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.     

Integration of Penman approach with complementary principle for evaporation research

Natural evaporation occurs with water transportation from an unsaturated land surface into an unsaturated atmosphere. The subprocesses at the land surface and in the atmosphere are one‐sidedly emphasized in the Penman approach and the complementary principle, in which the ratio of actual evaporation to the Penman potential evaporation is expressed as a function of the wetness state of the land surface and the atmosphere, respectively. The Penman approach and complementary principle can be integrated for completely conceptualizing the evaporation process, by expressing the evaporation ratio as a function of both the land surface and atmospheric wetness. The integrated approach has the potential to increase the accuracy of evaporation estimation while reducing the burdens of parameterization.     

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)     

Estimation of evaporation from the Dead Sea

A project to link the Dead Sea to the Red Sea via a canal is undergoing extensive study. As part of this study, a method to estimate evaporation from the Dead Sea is required as it is a hypersaline lake in which standard methods cannot be applied. Two methods based on Penman and Dalton formulae were examined. The method derived here is a modified Penman model that estimates the evaporation as a function of salinity, humidity, air temperature and wind speed. Other parameters such as water temperature are included implicitly in the model. The results obtained were verified as satisfactory agreement was achieved by comparison with previous measurements. A short‐cut relationship to estimate evaporation as a function of salinity only was also derived. Copyright © 1999 John Wiley & Sons, Ltd.     

A distributed approach for estimating catchment evapotranspiration: comparison of the combination equation and the complementary relationship approaches

In large river basins, there may be considerable variations in both climate and land use across the region. The evapotranspiration that occurs over a basin may be drastically different from one part of the region to another. The potential influence of these variations in evapotranspiration estimated for the catchment is weakened by using a spatially based distributed hydrological model in such a study. Areal evapotranspiration is estimated by means of approaches requiring only meteorological data: the combination equation (CE) model and the complementary relationship approach—the complementary relationship areal evapotranspiration (CRAE) and advection–aridity (AA) models. The capability of three models to estimate the evapotranspiration of catchments with complex topography and land‐use classification is investigated, and the models are applied to two catchments with different characteristics and scales for several representative years. Daily, monthly, and annual evapotranspiration are estimated with different accuracy. The result shows that the modified CE model may underestimate the evapotranspiration in some cases. The CRAE and AA models seem to be two kinds of effective alternatives for estimating catchment evapotranspiration. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Complementary relationships for near-instantaneous evaporation

The complementary relationship between actual and potential evaporation provides evaporation (i.e. evapotranspiration) estimates from minimal data. Some versions that require a land surface temperature instead of a humidity measurement could potentially be used with routine remotely sensed surface temperature data. A comparison of alternative complementary approaches, including those that require land surface temperatures, was made at small (10–30 min) time scales with point measurements spatially, using data from the FIFE, CASES, SGP, and Sahel field experiments. The advection-aridity version and a related version based on the Penman and the Priestley–Taylor equations performed the best overall. One of the four versions that incorporated land surface temperature performed fairly well. The complementary approach appears to remain viable, especially in remote sensing applications with sparse data.     

On the role of soil moisture in daytime evolution of temperatures

This paper explores the relationship between temperature, evaporation and soil moisture using a planetary boundary layer (PBL) model. It focuses on illustrating and quantifying the effect of soil moisture on the evolution of daytime temperatures. A simple convective PBL model coupled with the Penman–Monteith (PM) equation is used to estimate evapotranspiration. Following calibration and sensitivity analysis, the model was used to simulate the relative impact of dry and wet soil moisture conditions on daytime temperatures by changing the surface resistance parameter in the PM equation. It was found that the maximum temperature that can be reached during a day is constrained by the amount of soil moisture and the available net radiation, confirming previously published results. Higher temperatures can be reached with greater net radiation and dry soil moisture conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Studies and evaluations on interception processes during rainfall based on a tank model

Some analyses are carried out with regard to canopy interception processes during rainfall events based on a tank model. A hypothesis, rainfall interception rate is proportional to the product of potential evaporation and rainfall intensity, is formed from past experimental data, and is applied to the data in this study. Computational equations are proposed to the interception rate and accumulative interception loss under constant rainfall intensity. Data from the Shirakawatani experimental forested catchment are used in order to examine the relationship between the interception rate and rainfall intensity, the ratio of the interception rate to rainfall intensity and potential evaporation, accumulative interception loss and the rainfall duration, and accumulative interception loss and accumulative rainfall. These regression relations show that interception processes are described by rainfall intensity and potential evaporation. An equation relating the aerodynamic resistance in the Penman–Monteith equation to rainfall intensity is proposed to explain the fact that the interception rate exceeds net radiation.     

Pan evaporation and potential evapotranspiration trends in South Florida

Declining trends in pan and lake evaporation have been reported. It is important to study this trend in every region to evaluate the validity of the trend and water management implications. Data from nine pan evaporation sites in South Florida were evaluated to see if there is a trend and if the quality of the data is sufficient for such analysis. The conclusion is that pan evaporation measurements are prone to too many sources of errors to be used for trend analysis. This condition is demonstrated in South Florida and in other regions by differences in magnitude and direction between spatially related pan stations and unexplainable observations. Also, potential evapotranspiration (ET_p) was estimated with the Simple (Abtew equation) and the Penman–Monteith method. Both cases indicated no decline in evapotranspiration for the period of analysis. Based on the decline in humidity and the increasing trend in vapor pressure deficit for the short period of analysis, 1992–2009, it appears that South Florida is experiencing increase in evaporation and evapotranspiration at this time assuming no systematic error in the weather stations' observations. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaporation and energy balance of a wet grassland at Tadham Moor on the Somerset Levels

Wet grasslands are important both for their conservation value and for their important hydrological function. Evaporation is an important component of the water balance of a wetland. Where water is limited rainfall and/or surface (or sub‐surface) inflows are required to balance the summer evaporation and thus become a significant factor in the maintenance and environmental health of a wetland. This study presents an almost complete year of measurements of the water and energy balance of a wet grassland in the Somerset Levels in southwest England. The majority of the radiant energy at this site goes into evaporation. There is a strong seasonality of the controls on evaporation; the roughness length varies by a factor of 10 between winter and summer. The surface resistance to evaporation is low, close to zero, during the winter when the water table is at, or just below the surface. In the summer the water table drops to 80 cm below the surface; there is no sign of soil water stress on the evaporation but a clear effect of the senescence of grass during seed head production and of the subsequent harvest. There is clear evidence that water for evaporation is provided by the drainage ditches through sub‐surface flow. Standard evaporation formulae—such as the Penman‐Monteith equation with constant and standard parameters—provide a reasonable simulation of the total evaporation at this site, although they miss some of the seasonal detail. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimation of annual actual evapotranspiration from nonsaturated land surfaces with conventional meteorological data

Land surface evapotranspiration is an important component both in earth surface heat and water bal-ance, on whose budgets weather and climate depend, to a great extent, for their changes are responsible for the formation and variation of vegetation features on the globe. Besides, the evapotranspiration is an im-portant topic of short-term flood forecasting and the estimation of runoff from mountainous sides. As a result, the problem as to the evapotranspiration has been one of the concerns in …     

Spatial and temporal characteristics of actual evapotranspiration over Haihe River basin in China

Spatial and temporal characteristics of actual evapotranspiration over the Haihe River basin in China during 1960–2002 are estimated using the complementary relationship and the Thornthwaite water balance (WB) approaches. Firstly, the long-term water balance equation is used to validate and select the most suitable long-term average annual actual evapotranspiration equations for nine subbasins. Then, the most suitable method, the Pike equation, is used to calibrate parameters of the complementary relationship models and the WB model at each station. The results show that the advection aridity (AA) model more closely estimates actual evapotranspiration than does the Granger and Gray (GG) model especially considering the annual and summer evapotranspiration when compared with the WB model estimates. The results from the AA model and the WB model are then used to analyze spatial and temporal changing characteristics of the actual evapotranspiration over the basin. The analysis shows that the annual actual evapotranspirations during 1960–2002 exhibit similar decreasing trends in most parts of the Haihe River basin for the AA and WB models. Decreasing trends in annual precipitation and potential evapotranspiration, which directly affect water supply and the energy available for actual evapotranspiration respectively, jointly lead to the decrease in actual evapotranspiration in the basin. A weakening of the water cycle seems to have appeared, and as a consequence, the water supply capacity has been on the decrease, aggravating water shortage and restricting sustainable social and economic development in the region.     

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.     

Summer evapotranspiration in western Siberia: a comparison between eddy covariance and Penman method formulations

Evapotranspiration is difficult to quantify because of the many factors and complex processes that influence it. Several empirical methods have been developed over the years to estimate potential evapotranspiration based on easily available parameters. Directly measured data of actual evapotranspiration have been rather sparse in the past and still need to be improved in particular regions like western Siberia. The transition zone between the warm temperate and cold temperate continental climates is very sensitive to climate change, and water stress is an increasingly important issue in these regions with a highly dynamic agricultural activity. So there is a growing need to estimate actual evapotranspiration. Widely usable approximations are needed. In this study, the values of potential evapotranspiration computed with the original version, and eight modifications of the Penman formulation were compared and related to the actual evapotranspiration measured by eddy covariance over a grassland area in western Siberia. The original 1948 and 1963 Penman formulations are best for estimating potential evapotranspiration in the transition zone between the forest steppes and the pre‐taiga. A nearly linear relationship between the potential and actual evapotranspiration was found. A simple modification of the Penman equation (i.e. the multiplication of the result by a factor of 0.47) is suggested for approximating the actual evapotranspiration based on standard meteorological data for the region. The original Penman formulation is most robust and will provide the widest applicability in the future under changing climate and environmental conditions. In this context, it is further recommended not to neglect the ventilation term of the Penman equation, which is often assumed to be negligibly small. A detailed correlation analysis showed that under dry soil conditions, the vegetation largely contributed to the actual evapotranspiration and, in contrast to widely held expectations, that the Penman equation is best adapted to vegetated surfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

An objective assessment of soil-moisture deficit models

The performance of different soil-moisture deficit models was assessed by comparing model predictions with over 3000 neutron-probe observations of soil-moisture content at six grassland experimental sites operated by the Institute of Hydrology. The models were formulated using combinations of different equations for estimating potential evaporation and different regulating functions relating actual to potential evaporation via the moisture status of the soil. The inclusion of sophisticated evaporation equations (Priestley-Taylor, Penman, Thom-Oliver) gave no improvement in SMD prediction over a proposed simple evaporation formula requiring no direct meteorological measurements other than rainfall. The success of this formula demonstrates the conservative nature of annual potential evaporation within the U.K. both spatially and temporally and also suggests a possible natural feedback mechanism between atmospheric demand and grass transpiration.     

The effects of possible future climate change on evaporation losses from four contrasting UK water catchment areas

Evaporation losses from four water catchment areas under different land uses and climatic conditions were calculated using formulations developed from small plot studies. These formulations, dependent on rainfall inputs, potential evaporation and air temperature, were extrapolated to the catchment scale using land classifications based on analysing remotely sensed imagery. The approach adopted was verified by comparing the estimated annual evaporation losses with catchment water use, given by the difference between rainfall inputs and stream flow outputs, allowing for changes in soil moisture. This procedure was repeated using modified values of rainfall, potential evaporation and air temperature, as given by a climate change scenario. The computed evaporation losses were used in annual water balances to calculate stream flow losses under the climate change scenario. It was found that, in general, stream flow from areas receiving high rainfall would increase as a result of climate change. For low rainfall areas, a decrease in stream flow was predicted. The largest actual changes in stream flow were predicted to occur during the winter months, although the largest percentage changes will occur during the summer months. The implications of these changes on potable water supply are discussed. © 1998 John Wiley & Sons, Ltd.     

Issues and Options in the Delineation of Well Capture Zones under Uncertainty

The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT‐MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach. An alternative for all types of media is the capture probability (CP) approach, which is based on the solution of the standard advection‐dispersion equation in a backward mode, making use of the analogy between forward and backward transport processes. Within this context, we review the current controversy about the correct form of the conceptual model for transport, finding that the advection‐diffusion model, which represents the diffusive interchange between streamtubes with differing velocities, is more physically realistic than the conventional advection‐dispersion model. For mildly to moderately heterogeneous materials, stochastic theories and simulation experiments show that this process converges at the field scale to an effective advection‐dispersion process that can be simulated with conventional transport models using appropriate macrodispersivity values. For highly heterogeneous materials, stochastic theories do not yet exist but there is no reason why the process should not converge naturally as well. Macrodispersivities appear to be formation‐specific. The advection‐dispersion model can be used for capture zone delineation in heterogeneous granular media. For fractured porous systems, hybrid equivalent porous medium and discrete fracture network or CP‐based approaches may have potential. In general, capture zones delineated by PT without MC will always be too small and should not be used as a basis for land‐use decisions.     

High resolution water body mapping for SWAT evaporative modelling in the Upper Oconee watershed of Georgia,USA

Technological improvements in remote sensing and geographic information systems have demonstrated the abundance of artificially constructed water bodies across the landscape. Although research has shown the ubiquity of small ponds globally, and in the southeastern United States in particular, their cumulative impact in terms of evaporative alteration is less well quantified. The objectives of this study are to examine the hydrologic and evaporative importance of small artificial water bodies in the Upper Oconee watershed in the northern Georgia Piedmont, USA, by mapping their locations and modelling these small reservoirs using the Soil Water Assessment Tool. Comparative Soil Water Assessment Tool models were run with and without the inclusion of small reservoir surface area and volume. The models used meteorological inputs from 1990–2013 to represent years with drought, high precipitation, and moderate precipitation for both the calibration and evaluation periods. Statistical comparison of streamflow indicated that the calibration methodology produced results where the default model simulation without reservoirs fit observed flows more closely than the modified model with small reservoirs included (e.g., Nash–Sutcliffe efficiency of 0.72 vs. 0.64, r² of 0.73 vs. 0.66, and percent bias of 11.4 vs. 21.6). In addition, Penman–Monteith, Hargreaves, and Priestley–Taylor evapotranspiration equations were used to estimate actual evaporation from 2,219 small water bodies identified throughout the 1,936.8 km² watershed. Depending on the evaporation equation used, water bodies evaporated an average of 0.03–0.036 km³/year for the period 2003–2013. Using Penman–Monteith further, if the reservoirs were not considered and average actual evapotranspiration rates from the rest of the basin were applied, only 0.016 km³ of water would have left the basin as a result of evapotranspiration. This finding suggests construction of small reservoirs increased evaporation by an average of 0.017 km³ per year (approximately 46,500 m³/day). As the construction of small reservoirs continues and high resolution image data used to map these water bodies becomes increasingly available, watershed models that evolve to address the cumulative impacts of small water bodies on evaporation and other hydrologic processes will have greater potential to benefit the water resource management community.