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15 October 2020 Review of approaches for the estimation of sensible heat flux in remote sensing-based evapotranspiration models
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We recapitulate the approaches of sensible heat flux (H) estimation, which is a critical parameter in the remote sensing (RS)-based evapotranspiration (ET) models. We propose a classification scheme for the ET models considering their distinctions in approaches for the estimation of H. Adhering to the proposed classification scheme, the theoretical backgrounds of H estimation in the single-source and two-source RS-based ET models are discussed in brief, along with their unique characteristics. We addressed the role of critical parameters that influenced the H computation under each model and presented the related progress in the research. The importance of data assimilation techniques, as well as the application of unmanned aerial vehicles for the uninterrupted estimation of turbulent heat flux, are discussed in the context of single-source and two-source models. The influence of scale on the validation of the models and the impact of the aggregation methods are discussed. We compared the performance of the popular ET models for the estimation of H, utilizing the information obtained from peer-reviewed articles. The limitations related to the RS datasets in terms of spatial and temporal resolution and the scope of alleviating the shortcomings using the future satellite missions are discussed. We conclude by pointing toward the current challenges and the prospective domain of research, which needs to be addressed critically in the future.



The sensible heat flux (H) and latent heat flux (λET) of the energy balance equation, have a notable role in various domains of applications spanning from climate change to water resource management. In the remote sensing (RS) perspective, sensible heat flux computation gained more attention because of its sensitivity and computationally complex nature among all other components in the surface energy balance equation.1,2 The sensible heat flux parameter has a significant impact on the λET values as most of the RS-based models calculate λET as a residual of the surface energy balance equation as follows:3

Eq. (1)

where Rn is the net radiation (Wm2), G is the soil heat flux (Wm2), H is the sensible heat flux (Wm2), and λET represents the latent heat flux (Wm2).

The RS-based evapotranspiration (ET) models attained much importance in the last four decades due to the accelerated advancements in the satellite RS technology. Though the RS-based models are preferred to other approaches due to their better estimation of H capability under water-stressed conditions, there exist many challenges, such as lack of techniques for aerodynamic temperature measurements, use of radiometric temperature as a surrogate to aerodynamic temperature, and existence of heterogeneous partial canopy cover conditions.4

This review is an attempt to organize the outcomes obtained from the research carried out in the realm of sensible heat flux computation focusing on RS-based ET models. This review targets to create a comprehensive link between the approaches through a new classification scheme based on their mode of operation for the estimation of sensible heat flux.


Hybrid Nature of Sensible Heat Flux Estimation Approach

The sensible heat flux estimation could not be considered as a sole RS approach as many of the models utilize the combination of micrometeorological and RS concepts. Though the RS models consider land surface temperature (often referred as LST or Ts or Trad) as the primary boundary condition, they could not account for the uncertainty due to canopy cover and turbulence in the atmosphere. The parameters such as aerodynamic roughness of the surface and the wind velocity are also crucial under the non-neutral conditions of the atmosphere. Therefore, the estimation of H needs a hybrid approach by incorporating RS and micrometeorological concepts. This review mainly focuses on the RS aspects of the hybrid approach.


Organization of the Paper

This review starts with the concepts of resistance-based models with historical developments that guided the evolution of RS-based models. The RS-based ET models grouped under the proposed classification scheme are linked to form a comprehensive account of the progress in the sensible heat flux research in the succeeding sections. This review further discusses the importance of data assimilation techniques, the influence of scale changes on field validation of the models, and the recent developments in the use of unmanned aerial vehicles (UAVs) for the estimation of turbulent heat flux. This review concludes with a record of historical milestones along with the current developments in sensible heat flux related research.


Concepts of Resistance-Based Models for the Estimation of Sensible Heat Flux

The concept of resistance in plant physiology dates back to 1900, and later Monteith proved that the Ohm’s law-based resistance approach could simplify the estimation of H from natural surfaces.5 The “Penman–Monteith” (PM) equation (“big-leaf” approach), which follows the resistance-based concept, was the simple model used in the one-dimensional single-source descriptions of ET process, which is expressed as6

Eq. (2)

where raa is the aerodynamic resistance between the source (canopy) and the reference height, T0 is the aerodynamic temperature (K), Ta is the air temperature (K), Cp is the specific heat of air at constant pressure (Jkg1K1), and ρ is the mean air density (kgm3). One of the well-known practical application of the big-leaf approach is the FAO-56 (Irrigation and Drainage Paper No. 56) of Food and Agricultural Organisation.7 The performance of big-leaf based models mainly constrained to the rational calculation of an “excess resistance” term quantified by kB1. The term kB1 [which is equal to ln(z0m/z0h)] explains the difference between the height of the equivalent surfaces for momentum absorption (z0m) and heat transfer (z0h).8

The inability of the big-leaf concept to represent the canopy resistance for sparse vegetative conditions led to the development of two-source models where the estimation of component fluxes of soil and vegetation is essential.9 The two-source conceptual framework incorporated the influence of soil and vegetation components separately and categorized as series and parallel ET models.10 The presence of canopy structure with stacked multiple layers became the impetus for the development of multi-source models. The turbulence within the canopy and the counter-gradient fluxes, which are prominent in multi-layered canopies, make the multi-layered models complicated and limited.11


Importance of Radiometric Temperature and Aerodynamic Temperature in ET Models

The radiometric surface temperature (Ts) derived from RS platforms is used as a proxy for aerodynamic temperature (T0) in RS-based models.3 The single-source models primarily rely upon the relationship, which accounts for the difference between T0 and Ts. In the partially vegetated areas, the difference between Ts and T0 can even reach up to 10°C resulting in the overestimation of H.1216 To overcome this difference, an extra resistance term rex, derived from kB1 was incorporated in the bulk transfer equation.17 Due to the uncertainty regarding the dependency of kB1 on surface temperature, wind speed, and ground cover conditions, many methods were proposed without incorporating kB1 parameter.14,1820 Among them, the temperature gradient-based approaches reduced the errors contributed by the air temperature and successfully adopted in many of the current popular RS-based models.19,21


Atmospheric Stability Corrections and Aerodynamic Resistance

The earlier ET models assumed the existence of neutral atmospheric stability with homogeneous land surface temperature and stable wind velocity profile at the near-surface layers. The occurrence of such neutral stability condition is rare in heterogeneous canopy cover with varying soil moisture conditions.22 As the soil moisture depletes, the canopy temperature would rise, and the air density above the canopy would reduce, and it creates unstable conditions with increased heat transport. Similarly, at unstable conditions, the rate of decrease of air temperature with an increase in elevation is higher than the adiabatic lapse rate, which promotes the increased exchange of sensible heat flux. Contrary to this, at stable conditions, the rate of heat transfer decreases. The incorporation of atmospheric stability correction procedures in the estimation of aerodynamic resistance (rah) accounted for the aforementioned micrometeorological changes that influenced the sensible heat flux computations.23,24 Numerous studies proposed Monin–Obukhov (MO) stability parameter (ζ) or Richardson’s number (Ri) as the indicator of the atmospheric stability conditions.16,17,19,25,26 Generally, an iterative procedure is adopted while using ζ as a quantifier for atmospheric stability changes. Instead of ζ, many researchers had used Ri to avoid the iterative procedures in various surface energy balance models.3,27,28 Though the Richardson’s number found its place in various studies, it was not usually preferred over ζ since it is an unknown function of height and often approaches a constant value for near-surface layer applications.25


Classification of ET Models Based on Sensible Heat Flux Estimation Approach

The classification scheme unlocks opportunities to understand the characteristics of models systematically. One of the well-known classification methods developed by Courault et al. categorized the ET models into four different classes based on the complexity, considering the balance between the empirical and physical approaches applied in the models.29 The four categories are direct empirical methods, the residual methods of the energy budget, the deterministic methods, and the vegetation index-based methods. The direct empirical category includes RS-based semiempirical ET models, and the residual models use empirical and physical modules that are operational. The deterministic models are more complex models where the RS data are assimilated at different modeling levels. The vegetation index-based category of models uses RS data to compute reduction factors (e.g., crop coefficient and Priestley–Taylor coefficient) to estimate ET. Later, a new classification scheme by Bhattarai et al. grouped single-source energy balance models into three categories based on the methodology adopted for the estimation of H. The categories are hot and cold pixel-based full energy balance models, excess resistance-based full energy balance models, and partial energy balance models.30

The current population of RS-based ET models that include single- and multi-source models demands a generic theme of classification that facilitates a comprehensive approach with a better distinction between the classes. The approach should also improve the flexibility to update future developments. In view of these requirements, this review proposes a classification scheme for RS-based ET models as an extension of the classification scheme by Bhattarai et al. The current classification scheme considers the sensible heat flux estimation approach as the criterion for categorizing the models.

The classification scheme (Fig. 1) broadly divides the models into iterative and non-iterative models. The iterative models estimate H using an iterative procedure based on an initialization and termination condition. The non-iterative models are further classified into feature space-based and non-feature space-based models. The feature space-based models among non-iterative category utilize two-dimensional feature space [e.g., vegetation fraction cover-land surface temperature (VFC-LST) space] to estimate the parameters essential for the models. The non-iterative, non-feature space-based models are simple and straightforward that retrieve the model parameters without the aid of feature space or iterative procedure.


Sensible Heat Flux Estimation Approaches in Single-Source ET Models

Statistics of the peer-reviewed articles published during the last 10 years (source: Ref. 31) revealed that the surface energy balance algorithm for land (SEBAL), mapping evapotranspiration at high resolution with internalized calibration (METRIC), and surface energy balance system (SEBS) are the popular models of the single-source category [Fig. 2(b)]. Though these models are more suitable for semiarid regions, the spatial distribution of the sites chosen for executing these models are spread across all the climatic regions except polar group (as per Köppen–Geiger climate classification32). Refer to Fig. 2(a) for the spatial distribution of sites across the globe where popular models were tested.

Fig. 1

Classification of RS-based ET models based on sensible heat flux estimation approaches.


Fig. 2

(a) Study sites across various continents for single-source and two-source models; (b) statistics of articles published in peer-reviewed journals focusing RS-based single-source ET models; and (c) statistics of articles published in peer-reviewed journals focusing RS-based two-source ET models. Prepared using the data collected from Ref. 31.



Sensible Heat Flux Estimation Approaches in Iterative Single-Source ET Models

The SEBAL,19 METRIC,21 and SEBS33 are the iterative models that follow the H estimation procedure as a hybrid approach using micrometeorological and RS concepts. METRIC is an improved version of SEBAL that provides relatively more accurate estimates of ET at a higher spatial resolution and more suitable for advective conditions. The similarity of SEBAL and METRIC in their theoretical framework, underlying assumptions, and data requirements for H estimation makes both the models compatible with any common modifications.19,34 The limitations of SEBAL to operate at different atmospheric stability regimes and its semiempirical nature resulted in the development of a physically based model, SEBS.16 The SEBS uses relative evaporation fraction for computing the surface energy balance components using calibration limits called “wet” and “dry” limits using non-subjective procedure (use of equations). In contrast, METRIC and SEBAL use reference ET fraction, which is calibrated using hot and cold pixels (anchor pixels) selected by the subjective judgment of the user.

In SEBAL and METRIC, the two anchor pixels from the scene with extreme climatic and hydrological conditions (well-irrigated vegetation and dry open land) employed to calculate near-surface temperature gradient (dT) for the estimation of H. Stability corrected rah and stabilized dT values were obtained at the calibration pixels during the iterative stability correction procedure using MO theory. These calibration pixels establish an empirical linear relationship between dT and Ts that further calculates H for every Ts values. The iterative autocalibration procedure called calibration using inverse modeling of extreme conditions (CIMEC) mitigate the effect of error that occurred in Ts measurements METRIC and SEBAL.35 Due to the lack of arid open land with very high radiometric heating in agricultural areas, the assumption of zero latent heat flux (λEThot) in SEBAL was modified as non-zero latent heat flux in METRIC. This modified assumption also accommodates the presence of residual moisture content at hot pixels and avoid the underestimation of H.36 Similarly, the assumption that equated the ET at the cold pixel to 1.05 times the reference ET was not considered in METRIC due to its non-applicability during early growing seasons as well as non-growing seasons.34 The subjective nature of the anchor pixel selection process and the higher variability in the surface conditions for higher Ts values make the selection of hot pixels difficult.37 The utilization of available energy (RnG) as an additional input along with NDVI and Ts were useful in retrieving the candidate pixels with distinct variation.38 By considering the soil moisture and available energy as influencing auxiliary parameters for the endmember selection process, Mohan et al.39 proposed the integration of synthetic aperture radar (SAR) derived soil moisture into SEBAL for anchor pixel selection process. The semiautomatic statistical approach by Allen et al., a fully automatic procedure based on exhaustive search algorithm by Bhattarai et al. and the modified version ASEBAL with an automated endmember selection process are the recent related developments in the domain of anchor pixel selection process.4042

Single-source models use aerodynamic resistance as an essential parameter that captures the spatial variability of H. The aerodynamic resistance and its component parameters (surface roughness lengths) are characterized by spatially varying canopy architecture.43 The roughness length calculation is sensitive to the changes in wind speed, soil, and canopy temperature and may result in significant temporal variability. To account for these, a physically based model was developed by Su et al.16 to incorporate the surface condition and the aerodynamic variables from the ground. Such physical models require detailed information at the ground level at all scales of applications, and the scaling of the models from local to regional scales demanded a considerable amount of ground sampling.

RS-based ET models explicitly do not consider soil moisture variations for the estimation of H, relying upon the assumptions that the Ts and NDVI indirectly consider and incorporate the influence of soil moisture.44 However, at water-stressed conditions, the radiometric temperature is inadequate to represent the effect of soil moisture and biophysical parameters. At limiting conditions of soil moisture, z0h increases whereas z0m decreases, which leads to the changes in kB1 values. The influence of kB1 on varying soil moisture conditions contributed to the development of various empirical approaches, which included the soil moisture information into the bulk transfer equation in SEBS.4446 In METRIC, the incorporation of soil moisture related parameters is done through the Priestley–Taylor parameter (αPT) by choosing a value different from the usual value of 1.26 according to the changes in soil moisture content. This modified approach is often referred to as wMETRIC.47

In the case of METRIC and SEBAL, the estimate of Rn and H had a constant bias across the scene. The radiometric accuracy of the satellite data, the assumptions related to the models, and the uncertainties in the parameters used for the estimation of surface roughness and wind speed were the significant factors that influenced the magnitude of the bias.40 The application of METRIC and SEBAL in arid and non-agricultural areas resulted in the overestimation of H, inferring that both the models are not suitable for sites with extreme climatic conditions.48,49 Unlike SEBAL and METRIC, the application of SEBS in non-agricultural areas becomes versatile due to its non-subjective approach for the selection of the extreme wet and dry limits. Among the single-source models, SEBS is more sensitive to changes in the surface to the air temperature gradient (TsTa) for the computation of H compared to the individual effect of Ts, and it is more sensitive than the surface aerodynamic parameters.5052 The SEBAL and METRIC avoided the direct use of Ts by adopting the near-surface temperature gradient (dT) estimated by CIMEC process, which eliminates the systematic bias in the calculated Ts values.53 When comparing the performance of the single-source iterative models, the major difference was observed in the estimation of H. SEBAL consistently underestimated H and showed more than 65% variation from reference eddy covariance (EC) measurements.54 The deviations for METRIC and SEBS were 34% and 56%, respectively.55,56 For λET, all three models exhibited less variations (SEBAL-13.5%, METRIC-15.1%, and SEBS-20.6%) compared to H. The higher deviations of H in these models could be explained by their inability to partition the soil and vegetation component fluxes and their extreme sensitivity to the calibration pixels. A modified approach called M-SEBAL was introduced to decrease the bias in H in SEBAL by determining the anchor pixels from VFC-LST space. This approach minimized the deviation of H from 65% to 24.8%.54 The above values are only for reference to show the general trend of each model outputs.


Sensible Heat Flux Estimation Approaches in Single-Source Non-Iterative ET Models

The single-source models of non-iterative category compute H as a residual of other energy balance components, using evaporative fraction (EF). Models such as surface energy balance index (SEBI), simplified surface energy balance index (S-SEBI), simplified surface energy balance (SSEB) model, and operational simplified surface energy balance (SSEBop) model are listed under this category. Among these models, SSEB has tested for all climatic zones except the polar zone, whereas its operational version SSEBop was tested only for tropical and dry climatic zones. Minimal studies are available for SEBI and tested for very few locations grouped under continental and dry climatic zones. The S-SEBI, the simplified version of SEBI, has successfully applied at dry, temperate, and continental zones.


Feature space-based models

S-SEBI is a simplified operational RS-based model, in which the extreme temperatures at the boundary conditions are extracted from the Ts-reflectance spectral space. The two assumptions followed in S-SEBI are the existence of constant atmospheric conditions as well as the presence of calibration pixels within the area of application.57 S-SEBI utilizes Ts-reflectance feature space to determine EF without any ancillary data sets or meteorological data from the field.57,58 S-SEBI model is empirical, which restricts the extensive application of the model to global scales. Hence it is essential to calibrate the model for diverse climatic conditions. For instance, in semiarid areas with vegetation, EF exhibits very low values as a water deficit indicator, and therefore, a non-evaporative fraction-based approach was proposed for estimating sensible heat flux.59 Since S-SEBI is a pure image-based model that entirely relies upon the feature space for model parameters, the current focus of the research is to reduce the atmospheric and sensor related errors from the feature space. The use of surface albedo calculated by weighted surface reflectance approach is generally adopted for the feature space creation in S-SEBI. To improve its performance, a proper view zenith angle correction is essential. The surface broadband albedo calculated by the integration of bidirectional reflectance distribution function was found to be effective for the estimation of surface energy balance components in S-SEBI.60 Regarding the performance of the model compared to other single-source models, S-SEBI showed comparable performance with SEBAL and METRIC at arid conditions and the model was less suitable for wet conditions as it overestimated H.61


Non-feature space-based models

The SEBI became the precursor of RS-based ET models, which laid the strong theoretical foundations for all the present-day single-source models. It is the modified parametrization of crop water stress index developed by Jackson et al.62 and obtained by simultaneously solving the energy balance equation and the profile equations for sensible heat flux and latent heat flux at two extreme conditions of potential ET and zero ET in the study area. SEBI estimates the H based on the difference between the plant surface temperature and air potential temperature at the top of the atmospheric boundary layer.63 The model is unique because of its capability to handle situations when sufficient wet and dry pixels are not available in the study area. It uses the temperature difference obtained either from radio soundings or weather prediction models for estimating boundary conditions. The requirement of essential meteorological variables from the upper boundary of planetary boundary layer (PBL) made the model less operational as well as less compatible for RS datasets.64

SSEB is a regional scale model that inherits the concept of “near-surface temperature gradient (dT)” from SEBAL and METRIC for the actual ET estimation. The linearity assumption of sensible heat flux in SEBAL (H is proportional to dT) is extended for the estimation of latent heat flux in SSEB. The calibration pixels that correspond to zero ET and potential ET are used to establish a linear relationship between the temperature gradient and the actual ET, which further employed to derive the EF for any pixel within the study area. The SSEB model was modified to SSEBop by predefining the hot and cold extremes, which enhanced its potential as a large-scale operational RS model.65 The models such as SSEB, SEBAL, and METRIC designate the candidate pixels for a limited period, during which a uniform hydroclimatic condition exists. In actual field conditions, the candidate pixels change their locations within the same study area as per the variations of environmental factors. Contrary to this, the assumption of changing candidate pixels was discarded in SSEBop as it found to be less influential in the context of the accuracy of outputs obtained. Therefore, the candidate pixels were predefined and remained as same for the entire period for which the fluxes are estimated. The underestimation of H at dry open areas is a major limitation of the model. At vegetated areas, SSEB exhibits comparable performance with SEBAL and METRIC.66


Sensible Heat Flux Estimation Approaches in Two-Source ET Models

The two-source approach is more robust than the single-source approach due to its ability to partition the canopy and soil flux components. It also handles the influences of atmospheric and the sensor look angle effectively. The two-source models predict more accurate values of H in sparse canopy conditions and provide a reliable physical framework for capturing the variations of the aerodynamic resistance compared to single-source models.67,68 The two-source models are differentiated based on the approaches adopted for partitioning the directional radiometric surface temperature into canopy and soil temperatures (TC and TS). Among iterative models, two-source energy balance-Priestley–Taylor (TSEB-PT) and two-source time integrated model (TSTIM) and its operational versions such as atmosphere-land exchange inverse (ALEXI) model were tested for all climatic zones except polar. Only limited studies are available for two-source energy balance-Penman–Monteith (TSEB-PM), and it was tested only for dry climatic conditions. Among non-iterative models, the best performing model hybrid dual-source scheme and trapezoid framework-based evapotranspiration model (HTEM) was tested for dry and continental climates only. The two-source energy balance model-two angle (TSEB-2A) that utilizes two-directional surface temperature has few studies available and was tested for dry, tropical, and continental climates [refer Fig. 2(a)]. The statistics of the peer-reviewed articles published during the last 10 years showed that the TSEB-PT model gained more attention compared to other RS-based TSEB models [Fig. 2(c)].


Sensible Heat Flux Estimation Approaches in Iterative Two-Source ET Models

The TSEB-PM69 and TSEB-PT70 are the two different approaches, under the iterative category of two-source models, which differ mainly based on the fundamental equation used to estimate the initialization parameter (λEC) for iteration. The TSEB-PT model calculates λEC by the PT equation, assuming potential transpiration whereas, in TSEB-PM the calculation follows PM equation. In TSEB-PT, the iteration begins by assigning the value of PT coefficient (αPT) as 1.26, which progressively assumes smaller values in the subsequent iterations. The iteration procedure dynamically estimates various energy balance components as detailed by Norman et al.69 During each iteration, new values of TC and TS are calculated from Trad(θ) and used to estimate component sensible heat fluxes (HC and HS) by substituting in bulk transfer equation. The soil component of the latent heat flux (λES) is estimated during the progress of the iteration procedure as a residual of overall energy balance components. During each iteration, the value of component fluxes is progressively revised. When the λES stabilizes to a positive value the solution for component fluxes are achieved. In the case of the water-stressed condition, the value of λEC is overestimated, which converge to a negative value of λES. In such cases, the λES is set to zero, and HS and HC are recalculated. The use of the constant initial value of αPT (1.26) for all the cases of atmospheric, soil, and ground cover conditions is the major limitation of TSEB-PT approach. At advective conditions, the actual value of αPT is much higher than 1.26, which might lead to overestimation of H.71 In order to account for varying ground cover conditions, the fractional vegetation cover, f in the PT equation was modified by an empirical function of soil adjusted vegetation index.72 The influence of changing atmospheric and soil moisture conditions was addressed by a modified approach Gc-TSEB, which incorporated the canopy conductance Gc (a function of LAI, water vapor deficit, and visible radiation) in the model to calculate the energy balance components.73

Unlike the PT approach, the PM approach requires vapor pressure deficit and canopy resistance information to execute the model. This could account for the increased transpiration rate due to advective conditions as well as for the low relative humidity cases. TSEB-PM approach estimated more accurate soil and vegetation component temperatures and showed slightly superior performance compared to the PT approach at normal conditions.74 The unavailability of air temperature and wind speed measurements for a larger area hinder the applicability of TSEB-PT and TSEB-PM approaches for larger-scale applications. When comparing the performance of PT and PM approaches, both the models showed almost similar performance with a slight upper-hand for TSEB-PM. The root-mean-square error (RMSE) of estimated H was 44.9 and 47.5  Wm2 for TSEB-PM and TSEB-PT, respectively.75 The λET also showed a similar trend (TSEB-PM-70.6  Wm2 and TSEB-PT-75.3  Wm2).

TSTIM is a time-integrated iterative two-source model essentially meant for regional to continental-scale applications.76 The model is an extension of TSEB models that use two instantaneous satellite acquisitions to estimate the sensible heat flux. The two satellite observations, which are acquired just after the sunrise and before noon, reduce the effect of advection to a reasonable extent and avoid the requirement of local calibration and precise air temperature data.77 The two submodels associated with the TSTIM are surface layer component (SLC) and PBL component. The SLC follows the TSEB modeling schemes that compute instantaneous sensible heat fluxes H1 and H2 using radiometric temperature data at times t1 and t2 by assuming a linear increase in the sensible heat flux.78 The ALEXI model is a well-known time-integrated model that retrieve the surface energy fluxes at 5 to 10 km resolution using the two instantaneous values of sensible heat flux.79 Most of the studies related to ALEXI used the LST from GOES at a temporal resolution of 30 min or from Meteosat Second Generation (MSG) retrieved at every 15 min. The spatial resolution of GOES and MSG are 4 km and 3 km, respectively, at nadir.


Sensible Heat Flux Estimation Approaches in Non-Iterative Two-Source ET Models

The requirement of locally measured surface roughness length and wind speed narrowed the application potential of two-source iterative models for heterogeneous landscapes with non-linear surface characteristics. In iterative PT and PM formulations, the ambiguity of the initializing parameters induced significant biases in the H estimations. The use of directional radiometric temperature to estimate the soil and vegetation component temperatures eliminates the use of initializing parameter to estimate the canopy transpiration. The non-iterative two-source models estimate component temperatures either using simultaneous observations of directional temperatures from two viewing angles, or by surface temperature measurements from a single viewing angle. The retrieval of component temperatures by single Ts observation is complex and requires a “VFC-LST feature space” and in situ meteorological data sets. Those models that utilize the VFC-LST feature space are classified as non-iterative feature space-based models.


Non-iterative feature space-based models

The scatter plot of VFC versus LST forms a trapezoidal or triangular space for an area with a wide range of land-use and land-cover types. The trapezoidal spectral space could adequately account for the water stress, canopy transpiration, and the aerodynamic effects of the surface compared to triangular space.80,81 The VFC-LST space-based models gained attention due to its site-independent model parameterization capability. These models decompose the Trad(θ) into TC and TS using soil surface moisture availability isopleths superimposed on trapezoidal space.81 The warm edge and the cold edge of the trapezoidal space (Fig. 3) define the boundary condition for VFC-LST space-based models. There exist several isopeistic lines within these boundary conditions that represent the same soil surface moisture availability for the same TS values.82

Fig. 3

VFC-LST feature space, applicable to the models such as TTME, HTEM, and ETEML.


One of the earlier versions of the VFC-LST space-based patch model called two-source trapezoidal model for evapotranspiration (TTME) utilizes the trapezoid framework and isopleths of soil surface moisture availability to calculate energy balance components. The Ts,max that defines the upper boundary conditions requires stability corrected aerodynamic resistance through an iterative process (non-iterative for estimating surface energy balance components), and the Ts,min corresponds to the spatially averaged air temperature (Ta). The TTME uses these boundary conditions for decomposing radiometric temperatures into soil and canopy component temperatures. These component temperatures are subsequently used for calculating component evaporation fractions. The model estimates H as a residual of the energy balance equation, and the values are sensitive to the boundary conditions.83 HTEM is a modified form of TTME model that adopts a hybrid scheme of the layered and the patch approaches. The soil and vegetation components of H are estimated directly using component temperatures in bulk transfer equation. The procedure for the retrieval of component temperatures is the same as that of TTME model. Both TTME and HTEM rely upon the average value of Ta, albedo, aerodynamic resistance, and water vapor pressure of the entire image, which may lead to the incorrect temperature transformations.84 The modified version of trapezoidal approach enhanced two-source evapotranspiration model for land (ETEML) focuses on estimating canopy–air temperature gradient (TCTa) and soil–air temperature gradient (TSTa), which eliminates the need for spatially varying air temperature. In ETEML, physically based theoretical equations define the boundary conditions rather than the empirical equations. The conventional trapezoidal space used in TTME, HTEM, and ETEML assumed to have a horizontal wet edge, which was determined by the lowest air temperature in the study area. The invalid cold edge assumption often led to the underestimation of the EF. The modified two-stage LST-VFC feature space-based, “two-source model for estimating evaporative fraction (TMEF)” succeeded this limitation by calculating the cold edge by PT equation.85 The comparison of LST-VFC space-based models revealed that the H estimation of HTEM showed the least deviation (14.5%) from reference EC measurements compared to ETEML (18%) and TTME (24.5%).83,86,87 In the case of λET, the values are 9.1%, 1.5%, and 24.7% for HTEM, ETEML, and TTME, respectively.


Non-iterative non-feature space-based models

The directional radiometric surface temperature viewed from two different sensors can infer the canopy geometry and the vertical canopy temperature profile. It also nullifies the directional influences of TS while substituting for T0.88 TSEB-2A showed lesser mean absolute percentage error compared to single-source iterative models (λE-15% and H-35% from EC measurements89). The limited availability of sensors with simultaneous measurements in two view angles made this concept less operational. The along track scanning radiometer (ATSR) onboard ERS-1 satellite, advanced along-track scanning radiometer (AATSR) onboard Terra satellite, and ASTR-2 onboard ERS-2 were used in various studies to prove the strength of the dual view angle approach.90,91 The data from SLSTR of Sentinel-3 are a possible data source to implement the dual angular approach (refer to Table 4 in Appendix A for sensor details). The TSEB-2A calculates TC and TS, by solving two simultaneous equations for radiometric surface temperature (Trad(θ)={f(θ)TC4+[1f(θ)]TS4}14) from two different view angles (θ1 and θ2). The dual-angle approach eliminates the dumping of bias into H, as it directly calculates sensible heat flux from TC and TS. The H estimation is extremely sensitive to the clumping of vegetation cover, and its importance was proved in the initial trials of TSEB-2A using the airborne data collected during First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE).89 The simplified two-source energy balance (STSEB) model is a simplified patch version of TSEB model of non-iterative class, which excludes the PT approximation and estimates the total sensible heat flux as the weighted sum of canopy and soil component fluxes at the field scale. STSEB is an efficient model that requires fewer input variables compared to iterative TSEB models but necessary to collect the field-measured component temperatures.92


Unmanned Aerial Vehicles for Turbulent Heat Flux Estimation

The lack of sufficient in situ data sources for the validation of ET models and the requirement of the high-resolution dataset with frequent coverage prompted the utilization of UAV techniques in the domain of surface energy budget.93 The UAVs provide economic and compact instrumentation for real-time monitoring of fluxes in precision farming. The fixed-wing UAVs are preferred over rotary wings for large-scale field applications where heavy RS cameras and micrometeorological sensors are required. The multi-spectral and thermal infrared sensors attached to the UAV platform bridge the gap in scale between the field-based and satellite-based observations. Models such as SEBAL, METRIC, and TSEB-PT have been tested for UAV applications, and the TSEB-PT have exhibited better potential for UAV applications.94 These models are designed for satellite images with medium to coarse resolutions and modifications are required while using it for high-resolution UAV images. The larger data volume for smaller areas demands complex algorithms to achieve better results. TSEB-2T95 and deriving atmosphere turbulent transport useful to dummies using temperature (DATTUTDUT)96,97 are the two models that suit better for UAV applications. The TSEB-2T model employs contextual Trad-NDVI space to estimate the soil and vegetation component temperatures. The model identifies pure pixels of vegetation and soil from the high-resolution images for the estimation of TS and TC. In contrast to contextual models, DATTUTDUT model estimates EF solely from surface temperature information. The small multi-function research and teaching Sonde application proved the reliability of temperature and humidity measurements from UAV platforms for the estimation of sensible heat flux.98,99 Another recent research related to surface flux estimations revealed that the wind speed, temperature, and relative humidity from UAVs were in good agreement with ground-based values and the data quality was sufficient for the computation of the bulk heat transfer coefficient.100


LST and ET Models

The accurate estimation of LST is crucial in RS-based ET models due to its importance as a boundary condition. The first ISLSCP-FIFE reported an error of up to 100  wm2 for instantaneous H measurements due to variations in measured thermal infrared measurements.101 The appropriate calibration and atmospheric correction of satellite-based thermal infrared observations are essential to minimize these errors.102 Due to the complexities and cost of the technology, there are very few operational satellites with thermal bands available to the user community (refer to Table 4 in Appendix A for sensor details).


Thermal Remote Sensing Missions

The history of thermal RS related to ET models traces back to 1962 with the launch of TIROS-II. During the early 1970s, the aerial RS was the only mode of getting thermal images for understanding agricultural crop stress. The launch of GOES (in 1975) and NOAA/AVHRR (in 1979) satellites with thermal sensors became the significant milestones toward the use of satellite RS technology for surface energy balance studies. These missions delivered thermal images with a high temporal resolution (daily) and coarse spatial resolution (1 km). Landsat 5 mission (1985) was the first mission that collected thermal images with a relatively high spatial resolution (120 m) at the cost of its temporal resolution (16 days). Terra (1999) and Aqua (2002) missions with MODIS were of the same category as that of AVHRR, in spatial and temporal resolution, but with a large number of optical and infrared bands that could collect vegetation- and soil-related information along with thermal bands. Suomi NPP or JPSS-1 (2011) with VIIRS sensor improved the spatial resolution to 750 m keeping the daily temporal resolution. ERS-1 (1991) and ERS-2 (1995) satellites delivered thermal images of the same area from two view angles in tandem to facilitate the development of two-source ET models. The collection of thermal images with a high spatial and temporal resolution was a challenge for both polar and geostationary satellites. Use of two polar-orbiting satellites (Landsat) in tandem was a solution to this problem but constrained to the radiometric quality of the data due to two different sensors. ECOSTRESS mission is a new solution to the problem mentioned above, where the thermal scanner is onboard International Space Station, which would deliver thermal images with high spatial (69 m) and temporal (daily) resolution. ECOSTRESS is a unique mission where the users are provided with ready-made ET maps in 30-m resolution using ALEXI and PT-JPL (Priestley–Taylor Jet Propulsion Laboratory) algorithm. The latest version of ECOSTRESS is expected in 2020 or 2021. There are missions such as HyspIRI and TRISHNA in the conceptual and planning stage that could deliver similar products with high spatial and temporal resolution. Refer to Table 3 for a comprehensive list of operational and future thermal RS missions.


Data Assimilation Approaches

The two major approaches based on the use of LST for the estimation of turbulent heat fluxes are the diagnostic/retrieval-based approach and DA approach.103 The retrieval approach mainly focuses on instantaneous heat flux estimations from satellite images, and a variety of empirical and physical models discussed in this review comes under this category. The retrieval methods estimate the turbulent heat fluxes only for the available instances of LST observations. In contrast, the assimilation techniques capture the significant amount of information contained in the temporal datasets of LST and estimate the turbulent heat fluxes for instances without LST observations.104 The recent research in the field of DA techniques yielded numerous techniques that are mainly grouped into variational data assimilation (VDA) techniques and ensemble techniques. VDA techniques utilize the force-restore equation or full heat diffusion equation to predict LST by assimilating the known instances. By minimizing the difference between the RS derived LST and predicted LST, the optimum values of the unknown neutral bulk heat transfer coefficient (CHN) and EF are estimated. The CHN is a function of changing phenology that varies monthly, whereas the EF changes daily, and it is affected by soil moisture and LAI. The CHN scales the sum of turbulent heat fluxes, and EF scales the partitioning of turbulent heat fluxes.105 Among single-source and two-source VDA schemes, the performance of two sources is comparatively better due to the differences in cost functions for minimizing the observed and predicted LST.103 The VDA approach performed better for sparse vegetated dry regions compared to dense vegetated wet areas. The incorporation of daily precipitation as forcing input improved the results in wet areas.106 The main limitation of VDA is that it does not consider the mutual influence of water and energy in the soil plant atmosphere continuum. Therefore, soil moisture assimilation has a powerful influence on the improvement in heat flux predictions.107 When using predicted LST in surface energy balance models, the uncertainties in H estimation by VDA schemes are mainly due to errors in the CHN and LST estimates. Similarly, the uncertainties in λET are influenced by EF, CHN, and LST measurements.103

The ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS) are the two approaches that became better choices compared to the VDA approach. The ensemble approaches are efficient due to their easy formulation, non-linear capture, the ability to account for a wide range of measurement errors, and their capability to provide uncertainty estimates.108 The EnKF and EnKS mainly differ in their selection of inputs for the prediction process. In the EnKF, the prediction for a time t considers all available observations prior to and at time t, whereas in EnKS the observations that are available prior to and subsequent to the time t are used. The critical parameters related to the surface control and surface turbulence in ensemble methods are the same as that of the VDA approach (i.e., CHN and EF), but estimated by a different approach called “state augmentation method.” The H and λET estimates from the EnKS scheme revealed that the uncertainty of the estimated H is related to the errors in EF, CHN, incoming solar radiation, and air temperature. Similarly, the uncertainty of λET depends only on the predicted H and EF.108


Influence of Scale Effects and Validation of ET Models

Validation and comparison of ET models have been conducted across the world in various climatic zones by methods such as the Bowen ratio, lysimeters, EC system, and large aperture scintillometers. (refer Tables 1 and 2). It is essential to compare the performance of models by maintaining similar site conditions, sensor and field validation method. Adhering to these, this review compared the research outcomes of popular ET models at SMACEX site (Moisture–Atmosphere Coupling Experiment in central Iowa) and HiWATER-MUSOEXE site (Heihe Watershed Allied Telemetry Experimental Research in China) for various studies conducted between 2006 and 2018 (refer to Fig. 4). The SMACEX (41.87°N to 42.05°N, 93.83°W to 93.39°W) and HiWATER-MUSOEXE (41.87°Nto 42.05°N, 93.83°W to 93.39°W) fall under hot summer continental climate and cold desert climate, respectively. For SMACEX and MUSOEXE sites, satellite data from ETM+ and ASTER, respectively, were considered for comparison. The comparison based on RMSE and bias of λET and H showed that the VFC-LST feature space-based model HTEM exhibited an overall better performance, followed by TTME and ETEML for both the sites. Among single-source models compared at SMACEX sites, the SEBAL showed better performance statistics compared to SEBS and METRIC, and the same results were obtained in a site nearby Oklahoma using OLI/TIRS data.130 The superior performance of SEBAL could not be generalized for all the ground cover conditions and climatic zones.30

Table 1

RS-based single-source ET models and their uniqueness regarding sensible heat flux estimation.

ModelSpecialty regarding H estimationStrengthWeaknessSuitable scale of operationTimea resolutionSensors usedValidationb
SEBI63EF to estimate HSuitable when wet and dry pixels are not available in the study areaMeteorological variables from the upper boundary of PBL requiredRegionalDETM+ and ASTERGround-based EF63
S-SEBI57EF to estimate HImage-basedNeed constant atmospheric conditionsBasinD and METM+, MODIS, ASTER, AVHRR, TM5, and OLI-TIRSEC,57 LAS,57 and BR109
SEBAL19Use of near-surface temperature gradientCalibration by CIMECSubjective judgment of calibration pixelsField to regionalD, M, S, and YETM+, MODIS, ASTER, AVHRR, TM5, and OLI-TIRSEC,54 LAS,110 LM,111 and BR112
METRIC21Use of near-surface temperature gradientSoil moisture at hot pixel consideredSubjective judgment of calibration pixelsField to regionalD, M, S, and YETM+, TM5, OLI-TIRS, and MODISEC,55 LAS,110 LM,111 and BR109
SEBS33Uses MOS or BAS theory to estimate HModified kB1Too many input parametersLocal to regionalD and MATSR-2, ASTER, AATSR, TM5, ETM+, OLI-TIRS, AVHRR, MODIS, HJ1, and MERISEC,56 LAS,113 LM,114 and BR44
SSEB115EF to estimate HOperational modelHigh sensitivity to TsBasin to regionalD, M, and SASTER, MODIS, OLI-TIRS, AVHRR, TM5, and ETM+EC,65 LM,116 and BR112
SSEBop65Use predefined calibration pixelsOperational modelConstant dT induce bias on estimated fluxesBasin to regionalD, M, S, and YETM+, MODIS, and OLI-TIRSEC,65 LM,117 and BR109

aD, daily; M, monthly; S, seasonal; and Y, yearly. (For some of the models, research articles dealing with all types of time resolutions are unavailable.)

bEC, eddy covariance; LAS, large aperture scintillometer; LM, Lysimeter; and BR, Bowen ratio.

Table 2

RS-based two-source ET models and their uniqueness regarding sensible heat flux estimation.

ModelSpecialty regarding H estimationStrengthWeaknessSuitable scale of operationTimea resolutionSensors usedValidationb
TSEB-PT69Estimation of H by iteration initialized by PT parameterizationUseful at conditions of insufficient meteorological data (e.g., humidity)Use of αPT=1.26 for advective condition is not effectiveBasin to regionalD, M, and SETM+, MODIS, ASTER, TM5, and OLI-TIRSEC75, LAS,67 LM,70 and BR118
TSEB-PM70Estimation of H by iteration initialized by PM parameterizationUseful at conditions of high-vapor pressure deficitMarginal improvement compared to TSEB-PTFieldD and MASTEREC75 and LM70
TSTIM76H is estimated from surface brightness-temperatures taken at times t1 and t2In situ air temperature measurement is not requiredSatellite with high temporal resolution (2 times a day) is requiredRegional to continentalD, M, S, and YIMAGER (GOES), and SEVIRI (MSG)EC,119 LAS,110 and LM120
STSEB92Estimated H as the weighted sum of canopy and soil component fluxesExcludes the PT approximationRequirement of in situ soil and vegetation temperatureLocal to regionalDETM+, MODIS, TM5, and SPOT-5EC,92 LM,121 and BR121
TSEB-2A90Utilization of two-directional Ts observations to estimate HNo in situTa measurements requiredLess availability of satellites with multiple angle radiometersLocalDATSR, ATSR-2, and AATSREC90 and LAS122
TTME54H estimated as a residual of the energy balance equationFewer inputs and avoids the computation of resistance networksCold edge determination using local air temperature overestimates or underestimates fluxesRegionalDMODIS and ASTEREC83
HTEM86Estimated H using TC and TS from trapezoidal spaceHybrid framework using series and parallel resistance conceptSimple radiation transfer models are used, which might fail at complex surfacesRegionalDETM+, MODIS and ASTEREC86 and BR123
Simple Remote Sensing EvapoTranspiration (Sim-ReSET)124Calculated H without rahAll the inputs for the model are obtained from RS dataAssumed homogeneous atmospheric surface layer conditions (which may not be true always)Regional to continentalDMODISEC125 and BR109
ETEML87Estimated H using TC and TS from VFC-LST spaceApplicable for heterogeneous areasSensitive to Ts measurementsLocal to regionalDMODIS, ASTER, and ETM+EC87
ESVEP126Estimated H using TC and TS from VFC-LST spaceAccounts the differences in evaporation and transpiration ratesRequirement of many meteorological variablesLocal to regionalDMODIS, ASTER, and Sentinel-3EC,126 LAS,126 and BR127

aD daily; M, monthly; S, seasonal; Y, yearly. (For some of the models, research articles dealing with all types of time resolutions are unavailable.)

bEC, eddy covariance; LAS, large aperture scintillometer; LM, Lysimeter; and BR-Bowen ratio.

Fig. 4

(a) Comparison of RS-based ET models using SMACEX data (SEBAL,54 METRIC,55 SEBS,128 TSEB-PM,55 TTME,83 HTEM,86 and ETEML87) and (b) comparison of RS-based ET models using HiWATER-MUSOEXE data (SEBS,56 TSEB-PM,75 TSEB-PT,75 HTEM,75 and ETEML129).


The validation of the surface energy balance models depends on the spatial resolution of its outputs.131 The approach for validation of fine-resolution products is generally straightforward due to its scale correspondence with the ground measurements. For coarser-resolution products (>100  m, e.g., MODIS), the already validated fine-resolution products are used after up-scaling or aggregation.132 The methods such as simple averaging, nearest neighbor sampling, bilinear interpolation, or bicubic interpolation are the usual techniques used in the aggregation process. The aggregation of the input bands of the ET models or the aggregation of its fine resolution outputs (fluxes) are the two main aggregation approaches. The effect of aggregation varies with models as well as the resolution to which the aggregation is targeted. A study conducted on the aggregation of RS images from 5 m (very high resolution) to 1 km and its impact on surface energy balance components revealed that at spatial resolutions <30  m the difference in H values were negligible (2%) and it increased up to 24% at lower spatial resolutions.133 This could be due to the impact of aggregation on the actual values of NDVI and Ts, and calibration pixels, which could influence the values of estimated H. Scaling can affect the values of aerodynamic resistance, calculated empirically from vegetation indices. In SEBS, the input aggregation approach using a simple average of the pixel within a kernel window performed better in preserving the magnitude and the spatial distribution of fluxes. Contrary to this, the simple averaging procedure exhibited inferior performance in the case of flux aggregation.134 However, in the case of SEBAL, both the input and output aggregation showed similar spatial patterns.135 In the case of METRIC, the sensible heat flux exhibited higher sensitivity to the aggregation process than the latent heat flux due to the non-linear changes of surface roughness parameters in the model.133 In the VFC-LST feature space-based ET models, the aggregation process has a considerable impact on the shape of the trapezoidal scatter plot, which would change the boundary conditions for ET estimation. The other components Rn and G are relatively insensitive to the changes in spatial scales owing to the fact that these parameters are calculated from incoming solar radiation whose spatial variability is not intensive as in the case of vegetation and soil parameters.136 One of the main factors that hinder the scaling up of the popular RS-based ET models is the need of in situ air temperature data and wind speed data for the estimation of H. Though the single-source models such as METRIC and SEBAL avoided the use of near-surface air temperature by adopting dT approach, the requirement of u for the stability correction restricted its applications beyond the regional scale. Similarly, the dependence of TSEB-PT model on the in situ air temperature values limits its scalability for larger areas. In cases where the in situ air temperature data are unavailable, the capability of ALEXI to calculate Ta internally was utilized to estimate higher resolution turbulent heat fluxes. This is achieved by ALEXI flux disaggregation approach popularly known as DisALEXI.119 Though the disaggregation of ALEXI was proved to be efficient in estimating fluxes, the demand for computationally simple and disaggregation free method resulted in the TSEB-I method. The TSEB-I is a hybrid of single- and two-source approaches that estimates Ta by combining the self-calibration concept of SEBAL and the physically based land surface representation of TSEB. The air temperature was estimated using the cold pixel in the study area by sensible heat flux inversion method.137 A study conducted using DisALEXI, TSEB-I, and TSEB-PT revealed that the estimated air temperature showed an average difference in the order of 1 K only.137 Similarly, the need for spatially varying air temperature restricts the HTEM to scale its application from field to regional scales. By coupling with a simple time-integrated ABL model, the modified HTEM was able to perform better than its basic version and the RMSE was found to be <1  mmd1. The estimated value of Ta, by HTEM-ABL, was in close agreement with the in situ measured values.138 The research outcomes revealed that the architecture of a model free from in situ Ta measurement might not ultimately contribute to its scalability. The best instance is TSEB-PT, where the use of simultaneous directional radiometric temperatures could alleviate the need of Ta but its greater dependency on in situ wind speed disable the model for larger-scale applications. A simple temperature domain two-source model (TD-TSEB) is a model that does not use wind speed measurements to estimate sensible heat flux, but it requires in situ Ta as an input parameter. The moderate sensitivity of TSEB-TD to Ta values promoted its successful application for larger river basins.139



This review recapitulates the essential milestones of research and developments in the domain of sensible heat flux estimation through RS-based methods (Table 4 in Appendix A) for the last 120 years. The events are selected based on the contribution of research outcomes for further research associated with sensible heat flux. The milestones facilitate to categorize the research period into different focal periods of development. Till 1970, most of the research focussed on fundamental research related to micrometeorology, plant physiology, and its relation to ET, canopy temperature, and aerodynamic resistance. The RS-based ET estimation attained more importance between 1970 and 1990 due to the accelerated developments in the satellite RS technology. The evolution of the thermal imaging sensors and their capability to estimate LST has revolutionized the RS-based ET research. The period after 1990 till 2019 was the period of “RS-based ET models,” during which many single-source and two-source models were proposed and validated.


Current Research Activities

Though the two-source models are gaining more attention within the research community, the single-source models still continue to contribute through rigorous revisions for the last 10 years. Among the single-source models, SEBS, SEBAL, and METRIC are mainly modified intensively. In SEBS, the research activities are mainly focussed on the incorporation of the soil moisture information into the model for the improvement of the accuracy of H estimation. The domain of the anchor pixel selection process and its automation are the primary focus in the case of SEBAL and METRIC. In TSEB models, the non-iterative VFC-LST space-based models are getting more attention due to its simplicity and better performance. Current research activities focus on delineating VFC-LST space boundaries appropriately. In two-source iterative models, the research mainly focused on the value of αPT, which is an initialization parameter for the iteration process. Between the years of 1990 and 2020 (period of RS-based ET models), the main research focus was to improve the parameterization of roughness lengths, aerodynamic resistance, canopy resistance, and soil resistance. Statistics of the research activities for the last 10 years revealed that the parameterization of roughness length and aerodynamic resistance was the central area of research (Fig. 5). The application of UAV images in the context of turbulent heat flux estimation is one of the primary focus of the current area of research. There is an accelerated development in the UAV hardware and related algorithms in order to facilitate the transition of the ET models to replace satellite images with UAV products. The near real-time monitoring of ET is the need of the time by utilizing the UAV outputs as better inputs to two-source models such as TSEB-PT, TSEB-PM, and TSTIM. Field crop-based calibration of the models based on leaf area index or canopy height and growth stages makes the RS-based ET domain more crop and field-specific. The application of UAV images in the context of turbulent heat flux estimation need to be refined further by alleviating the challenges, which include the radiometric accuracy of thermal images attributed to low signal-to-noise ratio, camera noise, interimage sensor noise, and atmospheric conditions.140 The existing surface energy balance models rely mainly upon optical dataset for retrieving the parameters of the model either direct or in the indirect form and the potential of SAR dataset such as ESAs Sentinel-1A/1B with 6 days of temporal resolution is less explored. Its high spatial (20 m) and temporal resolution (6 days) make the mission suitable for exploring the possibilities of retrieving crop structural parameters and soil moisture that can be incorporated in the ET models. The thermal data with a high temporal and spatial resolution for surface energy balance models are an ideal requirement, and the possibility of disaggregating of MODIS LST using SAR data and Landsat 8 data is being explored.141

Fig. 5

Thrust area of research between 1990 and 2020. Prepared using the data collected from Ref. 31.



Current Challenges and Perspectives

The synapse between the challenges and the developments of RS-based H estimation techniques witnessed various facets of improvisations cornered mainly to the refinement of the architecture of classical ET models. The unwrapping of challenges of most of the RS-based models knocks at the role of the multitude of variant parameters that significantly contribute toward the robust model architecture. This review attempted to identify the prominent challenges related to the RS-based sensible heat flux estimation approaches using the insights obtained through the research outcomes across the globe. This review tried to address minor challenges related to each model along with model descriptions. The challenges listed below focussed entirely on the current thrust area of research related to turbulent heat flux estimations using RS-based ET models.

  • To modify the VFC-LST feature space-based models for ecosystems where the LST and VFC are positively correlated. The assumption of the inverse relationship between LST and VFC in trapezoidal feature space-based models will not be valid for all types of ecosystems. At mid- and high-latitude regions (forest steppe ecosystem, high mountains, and taiga), the increase in vegetation growth is proportional to the increase in temperature.142 At such conditions, the geometry of the trapezoidal space changes and the approaches for the retrieval of boundary conditions to be modified.

  • To incorporate a dynamic PT coefficient instead of a fixed value of 1.26 in RS-based TSEB-PT model for the initialization of iteration. The fixed value of 1.26 applies to saturated conditions and vary with a multitude of parameters such as soil water stress, vapor pressure deficit, VFC, air temperature, and ground cover conditions.143 The TSEB model did not account the changes in the vapor pressure deficit and stomatal conductance in the model formulation leading to higher TC and lesser H. Though the modified approach TSEB-PM has made a slight improvement in terms of RMSE of estimated flux, the night time ET by both the models showed negative values (not always).74 The TSEB-PT consistently showed this error and modification by a dynamic PT coefficient might address this limitation.

  • To modify the TSEB-2A model using satellite-based multi-angular thermal observations. Using airborne data, the TSEB-multi-angular model was successfully implemented for heterogeneous land surface conditions, which revealed its superior performance compared to TSEB-2A model.89 The multi-angular implementation requires new satellite missions that could procure more than two thermal images simultaneously.

  • To incorporate downscaled soil moisture products into ET models to enhance turbulent heat flux estimations. The spatial resolution available for soil moisture active passive mission (SMAP) is 30 to 40 km with a volumetric accuracy of 0.04  m3m3 in the top 5-cm soil layer, covered with moderately thick vegetation with canopy moisture content <5  kgm3.144 The feasibility of downscaling soil moisture products to 1- to 5-km resolution using thermal bands of MODIS or Sentinel-3, is to be checked in future studies to support regional to continental scale ET estimations. There are successful attempts reported in achieving soil moisture products at 10-km resolution using the synergy of SMAP, AMSR2, and Sentinel-1 datasets.145 The soil moisture products obtained by downscaling could be used to derive surface energy balance components for all-weather conditions.

  • Need for thermal remote sensing missions with high spatial and temporal resolutions. The need for increased cloud-free observations with the high spatial and temporal resolution is essential to estimate crop water requirements daily or weekly basis. The current thermal RS missions deliver thermal data with moderate resolutions at the cost of poor temporal resolutions. The future missions such as ECOSTRESS (new version), HysPIRI, and TRISHNA are promising thermal RS ventures that would provide better datasets for ET models. Refer to Table 3 for future thermal RS missions by various space agencies. Details of operational thermal RS missions are included in Table 4 in Appendix A.

Table 3

Details of operational and future satellite missions with thermal infrared sensors

SensoraSatellite or payloadLaunch (year)Revisit (days)Resolutionb (m)Space agency
Future missions
FCIMTG2021Daily2000TAS France
HyspIRI SBGConceptualPost-2023560NASA
TRISHNA(Feasibility stage)Post-2024350ISRO and CNES
Operational missions
ETM+Landsat 719991660NASA
MODISTerra and Aqua1999 and 2002161000NASA
SEVIRIMeteosat-8, 9, 10, 112002, 2005, 2012, and 2015Daily3000ESA
AVHRRNOAA-18, 192005 and 2009Daily1000NASA
AVHRR/3Metop-A, B, C2006, 2012, 2018Daily1000ESA
VIIRSSuomi NPP, JPSS-12011 and 2017Daily750ESA
AHIHimawari-8, 92015 and 2016Daily2000JAXA
ABIGOES-16, 172016 and 2018Daily2000NASA
SLSTRSentinel-3A, 3B2016 and 2018Daily1000ESA

aSensors with spatial resolution ≤3000  m are considered.

bSpatial resolution of thermal bands.

Table 4

Milestones of research activities related to sensible heat flux estimation.

YearKey research contributions
1900Concept of resistance for explaining the diffusion of water vapor from leaves5
1921The wind speed, the water surface temperature, the eddy diffusivity, distribution of water vapor above the surface, and their effect on evaporation was analyzed146
1930The main driving factor for fluctuations in evaporation is the mean air temperature147
1940The main resistance to evaporation from a surface is due to a thin layer of air just above the surface148
1948Penman’s equation1
1951Big-leaf model149
1954Experimental validation of MO similarity theory150
1956Modified Penman’s equation by adding stability correction151
1960Aerodynamic resistance could be calculated from wind speed and surface resistance152
1960The actual source/sink for mass, heat, and momentum are located at different levels153
1962Radiometric temperature and the air temperature difference is used for estimating ET154
1962Leaf temperature and its relation with transpiration was studied155
1962Surface temperature from meteorological satellite TIROS-II156
1968kB1 parameter8
1970Flux gradient relationship for momentum readdressed (Businger–Dyer concept)157
1970Formulation of Universal functions ψ for heat and mass transfer25
1972The areal thermal scanner was used to understand water stress in cotton canopies158
1972Priestley and Taylor equation159
1975Launched GOES-1. GOES continuity missions continue to produce LST images
1976The areal thermal scanner used for estimating ET160
1977ET is linearly related to the difference between the air and the leaf temperature22
1978Heat Capacity Mapping Mission data was used for evaporation mapping161
1979Start of NOAA-AVHRR missions
1985Landsat-5 mission (thermal sensor: TM, spatial resolution 120 m, and revisit: 16 days)
1985Shuttleworth and Wallace’s model was developed10
1985AVHRR data were used to show the importance of vegetation height and density162
1986Concept of blending height163
1987The formal theoretical base for ET estimation by RS of surface temperature164
1989EF, remained stable during daylight hours165
1991ERS-1 mission (thermal sensor: ASTR-1, spatial resolution 1000 m, and revisit: 2 to 3 days)
1995ERS-2 mission (thermal sensor: ASTR-2, spatial resolution 1000 m, and revisit: 2 to 3 days)
1997Two source approach by two radiometric temperature observations (TSEB-2A)90
1999Massman’s model for estimating kB1166
1999Landsat-7 mission (thermal sensor: ETM+, spatial resolution 60 m, and revisit: 16 days)
1999Terra satellite (thermal sensor: MODIS, spatial resolution 1000 m, and revisit: 1 to 2 days) (thermal sensor: ASTER, spatial resolution 90 m, and revisit: 16 days)
2002ENVISAT satellite (thermal sensor: AATSR, spatial resolution 1000 m, and revisit: 35 days)
2002AQUA satellite (thermal sensor: MODIS, spatial resolution 1000 m, and revisit: 1 to 2 days)
2002Meteosat-8 (thermal sensor: SEVIRI, spatial resolution 3000 m, and revisit: daily)
2005MTSAT-1R or Himawari-6 (thermal sensor: JAMI, spatial resolution 2000 m, and revisit: daily)
2005Pixel component arranging and comparing algorithm167
2005ET mapping algorithm168
2006Metop-A (thermal sensor: AVHRR/3, spatial resolution 2000 m, and revisit: daily)
2007METRIC model21
2008HJ 1B satellite (thermal sensor: IRMSS, spatial resolution 300 m, and revisit: 4 days)
2009Sim-ReSET estimation124
2011SNPP (thermal sensor: VIIRS, spatial resolution 750 m, and revisit: daily)
2013Landsat 8 mission (thermal sensor: TIRS, spatial resolution 100 m, and revisit: 16 days)
2014CBERS-4 satellite (thermal sensor: IRSCAM-4, spatial resolution 80 m, and revisit: 26 days)
2016GOES-16 satellite (thermal sensor: ABI, spatial resolution 2000 m, and revisit: daily)
2016Sentinel-3A satellite (thermal sensor: SLSTR, spatial resolution 1000 m, and revisit: daily)
2016Soil plant atmosphere and RS ET169
2016Backward-averaged iterative two-source surface temperature and energy170 balance solution170
2016NOAA-20 or JPSS-1 (thermal sensor: VIIRS, spatial resolution 750 m, and revisit: daily)
2018ECOSTRESS onboard ISS (spatial resolution 69 m, and revisit: daily)
2019Contextual TSEB for component temperature estimation (TSEB-2T)95



The current review spans across the research conducted to date in the area of sensible heat flux computations using RS-based ET models. The evolution of new-generation surface energy balance models for turbulent flux estimation, integrated with satellite sensor advances in the field of environmental RS, were discussed in the review, citing the milestones of developments starting from classical PM equation. The conceptual framework of classical models that triggered and accelerated the development of RS-based sensible heat flux models are emphasized in the beginning sections. The relevant research outcomes of each model were analyzed and summarized the essential characteristics related to sensible heat flux estimation in Tables 1 and 2. Spatial distribution of the sites where each model was executed is mapped based on the published articles under each model. It aids in the comprehensive understanding of climatic zones, in which the models are being tested. A simple classification scheme for the RS-based ET models was proposed based on the different approaches followed for the sensible heat flux estimation as iterative and non-iterative categories. This review also discussed the role of advance RS techniques such as UAVs and the DA techniques under the purview of turbulent heat flux estimations in ET models. The ET models tested at SMACEX and HiWATER-MUSOEXE sites revealed that the two-source feature space-based model, HTEM performed better compared to all other models.


Appendix A: Milestones

Table 4 presents the chronological order of research and developments in the domain of sensible heat flux estimation with emphasize on the remote sensing techniques.


We would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions, which helped to improve this work.



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M. M. Prakash Mohan is currently pursuing his PhD in the field of advanced remote sensing applications for surface energy balance models at BITS Pilani-Hyderabad Campus. He has 10 years of field experience as a designer for microirrigation systems for diverse environmental and terrain conditions. His expertise contributed relevant research publications in the domain of modification of approaches applied for remote sensing-based ET modeling using the SAR dataset.

Rajitha Kanchirapuzha received her PhD in remote sensing applications for water resources management at IIT Kharagpur in 2007. She is currently working as an assistant professor at BITS Pilani-Hyderabad campus. Her expertise mainly includes remote sensing applications for agriculture, aquaculture, natural resources, and wetland management. She is currently involved in the process of applying advanced remote sensing datasets for developing algorithms for various agriculture and allied areas.

Murari R. R. Varma received his PhD in watershed hydrology and management from the Indian Institute of Science, Bangalore, in 2010. He is currently working as an assistant professor at BITS Pilani-Hyderabad campus. He has expertise in the domains of experimental and field hydrology, hydrochemistry of watersheds, GIS applications in hydrology, and environmental hydrology.

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE)
M. M. Prakash Mohan, Rajitha Kanchirapuzha, and Murari R. R. Varma "Review of approaches for the estimation of sensible heat flux in remote sensing-based evapotranspiration models," Journal of Applied Remote Sensing 14(4), 041501 (15 October 2020).
Received: 23 January 2020; Accepted: 5 October 2020; Published: 15 October 2020

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