University Of Maryland



Angular Anisotropy of Land Surface Temperature

Version 6 July, 2012. To be submitted to GRL

Abstract

Angular anisotropy of land surface temperature (LST) is evaluated using one full year of simultaneous observation of two American geostationary satellites, GOES-EAST and GOES-WEST, at locations of five Surface Radiation (SURFRAD) stations. A technique is developed to convert directionally observed LST into hemispherical integrated temperature that can be used in land surface energy balance equations. The aAnisotropy model consists of an isotropic kernel, an emissivity kernel (land surface LSTemissivity dependence on viewing angle), and a solar kernel (effect of directional inhomogeneity of observed temperaturesolar 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 for scientific and practical use of global scale multi-year satellite monitoring of land surface temperature (LST) data.

• Diurnal cycle problem. Because of the rapid time variation of LST adjustment is required for near-simultaneous satellite observations.Time adjustment is very difficult for observation of polar orbiters but not for geostationary satellites. The sSimple solution of this problem is - to use climatology of diurnal/seasonal variations obtained using observation of geostationary satellites to adjust near-simultaneous satellite observations of LST.for time adjustment LST observation of polar orbiters.

• Cloudiness problem. An increase in spatial resolution of satellite radiometers decreases cloud contamination of LST observed data, improves spatial coverage, and permits interpretation of satellite observed LST as a new meteorological variable – clear sky LST.

• Angular anisotropy problem. It is obvious that at each specific location, and at each specific time, the angular dependence of LST on viewing geometry and sun position is absolutely unique. Nevertheless, we expect that these angular dependencies have only a few important causes.there is a lot in common in all these angular dependences. A universal 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 numerous modeling, experimental, and case study type investigations of angular anisotropy of land surface temperature in which found that observed variations reached 2 – 4 degrees Kin observed LST depending on radiometer viewing angle and on position of the sun at the time of observation may reach a few degrees K [Minnis and Khaiyer, 2000; Sobrino and Cuenca, 1999; Cuenca and Sobrino, 2004; Lagouarde et al., 1995; Pinheiro et al., 2006]. Experimental data showed that bare soil emissivity is decreasesing with increase of viewing zenith angle, but there is no any angular dependence for apparent emissivity of grass [Sobrino and Cuenca, 1999; 2004]. The same should be true for emissivity of dense forest. At nighttime, when land surface and green vegetation temperatures are in equilibrium and temperature field is relatively homogeneous, angular anisotropy of LST should depend on fractional amount of vegetation, which itself depends on viewing angle. During daytime, incoming solar radiation, inhomogeneity of evaporative flux and shadowing is a cause of spatial inhomogeneity and angular anisotropy of land surface temperature and it produces an additional directional dependence of LST on viewing zenith angle, its relative azimuth, and solar zenith angle.

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

1. Data

Data used here consists of full year 2001 time series of 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 SURFRAD stations is computed from the 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. AThe statistical cloud-detection algorithm that has been applied to eliminate cloud-contaminated data uses both satellite and SURFRAD observations [Ming et al., 2010]. The five SURFRAD stations are listed in Table 1.

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

Fifteen minuteSmall, about 15 minute, differences 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. Time adjustment Kostya, do you think section 1.1 is necessary? Has it been described in other papers that could be referenced?

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).

[pic] (2)

Above, t is time in days, N=365.25 days, and 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 t10 of observations |t8-t10|≤15 minutes. Interpolated values [pic] have been computed as:

[pic] (3)

Such pairs of observed T10(t10) GOES-10 LST and interpolated [pic] GOES-8 LST are considered to be simultaneous. The assumption that LST anomaly T(t8)-[pic] is not changing during 15-minute time interval, [pic], 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).

2. Three-kernel approach

The proposed statistical model to approximate angular dependence of satellite observed LST can be expressed by the following 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. 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(z) is the “emissivity kernel”, related to observation angleangular anisotropy of infrared land surface emissivity; ψ(z,zs≤90º,az) is the “solar kernel”, related to spatial inhomogeneity of surfacesolar heating and shadowing of different parts of land surface and its cover, ψ(z,zs≥90º,az)≡0 at nighttime; A and D are the coefficients that should be estimated from observations. These coefficients depend on land topography and land cover structure. Such a model follows traditional structure of the BRDF semi-empirical models based on linear combination of “kernels” as generalized by Jupp [2000].

Analytical expressions for the kernels φ(z) and ψ(z,zs≤90º,az) are developed using available simultaneous clear sky LST observations of two satellites, GOES-8 and GOES-10, at locations of five representative SURFRAD station during one full year 2001.

1. Emissivity kernel (can we think of a better name?)

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 emissivity kernel” φ(z) and to estimate A value. Using LST TE and TW, observed by GOES-EAST and GOES-WEST satellites, 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-WEST, TW, is biased compared to GOES-EAST 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)

The satellite zenith Viewing angles ZE and ZW are given in Table 1. EThe 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 the rather weak nonlinearity in (6). Best results have been obtained using the following simple approximations:

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

2. Solar kernel

Following 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 the effect of solar shadows; cos(zs-z)·represents the LST hot spot effect at z⟶zs and az⟶0; sin(z) is needed to satisfy the definition requirement ψ(z=0)=0. The analogues to 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 BW are known, equation (10), written for each pair of daytime simultaneous observations, has been used to obtain the least squares estimate of amplitude D:

D=0.0140 K-1. (11)

The function T(z,zs,az)/T0 for different sun zenith angles is shown in Figure 1.

3. Algorithm for angular correction of satellite observed LST.

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

[pic] (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)

[pic] (14)

[pic] (15)

[pic] (16)

C=0.9954. (17)

In such a way we can estimate unbiased annular corrected effective values of LSTs 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.

4. Statistics of errors

Decrease 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 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 (LSTE-LSTW) differences to 1.2°C and the RMS differences to values between 1.3 to 1.9 K. Angular adjustment that includes mean bias correction improves error statistics much 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 angular adjustment, at all five stations in Table 2, we obtained significant decrease of systematic error in differences between LST observed by GOES-EAST and GOES-WEST. At the first three stations we obtained very significant decrease of random error in this difference. The last two stations with very flat topography and homogeneous vegetation cover have only insignificant decrease 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 expectpermit LSTS to be noticeably biased because of small footprint size of the radiometer for measuring upward infrared flux Iu compared to much larger size of the satellite pixel. This may also causeThe same reason may result in larger RMS differences (θE-LSTS) or (θW-LSTS) in Table 2 than 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-EAST and GOES-WEST 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 LST isobserved at the DESERT Rock, NV station. This means that the observational plot at Desert Rockthis station doesis not well representative theo surrounding area, or theused emissivity value is underestimated, or there is an unknown instrumental problem.

For illustration, the statistical distribution of thedifference betweenof LST observed from GOES-EAST and GOES-WEST at location of the first station, Desert Rock, NV, is presented in the upper row of panels in Figure 2. The first panel displays an initial distribution of differences raw (LST*E-LST*W) data, which has asuffers 15-minute shift in time between observations of two satellites. After time shift adjustment, this distribution of (LSTE-LSTW-BW) is getting noticeablye taller and narrower (second panel). Angular correction makes thestatistical distribution (θE-θW) significantly taller and significantly narrower (third panel). This direction of evolution of the statistical distribution proves effectiveness of the proposed angular adjustment technique. In the third panel apanel 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 [pic] times by averaging observation of two satellites, θ = (θE+θW)/2. The statistical distribution of difference of θ and LSTS is shown in the top-right panel of Figure 2. LSTS here is land surface temperature obtained from observed infrared fluxes at SURFRAD station. This distribution is even sharper than thecompared to others and has asmaller standard deviation ofequal to 1.0°C. If weto 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], we can conclude that these estimates are consistent with an assumption that random errors in the angular adjusted satellite LSTobserved 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-EAST and GOES-WEST 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 shows thatproves an efficiency of the proposed angular adjustment technique removes much of the geometric inhomogeneity of satellite LST.

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. Under the assumption that parameters A=-0.0138 K-1 and BW=0.57 K, as estimated earlier 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. (Kostya, I am not sure this interpretation is correct. We need to discuss.)It is most interesting that D coefficient is decreasing with increasing smoothness of the topography and vegetation cover from 0.0165 K-1 at Desert Rock, NV to 0.0068 K-1 at Bondville, IL. It looks as if this parameter can be used as a 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 improvement of accuracy is not really significant and can be ignored.

5. Concluding Remarks

This analysis assumesis based on assumption that satellite retrieved LST is the 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.(What does this mean???) 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]. (again, I do not understand this)

Surface observed LSTS at SURFRAD stations are used here for model validation, not for model development. By definition (1), values of LSTS do not need angular adjustment but may be biased if computed with error in δ, broadband emissivity value. We found that LSTS data is not very useful in model developmenting - because theof small field of view of infrared Downwelling Pyrgeometer at SURFRAD stations cannot properly represent the much large footprint of satellite radiometers. Really, Oonly Desert Rock, NV observed LSTS 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. Nevertheless there are two pieces of evidencewe have two evidences that we are moving in the proper direction. The first of them is a significant decrease systematic and RMS differences between observed LSTE and LSTW afterin result of proposed angular adjustment shown in (Table 2). This evidence has some value if this decreasing is really significant. Some decreaseing 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 Table 2.

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

Other limitation is that there is no observations at small sun zenith angles, zs ................
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