Estimation Of The Land Surface Temperature Of Missing Pixels In MODIS LST Data Considering The Effect Of Solar-Cloud-Satellite Geometry

Land surface temperature(LST)is a key variable determined by the land surfaceatmosphere interactions and the energy fluxes between the atmosphere and ground.It is widely used in a variety of studies including climate change,hydrological cycle,vegetation monitoring,and ecosystem assessment.The LST data products from the Moderate Resolution Imaging Spectroradiometer(MODIS)onboard the Terra and Aqua satellites have become one of the most commonly used LST products due to their high spatial and temporal resolutions.However,the MODIS LST products contain a large number of missing data as a result of cloud contamination and high aerosol content.To recover the missing values in the MODIS LST data,many interpolation methods have been developed.Those methods can be primarily classified into three categories: spatiotemporal interpolation based methods,exogenous satellite data based methods and surface energy balance based methods.The category I methods is fast and simple,without the need for other auxiliary data,but the result obtained is only for the clear-sky conditions,without considering the effect of clouds on the LST.The category II methods resort to exogenous satellite data.As the passive microwave data are less interfered by the atmosphere conditions,it is frequently used to retrieve the cloud affected LST values.The category III methods is based on the surface energy balance equation and estimates the LST depending on numerous environmental and atmospheric parameters.This type of method has clear physical meaning,but is has not widely used at present application due to the difficulties in obtaining these parameters.At the same time,it should be noted that the cloudy pixels are identified by satellite remote sensing as a projection of the corresponding cloud from observing direction,rather than an orthographic projection on the ground.The orthogonally projected locations and the cloud projection of the cloud will have large departure if the observing and the solar illumination angles are relatively large.Thus considering the effect of the Solar-Cloud-Satellite geometry(SCSG)effects,each LST image influenced by cloud can be divided into four regions: Region A(clear-sky region),Region B(illuminated surface but with unknown LST),Region C(cloud shadow region with unknown LST)and Region D(cloud shadow region with known LST).Regions B and C are both recognized as missing data by the currently MODIS LST inversion algorithms.Considering the effects of SCSG,we should distinguish Region B from Region C because the former is actually under clear sky condition.This study uses a clear-sky interpolation method to estimate the missing LST values in Region B,and develops a cloudy-sky method for interpolating in Region C.Region D with known LST,however,is actually the region covered by cloud,and could provide cloud-affected instances for predicting the missing LST values in Region C covered by cloud.A clear-sky interpolation method combining an empirical orthogonal function method and a Bayesian data fusion method has been developed.The cloudy-sky interpolation method is based on the clear-sky method to initially estimate theoretical clear-sky LSTs,and then obtains cloudy sky LSTs by taking into account the cloud effects using the information from Region D.The process employs surface energy balance as a theoretical basis and applies the Multivariate Adaptive Regression Spline function with a variety of inputs including theoretical clear-sky LST time series and multi-source data(such as surface shortwave net radiation,DEM,NDVI,albedo,and others.).The performance was assessed from two aspects.One is for the verification of the clear-sky method by fabricating data voids on the Qinghai-Tibet Plateau(QTP)and comparing the interpolated results against the real values.The other is for the verification of cloudy-sky method,consisting of evaluating the interpolated values against left-out Region D data and against in suit observations collected from some past field campaigns.The experimental results show that the proposed approach is effective to estimate large-area missing LST data and can achieve favorable accuracy.The clear-sky interpolation accuracy is superior to the previous Yu method Harmonic Analysis of Time Series(HANTS)and the traditional geostatistical interpolation methods.In the experiment of the clear-sky condition,the interpolation accuracies of nighttime images are higher than those of the daytime images.The average absolute error(MAE)of night images is between 0.91 and 1.42 ?,the root mean square error(RMSE)between 1.19 and 1.92 ?,and the spatial correlation(SR)between 0.93 and 0.94.The MAE of the daytime images is between 1.43 and 2.78,the RMSE between 1.97 and 3.64 ° C,and the SR 0.90.In the experiments of the cloudy-sky condition,the SR between the estimates and the true data from Region D is between 0.71 and 0.77,MAE between 2.84 and 4.66 ° C,and RMSE between 3.59 and 5.88.In order to assess the interpolation accuracy,we should exclude the inherent biases existing in the MODIS LST data.We first evaluated the performance of MODIS LST data(Regions A and D)on the study area using the observations of a whole year of 2004.The results show there are very similar spatial patterns between MODIS LST and the measured data,with an SR of up to 0.95.There also exists apparent discrepancies,with an RMSE of 5.08 ? and a MAE of 3.85 ?.They are strongly related to heterogeneous land surfaces and complex terrains on the QTP,and the effects of mismatching scales between satellite and field observations.The developed cloudy-sky method yields favorable estimates with a SR of 0.94,a MAE of 3.89 ?,and a RMSE of 4.77 ? against in-situ observations.In view of the inherent biases in the MODIS LST data,the performance of our method is quite good and has been well demonstrated for its effectiveness in estimating the LST under the cloud.