Penman Potential Evaporation Research Articles

Sigmoid Generalized Complementary Equation for Evaporation Over Wet Surfaces: A Nonlinear Modification of the Priestley‐Taylor Equation

AbstractThe deviations of the Priestley‐Taylor (PT) coefficient from a fixed value around 1.26 indicate a nonlinear dependence of wet surface evaporation () on the equilibrium evaporation (, which is the radiation term in Penman potential evaporation []). The linear PT equation with a fixed coefficient underestimates for small but overestimates for large , whereas the Penman equation with calibrated linear wind function has the opposite bias. In this study, the sigmoid generalized complementary (SGC) equation by Han and Tian (2018a), https://doi.org/10.1029/2017wr021755 was applied to estimate the wet surface evaporation by setting its asymmetric parameter to infinity. The SGC equation with one fixed parameter captures the nonlinear dependence of on over wet surfaces by including the aerodynamic component of with a reference wind function, and amends the shortages of the linear PT and Penman equation. By using datasets over open water surfaces of lakes and ocean, wetlands, and paddy fields, the validation results indicate that the wet surface SGC equation performed better than the linear PT and Penman equations on evaporation estimation. The success of the wet surface SGC equation has implications for the extension of the complementary principle to consider varying aerodynamic conditions over wet surfaces.

A review of the complementary principle of evaporation: from the original linear relationship to generalized nonlinear functions

Abstract. The complementary principle is an important methodology for estimating actual evaporation by using routinely observed meteorological variables. This review summaries its 56-year development, focusing on how related studies have shifted from adopting a symmetric linear complementary relationship (CR) to employing generalized nonlinear functions. The original CR denotes that the actual evaporation (E) and “apparent” potential evaporation (Epa) depart from the potential evaporation (Ep0) complementarily when the land surface dries from a completely wet environment with constant available energy. The CR was then extended to an asymmetric linear relationship, and the linear nature was retained through properly formulating Epa and/or Ep0. Recently, the linear CR was generalized to a sigmoid function and a polynomial function. The sigmoid function does not involve the formulations of Epa and Ep0 but uses the Penman (1948) potential evaporation and its radiation component as inputs, whereas the polynomial function inherits Ep0 and Epa as inputs and requires proper formulations for application. The generalized complementary principle has a more rigorous physical base and offers a great potential in advancing evaporation estimation. Future studies may cover several topics, including the boundary conditions in wet environments, the parameterization and application over different regions of the world, and integration with other approaches for further development.

Evaluation of two generalized complementary functions for annual evaporation estimation on the Loess Plateau, China

Generalized complementary functions, which describe the relationship between the ratio of actual evaporation over the Penman potential evaporation (E/EPen) and the proportion of the radiation term in EPen (Erad/EPen) have not been widely used at annual time scales. In this study, the generalized nonlinear advection-aridity function (GNAA) and sigmoid generalized complementary function (SGCF) were evaluated for annual evaporation estimation with calibrated parameters in the Loess Plateau of China. For all 15 catchments, the lowest values of annual Erad/EPen were found to be much larger than zero, and the annual E/EPen increased approximately linearly with annual Erad/EPen. This complementary evaporation relationship at an annual timescale differs from those at daily timescales, and requires different parameterizations of the GNAA and SGCF. For the GNAA, parameter c, which is often set to zero for daily time scales, need to be well calibrated with available data. For the SGCF, the upper and lower limits of Erad/EPen must be constrained. After calibration, both the SGCF and GNAA performed well at estimating annual evaporation. In addition, the calibrated Priestley-Taylor coefficient from the SGCF was found to be closer to the widely accepted value (1.26) than that determined from the GNAA.

Integration of Penman approach with complementary principle for evaporation research

AbstractNatural 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.

Derivation of a Sigmoid Generalized Complementary Function for Evaporation With Physical Constraints

AbstractThe generalized complementary function to estimate actual evaporation, namely, the ratio of actual evaporation to Penman potential evaporation (E/EPen) as a function of the proportion of the radiation term in EPen (Erad/EPen), has been increasingly recognized. Existing analytical forms of this generalized function present deficiencies because they are limited by improper boundary conditions resulting from inadequate understanding of physical constraints. In this study, its zero‐ and first‐order boundary conditions were rigorously derived by adopting the physical constraints for E in Penman's combination theory, and a sigmoid feature of relationship between E/EPen and Erad/EPen was derived. Minimum and maximum limits of Erad/EPen were introduced based on the derived boundary conditions, and accordingly, a new sigmoid function was developed. By restricting it to be approximately equivalent to the linear advection‐aridity (Brutsaert & Stricker, 1979, https://doi.org/10.1029/WR015i002p00443) function under normal environments, the new sigmoid function satisfies the upper limits of Penman's open water evaporation and Priestley‐Taylor's minimal advection evaporation in parallel. The sigmoid feature and the new sigmoid function were validated by tower‐based data from FLUXNET. This work improves our understanding of the three‐stage pattern of the complementary behavior, and the new function demonstrates a favorable potential for use in evaporation estimation.

Observational study on complementary relationship between pan evaporation and actual evapotranspiration and its variation with pan type

Abstract The pan evaporation process is essential to understanding the climate change of pan evaporation. To study the physical process of pan evaporation and its interactions with the surrounding environment, an elaborate pan evaporation experiment was carried out by means of micrometeorological method in the arid region of northwest China, in which hourly pan evaporation was measured by E601B, Class A and D20 pans, the local actual evapotranspiration was measured using eddy correlation system. Our results show that the pan water surface and the surrounding land surface constitute a significant non-uniformity of heat and moisture, and the non-uniformity energy exchange between them has an important influence on pan evaporation rate. As the environmental humidity changes, daily actual evapotranspiration and pan evaporation rates have a contradictory tendency, with the relationship between these two evaporations presenting a clear asymmetrical complementary behavior. In addition, a simple pan non-uniformity intensity index (IE) is defined as the ratio of pan evaporation to the Penman potential evaporation (LEppman) (IE = LEpan/LEppman). This index reflects the non-uniformity intensity between pan water and the surrounding land. Meanwhile, the comparison of complementary relationship corresponding to three types of pans shows that the degree of complementary relationship asymmetry linearly rises as the intensity of non-uniformity between pan and surrounding environment increases.

Assessing climate change induced modification of Penman potential evaporation and runoff sensitivity in a large water-limited basin

Potential evaporation (Ep) reflects the combined effects of four key meteorological variables: (i) net radiation (Rn); (ii) wind speed (u); (iii) relative humidity (rh); and (iv) air temperature (Ta). Here, attribution analysis was conducted to investigate the contribution of the four key meteorological variables to changes of a physically-based Ep in a large water-limited basin, the Yellow River Basin (YRB), China. Then the influences of these changes, and precipitation (P) changes, on streamflow (Q) were explored analytically. Results show that: (i) Ep presented different temporal trends for the water yielding region (WYR) and water consuming region (WCR) with a overall changes of +0.16 mm a−2 and −0.66 mm a−2 during 1961–2010, respectively; (ii) trend analysis of Ep and the four key meteorological variables at the basin scale showed that increasing trend in Ta increased Ep during 1961–2010, while changes in Rn and u increased the 1961–1979 Ep rate and reduced it during 1980–1994 and 1995–2010; (iii) revealed by attribution analysis, Ep increased by changes in Ta and rh and reduced by changes of Rn and u in both WYR and WCR, in all, Ep rate presented positive and negative trends in the WYR and WCR, respectively; (iv) the changes of Q and actual evaporation (E) are much more sensitive to changes in P than the changes in Ep; and (v) of critical importance for water resource management of the YRB changes in Q are mainly attributed to changes in catchment-specific parameter (n) and P, while Ep reduced Q in WYR and increased Q in WCR. These results indicated that the causes of trend of Ep rates, influenced by combined effects of radiative and aerodynamic variables should be explicitly explained using fully physically based Ep formulations. Additionally, in the water-limited YRB, changes of Q are primarily controlled by the changes in catchment conditions, and secondarily by hydroclimatic factors where the available water (P) rather than energy condition (Ep) is more important. Better understanding all of these relationships and how they have varied will help water resource management in a changing climate.

A nonlinear function approach for the normalized complementary relationship evaporation model

AbstractA 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.

Potential evaporation trends over land between 1983–2008: driven by radiative fluxes or vapour-pressure deficit?

Abstract. We model the Penman potential evaporation (PE) over all land areas of the globe for the 25-yr period 1983–2008, relying on radiation transfer models (RTMs) for the shortwave and longwave fluxes. Penman's PE is determined by two factors: available energy for evaporation and ground to atmosphere vapour transfer. Input to the PE model and RTMs comprises satellite cloud and aerosol data, as well as data from reanalyses. PE is closely linked to pan evaporation, whose trends have sparked controversy in the community, since the factors responsible for the observed pan evaporation trends are not determined with consensus. Our particular interest is the temporal evolution of PE, and the provided insight to the observed trends of pan evaporation. We examine the decadal trends of PE and various related physical quantities, such as net solar flux, net longwave flux, water vapour saturation deficit and wind speed. Our findings are the following: Global warming has led to a larger water vapour saturation deficit. The periods 1983–1989, 1990–1999, and 2000–2008 were characterised by decreasing, increasing, and slightly decreasing PE, respectively. In these last 25 yr, global dimming/brightening cycles generally increased the available energy for evaporation. PE trends seem to follow more closely the trends of energy availability than the trends of the atmospheric capability for vapour transfer, at most locations on the globe, with trends in the Northern hemisphere significantly larger than in the Southern. These results support the hypothesis that global potential evaporation trends are attributed primarily to secular changes in the radiation fluxes, and secondarily to vapour transfer considerations.

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

AbstractA 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.

Assessing the ability of potential evaporation formulations to capture the dynamics in evaporative demand within a changing climate

Summary Rates of evaporative demand can be modelled using one of numerous formulations of potential evaporation. Physically, evaporative demand is driven by four key variables – net radiation, vapour pressure, wind speed, and air temperature – each of which have been changing across the globe over the past few decades. In this research we examine five formulations of potential evaporation, testing for how well each captures the dynamics in evaporative demand. We generated daily potential evaporation datasets for Australia, spanning 1981–2006, using the: (i) Penman; (ii) Priestley–Taylor; (iii) Morton point; (iv) Morton areal; and (v) Thornthwaite formulations. These represent a range in how many of the key driving variables are incorporated within modelling. The testing of these formulations was done by analysing the annual and seasonal trends in each against changes in precipitation (a proxy for actual evaporation), assuming that they should vary in an approximately inverse manner. The four-variable Penman formulation produced the most reasonable estimation of potential evaporation dynamics. An attribution analysis was performed using the Penman formulation to quantify the contribution of each input variable to overall trends in potential evaporation. Whilst changes in air temperature were found to produce a large increase in Penman potential evaporation rates, changes in the other key variables each reduced rates, resulting in an overall negative trend in Penman potential evaporation. This study highlights the need for spatially and temporally dynamic data describing all drivers of evaporative demand, especially projections of each driving variable when estimating the possible affects of climatic changes on evaporative demand.

EMPIRICAL FACTORS FOR ESTIMATING OPEN‐WATER EVAPORATION FROM POTENTIAL EVAPORATION

ABSTRACTFor many years, the standard method for estimating rates of evaporation from open water has been to apply empirical factors to potential evaporation data. However, significant errors can occur through the use of these factors, essentially due to the limitations of the measurements upon which they are based. New empirical factors are presented here for use with the Meteorological Office Rainfall and Evaporation Calculation System for grass potential evaporation and Penman potential evaporation. However, uncertainty in the estimated evaporation rates remains at least 5–12 mm per month.

Evaporation characteristics of wetlands: experience from a wetgrassland and a reedbed using eddy correlation measurements

Abstract. Measurements of evaporation were made from July to November 1999 using the eddy correlation method on two wetland types – wet grassland and reedbeds – in south west England. The evaporative water use of a reed bed exceeded that of the grassland wetland by 15% (or 50 mm over the 5 months). The evaporation rates at both sites exceed of the Penman Potential Evaporation estimates calculated for this area. The difference between sites results from the higher roughness length of the reed bed and the lower effective surface resistance of the reed/open water assemblage. At the grassland site, a significant relationship between the surface resistance and water table level has been demonstrated. The water table at this site is managed to maintain the plant diversity and allow some agricultural access. This regime specifies a water table below the surface during the summer period, which results in higher surface resistances and lower evaporation. The results have important implications for local water resources management, especially where wetlands are maintained by pumping from rivers or groundwater. Keywords: wetlands, evaporation, eddy correlation, wet grassland, reedbed, vapour pressure, water table level

Surface energy fluxes and control of evapotranspiration from a Swedish Sphagnum mire

The components of the energy budget for an open Swedish boreal bog were quantified over two growing seasons and an analysis of the influence of factors such as peat wetness, vapour deficit and radiative forcing was made, in order to understand how they can be represented by physically-based models. The presence of a pronounced micro-topography caused a variation of the surface wetness as well as the cover of vascular plants. This was reflected in the spatial variation in soil temperatures and the ground heat flux was almost twice as much in hollows as in ridges. A theoretical function of peat thermal conductance with porosity and water content agreed with calculated damping depths. The surface roughness was low (z 0=2–3 cm) and did not change during the season. Bluff-rough effects had to be considered for heat and vapour fluxes. Albedo changed little but significantly with development of vascular plants (from 0.11 to 0.14). The Bowen ratio did not change with temporal fluctuations in peat wetness but depended mainly on net radiation, air temperature and relative humidity. Consequently, there was a trend of falling Bowen ratio both during the day and during the season from May (monthly value 0.9) to September (monthly value 0.6). The bulk surface resistance ( r s) to evapotranspiration was seldom close to zero and varied little (mean r s±S.D.=160±70 s m −1). Its variation depended mainly on vapour pressure deficit and was not directly correlated to peat wetness. At least half the evapotranspiration was estimated to originate from the moss surface. The evapotranspiration was 60–80% of the Penman potential evaporation. The relatively large amount of non-transpiring biomass above ground gave an effect with a relatively high Bowen ratio and a large but stable r s. It was concluded that there exists a canopy layer, within which the distribution of heat and vapour sources may vary with time. As the sources of evapotranspiration probably vary, the stable surface resistance is not caused by a constant regulation of moss evaporation but by small-scale advection effects. The low coupling to the ambient vapour deficit resulted in the evapotranspiration fitting well with the Priestly–Taylor model, with an α value of 0.8. Simple models may then be very effective for a surface type like this. However, the influence of different surface properties on the parameterisation needs to be investigated further. The use of more complicated, but physically sound, models demands more detailed studies of both physical properties of mosses and effects of differences in surface cover and micro-topography.

Modelling the impact of Land-Use Change to Water Resources in the Uplands of Scotland

The predictions of a semi-empirical evaporation model, and their implications to water resources for the uplands of Scotland, are presented for a range of land-use and climatic scenarios. Three principal vegetation types (coniferous plantation forest, heather and upland grasses) are assessed. The model only requires daily rainfall, Penman potential evaporation, and snow line information as input data. A description of the modelling approach is given, and its performance is assessed by comparing its predictions to the water balances of nine partially afforested Scottish upland catchments.

Water use efficiency of C 4 perennial grasses in a temperate climate

The C 4 perennial grasses Miscanthus x giganteus and Spartina cynosuroides are potential biomass crops. Evaporation and growth rates of 3-year-old rainfed and irrigated stands were measured over one growing season in southeast England. Leaf gas exchange provided an independent measure of instantaneous water use efficiency. Total water use was similar in both species, in each treatment. However, due to the higher productivity of M. x giganteus, the above ground biomass formed per unit of water loss (‘water use efficiency’) was higher in M. x giganteus than S. cynosuroides. In irrigated crops the values were 9.1 and 7.4 g kg −1, respectively and in rainfed crops 9.5 and 8.2 g kg −1, respectively. When normalized by the daily maximum vapour pressure deficit, the values for both crops were comparable with typical values for C 4 crops in a range of environments; 7.3–9.4 g kPa kg −1. Soil water deficits reduced the crop coefficient (the ratio of water loss from the crop to Penman potential evaporation) in rainfed stands by ca. 50%. The crop coefficient of irrigated crops exceeded 1.5 in mid-season. Difficulties in making comparisons between values of water use efficiency derived from different measurements of leaf gas exchange and crop growth are discussed.

Climatic variability within the Balquhidder catchments and its effect on Penman potential evaporation

The Penman estimate of potential evaporation, E T, is widely used as a reference level for comparison and subsequent extrapolation of the results of catchment water use studies. The steep topography and 600 m altitude range of the Balquhidder catchments presented difficulties in determining representative values of E T and in the selection of the most appropriate sites for data collection. A network of three automatic weather stations, subsequently increased to four, was installed to sample climate and E T variability within the catchments. For comparison, an additional station was installed at a valley-bottom site typifying the probable location of a conventional meteorological site in a less intensive study. Despite reliability problems with the original logging equipment, the initial data led to well-defined between-site relationships which were used to infill gaps in the E T records. These synthesised records revealed that, contrary to expectations, the high-altitude exposed sites gave significantly higher E T values than the valley-bottom sites. Data obtained using more reliable logging equipment over a recent 12 month period have been analysed in some detail. The results confirm the higher E T values from the high-altitude sites, identify factors contributing to the trend and suggest that E T values obtained from valley-bottom meteorological stations, or from present methods of extrapolation from lowland sites, significantly underestimate potential evaporation in this type of mountain terrain.

The water balance of the Balquhidder catchments

The paper tabulates precipitation, streamflow and the Penman potential evaporation E T data for the Kirkton and Monachyle catchments from 1983 to 1989. The last 4 years of data relate to the period of land-use changes with felling of half of the forest in the Kirkton and planting of 14% of the Monachyle. The data are analysed to determine the water usage of the catchments and to compare this with the Penman E T. Further analysis using the Calder and Newson (1979, Water Resour. Bull., 15: 1628–1639) method provides information on the processes of water usage. No marked changes in water use have occurred so far in the 4 years since land-use changes began to be implemented.

Modelling catchment evaporation: An objective comparison of the Penman and Morton approaches

Water-balance data from the Shannon catchment are used to calibrate two simple models of catchment-scale evaporation. The first uses the more traditional approach: evaporation is taken as Penman potential evaporation ( PE), unless water is not freely available, in which case the reduction of actual evaporation ( AE) from PE is calculated using a simple Thornthwaite-style soil-moisture model. The second model makes use of the relatively recent work by Bouchet and Morton which suggests, inter alia, that AE and PE are inversely related in the absence of an abundant supply of moisture. The resulting objective criteria of efficiency for the final models are similar, but other results from the model calibration process indicate some of the relative strengths and weaknesses of the two models. In particular, it is shown that the Bouchet-Morton approach provides a valuable alternative to the empiricism of the Thornthwaite-style reduction of AE from PE, but that this is achieved at a high cost: the introduction of a strong degree of empiricism into the process of advection modelling.

Evaporation data from a Piche evaporimeter

Measurements with Piche evaporimeters have been conducted within a thermometer screen over a grass surface at several heights. The results show a good correlation with model calculations but differ somewhat in absolute value. Comparisons with the Penman potential evaporation results show a considerable overestimation. With a simple factor, or with a lower measuring position, the results can be brought in a better agreement. The idea of G. Stanhill was verified and proved to be useful only for long periods.