A minimalistic approach for evapotranspiration estimation using the Prophet model

ABSTRACT

This study aimed to evaluate the potential of the recently introduced Prophet model for estimating reference evapotranspiration (ETo). A comparative study was conducted for benchmarking the model results with support vector regression (SVR) and temperature-based empirical models (Thornthwaite and Hargreaves) in southern Japan. The performance of the Prophet, SVR and temperature-based empirical models was evaluated by Nash–Sutcliffe efficiency (NSE) and coefficient of determination (R²). The results indicate that temperature-based Prophet and SVR models have greater accuracy than the empirical models. The Prophet model with sole input of relative humidity, sunshine hours or windspeed showed acceptable accuracy (NSE > 0.80; R² > 0.80), while SVR models with similar inputs showed greater errors. Accuracy improved with increasing number of input parameters, giving excellent performance (NSE > 0.95; R² > 0.95) with all input parameters. Hence, the Prophet model is a new promising approach for modelling ETo with limited input variables.     

Blaney-Morin-Nigeria evapotranspiration model

An evapotranspiration model which parallels that proposed earlier by Blaney and Morin has been developed for application in Nigeria. The model, designated as the Blaney-Morin-Nigeria evapotranspiration model, predicts potential evapotranspiration with accuracy and consistency that are better than the Penman model, under Nigerian conditions. It is suggested that the Blaney-Morin evapotranspiration concept may have similar potential elsewhere when given specific form with appropriate constants derived to reflect climatic peculiarities.     

蒸散发时间尺度转换在日降雨径流过程模拟中的应用

针对目前研究蒸散发时间尺度转换方面的不足,构建了月蒸散发时间尺度转换模型,对淮河史灌河流域黄泥庄小流域1982-1987年月蒸散发能力进行逐栅格解集,并与改进后的AFFDEF分布式水文模型耦合进行日径流过程模拟.结果显示:解集产生的日蒸散发能力随时间在平均值附近波动变化,能很好地体现日蒸发量的时间变异特点;模拟的日径流过程的精度较高,平均Nash效率系数在80%以上,径流深相对误差都在10%以内,平均泊松相关系数为0.912,模拟流量过程曲线与实测值匹配的较好;经与采用平均解集模式的模拟结果对比发现,耦合蒸散发时间尺度转换模型后的模拟精度与前者大体相当,部分指标略优于前者.蒸散发时间尺度转换模型解集产生的日蒸散发量序列能够反映日蒸发量的时间变异特点,更能满足区域日降雨径流过程模拟的需要,可为解决资料匮乏区域水文模拟提供一个新途径.     

M5 model tree based modelling of reference evapotranspiration

This paper investigates the potential of M5 model tree based regression approach to model daily reference evapotranspiration using climatic data of Davis station maintained by California irrigation Management Information System (CIMIS). Four inputs including solar radiation, average air temperature, average relative humidity, and average wind speed whereas reference evapotranspiration calculated using a relation provided by the CIMIS was used as output. To compare the performance of M5 model tree in predicting the reference evapotranspiration, FAO–56 Penman–Monteith equation and calibrated Hargreaves–Samani relation was used. A comparison of results suggests that M5 model tree approach works well in comparison to both FAO–56 and calibrated Hargreaves–Samani relations. To judge the generalization capability of M5 model tree approach, model created by using the Davis data set was tested with the datasets of four different sites. Results from this part of the study suggest that M5 model tree could successfully be employed in modeling the reference evapotranspiration. Further, sensitivity analysis with M5 model tree approach suggests the suitability of solar radiation, average air temperature, average relative humidity, and average wind speed as input parameters to model the reference evapotranspiration Copyright © 2009 John Wiley & Sons, Ltd.     

Spatial modelling of reference evapotranspiration using adjusted Blaney-Criddle equation in an arid environment

Abstract

The Blaney-Criddle (BC) temperature-based equation is used in areas where the complete weather data to estimate reference evapotranspiration (ET₀) by the Penman-Monteith FAO-56 (PMF-56) standard model is complex. In this study, the BC equation was first tested and calibrated against the ET₀ values computed by the PMF-56 method using data from 17 weather stations in arid regions of Iran. Then, geographical information systems (GIS)-based spatially-distributed maps of ET₀ were prepared by means of geographic/topographic factors derived from a digital elevation model (DEM) for all months, separately. The results indicate that the original BC equation overestimated PMF-56 ET₀ by 4% at the study sites. The BC equation produced closer ET₀ estimates to the PMF-56 method after it was calibrated. The error rate of <3% for the spatial modelling approach suggests that the developed ET₀ maps are reliable.

Editor D. Koutsoyiannis; Associate editor D. Yang

Citation Tabari, H., Hosseinzadeh Talaee, P., and Shifteh Some'e, B., 2013. Spatial modelling of reference evapotranspiration using adjusted Blaney-Criddle equation in an arid environment. Hydrological Sciences Journal, 58 (2), 408–420.     

Long-term analysis of measured and simulated evapotranspiration and soil water content

In our study, we analysed a period from 2003 to 2012 with micrometeorological data measured at a boundary-layer field site operated by the Lindenberg Meteorological Observatory – Richard-Aßmann-Observatory of the German Meteorological Service (DWD). Amongst others, these data consist of real evapotranspiration (ETr) rates measured by eddy covariance and soil water contents determined by time domain reflectometry. Measured ETr and soil water contents were compared with those simulated by a simple soil–vegetation–atmosphere transfer (SVAT) scheme consisting of the FAO56 Penman-Monteith equation and the soil water flux model Hydrus-1D. We applied this SVAT scheme using uncompensatory and compensatory root water uptake (RWU). Soil water contents and ETr rates calculated using uncompensatory RWU showed an acceptable fit to the measured ones. In comparison, the use of compensatory RWU resulted in lower model performance due to higher deviations between measured and simulated soil moisture values and ETr rates during dry summer periods.     

A simple model to estimate monthly forest evapotranspiration in Japan from monthly temperature

The estimation of evapotranspiration (E) in forested areas is required for various practical purposes (e.g. evaluation of drought risks) in Japan. This study developed a model that estimates monthly forest E in Japan with the input of monthly temperature (T). The model is based on the assumptions that E equals the equilibrium evaporation rate (E_eq) and that E_eq is approximated by a function of T. The model formulates E as E (mm month⁻¹) = 3·48 T ( °C) + 32·3. The accuracy of the model was examined using monthly E data derived using short‐term water balance (WB) and micrometeorological (M) methods for 15 forest sites in Japan. The model estimated monthly E more accurately than did the Thornthwaite and Hamon equations according to regression analysis of the estimated E and E derived using the WB and M methods. Although the model tended to overestimate monthly E, the overestimation could be reduced by considering the effect of precipitation on E. As T data are commonly available all over Japan, the model would be a useful tool to estimate forest E in Japan. Copyright © 2010 John Wiley & Sons, Ltd.     

Intercomparison of evapotranspiration estimates

Abstract

Five methods of computing reference evapotranspiration from a reference crop (Penman, radiation, Blaney-Criddle, Hargreaves and pan evaporation) have been studied for their applicability under different climatic conditions. The Penman method was taken as the standard and the other four methods were compared against this method. Good correlation was obtained between the values estimated by the four methods and the Penman method although differences in magnitude were found. Regression equations were developed to correct those differences in magnitude. The method suitable for the estimation of reference evapotranspiration for each climatic condition is also suggested.     

A coupled surface resistance model to estimate crop evapotranspiration in arid region of northwest China

The Penman–Monteith (PM) model has been widely used to estimate crop evapotranspiration (ET), but it performs poorly with sparse vegetation. By combining the Jarvis canopy resistance model and the soil resistance model, we have developed a coupled surface resistance model to address this issue. Maize field and vineyard ET, measured by the eddy covariance method during 2007 and 2008, were used to test the estimations produced by the PM model combined with our coupled surface resistance model and Jarvis model, respectively. Results indicate that PM model combined with the coupled surface resistance model produces higher determination coefficient and lower root mean square error when compared with the PM–Jarvis method, either for maize field or for the sparse vineyard, on half‐hourly or daily time scales. Our study confirms that the coupled surface resistance model produces higher accuracy than the Jarvis model and provides a method to calculate resistance parameters for using the PM model to simulate the ET of sparse vegetation. Copyright © 2013 John Wiley & Sons, Ltd.     

Improving evapotranspiration estimation models through quantitative watershed parameter analysis and remote sensing applications

Numerous models had been developed to predict the annual evapotranspiration (ET) in vegetated lands across various spatial scales. Fu's (Scientia Atmospherica Sinica, 5, 23–31) and Zhang's (Water Resources Research, 37, 701–708) ET simulation models have emerged as highly effective and have been widely used. However, both formulas have the non-quantitative parameters (m in Fu's model and w in Zhang's model). Based on the collected 1789 samples from global long-term hydrological studies, this study discovered significant relations between m (or w) and vegetation coverage or greenness in collected catchments. Then, we used these relations to qualify the parameters in both Zhang's and Fu's models. Results show that the ET estimation accuracies of Fu's (or Zhang's) model are significantly improved by about 13.49 mm (or 6.74 mm) for grassland and cropland, 38.52 mm (or 29.84 mm) for forest and shrub land (coverage<40%), 19.74 mm (or 16.17 mm) for mixed land (coverage<40%), respectively. However, Zhang's model shows higher errors compared with Fu's model, especially in regions with high m (or w) values, such as those with dense vegetations or P/E₀ (annual precipitation to annual potential ET) smaller than 1.0. Additionally, this study also reveals that for regions with vegetation cover less than 40%, the annual ET is not only determined by vegetation types, but also relates to the sizes of vegetation-covered areas. Conversely, for regions with vegetation cover more than 40%, the annual ET is mainly determined by the vegetation density rather than vegetation types or vegetation coverage. Thus, linking m (or w) parameters with vegetation greenness allows leveraging remote sensing for forest management in data-scarce areas, safeguarding regional water resources. This study pioneers integrating vegetation-related indices with basin parameters, advocating for their crucial role in more effective hydrological modelling.     

Reedbed evapotranspiration rates in England

Measurements of evapotranspiration from contrasting stands of Phragmites australis [ET(Reed)] were obtained over several years at three sites within England between 1994 and 1998. A comparison with published ET(Reed) values showed the UK rates to be considerably lower than those measured in continental Europe. From the ET(Reed) data monthly crop coefficients [K_c(Reed)] have been developed, which when used with Reference Crop Evapotranspiration will enable reedbed water use to be determined. Due to the differences in study site characteristics, values for K_c varied widely, and it was not considered appropriate to combine results to produce a single set of monthly mean values. However, suggestions are made regarding the application of the K_c(Reed) values to wetland design. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing the impact of interannual variability of precipitation and potential evaporation on evapotranspiration

The impact of interannual variability of precipitation and potential evaporation on the long-term mean annual evapotranspiration as well as on the interannual variability of evapotranspiration is studied using a stochastic soil moisture model within the Budyko framework. Results indicate that given the same long-term mean annual precipitation and potential evaporation, including interannual variability of precipitation and potential evaporation reduces the long-term mean annual evapotranspiration. This reduction effect is mostly prominent when the dryness index (i.e., the ratio of potential evaporation to precipitation) is within the range from 0.5 to 2. The maximum reductions in the evaporation ratio (i.e., the ratio of evapotranspiration to precipitation) can reach 8–10% for a range of coefficient of variation (CV) values for precipitation and potential evaporation. The relations between the maximum reductions and the CV values of precipitation and potential evaporation follow power laws. Hence the larger the interannual variability of precipitation and potential evaporation becomes, the larger the reductions in the evaporation ratio will be. The inclusion of interannual variability of precipitation and potential evaporation also increases the interannual variability of evapotranspiration. It is found that the interannual variability of daily rainfall depth and that of the frequency of daily rainfall events have quantitatively different impacts on the interannual variability of evapotranspiration; and they also interact differently with the interannual variability of potential evaporation. The results presented in this study demonstrate the importance of understanding the role of interannual variability of precipitation and potential evaporation in land surface hydrology under a warming climate.     

Polynomial chaos expansion and response surface method for nonlinear modelling of reference evapotranspiration

The feasibility of polynomial chaos expansion (PCE) and response surface method (RSM) models is investigated for modelling reference evapotranspiration (ET₀). The modelling results of the proposed models are validated against the M5 model tree and multi-layer perceptron neural network (MLPNN) methods. Two meteorological stations, Isparta and Antalya, in the Mediterranean region of Turkey, are inspected. Various input combinations of daily air temperature, solar radiation, wind speed and relative humidity are constructed as input attributes for the ET₀. Generally, the modelling accuracy is increased by increasing the number of inputs. Including wind speed in the model inputs considerably increases their accuracy in modelling ET₀. Mean absolute error (MAE), root mean square error (RMSE), agreement index (d) and Nash-Sutcliffe efficiency (NSE) are used as comparison criteria. The PCE is the most accurate model in estimating daily ET₀, giving the lowest MAE (0.036 and 0.037 mm) and RMSE (0.047 and 0.050 mm) and the highest d (0.9998 and 0.9999) and NSE (0.9992 and 0.9996) with the four-input PCE models for Isparta and Antalya, respectively.     

Spatially distributed hydrotope‐based modelling of evapotranspiration and runoff in mountainous basins

River basins in mountainous regions are characterized by strong variations in topography, vegetation, soils, climatic conditions and snow cover conditions, and all are strongly related to altitude. The high spatial variation needs to be considered when modelling hydrological processes in such catchments. A complex hydrological model, with a great potential to account for spatial variability, was developed and applied for the hourly simulation of evapotranspiration, soil moisture, water balance and the runoff components for the period 1993 and 1994 in 12 subcatchments of the alpine/pre‐alpine basin of the River Thur (area 1703 km²). The basin is located in the north‐east of the Swiss part of the Rhine Basin and has an elevation range from 350 to 2500 m a.s.l. A considerable part of the Thur Basin is high mountain area, some of it above the tree‐line and a great part of the basin is snow covered during the winter season. In the distributed hydrological model, the 12 sub‐basins of the Thur catchment were spatially subdivided into sub‐areas (hydrologically similar response units—HRUs or hydrotopes) using a GIS. Within the HRUs a hydrologically similar behaviour was assumed. Spatial interpolations of the meteorological input variables wereemployed for each altitudinal zone. The structure of the model components for snow accumulation and melt, interception, soil water storage and uptake by evapotranspiration, runoff generation and flow routing are briefly outlined. The results of the simulated potential evapotranspiration reflect the dominant role of altitudinal change in radiation and albedo of exposure, followed by the influence of slope. The actual evapotranspiration shows, in comparison with the potential evapotranspiration, a greater variability in the lower and medium altitudinal zones and a smaller variability in the upper elevation zones, which was associated with limitations of available moisture in soil and surface depression storages as well as with the evaporative demand of the local vegetation. The higher altitudinal dependency and variability of runoff results from the strong increase in precipitation and the decrease in evaporation with increased altitude. An increasing influence of snow cover on runoff as well as evapotranspiration with altitude is obvious. The computed actual evapotranspiration and runoff were evaluated against the observed values of a weighting lysimeter and against runoff hydrographs. Copyright © 1999 John Wiley & Sons, Ltd.     

Estimation of land surface evapotranspiration over complex terrain based on multi‐spectral remote sensing data

Land surface evapotranspiration (ET) plays an important role in energy and water balances. ET can significantly affect the runoff yield of a basin and the available water resources in mountainous areas. The existing models to estimate ET are typically applicable to plains, and excessive data are required to calculate the surface fluxes accurately. This study established a simple and practical model capable of depicting the surface fluxes, while using relatively less parameters. Considering the complex terrain, solar radiation was corrected by importing a series of topographic factors. The water deficit index, a measure of land surface wetness, was calculated by applying the f_c (vegetation fractional cover)‐T_rad (land surface temperature) framework in the two‐source trapezoid model for evapotranspiration model to mountainous areas after corrections of temperature based on altitude variations. The model was successfully applied to the Kaidu River Basin, a basin with few gauges located in the east Tien Shan Mountains of China. Based on the time scale extensions, ET was analyzed at different time scales from 2000 to 2013. The results demonstrated that the corrected solar radiation and water deficit index were reasonably distributed in space and that this model is applicable to ungauged catchments, such as the Kaidu River Basin.     

Prediction of hourly actual evapotranspiration using neural networks,genetic programming,and statistical models

The complexity of the evapotranspiration process and its variability in time and space have imposed some limitations on previously developed evapotranspiration models. In this study, two data‐driven models: genetic programming (GP) and artificial neural networks (ANNs), and statistical regression models were developed and compared for estimating the hourly eddy covariance (EC)‐measured actual evapotranspiration (AET) using meteorological variables. The utility of the investigated data‐driven models was also compared with that of HYDRUS‐1D model, which makes use of conventional Penman–Monteith (PM) model for the prediction of AET. The latent heat (LE), which is measured using the EC method, is modelled as a function of five climatic variables: net radiation, ground temperature, air temperature, relative humidity, and wind speed in a reconstructed landscape located in Northern Alberta, Canada. Several ANN models were evaluated using two training algorithms of Levenberg–Marquardt and Bayesian regularization. The GP technique was used to generate mathematical equations correlating AET to the five climatic variables. Furthermore, the climatic variables, as well as their two‐factor interactions, were statistically analysed to obtain a regression equation and to indicate the climatic factors having significant effect on the evapotranspiration process. HYDRUS‐1D model as an available physically based model was examined for estimating AET using climatic variables, leaf area index (LAI), and soil moisture information. The results indicated that all three proposed data‐driven models were able to approximate the AET reasonably well; however, GP and regression models had better generalization ability than the ANN model. The results of HYDRUS‐1D model exhibited that a physically based model, such as HYDRUS‐1D, might be comparable or even inferior to the data‐driven models in terms of the overall prediction accuracy. Based on the developed GP and regression models, net radiation and ground temperature had larger contribution to the AET process than other variables. Copyright © 2010 John Wiley & Sons, Ltd.