Angular Anisotropy of Land Surface Temperature

1

Angular Anisotropy of Land Surface Temperature

Konstantin Y. Vinnikov1et al.

Abstract

Angular anisotropy of land surface temperature (LST) is evaluated using one full year simultaneous observations of two American geostationary satellites GOES-EAST and GOES-WEST at locations of five Surface Radiation (SURFRAD) stations. Technique is developed to convert directionally observed LST into hemispherical integrated temperature that can be used in land surface energy balance equations. Anisotropy model consists ofisotropic kernel, emissivity kernel (land surface emissivity dependence on viewing angle), and solar kernel (effect of directional inhomogeneity of solar heating). Application of this model decreases differences of LST observed from two satellites and between the satellites and SURFRAD stations observed LST.

(Key words: Land surface temperature, LST, Remote sensing, Angular anisotropy, Angular dependence, Land surface skin temperature)

Introduction

There are three main obstacles forscientific and practical use of data of global scale multi-year satellite monitoring of land surface temperature (LST).

• Diurnal cycle problem. Time adjustment is very difficult for observation of polar orbiters but not for geostationary satellites. Simple solution of this problem is - climatology of diurnal/seasonal variations obtained using observation of geostationary satellites can be used for time adjustment LST observation of polar orbiters.
• Cloudiness problem. An increasing of spatial resolution of satellite radiometers decreases cloud contamination of LST observed data, improves spatial coverage, and permits to interpret satellite observed LST as new meteorological variable – clear sky LST.
• Angular anisotropy problem. It is obvious that at each specific location, at each specific time, angular dependence of LST on viewing geometry and sun position is absolutely unique. Nevertheless, we expect that there is a lot of common in all these angular dependences, general empirical 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 angular anisotropy of land surface temperature[REFS] It is found that variations of observed LSTdepending on radiometer viewing angle, and on position of sun at the time of observation may reach a few degrees K. Experimental data showed that bare soil emissivity is decreasing with increasing of viewing zenith angle but there is no any angular dependence of emissivity of grass [Sobrino and Cuenca, 1999, 2004]. The same should be true for dense forest. At the nighttime, when land surface and green vegetation temperatures are in equilibrium and temperature field is relatively homogeneous,angular anisotropy of LST should dependon fractional amount of vegetation, which itself depends on viewing angle. At the daytime, incoming solar radiation is a reason of spatial inhomogeneity and angular anisotropy of land surface temperature and it produces an additional to the discussed above directional dependence of LST on viewing zenith angle, its relative azimuth, and solar zenith angle.

The main goal of this paper is to introduce simple statistical modelofangular anisotropy of LSTand estimate its parameters using available simultaneous land based and satellite, GOES-EAST and GOES-WEST, observations at locations of SURFRAD stations. The model should be usedin the algorithm for angular correction of satellite retrieved clear sky LST. The climatological approach is applied here. The main requirements to the angular correction algorithm is to convert satellite observed directional LST, T(z,zs,az), that depends on satellite viewing angle z, sun zenith angle zs, and relative sun-satellite azimuth az into the scalar (direction independent), unbiased value of LST, that can be used in land surface energy balance computation.

1. Data

Data used here consist of full year 2001 time seriesof LST computed from observed upward (Iu)and downward (Id) wide band hemispheric infrared fluxes at five SURFRAD stations listed in Table 1, and collocated hourly time series of LST retrieved at clear 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]. LST at the SURFRAD stations is computed from traditional equation

LSTS = {[Iu−(1−δ)Id]/(σ·δ)}0.25, (1)

where σ is Stefan-Boltzmann constant and δ - surface emissivity. Seasonally dependent 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 (MOD11) [Ming et al., 2010]. The baseline fit method [Wang et al., 2005; Seemann et al., 2008], based on a conceptual model developed from laboratory measurements of surface emissivity, is applied to fill in the spectral gaps between the six emissivity wavelengths available in MOD11. The statistical algorithm that has been applied to eliminate cloud contaminated data uses both satellite and SURFRAD observations[Ming et al., 2010].

Five stations in Table 1 are listed in order of increasing of smoothness and homogeneity of the land surface topography and vegetation cover. Such ranking has been accomplished using photos of stations vicinity available at the SURFRAD web site [

Small, about 15 minute, difference in observation time of two satellites has been taken into account using analytical approximations of seasonal and diurnal variations of LST at each of station as it has been demonstrated in [Vinnikov et. al., 2008; 2011].

1.1.Time adjustment

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

(2)

Above,t is time in days, N=365.25 days, akn – empirical least squares coefficients of approximation.

We then found all pairs of observed LST of satellites GOES-8 and GOES-10 with times t8 and t10of observations |t8-t10|≤15 minutes. 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)- is not changing during 15-minute time interval, , looks to be 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 angular dependence of satellite observed LST can be expressed by the next simple equation:

T(z,zs,az)/T0=1+A·φ(z)+D·ψ(z,zs≤90º,az),(4)

where: T0=T(z=0,zs) is LST in the nadir direction at z=0; one, the first term in the right side of (4), has sense of basic “isotropic kernel” that should be corrected by two other kernels;φ(z) is the “emissivitykernel”, related to angular anisotropy ofinfrared land surface emissivity;ψ(z,zs≤90º,az)is the “solar kernel”, related to spatial inhomogeneity of solar heating of different parts of land surface and its cover,ψ(z,zs≥90º,az)≡0at the nighttime; A and D are the coefficients, amplitudes, that should be estimated from observations. These coefficients depend on land topography and land cover structure. Such a model follows to traditional structure of the BRDF semi-empirical models based on linear combination of “kernels” as it is generalized by David L.B. Jupp in “A compendium of kernel & other (semi-)empirical BRDF Models,” available from

Analytical expressionsfor the kernelsφ(z)and ψ(z,zs≤90º,az) are developed using available simultaneous clear sky LST observations of two satellites, GOES-8 and GOES-10,atlocations of five representative SURFRAD stationduring 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 are used as one data set. Nighttime observations, z>90º only, have been used to find the best expression for “infrared kernel” φ(z) and to estimate A value. Using LST TE and TW, observed by GOES-E and GOES-Wsatellites,respectively, we have to assume that one of them, arbitrary chosen, is unbiased and the other one has constant bias in the observed LST. Let us assume that LST observed by GOES-W,TW, is biased compared to GOES-E and TW value should be substituted by TW+Bw, were BW is an unknown constant bias, to be determined. Using expression (1) for nighttime observations z>90º we can write:

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

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

TE-TW≈BW+A*[TW+BW]·φ(ZE)-TE·φ(ZW). (6)

Viewing angles ZE and ZW are given in Table 1. The equation (6) has been written for each pair of simultaneous nighttime observations of the satellites at locations of five SURFRAD stations. Total number of equations is equal to N=1619. Ordinary least squares technique is applied. Not more than three iterations are needed to resolve rather weak nonlinearity in (6). The best results have been obtained with the next simple approximations:

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

2.2.Solar kernel

Following to the same procedure as for infrared kernel, we selected the next simple analytical expression to approximate solar kernel for zs≤90°:

ψ(z,zs,az)=sin(z)·cos(zs)·sin(zs)·cos(zs-z)·cos(az).(8)

In this approximation, cos(zs)represents dependence of incoming solar radiation on solar zenith angle;sin(zs)·cos(az) represents effect of solar shadows; cos(zs-z)·represents LST hot spot effect at z⟶zs and az⟶0; sin(z) is needed to satisfy definitionrequirementψ(z=0)=0. The analogues to the equations (5) and (6) are:

TE·/[1+A·φ(ZE)+D·ψ(ZE,ZS,AZE)]≈[TW+BW]/[1+A·φ(ZW))+D·ψ(ZW,ZS,AZW)], (9)

TE·[1+A·φ(ZW)]-(TW+BW)·[1+A·φ(ZE)]≈D·[(TW+BW)·ψ(ZE,ZS,AZE)-TE·ψ(ZW,ZS,AZW)]. (10)

ZS here is zenith angle of sun at station location at the time of observation; AZE and AZW are relative satellite-sun azimuth angles. Assuming A and BWare known, equation (10), written for each pair of daytime simultaneous observations, has been used to obtain the least squares estimate ofamplitudeD:

D=0.0140K-1. (11)

The function T(z,zs,az)/T0for different sun zenith angles is shown in Figure 1.

2.3.Algorithm for angular correction of satellite observed LST.

Satellite observed angular dependent LSTshould be converted into the effective temperature,θ,which can be used in land surface energy balance computations. Let us define such land surface temperatureas the next:

(12)

T(z,zs,az) in (12) can be obtained from the observed T(Z,ZS,AZ) at satellite zenith viewing angle Z, solar zenith angle ZS, and relative azimuth AZ, using model (4).

T(z,zs,az)=T(Z,ZS,AZ)·[1+A·φ(z)+D·ψ(z,zs,az)]/[1+A·φ(Z)+D·ψ(Z,ZS,AZ)].(13)

(14)

(15)

(16)

C=0.9954.(17)

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

θE=C·TE/[1+A·φ(ZE)+D·ψ(ZE,ZS,AZE)]. (18)

θW=C·[TW+BW]/[1+A·φ(ZW)+D·ψ(ZW,ZS,AZW)]. (19)

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

Statistics of errors

Decreasing of mean and root mean squared (RMS) differences between GOES-10 (EAST) and GOES-8 (WEST) satellite observed LST is used as measure of efficiency of applied data adjustment. The estimates are shown in Table 1. Raw data at location of SURFRAD stations have mean differences of (LST*E-LST*W) in the range 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 noticeable the range of mean (LSTE-LSTW) differences to 1.2°C and RMS differences to values between 1.3 to 1.9 K. Angular adjustment that includes mean bias correction improves errors statistics much more. Mean differences for SURFRAD stations are in the range ±0.5 K and RMS differences are in the range from 1.2 to 1.4 K.

As a result of angular adjustment, atall five stations in Table 2,we obtained significant decreasing of systematic error in differences between LST observed by GOES-E and GOES-W. At the first three stations we obtained very significant decreasing of random error in this difference. The last two stations with very flat topography and homogeneous vegetation cover there is only insignificant decreasing of this random error. Let us compare angular adjusted satellite observed θE and θW with LSTS observed at SURFRAD stations. LSTS data is the only available analog to the LST ground truth for validation of satellite observed LST. The results are presented in Table 2. We should permit for LSTS to be noticeable biased because of a small footprint size of radiometer for measuring upward infraredfluxIu compared to much larger size of satellite pixel. The same reason may result in larger RMS difference (θE-LSTS) or (θW-LSTS) in Table 2 compared to the difference (θE-θW) in Table 1. An averaging of two LST angular adjusted observations obtained for the same pixel at the same time from two satellites GOES-E and GOES-W additionally decreases random error of observation. This can be seen in the Table 2. The largest, -1.5°C, bias of SURFRAD LSTS data compared to satellite observed is at DESERT Rock, NV stationmeans that observational plot at this station is not well representative to surrounding area, or used emissivity value is underestimated, or there is an unknown instrumental problem.

For illustration, statistical distribution of difference of LST observed from GOES-E and GOES-W at location of the first of our stations, Desert Rock, NV, presented in the upper row of panels in Figure 2. The first panel displays an initial distribution of differences raw (LST*) data which suffers 15-minute shift in time between observations of two satellites. After time shift adjustment, this distribution is getting noticeable taller and narrower (second panel). Angular correction makes this statistical distribution significantly taller and significantly narrower (third panel). This direction of evolution of the statistical distribution of proves effectiveness of the proposed angular adjustment technique. In the panel 3 distribution, 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 observation of two satellites, θ= (θE+θW)/2. The statistical distribution of difference of θ and LSTSis shown in the top-right panel of Figure 2. LSTShere is land surface temperature obtained from observed infrared fluxes at SURFRAD station. This distribution is even sharper compared to others and has smaller standard deviation equal to 1.0°C. If to use the estimate of RMS(θE-θW) = 1.3 K given in Table 1 and known standard error of LSTS which is equal to 0.6 K at Desert Rock station [Vinnikov et al., 2008]. These estimates are consistent with an assumption that random errors in the angular adjusted satellite observed and in the SURFRAD station observed LST are not just random but also statistically independent.

Systematic seasonal and diurnal variation of debiased difference (LSTE-LSTW-BW) between GOES-E and GOES-W observed LST at location of the same station, Desert Rock, NV, is shown in the bottom-first-left panel in Figure 2. This difference is approximated here with expression (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 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-LSTS]. This pattern proves an efficiency of the proposed angular adjustment technique.

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

1. Concluding Remarks

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

Surface observedLSTSatSURFRAD stationsare usedhere for model validation, not for model development. By definition (1), values of LSTS does not need angular adjustment but may be biased if computed with error in δ, broad band emissivity value. We found that LSTS data is not very useful in model developing - because of small field of view of infrared Downwelling Pyrgeometer at SURFRAD station cannot properly represent much large footprint of satellite radiometer. Really, only Desert Rock, NV observed LSTS is found to be significantly biased, 1.5°C warmer (Table 2), compared to satellite observed angular corrected θ=(θE+ θW)/2. Biases at other stations do not exceed ±0.5°C. Nevertheless we have two evidences that we are moving in proper direction. The first of them is significant decrease systematic and RMS differences between observed LSTE and LSTWin result of proposed angular adjustment shown in Table 2. This evidence has some value if this decreasing is really significant. Some decreasing 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 angular adjusted satellite observed(θE, θW, θ) and independently observed LSTS shown in Table2.

The weakest part of this research is that all five SURFRAD stations are in the very limited range of satellite viewing angles, from 43° to 66°. All observations at the same location have constant satellite viewing angles ZEandZW.Because of this limitation we are not able toproperly estimate emissivity kernel coefficients Afor each of stations. For stations with ZE≈ZW this is just impossible.

Other limitation is that there isnoobservation at small sun zenith angles, zs<10.75°, in our data set. Nevertheless, we have an adventure of using data for full year so all seasonal and diurnal variations of sun zenith and azimuth angles and evolution of land surface cover are well represented.