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Research ArticleRelationship between Evapotranspiration andLand Surface Temperature under Energy- and Water-LimitedConditions in Dry and Cold Climates

Zhigang Sun,1,2 Qinxue Wang,3 Ochirbat Batkhishig,4 and Zhu Ouyang1,2

1Key Laboratory of Ecosystem Network Observation and Modeling, Institute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences, Beijing 100101, China2Yucheng Comprehensive Experimental Station, Institute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences, Beijing 100101, China3Center for Regional Environmental Research, National Institute for Environmental Studies, Tsukuba 305-8506, Japan4Institute of Geography, Mongolian Academy of Sciences, 14192 Ulaanbaatar, Mongolia

Correspondence should be addressed to Zhigang Sun; [email protected]

Received 24 May 2015; Revised 29 September 2015; Accepted 7 October 2015

Academic Editor: Ke Zhang

Copyright © 2016 Zhigang Sun et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Remotely sensed land surface temperature- (LST-) dependent evapotranspiration (ET) models and vegetation index- (VI-) LSTmethods may not be suitable for ET estimation in energy-limited cold areas. In this study, the relationship of ET to LST wassimulated using the process-based Simultaneous Heat and Water (SHAW) model for energy- and water-limited conditions inMongolia, to understand the differences in ET processes under these two limiting conditions in dry and cold climates. Simulationresults from the SHAWmodel along with ground observational data showed that ET and LST have a positive relationship when airtemperature (𝑇

𝑎) is less than or equal to the temperature (𝑇tra) above which plants transpire and have a negative relationship when

𝑇𝑎is greater than 𝑇tra under the energy-limited condition. However, ET and LST maintain a negative relationship with changes

in 𝑇𝑎under the water-limited condition. The differences in the relationship between ET and LST under the energy-limited and

water-limited conditions could be attributed to plant transpiration and energy storage in moist/watered soil and plants. This studysuggests that different strategies should be used to estimate ET under the energy-limited condition in dry and cold climates.

1. Introduction

Terrestrial evapotranspiration (ET), defined as the loss ofwater from the land surface to the atmosphere, is a keyprocess in water cycles [1, 2]. ET closely relates to greenhousegas efflux and production [3], plant growth [4–6], anddroughts [7, 8].Therefore, it is essential to understand the ETphenomenon over wide ranges of space and time for waterresources management and climate change studies.

Regional or global ET maps are often obtained throughsatellite remote sensing [9, 10]. Among remote sensing-based ET estimation methods, remotely sensed land sur-face temperature- (LST) dependent methods, such as thevegetation index (VI) and LST scattered plot (VI-LST),and models that calculate ET as a residual of the land

surface energy balance equation have been widely used. TheLST-dependent ET models include SEBAL (remote sensingSurface Energy Balance Algorithm for Land) [11], Sim-ReSET(Simple Remote Sensing EvapoTranspiration model) [9],SEBI (Surface Energy Balance Index) and S-SEBI (Simplified-SEBI) [12], SEBS (Surface Energy Balance System) [13], andMETRIC (Mapping EvapoTranspiration at high Resolutionwith Internalized Calibration) [14, 15], among others. TheVI-LST methods use the VI-LST triangle/trapezoidal featurespace to derive an index, and this index is used to partitionsensible heat and latent heat fluxes from available energy(net radiation minus soil heat flux) [16–19]. Both LST-dependent ET models and VI-LST methods assume that ETcan cool land surfaces under the condition of homogeneousatmospheric forcing. In other words, land surfaces with larger

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016, Article ID 1835487, 9 pageshttp://dx.doi.org/10.1155/2016/1835487

2 Advances in Meteorology

Table 1: Main inputs to the SHAWmodel.

Date type Data item Unit Data source

Weather data

Air temperature ∘C AMSAir humidity % AMSPrecipitation Inch AMSWind speed mph AMS

Solar radiation W/m2 AMS

Soil data

Bulk density kg/m3 Soil sampleOrganic matter % Soil sample

Sand % Soil sampleSilt % Soil sampleClay % Soil sample

Soil temperature ∘C AMSSoil moisture m3/m3 AMS

Vegetation data

Vegetation canopy height m Vegetation sampleDry matter kg/m2 Vegetation sample

Leaf area index — Vegetation sampleRoot depth m Vegetation sample

General site information

Slope % Field surveyAspect Degree Field surveyLatitude Degree GPSElevation m GPS

ET have lower LST while air temperature (𝑇𝑎), air humidity,

wind speed, and solar radiation remain homogeneous overland surfaces of interest. However, this assumption may beinvalid in high latitudes (>50∘) and cold areas [2], where ETcommonly exhibits a positive relationship with LST [2, 20].A positive relationship between LST and VI has also beenobserved in Alaska tundra ecosystems [21] and in NorthAmerica above 45∘N [22]. These findings indicate that bothLST-dependent ET models and VI-LST methods may not besuitable for ET estimation in the energy-limited cold areas. Astudy to estimate water deficit (defined as the ratio of actualto potential ET) using the VI-LST method in southern Spainalso suggests that the VI-LST method should not be used tocalculate ET under energy-limited conditions [19].

Reasons for the incompetence of LST-dependent ETmodels and VI-LST methods in energy-limited cold areashave been seldom investigated so far. In this study, therelationship between ET and LST was investigated using theprocess-based Simultaneous Heat andWater (SHAW) modelfor energy- and water-limited conditions in Mongolia, tounderstand the difference in ET processes under such lim-iting conditions in dry and cold climates.

2. Methodology

2.1. SHAW Model. The Simultaneous Heat and Water(SHAW) model, a one-dimensional model that simulatesheat, water, and solute transfer within the atmosphere-plant-soil system, was used to simulate ET and LST in thisstudy. The SHAW model, developed by USDA AgriculturalResearch Service, has a detailed solution to simulate soil

freezing and thawing and a sophisticated approach to simu-late transpiration from a plant canopy and evaporation fromsoil [23, 24].The SHAWmodel has been documented that it iscapable to simulate heat and water movement through plantcover, snow, residue, and soil for investigating climate andanthropogenic effects on soil freezing, snowmelt, runoff, soiltemperature, water, evaporation, and transpiration [23, 24].Therefore, the calibrated SHAWmodel could be competent atnumerically simulating the relationship between ET and LST.

Vegetation, climate, and soil data are required to runthe SHAWmodel. These inputs include initial conditions forsnow, soil temperature, and water content profiles; daily orhourly weather data; and parameters describing the vegeta-tive cover, snow, residue, and soil. General site informationis also needed to initialize the model, including the slope,aspect, latitude, and surface roughness parameters. Detailedinformation on these input parameters is listed in Table 1.

2.2. Data

Weather Data. Hourly air temperature (𝑇𝑎), wind speed,

air humidity, precipitation, and solar radiation data werecollected from an auto-meteorological station (AMS; 47.75∘N107.33∘E) located near Ulaanbaatar in Mongolia. A dry andcold climate dominates the region around the AMS, withan annual mean air temperature of −2.8∘C and annual totalprecipitation of 260mm. Detailed information regarding theAMS can be found in Sun et al. [25].

Soil Data. Data for organic matter content, bulk density, andsoil component ratio of sand, silt, and claywere obtained from

Advances in Meteorology 3

ET versus LST

SHAW model

Weather data (wind speed, humidity, precipitation, and solar radiation)

Soil data (soil parameters, temperature, and moisture profile)

Vegetation data (height, dry matter, LAI, and root depth)

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

Inputs except of Ta and SWC remain the samecontent (SWC) in the top soil (0–25 cm)

Scenarios of air temperature (Ta) and soil water

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1

SWC = 0.4SWC = 0.3SWC = 0.2SWC = 0.1Ta = 15∘C

Ta = 12∘C

Ta = 10∘C

Ta = 7∘C

Ta = 5∘C

Ta = 3∘C

Ta = 1∘C

Ta = 0∘C

Ta = −1∘C

Figure 1: Strategies to simulate ET and LST using the SHAWmodel.

soil samples that were analyzed in the lab. Soil temperatureand moisture profile data were obtained from the AMS.

Vegetation Data. Grass height, dry matter, leaf area index(LAI), and root depth data were obtained by measuring grasssamples.

2.3. Strategies for ET and LST Simulations. In this study, ninescenarios of 𝑇

𝑎and four scenarios of topsoil water content

(SWC, 0–25 cm) were combined to simulate ET and LST forenergy- and water-limited conditions. 𝑇

𝑎was set at −1–15∘C

tomatch the local cold climate, and SWCwas set at 0.1–0.4 tocover the soil moisture range from dry to wet. Combinationsof𝑇𝑎and SWC could thereby simulate a wide range of energy

and water conditions under which ET and LST are simulatedusing the SHAW model (Figure 1). The scenario of SWC =0.1 represents the water-limited condition where ET ismainlylimited by soil water shortage.The scenario of SWC=0.4withlow 𝑇𝑎values represents the energy-limited condition where

ET is mainly limited by low incoming solar radiation. Sincelow incoming solar radiation leads to low𝑇

𝑎, the proxy of low

𝑇𝑎along with saturated soil water content could be used to

define the energy-limited condition. One combination of 𝑇𝑎

and SWC along with other inputs was used to run the model.For each model run, the SWC data were used to initialize the

moisture condition for the soil layer of 0–25 cm, and 𝑇𝑎data

along with other weather data representing typical weatherconditions at the AMS site in early spring were selected fromthe AMS dataset. A typical record of 𝑇

𝑎and other weather

data was repeated 84 times to simulate the condition ofhomogeneous atmospheric forcing. Therefore, ET and LSTvalues from each run of the SHAWmodel represent the waterand heat conditions of land surfaces under homogeneousatmospheric forcing. Outputted ET and LST values wereplotted and analyzed using the linear regression method, andthe slope and coefficient of determination (𝑅2) of the linearregression were used to understand the relationship of ET toLST under different energy and moisture conditions.

Before numerical simulations, intensive daily observa-tional data during the period of August 2008 to August2013 were used to calibrate the SHAW model by forcing thesimulated soil temperature and water content to be consistentwith observed values, respectively.

3. Results and Discussion

When the SHAW model was calibrated, simulations of ninescenarios of 𝑇

𝑎(−1 to 15∘C) and four scenarios of topsoil

water content (SWC = 0.1, 0.2, 0.3, and 0.4) were conducted


R2 = 0.98, MAE = 1.24

y = 0.91x + 0.31

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(d)

Figure 2: Comparison of simulated and observed soil temperature at the depths of 0.5m, 1m, 1.5m, and 2m, respectively. A linear analysiswas conducted for each comparison, where 𝑅2 is the coefficient of determination and MAE is the mean absolute error.

to estimate ET and LST. For each𝑇𝑎scenario, the relationship

of ET and LST for SWC = 0.2, 0.3, and 0.4 is similar, butfor SWC = 0.1 the relationship is quite different. Below aredetailed results and discussion regarding model calibrationand the relationship of ET and LST under energy- and water-limited conditions.

3.1. Calibration Results for the SHAWModel. The comparisonof simulated soil temperature and soil water content againstobserved values at four depths was used to evaluate theperformance of the calibrated SHAW model. Figure 2 showsthat simulated soil temperature matches observed one wellin magnitude and seasonal variation. A linear analysis wasconducted for each comparison. The coefficient of deter-mination (𝑅2) is greater than 0.9, and the mean absoluteerror (MAE) is less than 1.4∘C at four depths. Figure 3 showsthat simulated soil water content also matches observed onewell in magnitude. The mean absolute error (MAE) is lessthan 0.015 at four depths. The simulated soil water contentcan capture the soil water recharge from precipitation as

shown in Figure 3(a). Soil temperature and soil water contentare two key variables of water and thermal processes insoil. Therefore, the consistence of soil temperature and soilwater content between simulated and observed values couldindicate that the calibrated SHAWmodel could perform wellto investigate the relationship of ET and LST.

3.2. Relationship of ET and LST under the Energy-LimitedCondition in a Cold and Dry Climate. The relationship of ETand LST under the soil moisture condition of SWC = 0.4exhibited two patterns for nine simulations when 𝑇

𝑎varied

from −1 to 15∘C. As shown in Figure 4, simulations with 𝑇𝑎

from −1 to 5∘C show that ET increases as LST increases, butthis trend becomes progressively weaker with increases in𝑇𝑎.The slope of linear regression analysis gradually decreases

from 0.0059 to 0.0037, and the value of𝑅2 also decreases from0.8356 to 0.1153. The relationship of ET and LST abruptlychanges at 𝑇

𝑎= 7∘C, and the slope of linear regression

analysis becomes −0.0329 (𝑅2 = 0.1525). This negative trendbecomes stronger as 𝑇

𝑎increases from 7∘C to 15∘C; the slope


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y = 0.40x + 0.17


(d)

Figure 3: Comparison of simulated and observed soil water content at the depths of 0.5m, 1m, 1.5m, and 2m, respectively. A linear analysiswas conducted for each comparison, where 𝑅2 is the coefficient of determination and MAE is the mean absolute error.

of linear regression analysis decreases from −0.0329 to−0.0636, and the value of 𝑅2 increases from 0.1525 to 0.2946.

Figures 4(a)–4(e) show that higher land surface tem-perature enhances ET when air is cold (𝑇

𝑎≤ 5∘C) and

soil water is not limited. These results suggest that somecaution should be noted when ET is estimated from LST-dependent ET models and VI-LST methods. These methodsfor ET estimation assume that ET cools terrestrial surfacesthrough vegetation transpiration and soil (or water surface)evaporation and that moist/watered surfaces have relativelylow values of LST. However, these assumptions are invalidunder the energy-limited condition (𝑇

𝑎≤ 5∘C, SWC = 0.4).

3.3. Relationship of ET and LST under theWater-Limited Con-dition in aCold andDryClimate. Comparedwith the energy-limited condition, the relationship of ET and LST under thewater-limited condition (SWC = 0.1) is relatively straight-forward. As shown in Figure 4, the trend of decreasing ETwith increasing LST becomes more distinct as 𝑇

𝑎is increased

from −1 to 15∘C. The slope of linear regression analysisgradually decreases from −0.0022 to −0.0097, and the value

of 𝑅2 increases from 0.1323 to 0.6552. Results from Figure 4indicate that ET has an apparent cooling effect even when 𝑇

𝑎

is less than or equal to 5∘C under the water-limited condition(SWC = 0.1). Under such a condition, the assumption of ETcooling appears to be valid, and ET can be estimated fromLST-dependent ET models and VI-LST methods.

3.4. Effect of Plant Transpiration on the Relationship of ET andLST under the Energy- and Water-Limited Conditions in aCold and Dry Climate. Plant transpiration has a clear impacton the relationship of ET and LST under the energy-limitedcondition. As shown in Figure 5, the relationship of ET andLST becomes negative when 𝑇

𝑎is greater than 5∘C, which for

this study was set as the temperature above which plants startto transpire. It indicates that soil evaporation has no clearcooling function when 𝑇

𝑎≤ 5∘C, whereas plant transpiration

above 5∘C can cool land surfaces under the energy-limitedcondition.

Plant transpiration has less impact on the relationship ofET and LST under the water-limited condition. As shownin Figure 5, the relationship of ET and LST remains negative


R2 = 0.8356y = 0.0059x + 0.0353

R2 = 0.1323y = −0.0022x + 0.0556

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m/h

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Surface temperature (∘C)

Linear (SWC = 0.4)Linear (SWC = 0.1)

SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(a) 𝑇𝑎= −1∘C

R2 = 0.2663y = 0.0045x + 0.0427

R2 = 0.2188y = −0.003x + 0.0661

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(b) 𝑇𝑎= 0∘C

R2 = 0.2487y = 0.0045x + 0.0427

R2 = 0.2549y = −0.0034x + 0.0723

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(c) 𝑇𝑎= 1∘C

R2 = 0.163y = 0.004x + 0.0455

R2 = 0.2927y = −0.0039x + 0.0853

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/hr)

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(d) 𝑇𝑎= 3∘C

R2 = 0.1153y = 0.0037x + 0.0483

R2 = 0.3549y = −0.005x + 0.1072

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(e) 𝑇𝑎= 5∘C

R2 = 0.1525y = −0.0329x + 0.5203

R2 = 0.4284y = −0.006x + 0.1321

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(f) 𝑇𝑎= 7∘C

Figure 4: Continued.


R2 = 0.1666y = −0.0375x + 0.6784

R2 = 0.532y = −0.0075x + 0.1769

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(g) 𝑇𝑎= 10∘C

R2 = 0.2188y = −0.0479x + 0.9052

R2 = 0.6151y = −0.0085x + 0.2113

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(h) 𝑇𝑎= 12∘C

R2 = 0.2946y = −0.0636x + 1.3139

R2 = 0.6552y = −0.0097x + 0.2636

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SWC = 0.1 SWC = 0.4

SWC = 0.3

SWC = 0.2

(i) 𝑇𝑎= 15∘C

Figure 4: ET and LST under nine scenarios of air temperature and four scenarios of soil water content.

under the water-limited condition, and this negative relation-ship becomes more pronounced when 𝑇

𝑎> 5∘C (Figure 6).

This indicates that soil evaporation has a cooling functioneven when 𝑇

𝑎≤ 5∘C and that plant transpiration above

5∘C can enhance the cooling effect under the energy-limitedcondition.

Summarizing the inferences drawn from Figures 5 and 6,plant transpiration shows a cooling effect under both energy-and water-limited conditions, while soil evaporation has acooling effect under the water-limited condition only. Theseresults suggest that care should be taken with ET estimationfrom LST-dependent ET models and VI-LST methods attemperatures below which plants do not transpire (𝑇

𝑎≤ 5∘C

in this study).

3.5. Comparison of ET and LST Relationships between Energy-andWater-Limited Conditions. Under thewater-limited con-dition, the relationship of ET and LST is always negativeacross the 𝑇

𝑎range from −1 to 15∘C. With the assumption

of an ET cooling function under the dry and cold condition,therefore, LST-dependent ET models and VI-LST methodscan be used for ET estimation. Under the energy-limitedcondition, however, the ET estimating methods mentionedabove do not work and the assumption of an ET coolingfunction is invalid when 𝑇

𝑎≤ 5∘C. The reason for this

might be that the energy storage of moist/watered soil andplants is larger than that of dry soil and plants, and it iscomparable to available energy for moist/watered soil andplants. This suggests that ET estimation methods based on


SWC = 0.4

SWC = 0.1

−1 1 3 5 7 10 12 150Air temperature (∘C)

−0.07

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

0.00

0.01

Slop

e of l

inea

r reg

ress

ion

Figure 5: Slope of linear regression for ET and LST with ninescenarios of air temperature and two scenarios of soil water content.

SWC = 0.4

SWC = 0.1

−1 1 3 5 7 10 12 150Air temperature (∘C)

R2

of li

near

regr

essio

n

0.000.100.200.300.400.500.600.700.800.90

Figure 6:𝑅2 of linear regression for ET and LSTwith nine scenariosof air temperature and two scenarios of soil water content.

the land surface energy balance equation might be usefulunder the energy-limited condition if the energy storage bymoist/watered soil and plants is accounted for in the landsurface energy balance equation.

4. Conclusions

The energy- and water-limited ET processes should be con-sidered and included in the methods used for ET estimationin cold and dry climates. In this study, the process-basedSHAW model along with ground observational data wasused to simulate ET and LST in order to understand therelationship of ET and LST under energy- and water-limitedconditions. Simulation results indicated that ET and LSThave a positive relationship when 𝑇

𝑎≤ 5∘C and a negative

relationship when 𝑇𝑎> 5∘C under the energy-limited

condition (SWC = 0.4). However, ET and LST maintaina negative relationship under the water-limited condition(SWC = 0.1). Plant transpiration and energy storage in

moist/watered soil and plants can potentially explain thedifferences in the relationship of ET and LST simulatedunder the energy-limited and water-limited conditions. Planttranspiration likely affects the relationship of ET and LSTdue to its relatively strong cooling effect under the energy-limited condition. The energy storage of moist/watered soiland plants, which is comparable to the available energy, has arelatively large contribution to ET when 𝑇

𝑎≤ 5∘C.This study

suggests that different strategies should be used to estimateET under the energy-limited condition in a dry and coldclimate.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This research was supported by the 100 Talents Program ofthe Chinese Academy of Sciences. This research was alsosupported by the Grant-in-Aid for Encouragement, Centerfor Regional Environmental Research, National Institutefor Environmental Studies, Japan, and by the EnvironmentResearch and Technology Development Fund, the Ministryof Environment, Japan.

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