1

Angular Anisotropy of Land Surface Temperature

Konstantin Y. Vinnikov1, Yunyue Yu2, Mitchell D. Goldberg3, Dan Tarpley4, Peter Romanov3, Istvan Laszlo2, Ming Chen5

1Departament of Atmospheric and Oceanic Science, University of Maryland, College Park, MD, USA

2Center for Satellite Applications and Research/NESDIS/NOAA, College Park, MD, USA

3Joint Polar Satellite Systems Office,NESDIS/NOAA, College Park, MD, USA

4Short and Associates, Camp Springs, MD, USA

5IMSG at NESDIS/NOAA, College Park, MD, USA

Corresponding author: Konstantin Vinnikov , 301-405-5382

Abstract

Angular anisotropy of Land Surface Temperature (LST) is evaluated using one full year of simultaneous observation of twoGeostationary Operational Environment Satellites, GOES-EAST and GOES-WEST, at locations of five Surface Radiation (SURFRAD) stations. A technique is developed to convert directionally observed LST into direction-independent equivalent physical temperature that can be used in land surface energy balance equations. The anisotropy model consists of anisotropic kernel, an emissivity kernel (LST dependence on viewing angle), and a solar kernel (effect of directional inhomogeneity of observed temperature). Application of this model reduces differences of LST observed from two satellites and between the satellites and surface ground truth - SURFRAD stations observed LST. Proposed techniques of angular adjustment and temporal interpolation of satellite observed LST open way for blending together historical, current, and future observations of many geostationary and polar orbiters into homogeneous multi-decadal data set for climate change research.

Introduction

There are three main obstacles forscientific and practical useof global-scale multi-year satellite monitoring of Land Surface Temperature (LST) data:

  • Diurnal cycle problem. Because of the observation time variation,temporal adjustment is usually required for satellite observed LST. The simple solution of this problem is to use climatology of LST diurnal/seasonal variations from geostationary satellites to interpolate or extrapolate in time satellite observed LST.
  • Cloudiness problem. An increasein spatial resolution of satellite radiometers decreases cloud contamination of LST observed data, improves spatial coverage, and permits interpretation of satellite observed LST as anew meteorological variable – clear sky LST.
  • Angular anisotropy problem. It is obvious that at each specific location, and at each specific time, the dependence of LST on sun position and viewing geometry is absolutely unique. Nevertheless, we expect that these angular dependencies have only a few important causes. Auniversalempirical model of angular anisotropy of LST can be proposed and parameters of such a model can be statistically evaluated using available satellite observations. Angular correction of satellite retrieved LST must be applied before this data can be assimilated into weather prediction models or used in climate change research.

There are numerousmodeling, experimental, and case study type investigationsof the angular anisotropy of the land surface temperaturewhich report LSTvariations of up to 2 – 4 degrees Kdepending on the radiometer viewing angle and on the position of the sun at the time of observation [Minnis and Khaiyer, 2000; Sobrino and Cuenca, 1999; Cuenca and Sobrino, 2004; Lagouarde et al., 1995; Pinheiro et al., 2006]. Experimental data showed that the bare soil emissivity decreases with increasing viewing zenith angle,but there was no angular dependence forthe apparent emissivity of grass [Sobrino and Cuenca, 1999;2004]. The same should be true forthe emissivity of dense forest. At nighttime, when land surface, surface air,and green vegetation temperatures are in equilibrium and the temperature field is relatively homogeneous,angular anisotropy of LST should dependon the fractional amount of vegetation within the instrument field of view, which itself depends on the viewing angle. During daytime, incoming solar radiation, inhomogeneity of evaporative flux and shadowingproduce an additional dependence of LST on the viewing zenith angle, its relative azimuth, and solar zenith angle.

The main goal of this paper is to introduce a simple statistical modelofthe angular anisotropy of LSTand estimate its parameters using available simultaneous GOES-EAST and GOES-WEST, observations collocated at SURFRAD stations. The model should be usedin an algorithm for angular correction of satellite retrieved clear sky LST data. A climatological approach is applied here. The main requirement of the angular correction algorithm is to convert satellite observed directional LST, T(γ,ξ,β) that depends on the satellite zenith viewing angle γ, sun zenith angle ξ, and relative sun-satellite azimuth β, into adirection independentequivalent physical temperature that can be used in land surface energy balance computation.

  1. Data

Data used here consists of full year (2001)time seriesof “ground truth” LST computed from observed upward (Fu)and downward (Fd) wide band hemispheric infrared fluxes at five SURFRAD stations listed in Table 1, and collocated hourly time series of LST retrieved underclear sky conditions from observations of two geostationary satellites, GOES-8 (GOES-EAST, 75°W) and GOES-10 (GOES-WEST, 135°W). Satellite observed LST has been retrieved using a split window algorithm by Ulivieri and Cannizzaro [1985] as modified by Yu et al. [2009]. Random and systematic errors of this data are assessed and discussed in [Vinnikov et al., 2008; Yu et al., 2012]. LST atSURFRAD stations is computed from the traditional equation

TS = {[Fu−(1−ε)Fd]/(σ·ε)}0.25, (1)

where σ is Stefan-Boltzmann constant and ε - surface emissivity. Monthly mean values of spectral and broad-band land surface emissivity at station locations is estimated using data from the Moderate Resolution Imaging Spectroradiometer (MODIS) operational land surface emissivity product. The baseline fit method, based on a conceptual model developed from laboratory measurements of surface emissivity, is applied to fill in the spectral gaps between available emissivity wavelengths [Seemann et al., 2008]. Surface broadband emissivity at each station is obtained by the regression of the collocated emissivity values at three spectral bands[Wang et al., 2005; Ogawa et al., 2003]. No information is available on the accuracy of pixel-to-site emissivity estimates. Yet the maximum regression emissivity error is about 0.006 regardless of the surface types[Wang et al., 2005]. Athresholdcloud-detection algorithm has been applied to determine whether the surface scene is under strict clear-sky condition. The most important aspect of this algorithm is the use of both satellite and SURFRAD observations. To determine clear-sky background, the maximum brightness temperature of GOES Channel 4 during the previous 10 days iscomposited; andthe standard deviation of downwelling sky irradiance measured during the past 15 minutes at aSURFRAD site is checked. Eight parameters are chosen to characterize the essential differences of a cloudy pixel from a clear one. These parameters enable us to identify the possible spectral, spatial and temporal singularities of a target pixel due to cloud contamination.

Fifteen minute difference in the observation time of the two satellites has been taken into account using analytical approximations of seasonal and diurnal variations of LST as has been demonstrated in [Vinnikov etal, 2008; 2011].

1.1.Time adjustment

Seasonal and diurnal variations (time-dependent expected value) in time series T(t) of observed GOES-8 LST at locations of SURFRAD stations have been approximated as the product of two first Fourier harmonics of the annual cycle (n=-2,-1,0,1,2) and two first harmonics of the diurnal cycle (k=-2,-1,0,1,2).

(2)

Above,t is time in days, N=365.25 is the length of year in days, andaknare empirical least squares coefficients of approximation. Detailed description of such approach to approximation of seasonal/diurnal variations in meteorological variables is given in [Vinnikov et al., 2004]. Then, all the pairs of observed LST of satellites GOES-8 and GOES-10 with times t8 and t10of observations |t8-t10|≤15 minutes have been found. Interpolated valueshave been computed as:

(3)

Such pairs of observed T10(t10) GOES-10 LST and interpolated GOES-8 LST are considered to be simultaneous. The assumption that LST anomaly T(t8)-does not change during a 15-minute time interval, for |t8-t10|≈15 min,appears reasonable because this time interval is small compared to ~3 day decay scale of LST temporal variability [Vinnikov et al., 2008; 2011].

  1. Three-kernel approach

The proposed statistical model to approximate the angular dependence of satellite observed LST can be expressed by the following simple equation:

T(γ,ξ,β)/T0=1+A·φ(γ)+D·ψ(γ,ξ≤90º,β),(4)

where: T0=T(γ=0,ξ) is LST in the nadir direction at γ=0. The first term, 1,on the right side of (4), has sense of basic“isotropic kernel” that should be corrected by two other kernels;φ(γ) is the “emissivitykernel”, related to observation angle anisotropy;ψ(γ,ξ≤90º,β)is the “solar kernel”, related to spatial inhomogeneity of surface heating and shadowing of different parts of land surface and its cover,ψ(γ,ξ≥90º,β)≡0atnighttime; A and D are the coefficientsthat should be estimated from observations. These coefficients depend on land topography and land cover structure. Such a model followsa traditional structure of the BRDF semi-empirical models based on a linear combination of “kernels” as generalized by Jupp [2000].

Analytical expressionsfor the kernelsφ(γ)and ψ(γ,ξ≤90º,β)have been developed using described abovesynchronous clear sky LST observations of two satellites, GOES-8 and GOES-10,atthe location of five satellite pixel representative SURFRAD stationsduring one full year 2001.

2.1.Emissivity kernel

At this stage,LST observations of GOES-8 and GOES-10 satellites at locations of five SURFRAD stations were used as one data set. Nighttime observations, ξ90º only, have been used to find the best expression for the “emissivity kernel” φ(γ) and to estimate A value. Using LST estimates derived from GOES-EAST(TE) and GOES-WEST (TW),it is assumedthat one of them, chosen arbitrary, is unbiased and the other one has a constant bias in the observed LST. Assuming that LST observed by GOES-WEST,TW, is biased compared to GOES-EASTthen the TW value should be substituted by TW+BW, where BW is an unknown constant bias, to be determined. Using expression (4) for nighttime observationsξ90º we can write:

T0≈TE/[1+A·φ(γE)]≈[TW+BW]/ [1+A·φ(γW)]. (5)

This equation in the following form can be used for testing different approximations of φ(γ) and least square estimation of the unknowns BW and A:

TE-TW≈BW+A[TW+BW]·φ(γE)-TE·φ(γW).(6)

The satellite zenith angles γE and γW are given in Table 1. The angular sampling is very limited, only two zenith angles for site. One could fit many functions that go these two angles, yet have different shapes. In the assumption that commonuniversal shape of φ(γ) exists and can be found,equation (6) has been written for each pair of simultaneous nighttime observations of the satellites at locations of all five SURFRAD stations. Total number of equations is equal to 1619. Ordinary least squares technique has been applied. Less than three iterations are needed to resolve the rather weak nonlinearity in (6). The best results have been obtained usingthe followinganalytical expression for φ(γ) andBw and Avalues

φ(γ)=1-cos(γ), BW=0.57 K, A=-0.0138K-1.(7)

2.2.Solar kernel

Following the same procedure as for the emissivity kernel, the following simple analytical expression to approximate the solar kernel for ξ≤90° is recommended:

ψ(γ,ξ,β)=sin(γ)·cos(ξ)·sin(ξ)·cos(ξ-γ)·cos(β).(8)

In this approximation, cos(ξ)represents dependence of incoming solar radiation on solar zenith angle;sin(ξ)·cos(β) represents the effect of solar shadows; cos(ξ-γ)·represents the LST hot spot effect at γ⟶ξand β⟶0; sin(γ) is needed to satisfy thedefinitionrequirementψ(γ=0)=0. Nevertheless, the expressions (7) and (8) are pure empirical. The analogues to equations (5) and (6) which are for nighttime, for daytime observationsit can be written:

(9)

(10)

Assuming A and BWare known, equation (10), written for each pair of daytime simultaneous observations, has been used to obtain the least squares estimate ofthe amplitudeD:

D=0.0140K-1. (11)

The function T(γ,ξ,β)/T0for different sun zenith angles is shown in Figure 1.

  1. Algorithm for angular correction of satellite observed LST.

Satellite observed angular dependent LSTshould be converted into the isotropic, direction independent, equivalent physical temperature,θ,which can be used in land surface energy balance computations. Such equivalent temperaturecan be defined by the expression:

(12)

T(γ,ξ,β) in (12) can be obtained for eachsatellite observed temperatureT*(γ*,ξ*,β*) at known viewing angle γ*, solar zenith angle ξ*, and relative azimuth β*, using model (4).

T(γ,ξ,β)=T*(γ*,ξ*,β*)·[1+A·φ(γ)+D·ψ(γ,ξ,β)]/[1+A·φ(γ*)+D·ψ(γ*,ξ*,β*)].(13)

(14)

(15)

(16)

C=0.9954.(17)

In such a way we can estimate unbiased angular corrected equivalent values ofLSTs observed by GOES-EAST and GOES-WEST satellites.

(18)

(19)

For two observations for the same location, the best estimate should be obtained by averaging observations of both satellites θ =(θE+θW)/2.

  1. Statistics of errors

The decrease of mean and root mean squared (RMS) differences between GOES-10 (EAST) and GOES-8 (WEST)observed LST is used as a measure of efficiency of the applied data adjustment. The estimates are shown in Table 1. Raw data (uncorrected LST retrievals) at location of SURFRAD stations have mean differences of (TE-TW) in the range of 2.3 K(from 0.2 to 2.5 K) and RMS differences from 1.3 to 2.2 K. Adjustment for 15-minute shift in the time of observation of these two satellites decreases noticeably the range of mean (TE-TW) differences to 1.2°C and the RMS differences to values between 1.3 to 1.9 K. Angular adjustment that includes the mean bias correction improves the error statistics further more. Mean differences for SURFRAD stations are in the range of ±0.5 K and RMS differences are in the range from 1.2 to 1.4 K.

As a result of the angular adjustment atall five stations in Table 2,we obtained a significant decrease of the systematic error in differences between LST observed by GOES-EAST and GOES-WEST. At the first three stations in the Table (Desert Rock, NV; Boulder, CO; Goodwin Creek, MS)we obtained very substantial decrease of random error in this difference. The last two stations (Fort Peck, MT; and Bondville, IL) located in the region with very flat topography and homogeneous vegetation cover exhibit only small decrease of this random error. Let us compare temporally and angular adjusted satellite observed θE and θW with TS observed at SURFRAD stations. TS data is the only available analog to the LST ground truth for validation of satellite observed LST. The results are presented in Table 2. It is expectedthat TScould be noticeablybiased because of a small footprint size of the radiometer for measuring upward infraredfluxFucompared to much larger size of the satellite pixel. This may also cause larger RMS differences(θE-TS) or (θW-TS) in Table 2than the difference (θE-θW) in Table 1. Averaging of the two LST temporally and angular adjusted observations obtained for the same pixel at the same time from two satellites GOES-EAST and GOES-WESTfurther decreases the random error of observation. This can be seen in Table 2. The largest, -1.5 K, bias of SURFRAD LSTS data compared to satelliteLST is at the DESERT Rock, NV station. Thismeans that the observational plot at Desert Rockdoes not well representthe surrounding area, or theemissivity value is underestimated, or there is an unknown instrumental problem.

For illustration, the statistical distribution of thedifference between LST observed from GOES-EAST and GOES-WESTat Desert Rock, NV, is presented in the upper row of panels in Figure 2. The first panel displays an initial distribution of differences raw (TE-TW) data, which has a 15-minute shift in time between observations of two satellites. After time shift (and constant bias) adjustment, the distribution of (TE-TW-BW) is getting noticeably taller and narrower (second panel). Angular correction makes the distribution (θE-θW) significantly taller and significantly narrower (third panel). This direction of evolution of the statistical distribution proves the effectiveness of the proposed angular adjustment technique. In the third panel a significant part of angular anisotropy is corrected and we see manifestation of residual random error of satellite retrieved LST. This random error can be decreased times by averaging observations of two satellites, θ= (θE+θW)/2. The statistical distribution of difference of θ and TSis shown in the top-right panel of Figure 2. TShere is the land surface temperature obtained from observed infrared fluxes at the SURFRAD station. This distribution has even sharper shape than the others and has a standard deviation of 1.0°C. If we use the estimate of RMS(θE-θW) = 1.3 K given in Table 1 and known standard error of TS which is 0.6 K at Desert Rock [Vinnikov et al., 2008], we conclude that these estimates are consistent with an assumption that random errors in the angular adjusted satellite LST and in the SURFRAD station observed LST are not just random but also statistically independent.

Systematic seasonal and diurnal variation of the debiased difference (TE-TW-BW) between GOES-EAST and GOES-WESTobserved LST at Desert Rock, NV, is shown in the bottom-first-left panel in Figure 2. This difference is approximated here with expression analogous to (2). The next panel presents the same difference but for angular adjusted temperatures (θE-θW). The main components of seasonal and diurnal cycles have been removed by application of the angular adjustment (18-19). The bottom-right panel displays seasonal-diurnal cycles in the difference between two satellites average of angular adjusted and SURFRAD observed temperatures [(θE+θW)/2-TS]. This pattern shows that the proposed angular adjustment technique removes much of the geometric inhomogeneity of satellite LST.

The estimates presented in Tables 1 and 2 show that the effect of the angular adjustment of satellite observed LST is very strong for first three stations and is almost insignificant for the last two. Assuming that earlier estimates of parameters A=-0.0138 K-1 and BW=0.57K, are correct, we estimated optimal values of D anisotropy coefficients for locations of five SURFRAD station. The estimates of these coefficients and error statistics are given in Table 2. It is most interesting that estimates of D coefficient depend onthe satellite pixel topography and vegetation cover smoothness. They vary from 0.0165 K-1at Desert Rock, NV to 0.0068K-1at Bondville, IL. It looks as if this parameter can be used as a measure of thermal angular anisotropy of different land surfaces. Nevertheless, using optimal local estimates of D instead of its universal value increases accuracy of angular adjusted satellite observed LST, but this improvement of accuracy is not really significant and can be ignored.

  1. Concluding Remarks

This analysis assumes that satellite retrieved LST is the real physical temperature of land surface components within the field of view of a satellite radiometer. However, currently available algorithms for LST retrieval can inadvertently modify angular dependence of LST on viewing angle. Subsequently, the empirical model (4) has to be validated using independently observed data and different retrieval algorithms, for example, other algorithms listed by Yu et al., [2009].

Surface observedTSatSURFRAD stationsare usedhere for the model validation, not for the model development. By definition (1), values of TS do not need angular adjustment but may be biased if computed with an error in ε, broadband emissivity value. We found that TS data is not very useful in model development because thesmall field of view of infrared Downwelling Pyrgeometer at SURFRAD stations cannot properly represent the much large footprint of satellite radiometers. Nevertheless, only Desert Rock, NV observed TS is found to be significantly biased, 1.5°C warmer (Table 2), compared to satellite observed LST that has been angularly corrected θ=(θE+ θW)/2. Biases at other stations do not exceed ±0.5°C. There are two pieces of evidence that we are moving in the proper direction. The first is a significant decrease systematic and RMS differences between observed TE and TWafter angular adjustment (Table 2). Some decrease is guaranteed by using equations(6) and (10) to estimate the model’s parameters. The second, more important, evidence is decreasing systematic and RMS difference between the angular adjusted satellite observed(θE, θW, θ) and “ground truth”, independently observed TS, shown in Table2.