Land Surface Temperature Diurnal Analysis (Diurnal) to Validate the Performance of GOES-R Advance Baseline ImagerKonstantin Vinnikov; (NOAA Collaborator: Yunyue Yu) – KVKVLSAWG11

1. Background

The goals of this Task are: to statistically evaluate angular anisotropy of LST (Land Surface Temperature) using available simultaneous land based and satellite, GOES-E and GOES-W, observations at locations of SURFRAD stations; to develop algorithm for correcting GOES-R retrieved clear sky LST for angular anisotropy of LST field; to take into account angular anisotropy of LST in validation of GOES-R observed LST.

There are only a few modeling and case study type previous investigations on this subject, which includes empirical evaluation of “Anisotropy in the land surface temperature as observed with two geostationary satellites” by Peter Romanov and Dan Tarpley. They concluded that “at least 2-3 K temperature change may be caused by changing the relative solar-satellite azimuth from backscatter to approximately 90º. The difference between temperatures observed in the backscatter and forward scatter may be higher. The major reason for the temperature differences is the effect of shadows”.

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 azimuth az into the scalar, unbiased, energy effective value of LST, θ, that can be used in land surface energy balance computation.

2. Accomplishments

2.1. Two-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)/T(0) =1+A·φ(z)+D·ψ(z,zs≤90º,az), (1)

where: T(0) is LST in the nadir direction at z=0; φ(z) is “infrared kernel” (related to angular anisotropy of infrared radiation near land surface); ·ψ(z,zs≤90º,az) is “solar kernel” (related to angular anisotropy in solar radiation near land surface), ψ(z,zs≥90º,az)≡0; A and D are the coefficients that should be estimated from observations. These coefficients depend on land cover structure. Such a model follows 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 http://www.eoc.csiro.au/tasks/brdf/k_summ.pdf.

Statistical empirical models 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 five representative SURFRAD station locations during one full year 2001. Small, about 15 minute, difference in observation time of the 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). At this stage, dependence of the A and D coefficients on land cover structure has been ignored.

2.2. Infrared kernel

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-W 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 GOES-W observed LST, 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 observations at z>90º we can write:

T(0)≈TE /[1+A·φ(ZE)]≈[TW+BW]/ [1+A·φ(ZW)]. (2)

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). (3)

The equation has been written for each pair of simultaneous observations of the satellites at locations of five SURFRAD stations. Total number of equations is equal to N=1619. Not more than three iterations are needed to resolve rather weak nonlinearity in (3). Correlation coefficient between left and right parts of (3) has been used as measure of quality of selected approximation of φ(z) kernel. The best results have been obtained with next approximations:

φ(z)=A·[1-cos(z)], BW=0.57 K, A=-0.0138. (4)

The correlation coefficient is equal to 0.44. Recollect that random errors of satellite retrieved directional temperature from two GOES satellites are independent and their standard values are in the range of 0.7-1.3 K (Vinnikov et al., 2008), therefore the correlation coefficient is not too small. Blue line in Figure 1 displays empirically estimated angular dependence LST related to infrared kernel.

Figure 1. Blue line – nighttime angular dependence T(z)/T(0)=A·φ(z). Red line - angular correction function θ/T(z)=C/A·φ(z) of satellite observed nighttime LST.

2.3. Solar kernel

It is important to remind that infrared kernel does work at nighttime and during daytime. It was easier to estimate its shape and amplitude using nighttime observations only. This infrared kernel estimates should be used in the process of estimation of solar kernel’s shape and amplitude. There are a total

number of 3440 simultaneous daytime LST observations from GOES-E and GOES-W at locations of five SURFRAD stations during year 2001. Following to the same procedure as for infrared kernel, we selected the next simple analytical expression to approximate solar kernel:

ψ(z,zs,az)=[1-cos(z)]·sin(zs)·cos(zs)·cos(zs-z)·cos(az). (5)

The analogues to the equations (2) and (3) are:

T(0)≈TE /[1+A·φ(ZE)+D·ψ(ZE,ZS,AZE)]≈[TW+BW]/ [1+A·φ(ZW) )+D·ψ(ZW,ZS,AZW)], (6)

TE·[1+A·φ(ZW)]-(TW+BW)·[1+A·φ(ZE)]≈D·[(TW+BW)·ψ(ZE,ZS,AZE)-TE· ψ(ZW,ZS,AZW)]. (7)

Assuming A and BW are known, equation (7), written for each pair of observations, has been used to obtain the least square estimate of amplitude D in (1):

D=0.0313. (8)

The correlation coefficient between left and right sides of equation (7) is equal to 0.62.

2.4. Algorithm for angular correction of satellite observed LST.

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

θ4=π−1∫0

2 π

∫0

π2

T ( z ' , β )4 sin ( z ' )cos ( z ' )dz ' dβ (9)

T(z,β) in (9) 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 (1).

T(z,β)=T(Z,ZS,AZ)·[1+φ(z)+ψ(z,zs,az)]/[1+φ(Z)+ψ(Z,ZS,AZ)]. (10)

θ= T (Z , ZS , AZ )1+φ (Z )+ψ ( Z ,ZS , AZ )

¿ (11)

θ=T ( Z , ZS , AZ ) · C /[1+φ (Z )+ψ (Z , ZS , AZ ) ] . (12)

C=¿. (13)

C=0.9954. (14)

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

θE=TE (ZE)·C/[1+φ(ZE)+ψ(ZE,ZS,AZE)]. (15)θW= (TW(ZW)+BW)·C/[1+φ(ZW)+ ψ(ZE,ZS,AZE)]. (16)θ=TE, if GOES-EAST, only. (17)

θ=TW, if GOES-WEST, only. (18)

θ= (θE+θW)/2, if GOES-EAST and GOES-WEST data available. (19)Angular correction function for nighttime observations is shown in Figure 1 (Red line). Estimated angular dependence of satellite observed LST for different sun zenith angles is shown in Figure 2.Equations (15-19) give the first version of the algorithm for angular correction of GOES-R observed LST.

Figure 2. Estimated angular dependence of satellite observed LST for different solar zenith angles, T(z,zs,az)/T(0)=1+A·φ(z)+D·ψ(z,zs,az), is displayed in polar coordinate system (viewing zenith angle – radial coordinate 0-90º, relative azimuth-angular coordinate 0-360º)

3. Planned work

3.1. Work to be done to the end of the current period

The first version of the algorithm for angular correction of GOES observed LST will be assessed and improved using LST data retrieved from observations of upward and downward infrared fluxes at the SURFRAD stations. Work on improving the approximating expressions for infrared and solar kernels will be continued. Work on taking into account anisotropy of LST in validation of GOES-R observed LST will be continued.

3.2. Work plan for the next period

The goals of future work are in testing and improving of the developed algorithm using absolutely independent LST data sets. Plan of future work includes the following subtasks:

Collect and quality control full year of overlapping GOES-11 and GOES-13 GSIP archived LST data for Northern Hemisphere Extended Scan Sectors.

Adjust GOES-13 LST data to GOES-11 times of observation. Validate and improve infrared and solar kernels. Evaluate accuracy of proposed angular corrections Accomplish experimental blending historical GSIP GOES-11 and GOES-13 LST data

using proposed algorithm for LST angular anisotropy correction. Make Conclusion on usefulness and recommendation on blending LST data retrieved

from GOES-E and GOES-W satellites.

4. Publications and PresentationsResults of this work have not been published or presented at professional meetings, yet. Two

research papers are in preparation.