Evaluation of evapotranspiration using energy-based and water balance hydrological models

Evapotranspiration (ET) is the process by which water is transferred from the Earth's surface to the atmosphere and is a critical component of the Earth's water cycle to understand the link between land surface and atmosphere (Brutsaert 1982). It depends on both biophysical and environmental processes involved in the interaction between soil, vegetation, and atmosphere (Allen et al. 1998; Fisher et al. 2008; Ershadi et al. 2014). Therefore, considering ET has a major role in regulating climate and hydrology, it should be accurately quantified for proper decision-making in water resource management (Senay et al. 2011; Hwang & Choi 2013; Liaqat & Choi 2015).

The limited networks of ET monitoring stations pose challenges in providing global or regional quantification of ET (Long et al. 2014). Remotely sensed data provide an opportunity to estimate spatial and temporal variations of ET. One of the developed models that used satellite remote sensing is the surface energy balance system (SEBS). The SEBS model was developed by Su (2002) based on the energy balance equation. The SEBS is a widely validated model to calculate the turbulent heat fluxes for the hydrological model from the point scale to the regional scale and requires a high amount of data as inputs (Chen et al. 2013; Lu et al. 2013). The SEBS has been useful in estimating the actual ET in different river basins (Liaqat & Choi 2015; Liaqat et al. 2015) and different types of biomes, such as grassland, cropland, and evergreen needleleaf forest (Gokmen et al. 2012; Ma et al. 2012; Byun et al. 2014; Ershadi et al. 2014).

Another method to calculate ET is using hydrological models. In recent years, there has been a growing interest in using hydrological models to simulate ET. Hydrological models can be used to estimate ET at various scales, from local to regional to global, including different temporal scales. One of the newly developed hydrological models is spatial processes in hydrology (SPHY), introduced by FutureWater (Terink et al. 2015b; Eekhout et al. 2018). The SPHY model links the element of water balance components and simplifies the real-world complexity, requiring only temperature and precipitation as the main dynamical input data.

To address the tradeoff between data requirements and performance outcomes, this research compares and contrasts two models: one model has comprehensive data requirements, known for providing detailed energy-balance component results, while the other model estimates acceptable water balance component results with fewer inputs. This paper evaluates the performance of two energy-based and water balance hydrological models in simulating ET over southeast Africa. The two models are the surface energy balance system (SEBS) and the spatial processes in hydrology (SPHY) model, representing the energy-based and water balance-based hydrological models, respectively. In this study, we compare ET products from different model frameworks to evaluate the performance of models at different land covers. We also analyzed the relationship between hydrological variables and the ET output of the hydrological model. This work is expected to benefit future studies on machine-learning paradigms in terms of selecting data usage for ET prediction by examining the correlation between the amount of input data and model efficiency.

The Skukuza site is characterized by a subtropical arid steppe hot climate type based on the Köppen–Geiger climate classification, while the Mongu site experiences a tropical wet and dry climate. Both Skukuza and Mongu sites have the highest rainfall in the summer season, occurring from December to February (wet period), while the driest season occurs from June to August, with little to no rainfall (Queface et al. 2011).

The flux tower measures turbulent heat fluxes based on the eddy covariance method and uses them as a ground reference to validate the turbulent heat fluxes estimated by remote-sensing techniques. Flux-tower data were obtained from FLUXNET sites. For SEBS processing, inputs from surface meteorological variables such as pressure, wind speed, air temperature, specific humidity, and shortwave radiation are required, and these variables were measured every half hour.

A total of 15 Landsat 5 Thematic Mapper (TM) images of the 2008–2009 period were downloaded from Global Visualization Viewer USGS (http://glovis.usgs.gov/). Landsat 5 TM, launched in 1984 by NASA, has seven bands, including visible, thermal, and infrared bands. Each band has 30 m spatial resolution, while only band 6 has 120 m spatial resolution and 16 days temporal resolution (https://landsat.usgs.gov/). In this study, a threshold for the cloud cover was set at 10% as a filter to reduce the presence of clouds in the Landsat images. This threshold was to minimize the potential hidden biases in the land surface temperature (LST) result when using optical-based satellite images (Holmes et al. 2016; Khand et al. 2019). Thus, during the study period, nine images of Landsat 5 were available to be used for the ZM-Mon site and six images were available for the ZA-Kru site. Preprocessing of Landsat images including the conversion of digital numbers to spectral radiance and reflectance was performed, and these conversions were used to derive other inputs, such as albedo, surface emissivity, LAI, NDVI, and LST.

Terink et al. (2015a) developed the SPHY model, which is a grid-based distributed leaky bucket type of model written in Python language using the dynamical modeling framework of PCRaster. The model has similar soil-column structures to the variable infiltration capacity (VIC) model (Liang et al. 1994), including two upper soil storage layers and a groundwater storage layer. SPHY was developed to simulate terrestrial hydrology under various topographical and hydro-climatic conditions, integrating most of the hydrologic processes, and was capable of implementation in a wide range of applications (e.g., climate and land-use change impact, drought, etc.). Other advantages of this model are the lower input data requirement and ability to be forced using remote-sensing data. The differences in spatial resolution from the inputs were addressed by interpolating each dataset to 300 m resolution using bilinear interpolation while maintaining the quality of the data.

SPHY required static data and dynamic data as input. The static data were used in this study, which consist of the digital elevation model (DEM), land cover map, and soil characteristics. This model only uses temperature (average, maximal, and minimal) and precipitation as temporal hydro-meteorological data-forcing. In this study, we used daily data over the study period from 2008 to 2009.

The Climate Hazards Group InfraRed Precipitation with Station Data (CHIRPS), a 30+ year quasi-global rainfall dataset, was used as the source for the precipitation input. CHIRPS was developed in partnership with researchers at the Earth Resources Observation and Science (EROS) Center of the US Geological Survey (USGS) to provide accurate and comprehensive datasets for early warning purposes (such as trend analysis and seasonal drought monitoring). To construct a gridded rainfall time series for trend analysis, CHIRPS combines in situ station data with 0.05° resolution (5 km) satellite imagery starting in 1981 and continuing up to the present.

The Global Surface Summary of the Day (GSOD) is a gauge-based dataset that includes meteorological data from over 9,000 stations around the world, including mean, maximum, and minimum temperatures. The Integrated Surface Hourly (ISH) database served as the source for GSOD. Inverse distance interpolation has been used to interpolate this station data to 0.1° spatial resolution and the size of the chosen study area.

Data on soil hydraulic properties were obtained from the HiHydroSoil map, which was developed by FutureWater. De Boer (2016) showed that the HiHydroSoil map was made by deriving the soil hydraulic parameters from SoilGrids1km. To complete the SoilGrids1km, the Harmonized World Soil Database (HWSD) was used. According to Terink et al. (2015a), the SPHY model needed information for the top-soil's saturated water content (mm/mm), field capacity (mm/mm), wilting point (mm/mm), and permanent wilting point (mm/mm), as well as the subsoil layers' saturated water content (mm/mm), field capacity (mm/mm), and saturated conductivity (mm/day).

GlobCover, developed by the European Space Agency (ESA), was used as land cover data input in the SPHY model. GlobCover was created using data from the ENVISAT satellite mission's 300 m MERIS sensor (Bicheron et al. 2006). In this study, we also used DEM data with 3 arc-sec spatial resolution to derive other parameters such as slope and flow direction maps using the dynamic modeling framework of PCRaster.

Despite the biases, both models exhibit a reasonable correlation with the measured data. This implies that both SEBS and SPHY capture the underlying processes to some extent, albeit with some discrepancies. Furthermore, when evaluating the performance of the models at specific sites, the SPHY model demonstrates slightly better performance than the SEBS model. The coefficients of determination (R² value) of 0.86 for SPHY at the Mongu site and 0.78 at the Skukuza site indicate a relatively strong relationship between the estimated and measured ET values. These values suggest that the SPHY model explains approximately 86% and 78% of the variability in ET at the Mongu and Skukuza sites, respectively. The analysis of Figures 2 and 3 highlights the contrasting tendencies of the SEBS and SPHY models to overestimate and underestimate ET, respectively. The SPHY model demonstrates slightly better performance at the specific sites analyzed, as indicated by the higher coefficient of determination.

The SPHY model relies heavily on precipitation and temperature as the primary dynamic input data for calculating ET, utilizing water content variables from the current day and the previous day (Equation (16)). This dependency on precipitation and temperature can explain the overestimation during the summer season and the underestimation during the winter season, which might be influenced by the dependency of the SPHY model on water excess and water shortage stress parameters to calculate the actual ET (Terink et al. 2015c). In the summer, the model may overestimate ET due to high precipitation rates, which could result in the calculation of higher ET values. Conversely, during periods of low precipitation in the winter, the model may underestimate ET since there is less water available for ET. The dependency of the SPHY model on precipitation and temperature as the main dynamic input data for ET calculation is in line with the broader literature on ET modeling. For instance, Zhang et al. (2019) emphasized the significance of incorporating accurate precipitation and temperature data to improve ET estimation, as these variables strongly drive the availability of water for ET processes. The observation that zero precipitation and low water content lead to zero ET values and increased drought intensity aligns with the concept of water limitation on ET, as discussed by Teuling et al. (2013). These authors highlighted that drought conditions can severely restrict the availability of water for ET, resulting in reduced or even negligible ET rates.

In the middle of the winter season, the estimated ET values reach zero due to the combined effects of zero precipitation and low water content, leading to an increase in drought intensity. The SPHY model captures this phenomenon, as the lack of precipitation and minimal water content result in limited ET. At the ZM-Kru (savanna) site, the model only slightly underestimates ET due to temporal precipitation, even in small quantities (Figure 5).

Both models showed a good correlation with measured data from the flux tower, indicating their ability to capture the underlying processes. Overall, the two models showed better performance at the ZM-Mon site and marginal performance at the ZM-Kru site, perhaps because of the slightly higher elevation and more homogeneous vegetation at the ZM-Mon site, where woody vegetation predominates with around 60% coverage (based on the information from https://fluxnet.org), compared with the ZM-Kru site (savanna) characterized by vegetation heterogeneity, including various herbaceous and forest-canopy types covering around 10%–30%. This pattern of the ET model is in agreement with the result discussed in Liaqat & Choi (2015).

When comparing the RMSE between the two models, it was observed that the SEBS model exhibited a slightly lower RMSE (2.17 mm day⁻¹) at the ZM-Kru site, which is a savanna ecosystem, than the SPHY model (2.27 mm day⁻¹) (Table 2). These differences might be attributed to the SEBS model's ability to better depict ET in the heterogeneity of the savanna ecosystem due to the more detailed energy balance components in the SEBS than in the SPHY model, which used a water balance system in its algorithm. On the other hand, the SPHY model showed a lower RMSE (0.88 mm day⁻¹) than the SEBS model (1.90 mm day⁻¹) at the ZM-Mon site, representing a forest ecosystem with most of the land covered by woody vegetation. In the SPHY algorithm, the calculation of ET used an evaporation reduction parameter influenced by the soil saturation value instead of using detailed plant and soil properties as input to the model. Thus, the SPHY model can calculate reasonable ET at a site with more homogeneous vegetation than a site with heterogeneous vegetation types. These findings suggest that the performance of the two models varies depending on the ecosystem type. The SPHY model exhibited a reasonable performance compared with the SEBS model at the ZM-Mon site (forest), while the SEBS model performed slightly better at the ZM-Kru site (savanna). It is important to note that both models yielded high IOA values for both sites, indicating that they generally reproduced the observed data well.

This study aimed to compare the estimation of ET using two different framework models: the energy-based model (SEBS) and the water balance model (SPHY). The results were compared with ground observation data from the flux towers of FLUXNET sites (ZM-Mon and ZM-Kru), which are located in different PFT types across southeast Africa. The results demonstrate that both models exhibit a good correlation with the measured data from flux towers with R² (RMSE) values ranging from 0.76 to 0.86 (0.88 to 2.27 mm day⁻¹), indicating their ability to capture the underlying processes of ET. The performance of the SPHY model generally produced reasonable results compared with the SEBS model. Both models have their advantages and limitations in different land cover types. The SPHY model demonstrates a lower RMSE in forest areas with homogeneous vegetation, suggesting its reasonable performance in capturing ET dynamics in such ecosystems. On the other hand, the SEBS model shows slightly better performance in savanna areas, as indicated by lower RMSE values, than the SPHY model. These findings emphasize the importance of considering the specific characteristics of different land cover types, including the vegetation composition, when interpreting the results of ET models.

The sensitivity analysis reveals that the SPHY model is significantly influenced by the rate of precipitation as input data. During summer seasons with high precipitation rates, the model tends to overestimate ET, while in low precipitation periods, it underestimates ET, especially at the ZM-Mon site with forest ecosystems. These findings highlight the need for the accurate representation of precipitation dynamics in ET models to improve their performance. Furthermore, both models display seasonal variations in ET estimation, with overestimation in the wet period and underestimation in the dry period. The occurrence of near-zero ET values during periods of intense drought further emphasizes the sensitivity of the models to water availability.

To enhance the accuracy of estimated actual ET, future studies should focus on conducting uncertainty analyses for the input data of each model, especially precipitation data that majorly influence the ET result. Exploring uncertainties associated with various input variables can provide insights into the reliability and limitations of the estimated ET values. Improving the spatial resolution of input data is crucial as it can impact the model's output and enhance the representation of spatial heterogeneity in ET estimation. Additionally, using more satellite data from multiple sources in future studies can be an option to increase the number of samples to provide analysis for the long-term period and reduce biases due to the limited cloud-free satellite imagery available. This work is expected to benefit other studies that develop machine-learning paradigms in selecting data usage for ET prediction by evaluating the influence of the amount of input data and model efficiency correlates.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.