A complementary relationship evaporation model referring to the Granger model and the advection–aridity model

A complementary relationship evaporation model has been proposed and verified based on evaluations of the advection–aridity model and the Granger's complementary relationship model (Granger model) in dimensionless forms. Normalized by Penman potential evaporation, the Granger model and the advection–aridity model have been transformed into similar dimensionless forms. Evaporation ratio (ratio of actual evaporation to Penman potential evaporation) has been expressed as a function of dimensionless variable based on radiation and atmospheric conditions. Similar dimensionless variables for the different functions have been used in the two models. By referring to the dimensionless variable from the advection–aridity model and the function from the Granger model, a new model to estimate actual evaporation was proposed. The performance of the new model has been validated by the observed data from four sites under different land covers. The new model is an enhanced Granger model with better evaporation prediction over the aforementioned different land covers. It also offers more stable optimized parameters in a grassland site than the Granger model. The new model somewhat approximates the advection–aridity model under neither too wet nor too dry conditions, but without its system bias. Copyright © 2011 John Wiley & Sons, Ltd.     

QUELQUES EXEMPLES D'APPLICATION DES MESURES DE RAYONNEMENT À LA DÉTERMINATION DE L'ÉVAPO-TRANSPIRATION EN CLIMAT TROPICAL

ABSTRACT

From data obtained at stations set up in Chad, the Central African Republic and Congo-Brazzaville, stretching from the desert to the equatorial zone, it has been possible to compare measurements of evapotranspiration and of evaporation with results obtained by using the energy-balance method. Several difficulties arise in these comparisons since the scale of the measurements (small evaporating surfaces) is generally different from that of the climatic characteristics on which evaporation is dependent.

After proposing a model to resolve this problem and fitting the empirical coefficients of Penman's formula, the author has applied this formula to some results derived for stations in Congo-Brazzaville; the potential evapotranspiration calculated in this way is in good agreement with water balance data.

At these stations the evapotranspiration energy may be a constant percentage of global short-wave radiation.

Finally, the energy-balance method has been used at Brazzaville to measure the actual evapotranspiration over grass during the dry season. The result is that actual and potential evapotranspiration were found to be closely related.

These results indicate the importance of solar readiation in the field of hydrometeorology.     

A nonlinear function approach for the normalized complementary relationship evaporation model

A nonlinear function approach for the normalized complementary relationship evaporation model that is different from the methodology maintaining the symmetric complementary relationship with appropriate definitions of potential and wet‐environment evaporation is proposed and verified. This approach employs the definitions used in the advection‐aridity model, wherein the potential is estimated using the Penman equation. Normalized by Penman potential evaporation, the complementary relationship model is expressed as a function describing the relationship between the evaporation ratio (the ratio of the actual to the Penman potential evaporation) and the proportion of the radiation term in Penman potential evaporation. The new nonlinear function proposed in the current study is approximately equivalent to the advection‐aridity and the modified Granger models under conditions that are neither too wet nor too dry, but is more reasonable under arid and wet conditions. The new nonlinear function model performs well in estimating actual evaporation, as verified by the observed data from four sites under different land covers. Copyright © 2011 John Wiley & Sons, Ltd.     

Appraisal of Budyko formula in calculating long‐term water balance in humid watersheds of southern China

The Budyko formula for estimating the long‐term average annual evaporation is applied to calculate the long‐term water balance in 29 humid watersheds of southern China. As a result of overestimation of evaporation, the long‐term average annual runoff is underestimated, with the Nash‐Sutcliffe efficiency (NSE) at just ? 17%. A one‐variable linear regression model is employed to find that the Budyko scatter and the relative errors of Budyko runoff and evaporation estimates are all closely related to the long‐term aridity index. Through combining the original Budyko formula with the different linear regression models for estimating the Budyko estimation errors, three forms of revised Budyko equation for estimating the long‐term average annual runoff are derived, with all their NSE values to be around 66%. After calibration, both one‐parameter Turc‐Pike and one‐parameter Fu equations lead to the NSE value of 60% in estimating long‐term average annual runoff. Two conclusions are made, with the first one being that, the nonparametric Budyko formula, although very intuitive and very simple, does not apply well in calculating long‐term water balance in 29 humid watersheds in southern China. The second one is that, the parametric evaporation formulae, with locally optimized parameter values, can achieve better accuracy in estimating long‐term average annual evaporation and runoff than the nonparametric Budyko evaporation formula. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of the grid square technique to mapping of evapotranspiration

A grid-based technique for mapping potential evapotranspiration is described. An attempt is made to extrapolate the constituent parameters of Penman's equation (1962) over a grid, so that the equation can be evaluated for every grid square. Data for a part of Southwest England are used to demonstrate the technique. Aspect and slope, which determine evaporation to a considerable degree, have been included using a formula derived by Okanoue.     

On the influence of microphysics parametrization on the rainfall rates in numerical models of clouds

Accuracy of formulas for growth by accretion and evaporation of rain in bulk parametrization of these processes for the case of light and moderate precipitation is investigated. It is done by comparison of results from two simple models: with bulk approach and with exact calculations of growth or evaporation of drops in each size bin separately. Growth by accretion is accurately represented in bulk parametrization but rain evaporation is overpredicted. Corrected formula for rain evaporation is suggested.     

Comparison of varied complexity models simulating recharge at the field scale

Numerical models are frequently used for the regional quantification of groundwater recharge. However there is a wide range of potential models available that represent the land surface with varying degrees of complexity, but which are rarely tested against observations at the field scale. We compared four models that simulate potential recharge at four intensively monitored sites with different vegetation and soil types in two adjacent catchments. These models were: Penman–Grindley, UN Food and Agricultural Organization, SPAtial Distributed Evaporation and Joint UK Land Environment Simulator. Standardized, unoptimized land surface datasets and pertinent literature were used for parameterization to reflect practice in regional water resource management and planning in the UK. The models were validated against soil moisture observations at all sites, as well as observed transpiration and interception and calculated total evaporation over a year at a woodland site. Soil moisture observations were generally reproduced well, but there were significant differences in how the models apportioned precipitation through the hydrological cycle. This demonstrates that soil moisture data alone are not a good diagnostic for groundwater recharge models. Significant differences in potential recharge were produced by models at both grassland sites, although simulated average annual potential recharge varied by only 15% at the grassland site on permeable soil. At the woodland sites, soil moisture contents were reproduced least accurately, and there were large differences in potential recharge at both woodland sites. This predominantly resulted from varied and inaccurate simulation of evaporation, particularly in the form of interception losses where this was explicitly represented in models. Differences in model structure, such as runoff representation, and parameter selection also influenced all results. Hydrological Processes © 2013 John Wiley & Sons, Ltd.     

Estimating the sensitivity of mean annual runoff to climate change using selected hydrological models

Hydrological model sensitivity to climate change can be defined as the response of a particular hydrological model to a known quantum of climate change. This paper estimates the hydrological sensitivity, measured as the percentage change in mean annual runoff, of two lumped parameter rainfall-runoff models, SIMHYD and AWBM and an empirical model, Zhang01, to changes in rainfall and potential evaporation. These changes are estimated for 22 Australian catchments covering a range of climates, from cool temperate to tropical and moist to arid. The results show that the models display different sensitivities to both rainfall and potential evaporation changes. The SIMHYD, AWBM and Zhang01 models show mean sensitivities of 2.4%, 2.5% and 2.1% change in mean annual flow for every 1% change in mean annual rainfall, respectively. All rainfall sensitivities have a lower limit of 1.8% and show upper limits of 4.1%, 3.4% and 2.5%, respectively. The results for potential evaporation change are −0.5%, −0.8% and −1.0% for every 1% increase in mean annual potential evaporation, respectively, with changes rainfall being approximately 3–5 times more sensitive than changes in potential evaporation for each 1% change in climate. Despite these differences, the results show similar correlations for several catchment characteristics. The most significant relationship is between percent change in annual rainfall and potential evaporation to the catchment runoff coefficient. The sensitivity of both A and B factors decreases with an increasing runoff coefficient, as does the uncertainty in this relationship. The results suggest that a first-order relationship can be used to give a rough estimate of changes in runoff using estimates of change in rainfall and potential evaporation representing small to modest changes in climate. Further work will develop these methods further, by investigating other regions and changes on the subannual scale.     

Impact of flooded rice paddy on remotely sensed evapotranspiration in the Krishna River basin,India

Evapotranspiration (ET) is one of the major water exchange processes between the earth's surface and the atmosphere. ET is a combined process of evaporation from open water bodies, bare soil and plant surfaces, and transpiration from vegetation. Remote sensing-based ET models have been developed to estimate spatially distributed ET over large regions, however, many of them reportedly underestimate ET over semi-arid regions (Jamshidi et al., Journal of Hydrometeorology, 2019, 20, 947–964). In this work, we show that underestimation of ET can occur due to the open water evaporation from flooded rice paddies ignored in the existing ET models. To address the gap in ET estimation, we have developed a novel approach that accounts for the missing ET component over flooded rice paddies. Our method improved ET estimates by a modified Penman-Monteith algorithm that considered the fraction of open water evaporation from flooded rice paddies. Daily ET was calculated using ground based meteorological data and the MODIS satellite data over the Krishna River Basin. Seasonal and annual ET values over the Krishna Basin were compared with two different ET algorithms. ET estimates from these two models were also compared for different crop combinations. Results were validated with flux tower-based measurements from other studies. We have identified a 17 mm/year difference in average annual ET over the Krishna River Basin with this new ET algorithm. This is very critical in basin scale water balance analysis and water productivity studies.     

Validity of the Bouchet’s complementary relationship at 102 observatories across China

Bouchet in 1963 hypothesized that for large homogeneous land surface with minimum advection of heat and moisture, there exists a 1:1 complementary relationship of potential and actual evaporation coupled through land-atmosphere feedbacks. The complementary relationship has been widely used to estimate regional actual evaporation and explain the pan evaporation paradox. We examine the standardized potential evaporation (potential evaporation divided by wet environment evaporation) at 102 observatories at different elevations across China. Generally, the relationship is appropriate at the low elevations (<1000 m). With the increase of elevation, vapor transfer power becomes much less than radiation energy budget because of lower vapor pressure deficit and stronger global solar radiation. As a result, at the high elevations (over 1000 m), the excess energy resulted by limited moisture availability is not enough to be converted into drying power of the air. This result suggests that the complementary relationship is asymmetric at the high elevations. Supported by the Presidential Special Award Foundation, the Chinese Academy of Sciences (Grant No. O7R70020SD) and the National Key Technology R & D Program (Grant No. 2006BAC08B0408)     

Functional relationship to describe temporal statistics of soil moisture averaged over different depths

Detailed simulation studies, highly resolved in space and time, show that a physical relationship exists among instantaneous soil-moisture values integrated over different soil depths. This dynamic relationship evolves in time as a function of the hydrologic inputs and soil and vegetation characteristics. When depth-averaged soil moisture is sampled at a low temporal frequency, the structure of the relationship breaks down and becomes undetectable. Statistical measures can overcome the limitation of sampling frequency, and predictions of mean and variance for soil moisture can be defined over any soil averaging depth d. For a water-limited ecosystem, a detailed simulation model is used to compute the mean and variance of soil moisture for different averaging depths over a number of growing seasons. We present a framework that predicts the mean of soil moisture as a function of averaging depth given soil moisture over a shallow d and the average daily rainfall reaching the soil.     

Fuzzy logic model approaches to daily pan evaporation estimation in western Turkey / Estimation de l’évaporation journalière du bac dans l’Ouest de la Turquie par des modèles à base de logique floue

Abstract

Abstract Evaporation is one of the fundamental elements in the hydrological cycle, which affects the yield of river basins, the capacity of reservoirs, the consumptive use of water by crops and the yield of underground supplies. In general, there are two approaches in the evaporation estimation, namely, direct and indirect. The indirect methods such as the Penman and Priestley-Taylor methods are based on meteorological variables, whereas the direct methods include the class A pan evaporation measurement as well as others such as class GGI-3000 pan and class U pan. The major difficulty in using a class A pan for the direct measurements arises because of the subsequent application of coefficients based on the measurements from a small tank to large bodies of open water. Such difficulties can be accommodated by fuzzy logic reasoning and models as alternative approaches to classical evaporation estimation formulations were applied to Lake Egirdir in the western part of Turkey. This study has three objectives: to develop fuzzy models for daily pan evaporation estimation from measured meteorological data, to compare the fuzzy models with the widely-used Penman method, and finally to evaluate the potential of fuzzy models in such applications. Among the measured meteorological variables used to implement the models of daily pan evaporation prediction are the daily observations of air and water temperatures, sunshine hours, solar radiation, air pressure, relative humidity and wind speed. Comparison of the classical and fuzzy logic models shows a better agreement between the fuzzy model estimations and measurements of daily pan evaporation than the Penman method.     

Evaporation estimation models for Lake Eğirdir,Turkey

Lake E?irdir is located in the Lakes District in southwestern Turkey and it is the second largest freshwater resource lake. Evaporation is an important parameter in hydrological and meteorological practical studies. This study has three objectives: (1) to develop models for the estimation of daily evaporation using measured data from the automated GroWeather meteorological station located near Lake E?irdir; (2) to compare the evaporation models with the classical Penman approach; (3) to evaluate the potential of each model. The comparisons are based on daily and monthly available data from 2001 and 2002. The evaporation estimation models (EEMs) developed in this paper have lower mean absolute errors and higher coefficient of determination R² values than the Penman method. In order to evaluate the potential of the EEMs, daily evaporation values are calculated by the Priestley–Taylor, Brutsaert–Stricker, de Bruin, Makkink and Hamon methods. The EEMs are statistically indistinguishable from the classical methods on the basis of the parameters of mean, standard deviation, etc. In the evaluation of daily and monthly values, the relative error percentage for daily evaporation has lower values than for monthly evaporation. It can be seen that the EEMs help in calculating daily evaporation rather than monthly. Final evaluation and comparison indicate that there is a good agreement between the results of EEMs and the Penman approach than with the classical methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Retrieval of Large-Scale Hydrological Signals in Africa from GRACE Time-Variable Gravity Fields

Since its launch in April 2002, the Gravity Recovery and Climate Experiment (GRACE) mission is recording the Earth’s time-variable gravity field with temporal and spatial resolutions of typically 7–30?days and a few hundreds of kilometers, allowing the monitoring of continental water storage variations from both continental and river-basin scales. We investigate here large scale hydrological variations in Africa using different GRACE spherical harmonic solutions, using different processing strategies (constrained and unconstrained solutions). We compare our GRACE estimates to different global hydrology models, with different land-surface schemes and also precipitation forcing. We validate GRACE observations through two different techniques: first by studying desert areas, providing an estimate of the precision. Then we compare GRACE recovered mass variations of main lakes to volume changes derived from radar altimetry measurements. We also study the differences between different publicly available precipitation datasets from both space measurements and ground rain gauges, and their impact on soil-moisture estimates.     

Spatial variations and temporal changes in potential evaporation in the Tarim Basin,northwest China (1960–2006): influenced by irrigation?

The spatial pattern and temporal changes in potential evaporation (1960–2006) were evaluated using data from 48 meteorological stations in the Tarim Basin. These stations are located in four typical landscapes with varying irrigation influences. Mean annual potential evaporation is low in stations in the mountainous regions, next in the large oasis regions with extensive irrigation and small oasis regions with restricted irrigation, whereas they are high in the desert regions. The spatial pattern of annual mean potential evaporation is owing to the aerodynamic term, while the radiation term is relatively constant in different regions. The significant levels of the trends in potential evaporation and the radiation and aerodynamic terms in different regions were detected using the non‐parametric Mann–Kendall test. More significant decreasing trends in annual potential evaporation with relatively constant radiation term were found in the oasis regions (especially the large oasis regions) than that in the mountainous and desert regions. In the large oasis regions, the pronounced decrease in potential evaporation is mainly attributed to the decrease in wind speed and the increase in relative humidity. The long‐term mean and annual potential evaporation with an almost constant radiation term were found to be complementary with actual evaporation influenced by irrigation. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating daily lake evaporation from biweekly energy‐budget data

Estimates of daily lake evaporation based on energy‐budget data are poor because of large errors associated with quantifying change in lake heat storage over periods of less than about 10 days. Energy‐budget evaporation was determined during approximately biweekly periods at a northern Minnesota, USA, lake for 5 years. Various combinations of shortwave radiation, air temperature, wind speed, lake‐surface temperature, and vapour‐pressure difference were related to energy‐budget evaporation using linear‐regression models in an effort to determine daily evaporation without requiring the heat‐storage term. The model that combined the product of shortwave radiation and air temperature with the product of vapour‐pressure difference and wind speed provided the second best fit based on statistics but provided the best daily data based on comparisons with evaporation determined with the eddy‐covariance method. Best‐model daily values ranged from ?0.6 to 7.1 mm/day over a 5‐year period. Daily averages of best‐model evaporation and eddy‐covariance evaporation were nearly identical for all 28 days of comparisons with a standard deviation of the differences between the two methods of 0.68 mm/day. Best‐model daily evaporation also was compared with two other evaporation models, Jensen–Haise and a mass‐transfer model. Best‐model daily values were substantially improved relative to Jensen–Haise and mass‐transfer values when daily values were summed over biweekly energy‐budget periods for comparison with energy‐budget results.     

A formula for computation of time-varying recharge of groundwater

This paper presents a formula for computation of time-varying recharge of groundwater. The formula is derived from the basic equation of groundwater flow on an inclined impervious base. This analytical expression can also be used to compute evaporation rate if there is no recharge of groundwater. Readings from electronic data loggers show that recharge of groundwater is highly variable depending on the patterns of rainfall and antecedent conditions of the soil.     

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.     

Layer averaged Richard's equation with lateral flow

In this paper a formulation for layer averaged sub-surface moisture transport, that models the lateral flow, is developed using the Richard's equation. This formulation is consistent with the approach currently adopted in contemporary models used in land–atmosphere interaction studies. Explicit expressions are derived for layer averaged lateral transport contribution from diffusion, gravity, dispersion, and convergence due to land–surface curvature. It is argued that lateral contribution can be a significant component of the total soil-moisture flux. Ignoring these contributions can result in significant model error leading to inaccurate prediction or unrealistic calibration of parameters that compensate for these errors.     

Evaporation process modelling over northern Iran: application of an integrative data-intelligence model with the krill herd optimization algorithm

ABSTRACT

An integrated data-intelligence model based on multilayer perceptron (MLP) and krill herd optimization – the MLP-KH model – is presented for the estimation of daily pan evaporation. Daily climatological information collected from two meteorological stations in the northern region of Iran is used to compare the potential of the proposed model against classical MLP and support vector machine models. The integrated and the classical models were assessed based on different error and goodness-of-fit metrics. The quantitative results evidenced the capacity of the proposed MLP-KH model to estimate daily pan evaporation compared to the classical ones. For both weather stations, the lowest root mean square error (RMSE) of 0.725 and 0.855 mm/d, respectively, was obtained from the integrated model, while the RMSE for MLP was 1.088 and 1.197, and for SVM it was 1.096 and 1.290, respectively.