Complementary Relationship Areal Evapotranspiration Research Articles

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.

Modeling Actual Evapotranspiration using the Advection Aridity Model

Evapotranspiration is a major process in the hydrological cycle. Between 40 to 60% of precipitation is returned back to the atmosphere in the form of evapotranspiration. Therefore, estimation of Actual Evapotranspiration (AET) is important in studies related to hydrology, agriculture and climate. However, due to the fact that calculation of AET using conventional methods require data pertaining to climate, vegetation/crop and soil moisture levels, estimation of spatial AET becomes a very tedious task. The Complementary Relationship Areal Evapotranspiration (CRAE) hypothesis has been proposed as a simpler alternative to estimate AET from large spatial domains using only routinely observed meteorological data thereby circumventing the need for data on soil-vegetation. The objective of the present work was to apply the CRAE hypothesis in Karnataka State, India and evaluate the accuracy of estimates using MODIS satellite-derived AET estimates. The Advection Aridity (AA) model which is based on the CRAE hypothesis was chosen to estimate AET using historical climate records of the Afzalpur and Hungund stations. The AA model uses the Penman equation to estimate the Potential ET and the Priestley-Taylor equation to estimate Wet Environment ET which are needed to estimate AET. Accuracy of AET values obtained from the AA model were validated using the MODIS MOD16A2 evapotranspiration product, which provides an 8-day composite AET estimate at 500 m resolution. AET estimated by the AA model compared favorably with MOD16A2 with the average Coefficient of determination (R2)for the two stations being 0.8095. While the results of this study have shown that the AA model provides reasonably accurate AET estimates with minimum data, further studies need to be carried out to improve the accuracy through local calibration of parameters.

Complementary Relationship and Dual Crop Coefficient Approach-Based Study on Green Water Separation

Separating productive green water from non-productive green water could determine the potential for improving green water use through water-to-vapor conversion and the optimization of green water resource management. This study selected three typical planted forests of Robinia pseudoacacia, Platycladus orientalis, and Pinus tabulaeformis in the Nanxiaohegou sub-basin, a typical small sub-basin located in the gully region of the Loess Plateau. A combination of field monitoring, hydrological models, and statistical tests was used to obtain the crop coefficient and to differentiate productive green water from non-productive green water, based on the hydrological, climatic, and ecological processes in the basin. The results demonstrated that the complementary relationship areal evapotranspiration (CRAE) model was the most effective complementary relationship-based model for the simulation. Based on the calibrated parameters, it could be used for the simulation of green water flux of different vegetation types in the studied region. In the Nanxiaohegou sub-basin, the amounts of productive green water, non-productive green water, and total green water flux of R. pseudoacacia were the highest among all three types of vegetation, followed by those of P. orientalis and P. tabulaeformis forests during the growing seasons between 2015 and 2017.

PENENTUAN KOEFISIEN TANAMAN MENGGUNAKAN DATA PENGAMATAN IKLIM DAN INDEX VEGETASI DARI SETELIT NOAA/ AVHRR

One of the most important parameter of climatic water balance computation is crop coefficient (Kc). Unfortunately, the Kc is one of the most difficult parameter to measure in the field. This paper attempts to determine the crop coefficient by using climate observation data and the NDVI (Normalized Difference Vegetation Index) derived from NOAA (National Oceanic and Atmospheric Administration). Calculation using Morton’s Complementary Relationship Areal Evapotranspiration (CRAE) method that used elevation (m), annual precipitation (mm), monthly air temperature ( C), sunshine duration (%), as minimum requirement data, has been applied for more than 900 climatic stations over the Asian region that well documented by FAO-CLIM agroclimatic database to obtain the Kc value. The result was then related to NDVI derived from spectral reflectance of NOAA/AVHRR data. The relation results of NDVI and crop coefficient gave significant linear equation as Kc = 0.08 + 1.83 NDVI, with average correlation coefficient 0.72. It was high over humid area such as in Java island of Indonesia; on the other hand, it was low in semi arid area, such as west part of India. Even the results above were fit only for a specified area; this study has demonstrated a potential use of NOAA image for supplying the crop coefficient value that would be particularly necessary to determine actual evapotranspiration.

Modeling actual evapotranspiration with routine meteorological variables in the data‐scarce region of the Tibetan Plateau: Comparisons and implications

AbstractQuantitative estimation of actual evapotranspiration (ETa) by in situ measurements and mathematical modeling is a fundamental task for physical understanding of ETa as well as the feedback mechanisms between land and the ambient atmosphere. However, the ETa information in the Tibetan Plateau (TP) has been greatly impeded by the extremely sparse ground observation network in the region. Approaches for estimating ETa solely from routine meteorological variables are therefore important for investigating spatiotemporal variations of ETa in the data‐scarce region of the TP. Motivated by this need, the complementary relationship (CR) and Penman‐Monteith approaches were evaluated against in situ measurements of ETa on a daily basis in an alpine steppe region of the TP. The former includes the Nonlinear Complementary Relationship (Nonlinear‐CR) as well as the Complementary Relationship Areal Evapotranspiration (CRAE) models, while the latter involves the Katerji‐Perrier and the Todorovic models. Results indicate that the Nonlinear‐CR, CRAE, and Katerji‐Perrier models are all capable of efficiently simulating daily ETa, provided their parameter values were appropriately calibrated. The Katerji‐Perrier model performed best since its site‐specific parameters take the soil water status into account. The Nonlinear‐CR model also performed well with the advantage of not requiring the user to choose between a symmetric and asymmetric CR. The CRAE model, even with a relatively low Nash‐Sutcliffe efficiency (NSE) value, is also an acceptable approach in this data‐scarce region as it does not need information of wind speed and ground surface conditions. In contrast, application of the Todorovic model was found to be inappropriate in the dry regions of the TP due to its significant overestimation of ETa as it neglects the effect of water stress on the bulk surface resistance. Sensitivity analysis of the parameter values demonstrated the relative importance of each parameter in the corresponding model. Overall, the Nonlinear‐CR model is recommended in the absence of measured ETa for local calibration of the model parameter values.

Evapotranspiration model selection for estimation of actual evaporation from bare soil, as required in annual potential groundwater recharge studies of a semi-arid foothill region

Improved evapotranspiration estimation is instrumental in annual potential recharge (Re) evaluations of semi-arid regions, in the context of the water balance approach. Complementary relationship areal evapotranspiration (CRAE) and advection–aridity (AA) and a general combination equation proposed by Granger and Gray (GG) were evaluated for the estimation of actual evaporation (Ea) from bare soil under occurrence of Re. Model capability was evaluated by utilizing data from lysimeter measurements during the hydrological years [(2011–2012) and (2012–2013)]. Measured parameters included soil moisture (SM), rainfall and related meteorological data and Re (lysimeter output). All models with original parameters performed poorly during 2011–2012 and 2012–2013, underestimating annual Re values. The 2011–2012 data were used for model calibration, considering annual Ea [criterion (I)] and cumulative Ea during the occurrence period of Re [criterion(II)]. The calibrated CRAE model [criterion (II)] produced the best simulation for Ea (NRMSE < 30%). The 2012–2013 data were used to validate the models, and the calibrated CRAE model produced acceptable results (NRMSE < 10%) in SM simulation (both criteria). But calibrated CRAE under criterion (II) provided the best estimation of annual Re (ΔQ < 6%). According to the results, CR models can produce acceptable estimation of annual Re, if initially calibrated utilizing criterion (II).

Improving the complementary methods to estimate evapotranspiration under diverse climatic and physical conditions

Abstract. Reliable estimation of evapotranspiration (ET) is important for the purpose of water resources planning and management. Complementary methods, including complementary relationship areal evapotranspiration (CRAE), advection aridity (AA) and Granger and Gray (GG), have been used to estimate ET because these methods are simple and practical in estimating regional ET using meteorological data only. However, prior studies have found limitations in these methods especially in contrasting climates. This study aims to develop a calibration-free universal method using the complementary relationships to compute regional ET in contrasting climatic and physical conditions with meteorological data only. The proposed methodology consists of a systematic sensitivity analysis using the existing complementary methods. This work used 34 global FLUXNET sites where eddy covariance (EC) fluxes of ET are available for validation. A total of 33 alternative model variations from the original complementary methods were proposed. Further analysis using statistical methods and simplified climatic class definitions produced one distinctly improved GG-model-based alternative. The proposed model produced a single-step ET formulation with results equal to or better than the recent studies using data-intensive, classical methods. Average root mean square error (RMSE), mean absolute bias (BIAS) and R2 (coefficient of determination) across 34 global sites were 20.57 mm month−1, 10.55 mm month−1 and 0.64, respectively. The proposed model showed a step forward toward predicting ET in large river basins with limited data and requiring no calibration.

Evaluating actual evapotranspiration and impacts of groundwater storage change in the North China Plain

AbstractAs a critical water discharge term in basin‐scale water balance, accurate estimation of evapotranspiration (ET) is therefore important for sustainable water resources management. The understanding of the relationship between ET and groundwater storage change can improve our knowledge on the hydrological cycle in such regions with intensive agricultural land usage. Since the 1960s, the North China Plain (NCP) has experienced groundwater depletion because of overexploitation of groundwater for agriculture and urban development. Using meteorological data from 23 stations, the complementary relationship areal evapotranspiration model is evaluated against estimates of ET derived from regional water balance in the NCP during the period 1993–2008. The discrepancies between calculated ET and that derived by basin water balance indicate seasonal and interannual variations in model parameters. The monthly actual ET variations during the period from 1960 to 2008 are investigated by the calibrated model and then are used to derive groundwater storage change. The estimated actual ET is positively correlated with precipitation, and the general higher ET than precipitation indicates the contributions of groundwater irrigation to the total water supply. The long term decreasing trend in the actual ET can be explained by declining in precipitation, sunshine duration and wind speed. Over the past ~50 years, the calculated average annual water storage change, represented by the difference between actual ET and precipitation, was approximately 36 mm, or 4.8 km3; and the cumulative groundwater storage depletion was approximately 1700 mm, or 220 km3 in the NCP. The significantly groundwater storage depletion conversely affects the seasonal and interannual variations of ET. Irrigation especially during spring cause a marked increase in seasonal ET, whereas the rapid increasing of agricultural coverage over the NCP reduces the annual ET and is the primary control factor of the strong linear relationship between actual and potential ET. Copyright © 2013 John Wiley &amp; Sons, Ltd.

The impact of agricultural practices in China on land-atmosphere interactions

Human-induced land use changes and the resulting alterations in vegetation features are major but poorly recognized drivers of regional climatic patterns. In order to investigate the impacts of anthropogenically-induced seasonal vegetation cover changes on regional climate in China, harmonic analysis is applied to 1982–2000 National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVVHRR)-derived normalized difference vegetation index (NDVI) time series (ten day interval data). For two climatic divisions of South China, it is shown that the first harmonic term is in phase with air temperature, while the second and third harmonics are in phase with agricultural cultivation. The Penman-Monteith Equation and the Complementary Relationship Areal Evapotranspiration (CRAE) model suggest that monthly mean evapotranspiration is out of phase with temperature and precipitation in regions with significant second or third harmonics. Finally, seasonal vegetation cover changes associated with agricultural cultivation are identified: for cropped areas, the temperature and precipitation time series have a single maximum value, while the monthly evapotranspiration time series has a bimodal distribution. It is hypothesized that multi-cropping causes the land surface albedo to sharply increase during harvesting, thereby altering the energy distribution ratio and contributing to observed seasonal vegetation cover changes.

Estimating recharge rates for qanat-based water supply in northern Cyprus: a case study using remotely sensed and in-situ data

The qanat water supply technology, by which gravity drains mountain aquifers into valleys, is considered as a culturally appropriate and ecological sustainable design to meet freshwater development needs in northern Cyprus. This work provides a first-order analysis of the surface water budget to estimate qanat feasibility. The proposed qanat recharge area of 370 km2 is in the upper elevations of the limestone dominated Five Finger Mountain Range, is analysed using technical data reports, field visits, and satellite elevation data. Satellite based tropical rainfall measuring mission (TRMM) monthly rainfall totals at a 0.25° grid were tested for complementing sparse precipitation gauge data, but TRMM underestimated gauge observations by 43% in narrow zones of high rainfall during the wet winter months. A water budget for qanat supply used 30-year average gauge records within the qanat recharge region, which set annual precipitation at 529 mm year−1. A calibrated complementary relationship areal evapotranspiration model established atmospheric outputs at 222 mm year−1, slightly below the island-average of 280 mm year−1 estimated by the Cyprus Water Department. Recharge to the qanat aquifer was determined by subtracting evaporation from precipitation, and then allocating 50% of the remainder to environmental services. In the proposed qanat recharge region, this water budget yields an estimated recharge volume of 57 mm3 year−1. At less than 25% development, this volume satisfies the 13 mm3 annual deficit in northern Cyprus and protects against saltwater intrusion. Additional freshwater conservation measures in northern Cyprus are needed to ensure ecological sustainability in northern Cyprus.

Ancient eco-technology of qanats for engineering a sustainable water supply in the Mediterranean Island of Cyprus

The qanat water supply technology, which gravity drains mountain aquifers into valleys, is considered as a culturally appropriate and ecological sustainable design to meet northern Cyprus’ drinking water development needs. This research estimates the boundary and water budget for the proposed qanat recharge area of 370 km2, which is in the upper elevations of the limestone dominated Five Finger Mountain Range. The mountain drainage was analyzed using global elevation data from the Shuttle Ranging Topography Mission (SRTM). Efforts to use Tropical Rainfall Measuring Mission (TRMM) annual precipitation for water budget inputs failed due to extreme error when tested against 10–30 years of meteorological station data; TRMM under-estimated depths on the narrow mountain peaks. Gage records, while few in number, were area averaged to set average annual precipitation inputs at 530 mm year−1. Evaporation was estimated using a complementary relationship areal evapotranspiration (CRAE) model, setting average atmospheric outputs at 221 mm year−1. Recharge to the qanat aquifer was set by subtracting evaporation from precipitation, and then allocating 50% of the remaining water to environmental services. At 25% development, the qanat system supplies 14 mm3 year−1 of water, meeting the drinking water deficit of 13 mm3.

Evaluation of three complementary relationship approaches for evapotranspiration over the Yellow River basin

Regional evapotranspiration is an important component of the hydrological cycle. However, reliable estimates of regional evapotranspiration are extremely difficult to obtain. In this study, the evapotranspiration simulated by three complementary relationship approaches, namely the Advection–Aridity (AA) model, the Complementary Relationship Areal Evapotranspiration (CRAE) model and the Granger (G) model, is evaluated with the observations over the Yellow River basin during 1981–2000. The simulations on overall annual evapotranspiration are reasonably good, with mean annual errors less than 10% except in extreme dry years. The AA model gives the best estimation for the monthly evapotranspiration, and the CRAE and GM models slightly overestimate in winter. In addition, the AA model presents the same closure error of water balance over the Yellow River basin as model G, which was less than that by the CRAE model. In rather dry and rather wet cases (with higher or lower available energy), all three models perform less well. Empirical parameters of these models need to be recalibrated before they can be applied to other regions. The distribution of evapotranspiration over the Yellow River basin is also discussed. Copyright  2006 John Wiley & Sons, Ltd.

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

AbstractIn 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 &amp; Sons, Ltd.

The complementary relationship in estimation of regional evapotranspiration: The complementary relationship areal evapotranspiration and advection‐aridity models

Two implementations of the complementary relationship hypothesis for regional evapotranspiration, the Complementary Relationship Areal Evapotranspiration (CRAE) model and the Advection‐Aridity (AA) model, are evaluated against independent estimates of regional evapotranspiration derived from long‐term, large‐scale water balances (1962–1988) for 120 minimally impacted basins in the conterminous United States. The CRAE model overestimates annual evapotranspiration by 2.5% of mean annual precipitation, and the AA model underestimates annual evapotranspiration by 10.6% of precipitation. Generally, increasing humidity leads to decreasing absolute errors for both models, and increasing aridity leads to increasing overestimation by the CRAE model and underestimation by the AA model, with the exception of high, arid basins, where the AA model overestimates evapotranspiration. Overall, the results indicate that the advective portion of the AA model must be recalibrated before it may be used successfully on a regional basis and that the CRAE model accurately predicts monthly regional evapotranspiration.

Examination of Morton's CRAE model for estimating daily evaporation from field-sized areas

Morton's complementary relationship areal evapotranspiration (CRAE) model was originally designed to provide regional estimates of monthly evapotranspiration. Often, however, hydrologists and others require estimates of evapotranspiration for field-sized land units under a specific land use, for shorter intervals of time. This paper examines CRAE with respect to the algorithms used to describe different terms and its applicability to reduced spatial and temporal scales. Daily estimates by CRAE of atmospheric radiation fluxes during the summer months are compared with monitored values. It is shown that errors in estimation of the extra-terrestrial flux, the transmittancy of clouds to short-wave radiation, the surface albedo and the net long-wave flux result in standard deviations of the difference between ‘modelled’ and ‘measured’ net all-wave radiation for 1-, 5- and 10-day periods of 2.58, 1.8 and 1.50 MJm −2 day −1 respectively. The assumption in CRAE that the vapour transfer coefficient is independent of wind speed may lead to appreciable error in computing evapotranspiration. A procedure for incorporating a wind correction factor is described and the improvement in estimating regional evaporation is illustrated. Comparisons of evapotranspiration estimates by CRAE and measurements obtained from soil moisture and precipitation observations in the semi-arid, cold-climate Prairie region of western Canada demonstrate that the assumptions that the soil heat flux and storage terms are negligible, lead to large overestimation by the model during periods of soil thaw.

Evaluation of three evapotranspiration models in terms of their applicability for an arid region

Evapotranspiration has a major controlling influence on all hydrological processes. Unfortunately, reliable estimates are extremely difficult to obtain, especially in arid regions. In this research, three evapotranspiration models are evaluated, namely, the Advection-Aridity, the Complementary Relationship Areal Evapotranspiration (CRAE), and the Penman-Monteith models. By applying these models to an arid river basin in Xinjiang, China, the consistency and reliability of the models are examined. It is found that the Penman-Monteith model is particularly sensitive to the canopy resistance r c, but is not sensitive to the surface albedo. In arid regions canopy resistance may range from 400 to 1000 sm −1 for crops and grassland and a 10% error in r c results in a 10% error in the estimated evapotranspiration. The use of the surface roughness length and surface albedo have significant effects on the estimates of evapotranspiration in the Advection-Aridity model. To estimate regional evapotranspiration, a weighted average method is proposed. By using this method, regional evapotranspiration is obtained from point estimates (Advection-Aridity and Penman-Monteith models) which are weighted according to their relative surface areas. The actual evapotranspiration for the river basin obtained by this method is very close to water balance estimates. From this study, it can be concluded that the Advection-Aridity, the CRAE, and the Penman-Monteith models are applicable to arid regions, and that the Penman-Monteith model yields the best results.

Operational estimates of areal evapotranspiration and their significance to the science and practice of hydrology

Reliable estimates of areal evapotranspiration are essential to significant improvements in the science and practice of hydrology. Direct measurements, such as those provided by lysimeters, eddy flux instrumentation or Bowen-ratio instrumentation, give point values, require constant attendance by skilled personnel and are based on unverified assumptions. A critical review of the methods used for estimating areal evapotranspiration indicates that the conventional conceptual techniques, such as those used in current watershed models, are based on assumptions that are completely divorced from reality; and that causal techniques based on processes and interactions in the soil-plant-atmosphere system are not likely to prove useful for another generation. However, the complementary relationship can do much to fill the gap until such time as causal techniques become practicable because it provides the basis for models that permit areal evapotranspiration to be estimated from its effects on the routine climatological observations needed to estimate potential evapotranspiration. Such models have a realistic conceptual and empirical basis, by-pass the complexity of the soil-plant system and require no local calibration of coefficients. Therefore, they are falsifiable (i.e. can be tested rigorously) so that errors in the associated assumptions and relationships can be detected and corrected by progressive testing over an ever-widening range of environments. Such a methodology uses the entire world as a laboratory and requires that a correction made to obtain agreement between model and river-basin water budget estimates in one environment must be applicable without modification in all other environment. The most recent version of the complementary relationship areal evapotranspiration (CRAE) models is formulated and documented. The reliability of the independent operational estimates of areal evapotranspiration is tested with comparable long-term water-budget estimates for 143 river basins in North America, Africa, Ireland, Australia and New Zealand. The practicality and potential impact of such estimates are demonstrated with examples which show how the availability of such estimates can revitalize the science and practice of hydrology by providing a reliable basis for detailed water-balance studies; for further research on the development of causal models; for hydrological, agricultural and fire hazard forecasts; for detecting the development of errors in hydrometeorological records; for detecting and monitoring the effects of land-use changes; for explaining hydrologic anomalies; and for other better known applications. It is suggested that the collection of the required climatological data by hydrometric agencies could be justified on the grounds that the agencies would gain a technique for quality control and the users would gain by a significant expansion in the information content of the hydrometric data, all at minimal additional expense.

Operational estimates of lake evaporation

The complementary relationship between areal and potential evapotranspiration takes into account the changes in the temperature and humidity of the air as it passes from a land environment to a lake environment. Minor changes convert the latest version of the complementary relationship areal evapotranspiration (CRAE) models to a complementary relationship lake evaporation (CRLE) model. The ability of the CRLE model to produce reliable estimates of annual lake evaporation from monthly values of temperature, humidity and sunshine duration (or global radiation) observed in the land environment with no locally optimized coefficients is tested against comparable water-budget estimates for 11 lakes in North America and Africa. Maps of annual lake evaporation and annual net reservoir evaporation (i.e. the difference between lake evaporation and areal evapotranspiration) for the part of Canada to the east of the Pacific Divide and for the southern U.S.A. are presented. An approximate routing technique, which takes into account the effects of depth and salinity on the seasonal pattern of monthly lake evaporation, is formulated and tested against comparable water-budget estimates for 10 lakes in North America and Africa. The results indicate that the CRLE model, with its associated routing technique, is much superior to the other techniques in current use that rely on climatological or pan observations in the land environment.

Technical note no. 126: Comparison between pan and lake evaporation

The complementary relationship between areal and potential evapotranspiration takes into account the changes in the temperature and humidity of the air as it passes from a land environment to a lake environment. Minor changes convert the latest version of the complementary relationship areal evapotranspiration (CRAE) models to a complementary relationship lake evaporation (CRLE) model. The ability of the CRLE model to produce reliable estimates of annual lake evaporation from monthly values of temperature, humidity and sunshine duration (or global radiation) observed in the land environment with no locally optimized coefficients is tested against comparable water-budget estimates for 11 lakes in North America and Africa. Maps of annual lake evaporation and annual net reservoir evaporation (i.e. the difference between lake evaporation and areal evapotranspiration) for the part of Canada to the east of the Pacific Divide and for the southern U.S.A. are presented. An approximate routing technique, which takes into account the effects of depth and salinity on the seasonal pattern of monthly lake evaporation, is formulated and tested against comparable water-budget estimates for 10 lakes in North America and Africa. The results indicate that the CRLE model, with its associated routing technique, is much superior to the other techniques in current use that rely on climatological or pan observations in the land environment.