[11].A minor difference in management over similar patches can result in different energy fluxes[12].Differences in surface radiation and energy balance at local scales also have important implications in many bound-ary layer variables,such as wind speed,air temperature,and relative humidity[13].High-resolution data of surface radiation are also needed in the study of heterogeneous urban landscapes [14].The surface roughness and surface energy budget of urban areas are unique and serve important roles in modern atmo-spheric models[15].Nevertheless,the study of urban energy budget is still limited partially due to the availability of spatially explicit data[16].With the time coverage dated back to1980s [17],the Landsat multispectral data record[Thematic Mapper (TM),Enhanced Thematic Mapper Plus(ETM+)]is a valuable data source for mapping SSNR at such high spatial resolution. It is common to estimate SSNR from incident solar radiation and surface albedo data,based on its definition[18]–[20].How-ever,high-resolution products of both incident solar radiation and surface albedo are unavailable.Many studies have used Landsat reflectance and downward radiation calculated from preset atmospheric parameters[13],[21].This type of approach typically works better for clear-sky conditions[22],[23].An-other problem with such albedo-based methods is that each of the two products contains uncertainties.To avoid the possibility of error addition from the two variables,an alternative is to estimate SSNR as one variable.Kim and Liang developed a hy-brid method to retrieve SSNR from Moderate Resolution Imag-ing Spectroradiometer(MODIS)top-of-atmosphere(TOA)and surface reflectance data[7].Their hybrid method estimates SSNR without separating cloudy and clear-sky conditions.Kim and Liang compared their hybrid method with the existing method[6]and found that results improved in terms of reducing both root mean square error(RMSE)and bias[7].This hybrid method also performs well when compared to another method where all inputs are from MODIS high-level products[24]. The method in Kim and Liang[7]is designed for retrieving instantaneous SSNR,and a daily value has to be interpolated approximately from a sinusoidal model[25].In this letter,we modify the hybrid method to estimate SSNR directly from Landsat TOA reflectance by separating clear and cloudy models according to cloud coverage.We also extend the method to derive daily SSNR by assuming a stable atmospheric condition during the daytime.Atmospheric water vapor is a key factor af-fecting SSNR.In addition to the water vapor correction method proposed by Kim and Liang[7],we evaluate two other methods of treating water vapor.A brief summary of our methodology is1545-598X©2013IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.Fig.1.Model predictability in terms of relative RMSE for three types of sky conditions.Results from the method of generic LUT (WV3)are shown here.given in Section II.Data and results will be in Section III,and the final section is a discussion and some concluding remarks.II.M ETHODOLOGYThe basic idea of hybrid retrieval methods is to link variables of interest to satellite observations through simulation of physi-cal models.Kim and Liang found a strong relationship between SSNR,MODIS surface and TOA reflectance [7].The hybrid retrieval method cannot be applied to Landsat data directly since the surface method is not a standard product of Landsat.Although atmospheric correction of Landsat data is rather mature [26],surface reflectance is available only for clear-sky conditions.It is difficult to interpolate surface reflectance on cloudy days from temporally sparse Landsat data.Therefore,we constructed regression models that link SSNR directly to spectral TOA reflectance.The model is given asS n =c 0+r i •c i (1)where S n is instantaneous SSNR,r i is the Landsat TOAspectral reflectance at Band i (i =1,2,3,4,5,7),c i is the regression coefficient for the band,and c 0is the offset.We build regression models for separate cases of clear-sky or cloudy-sky conditions and mixed cases of all-sky conditions.Our analysis found that SSNR can be estimated more reliably from TOA reflectance if clear-sky and cloudy-sky conditions are separated (see Fig.1in the next section for more details).The regression coefficients are stored in a look-up table (LUT)and depend on solar zenith angle (SZA).Based on the method used for treating water vapor,the coefficients may also depend on water vapor concentration.Kim and Liang derived regression coefficients for one fixed level of water vapor u 0[7].An empirical correction is then applied to adjust the retrieved SSNR to any level of water vapor u .The correction coefficient C w is calculated as [7]C w = a −b lg u c√d cos 2θs +1a −b lg u 0c√d cos 2θs +1(2)where θs is SZA,a ,b ,c ,and d are constants derived from simu-lation,and their values are taken from Kim and Liang’s paper [7].We call this empirical correction method WV1.We also evaluated two other methods that account for atmospheric water vapor:WV2and WV3.In WV2,the concentration of water vapor is used as an additional dimension of LUT.The regressioncoefficients are derived for various levels of water vapor (five inthis letter:0.5,2.0,4.0,6.0,and 12.0g/cm 2).A suitable set of coefficients is selected or interpolated according to the actual value of water vapor.In WV3,there is only one set of generic regression coefficients,and they are based on a simulation of all five levels of water vapor.The generic LUT is supposed to consider the effects of water vapor implicitly.The critical part of developing the hybrid algorithm is radia-tive transfer simulation.MODTRAN 5[27]is used to establish the training data sets in this letter.In our simulation,ten SZA values are used (0◦,15◦,30◦,45◦,55◦,60◦,65◦,70◦,75◦,and 80◦).For each SZA,a database containing 245surface spectra is used as the inputs of surface reflectance.The spectra database is extracted from ASTER [28]and U.S.Geological Survey (USGS)[29]spectral libraries.The atmospheric parameters mainly include information about water vapor and aerosols,for clear-sky cases,or clouds,for cloudy-sky cases.A previous study found that aerosol and cloud type are not the main factors affecting retrieval accuracy [30].One aerosol type (rural)and one cloud type (stratus)is used in this study.Eight aerosol optical depth (AOD)values at 550nm (0.00,0.05,0.10,0.15,0.20,0.40,0.60,and 0.80)and five cloud extinction coefficients (5.0,20.0,50.0,128.0,and 200.0)are used.Elevation is set to the sea level in all the simulations.The normalized elevation coefficients in [7]are used to correct the impacts of elevation on SSNR.Compared with instantaneous SSNR,daily SSNR is more important for the study of daily surface energy budget.To calculate daily SSNR,atmospheric conditions are assumed tobe fairly invariant during the day.Thus,daily SSNR,S dailyn ,can be computed as the integral of instantaneous SSNR,S instn ,over the daytimeS daily n =daytimeS inst n (t )dt.(3)Given latitude and day of year,SZA can be calculated easily forany time of the day,and S instn can be simulated from the radia-tive transfer model for the given SZA.Then,S daily n is obtained through integration for various combinations of latitude,day of year,atmospheric condition and surface condition.Similar to the instantaneous model,the regression models are used to link the TOA reflectance and daily shortwave net radiationS dailyn =c 0+r i •c i .(4)Different from the LUT for instantaneous SSNR,the LUT fordaily SSNR has two more variables as an index,latitude,and day of year.For the purpose of comparison,we also apply the albedo-based method to calculate SSNR for the clear-sky cases.The incoming solar radiation S ↓is calculated using the following equation [23]:S ↓=I 0dcos θs τm (5)where I 0is the solar constant,d is the Sun-Earth distance,τis atmospheric transmittance,and m is a unitless number for air mass.The narrow-to-broadband conversion coefficients [31]are used to calculate surface albedo from Landsat spectral surface reflectance,which is generated by the LEDPAS software [26].WANG et al.:MAPPING HIGH-RESOLUTION SURFACE SHORTWAVE NET RADIATION FROM LANDSAT DATA 461TABLE II NFORMATION OF S IX A MERI F LUX S ITES AND C ORRESPONDINGL ANDSAT D ATA U SED FOR VALIDATIONIII.D ATA AND R ESULTSLandsat 5/TM and Landsat 7/ETM+data from 2003to 2005over six AmeriFlux sites were used in the study (Table I).The Landsat L1T data were downloaded from the U.S.Geological Survey data archive and have been geometrically and radiomet-rically corrected.To ensure the quality of geometric registration and cloud detection,we selected 101scenes with nominal cloud cover less than 30%.The LEDAPS software [26]was applied to each scene to obtain the cloud mask and surface reflectance.In situ measurements at the six AmeriFlux sites were used to validate Landsat SSNR retrievals.Measurements of flux vari-ables are available every 30min.The measurement closest to the Landsat overpass time was chosen to validate instantaneous SSNR.The integrated value on the overpass day was used to validate daily SSNR.For WV1and WV2,the concentration of water vapor is needed to perform water vapor correction or choose suitable regression coefficients from the LUT.The daily North American Regional Reanalysis (NARR)data of total precipitable water produced by National Centers for En-vironmental Prediction (NCEP)were used in this study [32].For each method of handling water vapor,the clear-sky and cloudy-sky models were constructed separately.When the cloud mask was available,a model was chosen according to whether cloud was present.We also generated regression coefficients for all-sky conditions.When the cloud mask was unavailable,the all-sky model was used.Fig.1compares the uncertainties of the regression models under various sky conditions.All models have increased errors with an increase in SZA.However,for the cloudy-sky cases,the change of relative error with SZA is very small.When SZA is small,the relative RMSE (root mean square relative error)of the clear-sky model is much smaller than that of the cloudy-sky model.This feature is expected because surface information is limited when cloud is present.An increase in SZA creates longer atmospheric scattering paths,which lead to larger errors in the clear-sky model.When SZA is greater than 65◦,the clear-sky model produces an even larger error than the cloud-sky pared with the clear-sky or cloudy-sky model,the all-sky model has a much larger error.When the cloud mask is available,it is better to use the separate model of clear-sky or cloudy-sky instead of the mixed all-sky model.Fig.2shows the predictability of the clear-sky models with various methods of treating water vapor.For all models,un-certainties increase with SZA.One generic group of regression coefficients for all levels of water vapor (WV3)producestheFig.2.Model predictability in terms of relative RMSE for clear-sky models with various methods to treat the atmospheric water vapor.Results from WV2at three concentrations (0.5,2.0,and 6.0g/cm 2)of water vapor and WV3are shown here.TABLE IIS UMMARY OF V ALIDATION R ESULTS OF I NSTANTANEOUS AND D AILY SSNR.RMSE AND B IAS A RE IN THE U NIT OF W/m 2.T HE N UMBERS IN P ARENTHESES A RE R ELATIVE RMSE (R OOT M EAN S QUARE R ELATIVEE RROR )OR R ELATIVE B IAS (M EAN OF R ELATIVE D IFFERENCE)largest error.When water vapor concentration is known (WV2),the models have similar but much smaller RMSE values,and RMSE slightly increases as the concentration of water vapor increases.The validation results of instantaneous and daily SSNR retrievals are given in Table II and Fig.3.A total of 382pixels from year 2003to 2005covering the six AmeriFlux sites were extracted from the downloaded Landsat images.Instantaneous SSNR retrievals from the method using water vapor as additional dimension of LUT (WV2)have an RMSE of 77.5W/m 2(Fig.3).The majority of retrieved SSNR results are close to the 1:1line.Retrievals with large differences exist for both clear-sky and cloudy-sky conditions.One reason is that clear pixels on Landsat images may be blocked by a cloud,and vice versa,because of the relative location of cloud,sun and sensor in space (Fig.4).The RMSE of retrieving daily SSNR is 36.1W/m 2.The relative RMSE of daily retrievals (21.5%)is slightly larger than that of instantaneous SSNR (16.2%).The daily algorithm assumes the stability of atmospheric conditions.However,clear pixels are not always sunny and cloudy pixels are not always overcast during an entire day.This also explains why large overestimation exists for some clear pixels,and large underestimation exists for some cloudy pixels.With regard to the different methods of treating water vapor,WV1and WV2,which rely on the external information of water vapor,have smaller RMSE (Table II).The generic LUT for all levels of water vapor (WV3)produces an RMSE as large as 101.4W/m 2for instantaneous SSNR.In terms of daily SSNR,the results of WV3are similar to those from the other two methods.We compared the hybrid method with the albedo-based method for the clear-sky cases (Table III).Two numbers of transmittance were tested in the albedo-based method.The value of 0.7from [23]leads to a large underestimation of SSNR (−20.4%)in our test.We then increase transmittance to 0.75,which represents a very clear atmosphere [23].This mitigates the problem of underestimation,but the accuracy of the albedo462IEEE GEOSCIENCE AND REMOTE SENSING LETTERS,VOL.11,NO.2,FEBRUARY2014Fig. parison between instantaneous and daily SSNR retrievals (in W/m 2)from WV2(using water vapor as an additional dimension of LUT)and in situ measurements at six AmeriFlux sites.Numbers in parentheses are counts ofobservations.Fig.4.Illustration of view geometry among sun,cloud and sensor,which may cause large errors in retrieving SSNR for clear pixels (a)and cloudy pixels (b)on the Landsat images.TABLE IIIC OMPARISON B ETWEEN THE H YBRID M ETHOD (WV2)AND THE A LBEDO -B ASED M ETHOD FOR E STIMATING I NSTANTANEOUSSSNR U NDER THE C LEAR -S KY CONDITIONSbased method is still worse than that of the hybrid method,in terms of both RMSE and bias.The mapping ability of the presented method is demonstrated in Fig.5.Maps of instantaneous and daily SSNR were gen-erated from one Landsat 5TM scene.The SSNR maps agree well with the color composite image.The dark targets (water,dense vegetation)have larger SSNR values due to smallalbedo,Fig.5.Color composite (Band 3,2,1)of the Landsat 5/TM scene (path 25,row28)acquired on 08/22/2005and the derived maps of instantaneous and daily SSNR (W/m 2).Fig. 6.Spectral response functions of Landsat5/TM reflective bands (Bands 1–5and 7)and downward solar radiation at two concentrations of atmospheric water vapor (0.5and 6.0g/cm 2).whereas the cloudy pixels show smaller SSNR values because of the small amount of incident solar radiation.IV .D ISCUSSIONTo map high-resolution SSNR from Landsat data,this letter modifies the hybrid method proposed by Kim and Liang [7]by directly linking SSNR to Landsat TOA spectral reflectance.The method is extended further to estimate daily SSNR by assuming stable atmospheric conditions within the daytime.Validation re-sults show that the presented method can estimate instantaneous and daily SSNR accurately.RMSE of instantaneous SSNR is 77.5W/m 2,smaller than the error Kim and Liang obtained from MODIS 1km data (93.8W/m 2)[7].RMSE of daily-integrated SSNR in [7]is 3.5MJ/m 2,equivalent to daily mean SSNR of 41.0W/m 2,larger than our error (36.1W/m 2).This improvement can be attributed partially to the finer resolution of the Landsat data,which provides a better match to field measurements.Atmospheric water vapor affects SSNR by regulating the total amount and spectral distribution of shortwave radiation.Water vapor information is needed for accurately estimating SSNR.This letter evaluates three methods of treating water vapor.The inclusion of an external source of water vapor generally produces higher accuracy.The WV3method,which employs a generic LUT to estimate SSNR without the input of water vapor,has the largest error.This result may occur because the six Landsat bands are all in the atmospheric window and carry little information about water vapor (Fig.6).At the Landsat scale,topography is an important factor affecting SSNR.The effects of elevation are corrected using the empirical method proposed by [7].In addition to elevation,slope and azimuth of rugged terrain greatly affect SSNR by changing incoming radiation and surface albedo [33].The incoming radiation changes not only because of the change of incident angle but also due to the variation of diffuse and terrainWANG et al.:MAPPING HIGH-RESOLUTION SURFACE SHORTWAVE NET RADIATION FROM LANDSAT DATA463irradiance[34].Such effects are not well handled by the pre-sented hybrid method.On the contrary,albedo-based methods are able to take the variation of slope and azimuth into account, with the parameterization of incoming radiation[35],[36]. The mismatch between clouds observed from the ground and clouds on a Landsat image(as illustrated in Fig.4)is another major source of error in retrieving SSNR at a30m resolution. The presented method will treat pixels in a cloud shadow as either a dark surface(in clear-sky models)or a thin cloud(in cloudy-sky models).SSNR will be overestimated in either case. 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