A Two-Source Energy Balance (TSEB) model computes surface energy fluxes using soil surface temperature and canopy temperature. An experiment was carried out in a research farm near the agrometeorological observatory, at Anand, India to parameterize the TSEB model for the mustard (Brassica Juncea) crop, to estimate surface energy fluxes and validate the TSEB-2T model. The TSEB-2T model was validated using net radiation measurements. Results revealed that modeled net radiation under all sowings. Very late sowing had comparatively high dr 0.61, r 0.78** and low RMSE 58.12 Wm−2, MAE 46.47 Wm−2 and low MBE 1.66. Net radiation over mustard ranged from 269 to 538 Wm−2 with relatively high peaks in the second sowing date. Sensible heat flux was relatively high during early growth and after the seed development phase. Latent heat flux and sensible heat flux had inverse partitioning patterns during the crop cycle of the mustard. Ground heat flux had negligible partitioning from net radiation after the seed initiation stage. During vegetative to pod initiation phases, the net radiation fraction for latent heat was high compared to sensible heat. Peak daily evapotranspiration based on modeled latent heat during the flowering to pod initiation phase was about 3.7 mm day−1.

  • A Two-Source Energy Balance (TSEB) model was used to estimate surface energy fluxes over mustard crops.

  • The TSEB-2T model was validated using net radiation measurements. The model performed well under all sowings.

  • Latent heat flux was high during the vegetative and pod initiation phases, while sensible heat flux was high during early growth and after the seed development.

  • Peak evapotranspiration (3.7 mm day-1) was estimated during flowering and pod initiation.

  • The seasonal evapotranspiration of mustrard varied between 192.51 and 316.74 mm under different growing environments.

Water resource managers need to know the actual crop evapotranspiration (ETc) to plan and supervise water resources. Crop water requirements vary significantly during the growing period, primarily due to variations in crop canopy and climatic conditions (Doorenbos & Pruitt 1975; Moursy & Wasfy 2022). This knowledge is a critical practical consideration for improving the water use efficiency in irrigated agriculture. Proper irrigation scheduling, largely governed by ETc (Tyagi et al. 2000; Bwambale et al. 2022), offers substantial potential for enhancing water use efficiency in crop cultivation. In-field ETc estimation and water stress play a crucial role in managing and improving crop water productivity (Zwart & Bastiaanssen 2007; Evans & Sadler 2008; Ahmad et al. 2009; Senay et al. 2009). This becomes particularly crucial in areas where water usage is regulated due to limited resources or competitive demand (Piccinni et al. 2009).
Figure 1

Location of the study (22.54°ʹ N, 72.98°ʹ E, 45.1 m).

Figure 1

Location of the study (22.54°ʹ N, 72.98°ʹ E, 45.1 m).

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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 (Ts) 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.

Study area

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).

Data and measurements

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).

Data pre-processing

Encrypted data matrices were extracted from each image using CAmReport software (CHAUVIN ARNOUX) and saved as comma-separated value (csv) files. Extracted temperature data and visible images were used to classify the canopy and soil. A tool was developed using MATLAB to classify the image by adjusting the threshold for retrieval of canopy temperature and soil temperature. Thresholding was done by visually inspecting the binarization of the data matrix overlayed on the true color image. The screenshot of the tool sowing the process is depicted in Figures 2 and 3. Then soil and canopy temperatures were converted to Kelvin. Soil temperature and canopy temperature were computed from thermal digital numbers and emissivities of loamy sand soil and mustard (0.91 and 0.96, respectively; Rahkonen & Jokela 2003). Thus, soil and canopy temperatures were retrieved from the imagery collected at solar noon on alternate days, so the energy fluxes could be derived directly from the component temperatures without the need for a separate parameterization for the canopy transpiration. Vegetation fractional cover was estimated by processing digital photographs. Daily irradiance value in Wm−2 computed from irradiance measured by pyranometer and logged in MJ m−2 at 10-minute intervals. Percent available soil moisture (PASM) was calculated for loamy sand soil from gravimetric soil moisture. Modeled ET fraction and daily net radiation were used for the estimation of ET.
Figure 2

The tool (CAmReport) used for extraction of thermograph temperature values.

Figure 2

The tool (CAmReport) used for extraction of thermograph temperature values.

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Figure 3

Segmentation of soil and canopy using an application developed in MATLAB to retrieve canopy temperature and soil temperature.

Figure 3

Segmentation of soil and canopy using an application developed in MATLAB to retrieve canopy temperature and soil temperature.

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Figure 4

Schematic representation of the TSEB model (redrawn from Sanchez et al. 2008; Nieto et al. 2019).

Figure 4

Schematic representation of the TSEB model (redrawn from Sanchez et al. 2008; Nieto et al. 2019).

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TSEB-2T model

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.

The fundamental equation of the energy balance at the surface can be expressed as:
(1)
(2)
(3)

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).

The TSEB model partitions fluxes into the canopy cover and soil layers, which depends on the soil temperatures (TS) and canopy temperatures (TC). The resistances network in TSEB considers an interaction between the fluxes of canopy cover and soil, due to an expected heating of the canopy–air by heat transport from the soil. So, H can be estimated as (Norman et al. 1995):
(4)
where Hs and Hc are expressed as:
(5)
(6)
(7)
where ρCp is the volumetric heat capacity of air (J K−1 m−3), TAC is the air temperature at a reference height (K), Tc (K), and Ts (K) are canopy and soil temperature, respectively. Ra is the heat transport aerodynamic resistance (m s−1), Rx is the boundary layer resistance of the canopy leaves (m s−1), and Rs is the resistance to heat flow in the boundary layer immediately above the soil surface (m s−1).
The mathematical expressions of these resistances are detailed in the following equations (also in (Norman et al. (1995)) and Nieto et al. 2019:
(8)
where is the friction velocity (m s−1) computed as:
(9)
(10)
(11)
where L is the Monin–Obukhov length (m) and is expressed as:
(12)
zT and zu are the measurement height for air temperature (K) and wind speed (m s−1). d is the zero-plane displacement height, and z0H and z0M are the roughness length for heat transport and momentum (all those magnitudes expressed in m). and are the stability functions for heat and momentum, respectively. In the version of TSEB, z0H is assumed equal to z0M. k is the von Karman's constant, c, b, C′ are model constants, us is s is the wind speed at height above the soil surface where the effect of soil surface roughness on the free wind movement can be neglected. This wind speed is determined assuming a logarithmic wind profile (Ud) in the air space above the soil.
A similar expression is used to combine the soil and canopy contributions, LEs and LEc, respectively, to the total latent heat flux:
(13)
According to this configuration, a complete and independent energy balance between the atmosphere and each component of the surface is recognized, from the assumption that all the fluxes act vertically. In this way, the component fluxes to the total latent heat flux can be written as:
(14)
(15)
Finally, G can be estimated as a fraction (CG) of the soil contribution to the net radiation (Choudhury et al. 1987):
(16)
where CG can vary in a range of 0.2–0.5 depending on the soil type and moisture. Recent studies have also expressed CG as a function of time to accommodate temporal variation in this fraction (Santanello & Friedl 2003).

Modeling of fluxes

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 (dr). 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 dr 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.

Table 1

Validation statistics for net radiation modeling by TSEB-2T

Early sowingTimely sowingLate sowingVery late sowingGeneral
10 October20 October30 October10 November
R 0.73** 0.37 0.51** 0.78** 0.62** 
dr 0.59 0.40 0.5 0.61 0.54 
RMSE (Wm−259.8 77.49 84.01 58.12 70.84 
MAE (Wm−247.86 61.59 65.43 46.47 55.42 
MBE (Wm−25.99 7.17 −10.53 1.66 1.16 
Early sowingTimely sowingLate sowingVery late sowingGeneral
10 October20 October30 October10 November
R 0.73** 0.37 0.51** 0.78** 0.62** 
dr 0.59 0.40 0.5 0.61 0.54 
RMSE (Wm−259.8 77.49 84.01 58.12 70.84 
MAE (Wm−247.86 61.59 65.43 46.47 55.42 
MBE (Wm−25.99 7.17 −10.53 1.66 1.16 

*Significant (at 5% level) and **highly significant (at 1% level).

Validation of TSEB-2T model for net radiation

Figure 5 shows validation of the model done by comparing modeled and measured net radiation for four growing environments. Figure 5(a)–5(d) illustrates the moderate agreement between modeled and measured Rn for all sowing environments in clear sky conditions. Very late sowing environment had moderately high dr (0.61), highly significant r (0.78**) and low RMSE (58.12 Wm−2), low MAE (46.47 Wm−2) and low MBE (1.66) (Table 1). A similar result was obtained for early sowing with highly significant r, RMSE, MAE and MBE of 0.73**, 59.8, 47.86, and 5.99 Wm−2, respectively. Large differences with a small correlation coefficient (0.37), maximum MBE (7.17 Wm−2), and relatively low agreement index (0.40) were in timely sowing date (Table 1). Overall, the scatter plot (Figure 6) with all observations (n = 207) shows that the model had estimated net radiation fairly precisely. The general validation, resulted r (0.62**), dr (0.54), RMSE (70.84 Wm−2), MAE (55.42 Wm−2), and MBE (1.17 Wm−2) also indicate precision in modeling of net radiation.
Figure 5

Comparison between modeled Rn and measured Rn: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 5

Comparison between modeled Rn and measured Rn: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Close modal
Figure 6

Comparison between modeled Rn and measured Rn for all treatments together (n = 207).

Figure 6

Comparison between modeled Rn and measured Rn for all treatments together (n = 207).

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Surface energy fluxes modeled by TSEB-2T

Day time variation of surface energy fluxes over different growth stages for different growing environments

Daytime energy balance fluxes from 30 to 120 Days after Sowing (DAS) for various growing environments are depicted in Figure 7. In all treatments, energy fluxes followed a typical daytime pattern, with the maximum values occurring at noon and the minimum values in the morning and evening. In Figure 7(b), it is evident that during the vegetative growth stage (30 DAS), the maximum values for Rn (496 Wm–2), LE (387 Wm–2), and the minimum for H (200 Wm–2) were modeled at noon in the growing environment with timely sowing. The minimum and maximum values for G (61 and 83 Wm–2, respectively) were observed at noon in both timely and very late growing environments. In all other growing environments and phases, G remained low. During the flowering stage (70 DAS), Rn and LE reached their maximum values among all phenological stages in all the growing environments. This increase in latent heat flux is attributed to active transpiration by the canopy cover compared to other surface energy fluxes. In Figure 7(b), the maximum values for Rn (538 Wm–2), LE (495 Wm–2), and the minimum values for H (53 Wm–2) and G (9 Wm–2) were observed at noon in the timely sowing date. After 80–120 DAS (Maturity-harvesting phase), LE decreased, and H increased across all growing environments. The maximum values for H (232 Wm–2) and G (20 Wm–2) were observed at noon in the environment starting from very late sowing, possibly due to senescence and rising temperatures at the end of the winter season during the maturity-harvesting phase. There were no significant variations in daytime fluxes among the different varieties.
Figure 7

Day time variations of surface energy fluxes over different growth stages: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 7

Day time variations of surface energy fluxes over different growth stages: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Close modal

Seasonal variation of surface energy fluxes near solar under different growing environments

In the early stages of crop growth, modeled G was more than that of the later phase. Due to the higher soil exposure during early growth phases, the growing environment starting from first sowing had high H (233 Wm−2), high G (98 Wm−2), and high LE (199 Wm−2) than other sowings (Figure 8(a)). During the flowering to pod initiation phase (30 DAS–70 DAS) LE and H were the highest and lowest, respectively among all phonological stages for all growing environments because of canopy cover. Maximum LE (505 Wm−2) and minimum H (61 Wm−2) were observed during the flowering phase from 20 November to 20 December (Figure 8(b)). At pod development to maturity phase (90 DAS-130 DAS), LE was low and H was high under all growing environments, it might be due to the decreased vegetation cover. Figure 8 shows that minimum LE (95 Wm−2) and maximum H (227 Wm−2) were observed at maturity in the last growing environment. Ground heat flux was consistently low after 60 DAS under all growing environments because of lower soil exposure. Varietal variation in seasonal surface energy fluxes was negligible.
Figure 8

Seasonal variations of surface energy fluxes at near solar noon: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 8

Seasonal variations of surface energy fluxes at near solar noon: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

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Relative proportions of heat fluxes

Seasonal relative proportions of heat fluxes

During the crop growing period (Rabi season, 2019–2020) over different phenological phases relative proportion ratio of sensible, latent and ground heat fluxes was explored to associate with prevailing weather, soil moisture and crop growth status. Net radiation (Rn) is one of the prime factors contributing to different surface energy flux components. Rn changes correspond with changes of crop canopy, time and day of the year. Generalized seasonal patterns of fluxes partitioning were identical among sowing dates (Figure 9). During the initial period due to low canopy coverage, radiation partitioned into soil heat flux was of higher magnitude. LE/Rn during the sowing-emergence phase (1–15 DAS) was less than the early vegetative phase due to less canopy cover and Rn mostly contributed to sensible heat flux and soil heat flux. High H/Rn (0.53) and LE/Rn (0.48) were observed on the early sowing date (Figure 9(a)) and due to the more soil exposure maximum G/Rn (0.22) were observed in early sowing and very late growing environment during sowing and emergence phase as compared to other treatments. High LE/Rn attributes active ET by a well-developed canopy in all growing environments. The minimum value LE/Rn (0.40) was observed at the emergence phase at very late sowing date among all growing environments (Figure 9(d)). During the vegetative to seed development (20–90 DAS) phase LE/Rn was higher than H/Rn due to high transpiration except the last growing environment where maximum LE/Rn was only up to the pod initiation phase. The peak value of LE/Rn (0.98), the lowest value of H/Rn (0.13) and G/Rn (0.07) were observed at the flowering to pod initiation phase in timely sowing date (Figure 9(b)). As the crop attained maturity, transpiration reduced, and net radiation was partitioned more in the sensible heat flux and ground heat flux. The result in Figure 9(d) showed that maximum H/Rn (0.84) was in very late sowing among all.
Figure 9

Seasonal trend of net radiation partitioning to sensible and latent heat fluxes: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 9

Seasonal trend of net radiation partitioning to sensible and latent heat fluxes: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Close modal

Day time relative proportion of sensible heat and latent heat fluxes

Daytime LE/Rn and H/Rn ratios over different phenological stages are illustrated in Figure 10. In all treatments, the partitioning of radiant energy into LE, G, and H peaked at noon and was at its minimum during the morning and evening. During the early vegetative phase (30 DAS), H partitioning increased sharply at noon compared to the morning and afternoon. In late sowings (Figure 10(c) and 10(d)), H/Rn and LE/Rn were notably high during the daytime. The fractions of H and LE in the morning and afternoon were similar at 110 DAS in all sowings. In late growing environments, noon partitioning was also identical at this stage. At complete maturity (120 DAS), sensible heat flux dominated, resulting in a high H/Rn ratio.
Figure 10

Day time net radiation energy partitioning to sensible and latent heat fluxes: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 10

Day time net radiation energy partitioning to sensible and latent heat fluxes: (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Close modal

ET and PASM during rabi season (2019–2020)

Seasonal ET (mm) with PASM (%) at different sowing dates is presented in Figure 11. ET gradually increased from the seedling phase (1–20 DAS) to the pod initiation phase (61–70/75 DAS), and later, it decreased. The mean requirement and cumulative ET from the seedling to the maturity phase are presented in Table 2. Gupta et al. (2017) reported nearly similar results for mustard ET estimation. Daily ET was high after the first irrigation in early and timely sowings (Figure 11(a) and 11(b)), while in late and very late sowings, ET rose after the second irrigation. There were peak ET levels at 70 DAS (pod initiation stage) in all growing environments. Daily ET appears to follow the pattern of canopy development in all growing environments. This pattern also reveals that available soil moisture during the crop growth cycle was generally sufficient, with no marked influence on the ET rate. However, late sowing and very late sowing had very low PASM levels just before scheduled irrigations during the season. Therefore, irrigation scheduling in late sowings is particularly crucial for influencing fluxes and their partitioning. Figure 12 displays cumulative ET for different sowing dates of the mustard crop. Cumulative ET for the season is considered as the crop's water requirement. Consequently, the crop water requirements were estimated at 264.45 mm for early sowing, 316.74 mm for timely sowing, 238.62 mm for late sowing, and 192.51 mm for very late sowing.
Table 2

Cumulative and average evapotranspiration at different phenological phases of the mustard crop during Rabi season 2019–2020

Phenological phasesEarly sowing (10 October)
Early sowing (20 October)
Early sowing (30 October)
Early sowing (10 November)
Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)
Vegetative (1–30 DAS) 37.09 1.27 30.95 1.03 27.89 0.96 24.75 0.83 
Flowering (31–75 DAS) 112.12 2.80 164.25 2.89 99.48 2.35 87.46 2.02 
Pod development (76–90/95 DAS) 74.12 2.84 82.13 2.99 70.13 2.97 50.16 2.65 
Maturity (96–130 DAS) 41.12 0.75 39.41 0.99 41.12 1.14 30.14 1.09 
Seasonal 264.45 1.91 316.74 1.97 238.62 1.85 192.51 1.64 
Phenological phasesEarly sowing (10 October)
Early sowing (20 October)
Early sowing (30 October)
Early sowing (10 November)
Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)Cumulative ET (CET) (mm)Average ET (mm day−1)
Vegetative (1–30 DAS) 37.09 1.27 30.95 1.03 27.89 0.96 24.75 0.83 
Flowering (31–75 DAS) 112.12 2.80 164.25 2.89 99.48 2.35 87.46 2.02 
Pod development (76–90/95 DAS) 74.12 2.84 82.13 2.99 70.13 2.97 50.16 2.65 
Maturity (96–130 DAS) 41.12 0.75 39.41 0.99 41.12 1.14 30.14 1.09 
Seasonal 264.45 1.91 316.74 1.97 238.62 1.85 192.51 1.64 
Figure 11

Evapotranspiration and percent available soil moisture (PASM): (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

Figure 11

Evapotranspiration and percent available soil moisture (PASM): (a) sowing on 10th October; (b) sowing on 20th October; (c) sowing on 30th October; and (d) sowing on 10th November.

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Figure 12

Total evapotranspiration over the crop growth cycle under different growing environments.

Figure 12

Total evapotranspiration over the crop growth cycle under different growing environments.

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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.

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