Plot-scale retrieval of land surface temperature (LST) and emissivity (ε)) estimation

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Plot-scale retrieval of land surface temperature (LST) and emissivity (ε)) estimation

Supported by the Luxembourg National Research Fund (FNR) ATTRACT programme (WAVE, A16/SR/11254288)

Gitanjali Thakur, Stan Schymanski, Kaniska Mallick, Ivonne Trebs Luxembourg Institute of Science and Technology

Conclusions

INTRODUCTION METHODOLOGY RESULTS

MOTIVATION BACKGROUND

PROBLEM

RESEARCH QUESTIONS

LST ESTIMATION ε ESTIMATION

UNCERTAINTY

PLOT-SCALE LST PLOT-SCALE ε LST COMPARISON LST UNCERTAINTY

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Previous Home Next

1. Introduction 1.1 Motivation 1.2 Background

1.3 Problem

1.4 Research questions 1.5 Study sites

2. Plot-scale LST 2.1 Methods 2.2 Result

3.Plot Scale emissivity 3.1 Holmes et al. (2009) 3.2 Result

4.LST uncertainty 4.1 Method 4.2 Result 5. Conclusions

SURFACE ENERGY BALANCE AND SURFACE TEMPERATURE:

2

Radiometer

H (W m

^-2

) is sensible heat, LE (W m

^-2

) is latent heat, G (W m

^-2

) is ground heat flux, σ is Stephan-

Boltzmann constant and ε is the surface emissivity, T

_s

(K) is surface temperature, T

_a

(K)

is air temperature, K is the conductance to heat transport between surface and atmosphere.

Eddy covariance system

H LE G

●

Surface energy balance (R

_net

) depends on surface temperature (T

_s

)

H, T

_a

are

measured

●

K is an important parameter determining surface

atmosphere coupling T

_s

is

required

to derive K

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3

1.3 Problem

RADIATIVE ENERGY BALANCE AND SURFACE TEMPERATURE:

3

Radiometer

R

_net

(W m

^-2

) is net radiation, R

_ldwn

is down-welling longwave, R

_lref

is reflected longwave, R

_sref

is reflected shortwave, R

_lem

is emitted longwave, R

_lup

is up-welling longwave, σ is the Stephan-Boltzmann constant and ε is the surface emissivity and T is surface temperature

Eddy covariance system

R

_sdwn

+ R

_ldwn

R

_sref

+ R

_lref

R

_lem

R

_lup

●

Net radiation (R

_net

) is difference between the down- welling and up-welling radiative components

●

Radiometer measures up-welling longwave ( i.e emitted longwave + reflected longwave)

●

Land surface temperature at plot-scale is calculated by inverting R

_lup

equation

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1.3 Problem

PLOT-SCALE LST ESTIMATION : INCONSIS -TENCY IN EQUATION

4

Simplified equation (seq) Complete equation (leq)

Assuming ε ≈ 1

●

In past R

_ldwn

was not measured routinely at Eddy covariance sites, resulting omission of reflected longwave component, and simplification of equation.

Even now with the availability of R

_{ldwn ,}

use

of simplified equation for LST estimation is a

common practice

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1.3 Problem

LST AND EMISSIVITY AT PLOT SCALE :

RQ 1. Is simplified equation adequate to estimate LST at plot-scale?

RQ 2. How to obtain correct emissivity needed for plot-scale LST retrievals using tower-based measurements?

RQ 3. What is the resulting uncertainty in diurnal LST due to measurement uncertainties using complete and simplified equation?

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1.3 Problem

LAND COVER TYPES:

●

Ten sites

^[1][2]

having good record of eddy covariance data

Site Name Land cover types Adelaide River (AR) Savanna dominated by

Eucalyptus Alice Spring (AS) Mulga Canopy Daly uncleared (DU) Woodland savana Howard Spring (HS) Woodland Savanna Litchfield ( LF) Tropical Savanna

Sturt Plains (SP) Grassland (Mitchell grass) Ti Tree East (TT) Grassy mulga woodland &

Triodia savanna Tumbarumba (TUM) Wet Sclerophyll forest Brookings (BR) Cropland

Yatir Forest (YF) Evergreen needle forest

1) http://data.ozflux.org.au/portal/home.jspx 2) https://ameriflux.lbl.gov/

Table 1: Study sites for the analysis

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1.3 Problem

METHODS : RESEARCH QUESTION 1

Plot scale LST using complete and simplified equation?

Step 1: MODIS spectral emissivity for Channel 31 & 32 provides landscape-scale broadband emissivity

Step 2: Daytime longwave measurement and landscape-scale emissivity (ε

_MODIS

) is used to calculate plot-scale LST using complete equation (T

_leq

) and simplified equation (T

_seq

).

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1.3 Problem

Fig. 1 : Distributions of diurnal surface temperature for a representative year at each study site. Surface temperatures based on short equation (T_seq ) and complete equation (T_leq) using landscape-scale emissivity (ε_MODIS). ε_MODISis derived using spectral emissivity from channel 31 & 32. The median values of T_s are shown at top of the plot and the emissivity used for the T_s retrieval are shown at bottom in orange.

ε

_MODIS

PLOT SCALE LST : USING LEQ AND SEQ

How different are T

_seq

, T

_leq

using landscape scale emissivity (ε

_MODIS

) ?

Simplified equation leads to higher values than complete equation

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1.3 Problem

SENSITIVITY OF T

_SEQ

AND T

_LEQ

TO EMISSIVITY:

Fig. 2: An illustration of surface temperature (T_s ) sensitivity to emissivity using complete and simplified equation.

Longwave measurement (R_lup, R_ldwn) used for the plot is from Alice Springs on 15/06/2018 at midday

How sensitivity of T

_s

to emissivity differs using complete and simplified equation?

T_leq is less sensitive to emissivity used

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1.3 Problem

Linear regression between H And T_s – T_a should pass through

origin if estimated T_s is correct

H=0 when T

_s

−T

_a

= 0

Step 1: Segregating each month daytime data (H, R

_ldw

, R

_lup

, T

_a

) Step 2: Assuming ε range between 0.4 to 0.998

Step 3: Calculate T

_s

for each value of emissivity

Step 4: Linear regression between sensible heat (H) and (T

_s

-T

_a

) is forced through origin and coefficient of determination (R

²

) and root mean square error (RMSE) is calculated

Step 5: If R

²

> 0.5, select ε resulting in lowest RMSE

Sensible heat is driven by surface-air temperature difference (T_s-T_a )

METHODS: RESEARCH QUESTION 2

Theory

EXAMPLE

H= K (T

_s

−T

_a

)

How to estimate plot-scale emissivity using H and T

_s

- T

_a

?

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1.3 Problem

PLOT-SCALE EMISSIVITY: USING SEQ AND LEQ

Lower sensitivity of T_leq results in lower value of ε

Fig. 3: Sensible heat (H) vs ∆T (T_s − T_a) regression based on the simplified and complete equation is presented for August 2005 at Brookings. (a) Reproduction of analysis presented in Fig. 2 (a) in Holmes et al. (2009) based on simplified equation. (b) Replication of Fig. 2 (a) using complete equation. Blue crosses mark data points satisfying the filtering criteria while black dots mark points not considered in the analysis. N is the number of blue crosses used for regression (red line), m is the slope of regression, RMSE is the root mean square error and R² is the coefficient of determination. The fitted ε value is reported in the title.

How T

_seq

and T

_leq

results into different plot-scale emissivity?

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1.3 Problem

COMPARISON: PLOT-SCALE AND MODIS EMISSIVITY

Site Name MODIS emissivity Plot-scale emissivity

SEQ LEQ

Adelaide River (AR) 0.985 0.99 0.96

Alice Spring (AS) 0.974 0.96 0.82

Daly uncleared (DU) 0.985 0.99 0.98

Howard Spring (HS) 0.985 0.92 0.60

Litchfield ( LF) 0.985 0.92 0.60

Sturt Plains (SP) 0.974 0.96 0.85

Ti Tree East (TT) 0.974 0.95 0.80

Tumbarumba (TUM) 0.983 0.99 0.97

Brookings (BR) 0.983 0.98 0.82

Yatir Forest (YF) 0.974 0.97 0.83

Table 2: MODIS emissivity (ε_MODIS ) are obtained using channel 31 and 32 . The plot-scale emissivity represented above are median of monthly emissivity obtained analysing three years of H vs T_{s –} T_a plots for Australian site and one year data for Brookings and Yatir.

How different are plot-scale emissivity to the landscape-scale emissivity (MODIS) ?

Complete equation has lower sensitivity resulting into lower emissivity

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1.3 Problem

LST COMPARISON:

How plot-scale T

_s

calculated using ε

_MODIS

, ε

_opt

compares to MODIS LST ?

Fig. 4: Comparison of plot-scale LST (T_seq, T_leq) with landscape-scale LST (T_MODIS) derived from daily MODIS overpass. (a) T_seq based on short equation and MODIS derived landscape-scale emissivity; (b) Same as (a), but T_leq based on complete equation; (c) T_seq based on short equation and monthly plot-scale emissivity; (d) Same as (c), but T_leq based on complete equation. Bias is mean of T_{plot scale} − T _MODIS , N is the number of daily overpasses of MODIS between 2016 and 2018. c is the intercept, m the slope, RMSE is the root mean square error and R² is coefficient of determination

Use of plot-scale emissivity

reduces the bias between landscape and plot-scale LST

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1.3 Problem

How do errors in measured fluxes result in ε and Ts uncertainty?

Step 1 : Select uncertainty bounds for each input variable (H, T

_a,

R

_lup

,R

_ldwn

)

Step 2 : Uniformly distributed samples are generated using Saltelli sample generator Step 3 : Optimum emissivity range for each sample (measured + error sample) is generated

Step 4: Uncertainty in hourly LST resulting due to uncertainty in ε is estimated

H bound = [-20, 20]

R_lupbound = [-5, 5]

R_ldwnbound = [-5, 5]

T_abound = [-1, 1]

Uniformly distributed samples

generated within bounds

Measured (H , R_lup , R_ldwn, T_a) +

generated samples

Uncertainty in

Hourly LST

Range of optimum emissivity for each month

UNCERTAINTY: PLOT-SCALE LST

Saltelli sample generator

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1.3 Problem

UNCERTAINTY: DIURNAL LST

Fig.6: Uncertainty in hourly T_s − T _a for 15 August 2017. (a) Hourly daytime uncertainty in T_leq − T_a due to perturbed fluxes and optimum ε using complete equation in blue and perturbed fluxes with MODIS based ε in orange. (b) Hourly daytime uncertainty in T_seq − T_a due to perturbed fluxes and optimum ε using simplified equation in black and perturbed fluxes with MODIS based ε in orange. Unperturbed optimum ε values and T_s − T_avalues correspond to the median of perturbed values. Uncertainty in ε

Uncertainty in hourly T _s − T _a reduced when plot-scale ε is

used

Comparison of uncertainty in hourly T

_s

- T

_a

using plot-scale and landscape-scale ε ?

Additional input (R_ldwn ) in complete equation is not increasing T_s - T_auncertainty

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1.3 Problem

●

Simplified equation produces different results (LST, ε) to complete equation and therefore should not be used

●

The use of plot-scale emissivity for LST retrieval reduces the bias between tower based in-situ LST and landscape-scale (MODIS) LST

●

The uncertainty in T

_s

-T

_a

is reduced using plot-scale emissivity in comparison to MODIS based constant emissivity

Results

CONCLUSIONS:

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Previous Home

1) Holmes, T. R. H., De Jeu, R. A. M., Owe, M., & Dolman, A. J. (2009). Land surface temperature from Ka band (37 GHz) passive microwave observations. Journal of Geophysical Research: Atmospheres, 114(D4)

2)Holmes, T. R., Hain, C. R., Anderson, M. C., & Crow, W. T. (2016). Cloud tolerance of remote-sensing technologies to measure land surface temperature. Hydrology and Earth System Sciences, 20(8), 3263-3275

REFERENCES :

ACKNOWLEDGMENTS:

We would like to thank Dr. Maik Renner for pointing us to the work by Holmes et al. and Dan Yakir’s lab for providing Yatir Forest data and helpful discussions. We are also grateful to

Thomas Foken, Jason Beringer, Lindsay Hutley and Mauro Sulis for insightful discussions.This

work is supported by the Luxembourg National Research Fund (FNR) ATTRACT programme

(WAVE, A16/SR/11254288).

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Calculation of Ts using

different epsilon values from the range defined. (Step 3)

RMSE values calculated for the corresponding epsilon values. (Step 4)

Optimized value of epsilon giving the least RMSE value. (Step 5)

Fig. A: H vs ΔT (T

_leq

-T

_a

) plots illustrating the steps for obtaining optimized emissivity

EXAMPLE ESTIMATION OF EMISSIVITY

To method

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RANGE OF UNCERTAINTY FOR EMISSIVITY

Seq resulted in more constrained values

between 0.94 and 0.9

Fig. A1: Uncertainty in plot scale monthly emissivity for 2017 due to perturbation in H, R

_lup

, R

_ldw

, T

_a

at using complete and simplified equation shown in Blue and black at Alice Springs

To Result