Complementary Relationship Model Research Articles

Revisiting the global distribution of the exponent of the power-function complementary relationship of terrestrial evaporation: Insights from an isenthalpic index

The complementary relationship (CR) of evaporation is one of widely-used approaches in estimating terrestrial evapration (E). However, the determination of the parameter values in CR-based models remains a difficult task. This is especially true for the new power-function complementary relationship (PCR) model developed recently, in which the key parameter that accounts for the effect of moisture advection over the drying land, b, must be well calibrated with consideration of an approporiate physical basis. Here, by proposing a new isenthalpic index that can be used for determining b directly without resorting to any a priori information of global E, this study found that the resulting b values (median = 1.64, standard deviation = 0.73) are generally smaller and display a narrower range than those reported recently by Kim et al. (2024). When applied with monthly input variables of 124 FLUXNET stations, the gridded b values improve upon E estimates that employ either i) a standard value of b (=2), or; ii) a calibrated value (same for all stations). The global distribution of the gridded b values –in contrast to those obtained by Kim et al. (2024) –aligns with its physical interpretation: low values (1 < b < 2) where the effect of moisture advection is weak (i.e., permanently/periodically wet, humid regions or regions far away from any significant external moisture source) and high ones (b > 2) when strong (i.e., warm arid/semi arid regions near a sea or high mountains of abundant moisture). The gridded b values improve the calibration-free PCR that employs a constant b (=2) and a Priestley-Taylor coefficient linked to the wet-environment air temperature.

Estimation of actual evapotranspiration from different ecosystems on the Tibetan Plateau based on a generalized complementary evapotranspiration theory model

AbstractActual evapotranspiration constitutes a vital component of the exchange of energy and water vapour between the soil‐vegetation and atmospheric systems on terrestrial terrain. Nevertheless, the Tibetan Plateau, owing to its austere environmental conditions, harbours a scarcity of terrestrial monitoring stations. This circumstance presents a formidable challenge in attaining precise estimations of actual evapotranspiration. The complementary relationship method is a potential approach because it requires only routine meteorological data to estimate actual evapotranspiration on a regional or global scale. However, the suitability of the complementary relationship model across diverse ecosystems on the Tibetan Plateau necessitates further investigation. In this study, we scrutinized the simulation of daily and monthly actual evapotranspiration across 18 observation sites spanning eight distinct land use categories on the Tibetan Plateau. We employed the polynomial generalized complementary function introduced by Brutsaert (B2015), alongside its enhanced rendition proposed by Szilagyi (S2017) and Crago (C2018). The outcomes reveal that all three models adeptly replicate the fluctuations in actual evapotranspiration, irrespective of land use category or temporal scale—whether daily or monthly. This is true regardless of whether original or calibrated parameter values are applied. However, there exist significant variations in the performance of these models. In general, the C2018 model demonstrates superior performance across most ecosystems when original parameters are employed. Following parameter calibration, the simulation efficacy of the models experienced marked enhancement. Post parameter calibration, the B2015 model outperforms the other two models notably in desert and wetland environments. Furthermore, the simulation outputs from all three models display heightened sensitivity to parameter α, particularly in the context of the C2018 and S2017 models. These findings suggest that accurate estimation of parameter values is critical to improving the accuracy of estimating actual evapotranspiration. Calibrated parameter values, contingent on a fusion of vegetation, meteorology and surface roughness, exhibit variability across diverse ecosystems.

Assessing the utility of common arguments used in expert review of in silico predictions as part of ICH M7 assessments

Expert review of two predictions, made by complementary (quantitative) structure-activity relationship models, to an overall conclusion is a key component of using in silico tools to assess the mutagenic potential of impurities as part of the ICH M7 guideline. In lieu of a specified protocol, numerous publications have presented best practise guides, often indicating the occurrence of common prediction scenarios and the evidence required to resolve them. A semi-automated expert review tool has been implemented in Lhasa Limited's Nexus platform following collation of these common arguments and assignment to the associated prediction scenarios made by Derek Nexus and Sarah Nexus. Using datasets primarily donated by pharmaceutical companies, an automated analysis of the frequency these prediction scenarios occur, and the likelihood of the associated arguments assigning the correct resolution, could then be conducted. This article highlights that a relatively small number of common arguments may be used to accurately resolve many prediction scenarios to a single conclusion. The use of a standardised method of argumentation and assessment of evidence for a given impurity is proposed to improve the efficiency and consistency of expert review as part of an ICH M7 submission.

Trade‐Offs Between Spatial and Temporal Accuracy of Complementary Relationship Models for Evaporation in an Ungauged Basin

AbstractThe complementary relationship (CR) between actual and potential evaporation has undergone rapid development over the past decades. Commonly, the evaluation of CR models does not comprehensively cover spatial and temporal aspects of model performance; thus, the spatial and temporal accuracy and parameter sensitivity of different CR models remain relatively unknown, especially in ungauged basins. We examine the spatial and temporal performance and parameter sensitivity of four CR models with fixed parameters at the monthly scale over the source region of the Yellow River in China. Additionally, two CR models with distributed parameters were selected as comparisons. Because of the lack of evaporation spatiotemporal “true” values, the corrected water‐balance‐derived evaporation was used as the temporal reference, and the ensemble mean of multiple evaporation products was used as the spatial reference. We find that trade‐offs between the spatial and temporal accuracy of CR models with fixed parameters for basin evaporation should be considered in the application. Although four CR models with fixed parameters exhibited different spatial and temporal performances, their overall performance was generally similar. The parameters of CR models had consistent spatial and temporal sensitivities, and the sensitivity of parameter αe was stronger than that of other parameters. This study demonstrates that CR models with distributed parameters have a promising future in estimating basin or regional evaporation. An integrated spatial and temporal evaluation framework can better distinguish the performance of CR models. The methodologies can be used as a guideline for evaluating and calibrating CR models that match an application's needs.

Estimating the Temporal and Spatial Variations in Evapotranspiration with a Nonlinear Evaporation Complementary Relationship Model in Hyper-arid Areas

Estimating the Temporal and Spatial Variations in Evapotranspiration with a Nonlinear Evaporation Complementary Relationship Model in Hyper-arid Areas

Attribution of decadal runoff changes by considering remotely sensed snow/ice melt and actual evapotranspiration in two contrasting watersheds in the Tienshan Mountains

Water processes in the Tienshan Mountains have undergone great changes under the impacts of climate warming and human activities. Here, based on the Budyko framework, we investigated the respective contributions of climate change and human activities to decadal runoff changes (1982–2014) in two contrary watersheds, i.e., the humid Kashi watershed in the Yili River valley and the arid Boertala watershed in the Ebinur Lake basin, in the Tienshan Mountains, where closing the water balance is difficult due to the scarcity of precipitation gauges. To achieve closure of the decadal water balance of the study watersheds, we estimated evapotranspiration from a complementary relationship model and snow/ice melt using the degree-day method with the remote sensing snow cover product. We found that the increase of rainfall (+61.6 mm) and snow/ice melt (+57.3 mm) dominated the increase of runoff (+87.2 mm, from 398.2 mm in 1982–1992 to 485.4 mm in 1993–2014) in the Kashi watershed, contributing 47.1 mm (54.8%) and 43.8 mm (51.0%), respectively, to the increase of runoff. Unlike the Kashi watershed, human activities contributed −13.8 mm (−103.7%) to the runoff (+13.9 mm, from 61.4 mm in 1982–1997 to 75.3 mm in 1998–2014) in the Boertala watershed. Most of the increase in rainfall (+62.5 mm) and snow/ice melt (+13.6 mm) was consumed by the increase of ET (+64.0 mm) instead of runoff. Further analysis showed that most of the increases in snow/ice melt and ET were contributed from the high (>2500 m) and low (<1500 m) elevation regions, respectively. Snowmelt showed a decreasing trend in low elevation regions. Our study highlighted the importance of snow/ice melt and ET in understanding decadal changes in runoff in the Tienshan Mountains.

Assessment of long-term water stress for ecosystems across China using the maximum entropy production theory-based evapotranspiration product

Water demand growth coupled with its high spatial-temporal mismatch of water resources will lead to an increasing water scarcity worldwide. In order to investigate a robust long-term water stress for ecosystems and regions across China, the improved maximum entropy production (MEP) method was utilized to obtain a reliable evapotranspiration (ET) product during 1982–2015. Afterwards four water stress indices were constructed based on the MEP, Penman, Priestley-Taylor and complementary relationship model. The MEP estimated ET showed a close agreement with measurements at eddy covariance sites, with R2 = 0.89 and RMSE ranged from 5 to 12 mm/month. All ecosystems were indicated to suffer from a high risk of water stress, and were ranked by desert (0.67–0.93), grassland (0.60–0.78), settlement (0.49–0.63), farmland (0.48–0.63), and forest ecosystem (0.45–0.58) with four indices. Patterns of water stress at the provincial levels were revealed. Provinces including Xinjiang, Qinghai, Inner Mongolia, and Gansu in the northern regions displayed the highest water stress, and months from December to February were most vulnerable to extreme water stress. Overall, results revealed that the MEP model-based water stress index can well characterize the water stress footprints for all ecosystems and regions in China. This study can support the policy-making for improving water use efficiency and optimizing water resource management to alleviate water stress on large scales.

Evaluations of Remote Sensing-Based Global Evapotranspiration Datasets at Catchment Scale in Mountain Regions

Evapotranspiration (ET) is essential for connecting ecosystems and directly affects the water consumption of forests, grasslands, and farmlands. Eight global remote sensing-based ET (RS_ET) datasets generated using satellite imagery and ground-based observations were comprehensively assessed using monthly ET time series simulated by the water balance (WB) method at the catchment scale in the Hengduan Mountain (HDM) region, including the Nu River, Lancang River, and Jinsha River basins. The complementary relationship (CR) model, which derives ET from meteorological data, was also evaluated against WB-based ET (WB_ET). In addition, WB_ET, RS_ET, and CR-based ET (CR_ET) data were used to investigate ET spatial and temporal variations at the catchment, grid, and site scale, respectively. Most RS_ET datasets accurately simulated monthly ET with an average index of agreement ranging from 0.71–0.91. The Operational Simplified Surface Energy Balance dataset outperformed other RS_ET datasets, with Nash–Sutcliffe efficiency coefficient (NSE) and Kling–Gupta efficiency values of 0.80 and 0.90, respectively. RS_ET datasets generally performed better in northern semiarid areas than in humid southern areas. The monthly ET simulation by the CR model was consistent with that of the WB_ET in the HDM region, with mean values of correlation coefficient (cc) and NSE at each site of 0.89 and 0.68, respectively. The model showed better performance in simulating monthly ET in the Lancang River Basin than in the Nu River and Lancang River basins, with mean cc and NSE of 0.92 and 0.83, respectively. Generally, annual ET trends were consistent at the catchment, grid, and site scale, as estimated by the WB method, RS_ET datasets, and CR model. It showed a significant decreasing trend in the northern semiarid region of the HDM while exhibiting an increasing trend in the humid southern region.

Calibration‐Free Complementary Relationship Estimates Terrestrial Evapotranspiration Globally

AbstractWhile large‐scale terrestrial evapotranspiration (ET) information is essential for our understanding of the Earth's water and energy cycles, substantial differences exist in current global ET products due partly to uncertainties in soil‐ and vegetation‐related parameters and/or precipitation forcing. Here a calibration‐free complementary relationship (CR) model, driven purely by routine meteorological forcing (air and dew‐point temperature, wind speed, and net radiation), mainly from ERA5, was employed to estimate global ET rates during 1982–2016. Modeled ET agrees favorably with (a) monthly eddy‐covariance measurements of 129 global FLUXNET sites, and; (b) water‐balance‐derived ET of 52 basins at the multiyear mean and annual scales. Additional evaluations demonstrate that the CR is very competitive, in comparison with other 12 widely used global ET products. The 35‐years mean global land ET rate from the CR is 500 ± 6 mm yr−1 (72.3 ± 0.9 × 103 km3 yr−1) with more than 70% of the land area exhibiting increasing annual ET rates over the study period. Globally, CR ET significantly increased at a rate of 0.31 mm yr−1 during 1982–2016, suggesting a 2.2% increase in global land ET over last 35 years. Model inter‐comparisons indicate that global annual CR ET values and their trend are close to the median of not only the 12 ET products chosen but also that of 20 CMIP6 models. Since this calibration‐free CR model requires no precipitation (except in sea‐shore deserts for a subsequent ET correction), vegetation or soil data, it could be incorporated into complex hydrological and/or climate models, thereby facilitating large‐scale hydrological and climate simulations.

Investigation of a non-linear complementary relationship model for monthly evapotranspiration estimation at global flux sites

AbstractProper parameterization of the parameter (αe) that governs the wet environment evaporation is critical for the regional estimation of evapotranspiration (ET) using the generalized complementary relationship (GCR) model. Here, we proposed a global parameterization for the GCR model. We found that the GCR model is sensitive to the parameter αe, which varies spatially with the climate aridity index (AI, the ratio between the apparent potential ET and the precipitation) across 60 sites that span a large variety in climate types worldwide. We found that αe and the AI are generally more strongly correlated in drier climates (AI &gt; 2) where water supply instead of energy supply is the limiting factor for actual ET. The strong correlation between αe and AI can be partly explained by 1) the usage of the air temperature measurements in the non-potential conditions instead of potential conditions, and 2) the insensitivity of the actual ET to the apparent potential ET in the drier climate. Temporally, the parameter αe exhibits seasonal courses at monthly scales and decreases with increasing of vapor pressure deficit (VPD) in a hysteresis loop. Incorporation of the seasonal course and hysteresis significantly improved the model performances at most of the sites. The global parameterization we established can help the GCR model to be a more useful tool for regional and global ET estimations.

Comment on “A Calibration‐Free Formulation of the Complementary Relationship of Evaporation for Continental‐Scale Hydrology” by J. Szilagyi et al.

AbstractSzilagyi et al. (2017) proposed an approach to accommodate Brutsaert's (2015) cubic complementary relationship model by scaling down its independent variable xB. This scaling down approach can work under a condition that xB is larger than its counterparts in the cubic equation, but decreases the performance of the model when xB is smaller than its counterparts.

Evaluation of five complementary relationship models for estimating actual evapotranspiration during soil freeze-thaw cycles

AbstractThe actual evapotranspiration (ETa) estimated models based on the complementary relationship (CR) theory have been applied in various climatic conditions around the world. However, in cold regions, the evaluation of the adaptability of the CR models was performed through complete freeze-thaw cycles, and the adaptability during various periods of soil freeze-thaw cycles has not been evaluated separately. Daily ETa was measured by lysimeters on alpine grassland in the Qilian Mountains from 2010 to 2017, and the measurements were used to evaluate five CR models during the thawing, thawed, freezing, and frozen periods, respectively. The five models comprised the advection-aridity (AA) model of Brutsaert and Stricker, the GG model proposed by Granger and Gray, Morton's CR areal evapotranspiration (CRAE) model, the Han model, and Brutsaert model. The results show that all five CR models were only able to estimate daily ETa during the thawed period. None of the models could estimate the daily ETa during the thawing, freezing, or frozen periods. The basic assumptions of the CR may not be suitable for non-thawed periods with complex energy processes, and no complementary behavior was shown in the non-thawed periods. The CR models must be applied with caution during freeze-thaw cycles in cold regions.

A Comparison of SSEBop-Model-Based Evapotranspiration with Eight Evapotranspiration Products in the Yellow River Basin, China

Accurate evapotranspiration (ET) estimation is important in understanding the hydrological cycle and improving water resource management. The operational simplified surface energy balance (SSEBop) model can be set up quickly for the routine monitoring of ET. Several studies have suggested that the SSEBop model, which can simulate ET, has performed inconsistently across the United States. There are few detailed studies on the evaluation of ET simulated by SSEBop in other regions. To explore the potential and application scope of the SSEBop model, more evaluation of the ET simulated by SSEBop is clearly needed. We calculated the SSEBop-model-based ET (ETSSEBopYRB) with land surface temperature product of MOD11A2 and climate variables as inputs for the Yellow River Basin (YRB), China. We also compared the ETSSEBopYRB with eight coarse resolution ET products, including China ETMTE, produced using the upscaling energy flux method; China ETCR, which is generated using the non-linear complementary relationship model; three global products based on the Penman–Monteith logic (ETPMLv2, ETMODIS, and ETBESS), two global ET products based on the surface energy balance (ETSEBS, ETSSEBopGlo), and integrated ET products based on the Bayesian model averaging method (ETGLASS), using the annual ET data derived from the water balance method (WB-ET) for fourteen catchments. We found that ETSSEBopYRB and the other eight ET products were able to explain 23 to 52% of the variability in the water balance ET for fourteen small catchments in the YRB. ETSSEBopYRB had a better agreement with WB-ET than ETSEBS, ETMODIS, ETCR, and ETGLASS, with lower RMSE (88.3 mm yr−1 vs. 121.7 mm yr−1), higher R2 (0.49 vs. 0.43), and lower absolute RPE (−3.3% vs. –19.9%) values for the years 2003–2015. We also found that the uncertainties of the spatial patterns of the average annual ET values and the ET trends were still large for different ET products. Third, we found that the free global ET product derived from the SSEBop model (ETSSEBopGlo) highly underestimated the annual total ET trend for the YRB. The poor performance of the land surface temperature product of MOD11A2 in 2015 caused the large ETSSEBopYRB uncertainty at eight-day and monthly scales. Further evaluation of ET based on the SSEBop model for site measurements is needed.

Estimating daily evapotranspiration in the agricultural-pastoral ecotone in Northwest China: A comparative analysis of the Complementary Relationship, WRF-CLM4.0, and WRF-Noah methods

Accurate estimation of evapotranspiration (ET) over regional scale is essential for ecohydrological research, agricultural production, and water resources management. However, few studies have been done to estimate regional ET in data lacking, highly heterogeneous arid areas such as the Agricultural-Pastoral Ecotone in Northwest China (APENC). In this study, we compared three actual ET-estimation methods driven by Weather Research and Forecasting (WRF) model in a semi-arid region. We selected the state of the art Weather Research and Forecasting-Community Land Model 4.0 (WRF-CLM4.0) model, the widely used WRF-Noah model and an empirical Complementary Relationship (CR) model to compare their model structures and mechanisms of estimating daily ET in the study region. The WRF model was chosen to address the problem of data scarcity in the study region and to derive model input for ET estimation with high spatial resolution. The seasonal and pooled performances of the three models were verified with in situ observations. Results indicate that the WRF-CLM4.0 model shows a better applicability in the study region, with a superior performance for the pooled datasets (Pearson correlation coefficient [r] = 0.89, root-mean-square error [RMSE] = 0.66 mm/d and Nash-Sutcliffe efficiency coefficient [NSE] = 0.90), while the CR model has a comparable performance (r = 0.91, RMSE = 0.86 mm/d and NSE = 0.85) and the WRF-Noah model shows the worst performance (r = 0.82, RMSE = 0.94 mm/d and NSE = 0.81). The differences are mainly caused by different representations of the land surface characteristics and hydrology of the study region by the three different models. Our analysis shows that the WRF-CLM4.0 model and the CR model are more applicable to the APENC than the WRF-Noah model. For regional applications, the CR model, with fewer parameters and simpler structure, is able to capture the local characteristic and well-suited for data lacking, highly heterogeneous landscapes such as the APENC.

Inferring transpiration from evapotranspiration: A transpiration indicator using the Priestley-Taylor coefficient of wet environment

Abstract Transpiration (T) from plant tissues is an important variable in ecological and agricultural studies. T is usually estimated using the Priestley-Taylor (PT) equation by an analog to the wet environment evaporation (ETw), because vegetation can use water from deep soils. However, the relation between the PT coefficients of T and ETw (αc and αe) was still unclear. In this paper, we tested whether αe can be used as a reasonable indicator of αc at intra-annual and annual scales. We obtained αe by inverting a complementary relationship model with measured evapotranspiration (ET) at the flux sites and obtained αc after ET was partitioned into evaporation (E) and T. We found that αc tends to converge to αe at annual scales, and a linear equation can adequately fit the αc = f(αe) functions at annual scales. With the αc = f(αe) functions determined, satisfactory accuracy (R2 = 0.89) was achieved in estimating T from ET following the “ET → αe → αc → T” calculating process at annual scales. In comparison, the αc ~ αe relationship at 8-day scales are modulated by leaf area index and vapor pressure deficit. However, similar αc = f(αe) functions are identified in the region with the same climate type at 8-day scales, indicating that a single αc = f(αe) function is applicable in the same region. The accuracy in T predictions at 8 day scales deteriorated compared to those at annual scales. However, R2 were still larger than 0.58 at most of the sites. Because great progress in ET estimation has been achieved with the help of thermal remote sensing technique in the last two decades, our results here can provide a new method to estimate T from remotely sensed ET.

Combining generalized complementary relationship models with the Bayesian Model Averaging method to estimate actual evapotranspiration over China

Evapotranspiration, commonly classified as actual evapotranspiration (AET), wet evapotranspiration (WET), and potential evapotranspiration (PET), is an important component of hydrological processes. Several models have been developed for estimating AET, but none are applicable under all conditions due to the complexity of the algorithms and limitations in parameterization. However, PET and WET can be easily calculated using several simple equations based on available climate data. In this study, a regional reanalysis dataset, the China Meteorological Assimilation Driving Dataset for the SWAT model (CMADS), was used to estimate PET and WET, and a generalized complementary relationship (GCR) was used to convert from PET and WET to AET. Then a Bayesian Model Averaging (BMA) method was applied to merge the GCR-based AETs to improve the accuracy of AET estimations in China. After examining the performance of GCR and BMA models at the flux tower sites in different climate zones, we found that other PET models were better than the PM model for predicting AET using GCR. In addition, the BMA estimations were closer to flux tower observations than were those of the GCR-based AET in each climate zone. The average RMSE of BMA-merged AET was reduced to 0.66 mm/day, compared to 1.82 mm/day in the original GCR model. Moreover, the performance of AET estimated by CMADS and other AET products, such as the Global Land Data Assimilation System and the Moderate Resolution Imaging Spectroradiometer Global Evapotranspiration Project was examined at the flux tower sites. The results showed that the CMADS AET product performed better than other AET products in each climate zone with better statistical values. In general, the results showed that the GCR estimates are promising when combined with BMA for future studies to characterize global AET.

The characteristics of moisture recycling and its impact on regional precipitation against the background of climate warming over Northwest China

AbstractFrom 1961 to 2015, annual and seasonal precipitation have shown a significant increase over Northwest China (NW). The change of precipitation is a combination result of the changing recycling precipitation (Pw) contributed by local evapotranspiration (ET) and changing precipitation contributed by advection moisture (Po). In this paper, we calculated the ET based on the observation data of meteorological stations and the complementary relationship model. Then used an improved precipitation recycling model to analyse influential factors on the variation of precipitation over the NW from aspects of ET and advection moisture. The annual precipitation recycling ratio (ρ) fluctuates between 4% and 10% and shows an increasing trend at a rate of 0.3% /10a with a significance level of 0.01. ET, which is the internal supplier of the precipitable water, and advection moisture, which is the outside supplier of the precipitable water, both have displayed significantly increasing trends over the NW. The advection moisture contributes precipitation much more than ET, no matter in the annual scale or seasonal scales. In view of the spatial distribution, Pw shows an increasing trend over the whole NW, but distinctly opposite spatial patterns of Po are found between the western area of NW (WNW) and the eastern area of NW (ENW). Such differences caused the precipitation is characterized by a wetting trend in WNW but a drying trend in ENW.

Complementary‐Relationship‐Based Modeling of Terrestrial Evapotranspiration Across China During 1982–2012: Validations and Spatiotemporal Analyses

AbstractHaving recognized the limitations in spatial representativeness and/or temporal coverage of (i) current ground ETa observations and (ii) land surface model‐ and remote sensing‐based ETa estimates due to uncertainties in soil and vegetation parameters, a calibration‐free nonlinear complementary relationship (CR) model is employed with inputs of air and dew‐point temperature, wind speed, and net radiation to estimate 0.1°, monthly ETa over China during 1982–2012. The modeled ETa rates were first validated against 13 eddy‐covariance measurements, producing Nash‐Sutcliffe efficiency values in the range of 0.72–0.94. On the basin scale, the modeled ETa values yielded a relative bias of 6%, and a Nash‐Sutcliffe efficiency value of 0.80 in comparison with water‐balance‐derived evapotranspiration rates across 10 major river basins in China, indicating the CR‐simulated ETa rates reliable over China. Further evaluations suggest that the CR‐based ETa product is more accurate than seven other mainstream ETa products. The 31‐year mean annual ETa value decreases from the southeast to the northwest in China, resulting in a country average of 406 ± 15 mm/year. The country‐representative annual ETa rates slightly decreased with a rate of −0.5 mm/year (p = 0.86) during 1982–2012. Annual ETa increased significantly over most parts of western and northeastern China but decreased significantly in many regions of the North China Plain as well as in the eastern and southern coastal regions. The present CR‐based method, with its calibration‐free nature and minimal data requirement, could help future calibrations/verifications of the more complex and more data‐intensive land surface model‐ and remote sensing‐based models.

A comparative assessment of SWAT-model-based evapotranspiration against regional-scale estimates

We attempted to assess the actual evapotranspiration (ETa) rates estimated by the Soil and Water Assessment Tool (SWAT) model in an arid region by comparing other regional-based ETa estimates: the Operational Simplified Surface Energy Balance (SSEBop) products, the MODerate Resolution Imaging Spectroradiometer (MODIS) Global Evapotranspiration product (MOD16), and the Generalized Complementary Relationship (GCR) model. The results by the SWAT model clearly showed that ETa rates in the SWAT model are limited by soil water availability. From the comparison of the annual ETa estimates, the GCR model among those ETa estimation methods simulated slightly higher values than the water-balance derived ETa rates (i.e., the difference between annual precipitation and annual stream flow rates). The annual ETa rates of the SSEBop products showed the closest slope of the regression line to 1.0, while the highest R2 (coefficient of determination) value was found from the annual ETa estimates by the SWAT model. The monthly ETa by the GCR model had the highest linear relationship with those of the SSEBop products. However, the SWAT model did not have a strong linear relationship with the monthly ETa of the SSEBop products unlike the comparison against the MOD16 products. This study recommends a further study on more reliable ETa estimates in arid or semi-arid regions by the SWAT model.

Developing an Integrated Complementary Relationship for Estimating Evapotranspiration

The complementary relationship for estimating evapotranspiration (ET) is a simple approach requiring only commonly available meteorological data; however, most complementary relationship models decrease in predictive power with increasing aridity. In this study, a previously developed Granger and Gray (GG) model by using Budyko framework is further improved to estimate ET under a variety of climatic conditions. This updated GG model, GG-NDVI, includes Normalized Difference Vegetation Index (NDVI), precipitation, and potential evapotranspiration based on the Budyko framework. The Budyko framework is consistent with the complementary relationship and performs well under dry conditions. We validated the GG-NDVI model under operational conditions with the commonly used remote sensing-based Operational Simplified Surface Energy Balance (SSEBop) model at 60 Eddy Covariance AmeriFlux sites located in the USA. Results showed that the Root Mean Square Error (RMSE) for GG-NDVI ranged between 15 and 20 mm/month, which is lower than for SSEBop every year. Although the magnitude of agreement seems to vary from site to site and from season to season, the occurrences of RMSE less than 20 mm/month with the proposed model are more frequent than with SSEBop in both dry and wet sites. Another finding is that the assumption of symmetric complementary relationship is a deficiency in GG-NDVI that may introduce an inherent limitation under certain conditions. We proposed a nonlinear correction function that was incorporated into GG-NDVI to overcome this limitation. As a result, the proposed model produced much lower RMSE values, along with lower RMSE across more sites, as compared to SSEBop.