Estimation of evapotranspiration fluxes over mustard using a Two-Source Energy Balance model

The surface energy balance is a widely applied concept, especially in micro-meteorological analysis related to the management of Earth's resources. It significantly influences the microclimate of plant canopies, impacting parameters such as temperature, humidity, evapotranspiration (ET), and, ultimately, plant growth. The growing interest within meteorological, climatic, and hydrological scientific communities in the various components of the surface energy balance, particularly ET, has spurred the development of different micro-meteorological models for estimating surface energy fluxes (Sanchez et al. 2008). However, most of these approaches have its drawbacks, such as fetch requirements, dependence on sophisticated and costly instruments, stability correction, and invalidity under moisture stress conditions (Mohan et al. 2020). Recently, substantial efforts and progress have been made in estimating fluxes and ET from remotely sensed thermal infrared data. The utility of soil temperature and crop surface temperature to detect crop water stress is based on the principle that, under non-stress conditions, plant-transpired water evaporates and cools the leaves. Conversely, in a water deficit situation, transpiration is limited, leading to an increase in canopy temperature (Jackson 1985; Gardner et al. 1992; Pinter et al. 2003; Gonzalez-Dugo et al. 2006). This concept has been leveraged to develop indices that combine meteorological data with remotely sensed thermal information to provide a relative measure of plant water status and health (Hatfield et al. 1983; Moran et al. 1994; Wang & Gartung 2010).

The use of remotely sensed surface temperature (T_s) to estimate the temperature gradient at the ground is motivated by the inability to measure aerodynamic temperature in the One Source Energy Balance Model (OSEB), which does not distinguish between vegetation and soil as sources or sinks. The Two-Source Energy Balance Model (TSEB), developed by Norman et al. (1995), has been demonstrated to outperform the OSEB model (Peddinti & Kisekka 2022). TSEB avoids the estimation of excess resistance resulting from using surface temperature to replace aerodynamic temperature in the OSEB model. The TSEB model can provide the difference between radiometric and aerodynamic surface temperature by considering satellite or sensor view geometry, allowing for the partitioning of surface energy and temperature into soil and vegetation components (Tang et al. 2013). Two-source models, considering both soil and vegetation cover, have been developed to accommodate partial canopy cover conditions and interactions between soil and canopy elements. The TSEB model has been also shown to be more accurate in calculating surface energy fluxes using soil and canopy temperature than other thermally based models (Gao & Long 2008). The model combines the biophysical characteristics of vegetation with the energy balance of the canopy and soil, requiring less information compared to other thermal-based two-source modeling approaches. TSEB-2T variant directly uses canopy temperature and soil temperature, obtained from thermal imagery as opposed to TSEB-PT (Priestley–Taylor formulation) in which the temperatures need to be estimated by iterative process. Evaluation of turbulent fluxes thermal and multispectral imagery showed that TSEB-2T performed notably well compared to other methods (Nieto et al. 2019; Bellvert et al. 2020).

Mustard (Brassica Juncea) is a Rabi crop, requiring relatively cool temperatures during the growing season from October to December in India. It is the third most important oilseed crop globally, following soybean (Glycine max) and palm (Elaeis guineensis Jacq). In India, mustard contributes 28.6% to the total production of oilseeds. The area and production of mustard seeds have been consistently increasing (Shekhavat et al. 2012). In India, the total area under mustard cultivation is 60.09 lakh hectares, with a total production of 80.41 lakh tonnes and an average yield of 1,339 kg ha⁻¹. Because mustard depends on irrigation and grows in large areas, accurate irrigation management and efficient water use need the monitoring and estimation of actual ET. Studies on ET and surface energy balance over mustard fields are scarce (Ramakrishna et al. 1990; Chaudhary et al. 2014; Mukherjee et al. 2016). Surface energy balance study using imaging infrared thermometry is also rarely attempted for the purpose. Given the importance of ET estimation and the paucity of previous studies, the objective of this study is to parameterize and assess the TSEB-2T model for estimating the energy fluxes and ET needs of mustard crops.

The location of the field experiment is at 22.54°ʹ N latitude and 72.98°ʹ E longitude and at an altitude of 45.1 m above mean sea level and the research farm falls under Middle Gujarat Agro-Climatic Zone-III of the Gujarat State (Figure 1). The climate of Anand is categorized as semi-arid tropical with intense hot summer and mild winter. In this region, most of the rainfall is received from the southwest monsoon currents and the average annual rainfall of Anand is 860 mm. Considerable fluctuations in the magnitude of the average maximum and minimum temperatures are observed during different seasons of the year. The air temperature during the summer often rises to a maximum of 45 °C in the month of May and drops down to a minimum of 7 °C during January. On average minimum temperature in winter months is about 11 °C. The field experiment was set up using a split-plot design, involving four sowing environments: early (10th October), timely (20th October), late (30th October), and very late (10th November). Additionally, three varieties (Bio-902, GM-3, and GDM-4) were included in the study, each with four replications. The experiment was conducted at the agrometeorological observatory, B. A. College of Agriculture, AAU, Anand (Gujarat), India during Rabi season of the year 2019–2020. The experiment was conducted on loamy sand soil, a true representative soil of the region. The soil is locally known as ‘Goradu’ soil. The soil is loamy sand with alluvial in origin and belongs to Entisols (type: ustorthents).

Canopy and soil temperatures were regularly measured near solar noon with an imaging infrared thermometer (Thermal Camera DiaCAm 2, CHAUVIN ARNOUX) every other day for each treatment within a single replication. Thermal images were captured using the DiaCAm 2.

Dry bulb and wet bulb temperatures were taken using an Assmann psychrometer, representing the ambient air temperature of the canopy for each treatment near solar noon. These measurements were used to calculate the vapor pressure above the crop canopy. Net radiation was recorded at weekly intervals, around solar noon, for each treatment within a single replication, using a net radiometer (NRLite; Kipp & Zonen, The Netherlands). The measured net radiation data were then used to compute daily net radiation through temporal integration of 10-minute intervals records. Radiance spectra of leaves and soil were measured weekly using a spectroradiometer (UniSpec-DC, PP Systems, USA). Wind speed was measured using a pocket weather meter (Kestrel Instruments, Boothwyn, PA). These measurements were taken in parallel with canopy temperature and psychrometric observations for each treatment. Soil moisture levels were estimated using the gravimetric method every other day. Crop height, measured from the ground level to the last terminal leaf, was recorded using a measuring ruler. Leaf width was also measured weekly using a ruler scale. The Leaf Area Index (LAI) was calculated based on measurements of green leaf area using a leaf area meter (LI-3100; LI-COR Inc., USA).

The TSEB model was developed by Norman et al. (1995) and improved by other researchers. Nieto et al. (2019) have developed a Python source code and implemented two-source code (2T) variant of the model. Schematic representation of the model is depicted in Figure 4.

Here, Rn is net radiation, H, LE, and G are the the sensible heat flux, latent heat flux, and soil heat flux, respectively. ‘C’ and ‘S’ subscripts are assigned to canopy and soil layers, respectively. The symbol ‘ ≈ ’ indicates that there are additional components of the energy balance that are usually neglected, like heat advection, and energy for the fixation of CO₂ (Hillel 1998).

Canopy temperature, soil temperature, day of year, time, wind speed, LAI, vegetation fractional cover, air temperature, actual vapor pressure over canopy, incoming short wave irradiance, canopy height and view zenith angle are the main inputs for TSEB-2T model. Leaf width is used for estimating the canopy boundary resistance. The model uses measurement heights for wind profile estimation and to calculate resistances to heat transport. Day of the year, latitude, longitude, and observation time were used to calculate solar angles. Once TSEB is configured, it parses all the information for computation. The configuration file includes site and canopy description, types of TSEB model, spectral properties, and additional input with constant soil heat flux to net radiation ratio. The main outputs of the TSEB-2T model are net radiation, sensible heat flux, latent heat flux and soil heat flux. ET fraction, daily net radiation and latent heat of vaporization could be used for the estimation of ET using the following formula. TSEB-2T model was validated only for net radiation with measured value of net radiometer. Statistical parameters (Table 1) used for validation are Pearson correlation coefficient (r), Mean Bias Error (MBE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and refined agreement index (d_r). The correlation coefficient r, was considered a measure of the strength of association and its direction. The values of r range from −1 to +1, where ±1 indicates the perfect positive or negative agreement and 0 the perfect disagreement. The d_r is a statistical index of performance, considered to be more rationally related to model accuracy than other indices (Willmott et al. 2012). It ranges from − 1.0 to 1.0 for no agreement to perfect agreement.

Understanding energy fluxes over geographical areas with extensive mustard cultivation is crucial to characterize microclimatic conditions and water demans. The modeling of net radiation by the TSEB model, based on the canopy–air temperature difference, demonstrates a relatively high level of accuracy. Notably, the modeling is more precise when applied to the very late sowing of mustard. Net radiation values over mustard fields vary, ranging from 269 to 538 Wm⁻², with relatively high peaks observed during timely sowing. Sensible heat flux exhibits higher values during the early growth stage (30 DAS) and after the seed development phase (90 DAS) compared to other phases of the crop cycle. Ground heat flux, on the other hand, shows negligible partitioning from net radiation after the seed initiation stage (80 DAS). During the vegetative to pod initiation phases, there are significant ET losses, resulting in a higher fraction of net radiation allocated to latent heat compared to sensible heat. The peak daily ET is modeled during the flowering to pod initiation phase, approximately at 3.7 mm per day. For mustard sown on 20th October, the estimated water loss through ET is approximately 316.74 mm. In contrast, very late sowing (on 10th November) results in the lowest ET loss, approximately 192.51 mm.

R.V. collected and analyzed the research data, prepared and wrote the manuscript. M.M.L. contributed to the ideas, methodology, visualization, developed a tool to classify thermal imagery, mentorship, and review/commentary.

The MATLAB-based tools used in this study are available on request.

The manuscript is conducted within the ethical manner advised by the Water & Climate Change. This study is our own original work, which has not been previously published elsewhere.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.