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

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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.

Introduction

Analyses of catchment hydrological dynamics require estimates of the supply of water and of the evaporative demand for water. Estimates of potential evaporation are generally used to represent evaporative demand. Conceptually, potential evaporation represents the maximum possible evaporation rate (e.g., Granger, 1989, Lhomme, 1999) and is the rate that would occur under given meteorological conditions from a continuously saturated surface (e.g., Thornthwaite, 1948). Notionally, the concept of potential evaporation is simple. However the practical implementation of the concept is problematic and ambiguous due to the many ways that potential evaporation can be, and has been, formulated. Here we focus on the number of input variables used in formulations and the effect this has on the dynamics of estimated potential evaporation.

Even though potential evaporation is primarily driven by four key meteorological variables (net radiation, vapor pressure, wind speed and air temperature) it is a conceptual entity that can not be measured directly (Thornthwaite, 1948). Many different methods of estimating potential evaporation from one or more of these four variables have been developed according to local climatic conditions and the availability of suitable data (see Shuttleworth, 1993, Singh and Xu, 1997, Xu and Singh, 2000, Xu and Singh, 2001). Some formulations, such as Thornthwaite’s (1948), use a single variable (i.e., air temperature) that is related to potential evaporation rates via empirical relationships. These typically need to be recalibrated to maintain accuracy when applied outside the original spatial and temporal contexts (Xu and Singh, 2001). Other formulations, by assuming the surface is extensive and continually saturated, omit the effects of the ‘advective’ variables (i.e., wind speed and vapor pressure), and account only for the vertical heat and mass fluxes. Such formulations are often referred to as ‘areal’ or ‘wet area’ potentials (e.g., Morton, 1983, Priestley and Taylor, 1972) and are best suited to energy-limited environments. Alternatively, fully physical models, such as the Penman and the Penman–Monteith equations (Monteith, 1981, Penman, 1948), are physically derived (except for any resistance terms) and explicitly incorporate all the driving variables. Although these formulations are universally applicable they are data intensive.

This research was prompted by the need for spatially explicit potential evaporation data that are suitable for the analysis of long-term dynamics in evaporative demand. Wide-spread changes in climatic conditions have been reported, with long-term trends observed in global average air temperature (e.g., IPCC, 2007), vapour pressure (e.g., Durre et al., 2009), precipitation (e.g., New et al., 2001), net radiation (e.g., Wild, 2009), and wind speed (e.g., McVicar et al., 2008). This is no less true for Australia, where temperature and precipitation have been increasing on average over the past 3 or so decades (Bureau of Meteorology, 2007) as has vapour pressure (this study), whilst wind (McVicar et al., 2008, Rayner, 2007, Roderick et al., 2007) and net radiation (this study) have been decreasing. All these changes will have inevitably led to changes in evaporative demand. Given the extremely variable nature of the drivers of potential evaporation, any methods used to examine long-term analyses of evaporative demand need to be capable of accounting for the observed, and expected, changes in all relevant input variables (McKenney and Rosenberg, 1993) and should ideally be applicable in both water- and energy-limited environments.

Our aim is to test a variety of potential evaporation formulations, assessing how well each captures the dynamics in evaporative demand. Towards this end, we generated datasets of daily potential evaporation—spanning Australia and extending from 1981 to 2006—using the five formulations outlined in Table 1. These were selected as they represent a range in how the key input variables are treated, varying from the fully physical, four-variable Penman model to the empirical Thornthwaite model that contains only one variable. In this paper we analyse the annual and seasonal trends of each formulation, comparing these against equivalent trends in precipitation, assessing the suitability of each formulation for representing long-term dynamics in evaporative demand. An attribution analysis is then performed on the formulation identified as most suitable in order to see how each input variable contributes to the overall trend in potential evaporation.

Validation of modelled potential evaporation data is an important initial step when assessing the suitability of modelled data. Yet potential evaporation can not be measured directly and so spatial and temporal validation of such data is difficult. Instead, the input data used to generate potential evaporation estimates can be validated. Spatial surfaces of meteorological variables are increasingly being used in hydro-meteorological analyses. To date, little attention has been given to assessing the temporal accuracy of such surfaces. Prior to conducting analyses of potential evaporation dynamics, we undertook two rigorous tests of the temporal accuracy of the input surface data. In the first, which is reported in Donohue et al. (2009b), we compared surface-derived trends in the input variables with trends present in the underlying point data from which the surfaces were generated. In the second test, reported here, we use the input data and the Penpan model (Rotstayn et al., 2006) to estimate US Class A pan evaporation rates and trends, and compare these with rates and trends in observed point-based pan evaporation data.

This paper is organised as follows. In the next Section ‘Data and Methods’ we describe: (i) the data used in these analyses and the validation performed to test their accuracy, including the generation and validation of Australia-wide daily net radiation surfaces and the five different potential evaporation formulations used; (ii) the assessment of potential evaporation dynamics; and (iii) an attribution analysis to quantify the contribution of each input variable to potential evaporation trends. Results are presented using a similar structure, followed by a discussion of results and some concluding remarks. A more detailed description of the data, validation and methods is given in Donohue et al. (2009b).

Section snippets

Background datasets

Data in the form of daily grids were used for these analyses, spanning January 1981–December 2006 (see Table 2). This time-span was chosen to match that of the remotely sensed vegetation cover data of Donohue et al. (2008) from which estimates of albedo and surface emissivity were derived. Elevation was derived from the DEM-9S dataset of Geoscience Australia (2007). Meteorological data describing precipitation, air temperature and vapour pressure were sourced from Jones et al. (2009). A spatial

Background datasets

The comparison of rates and trends in modelled Penpan evaporation (Epp) with rates and trends in pan observations (Epan) provides a robust test of the input data (Fig. 2). Here, these comparisons are quantified by linear regressions. Fig. 2a shows that, modelled Epp rates compare well with Epan rates, with a slope of 0.99, an r2 of 0.92, and an RMSE (Root Mean Square Error) of 27 mm mth−1. A similar level of accuracy between modelled and observed rates was attained by Roderick et al. (2007) using

The availability and quality of appropriate input data

A critical requirement of being able to examine dynamics in evaporative demand, regardless of which formulation is used, is the availability of data describing all the relevant input variables. Recently Roderick et al., 2007, McVicar et al., 2008 demonstrated that wind speed across Australia has been declining over the past three decades, and that this decline has been the main cause of the observed declines in pan evaporation (Rayner, 2007, Roderick et al., 2007). Donohue et al. (2009a) have

Summary and conclusions

A main finding of this research is that the fully physical Penman formulation of potential evaporation, calculated using spatially and temporally dynamic input data, yields the most realistic estimates of potential evaporation dynamics. This supports the premise that the greater the number of the four key variables that are incorporated in a formulation, the more realistic the trends from that formulation become (Chen et al., 2005, Garcia et al., 2004, McKenney and Rosenberg, 1993, Shenbin et

Acknowledgements

We would like to thank David McJannet, Tom Van Niel and two anonymous reviewers for helpful comments that improved the manuscript. We are grateful to Michael Hutchinson of the Australian National University and to David Jones and Andrew Frost, both of the Bureau of Meteorology, for useful discussions on the accuracy of spline-interpolated data.

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