Pan evaporation can be modeled using a suitably generalized form of Penman's equation [Thom et al., 1981],
where Ep is the pan evaporation rate (kg m−2 s−1), L is the latent heat of vaporization of water (J kg−1), Rn is the net irradiance of the pan (W m−2), s is the slope of the saturation vapor pressure (es) curve in Pa K−1, evaluated at air temperature Ta (K), δe = es(Ta) − e is the vapor pressure deficit (VPD, in Pa), γ is the psychrometric constant (Pa K−1), u is wind speed at two meters (m s−1), and fh(u) and fq(u) are the wind functions for transfer of heat and water vapor respectively (kg m−2 s−1 Pa−1). Strictly, Thom et al.  required that δe be calculated using the properties of the air just above the surface of the pan (0.41 m above the ground), but they assumed that this was the same as at two meters, except for some hourly calculations at night (when dew was on the ground). We use the properties of the air at two meters, to enable the use of standard GCM output. Further, γ = cpp*/(0.622L), where p* is surface pressure and cp is the specific heat of dry air at constant pressure, and s = Les/(RvTa2), where Rv is the specific gas constant for water vapor. S is the storage of heat in the pan, which can be neglected for time periods longer than a few days [Thom et al., 1981]. If we define a = fh(u)/fq(u) (the ratio of the effective surface areas for heat and water-vapor transfer), equation 1 can be written as
We use a = 2.4 [Linacre, 1994], larger than the value (2.1) from Thom et al. , but smaller than the value (2.5) from Kohler et al. . We use the wind function
derived by Thom et al.  using measurements of evaporation from a pan located in a field at the University of Grenoble, France, during the autumn of 1979.
 Calculation of Rn needs to account for the extra shortwave (SW) radiation intercepted by the sides of the pan (including direct, diffuse and reflected radiation). The total SW irradiance of the pan can be estimated as [Linacre, 1994]
where Rs is the downward solar irradiance at the surface, fdir is the fraction of Rs that is direct, As is the albedo of the ground surrounding the pan, and Prad is the pan radiation factor, which accounts for the extra direct irradiance intercepted by the walls of the pan when the sun is not directly overhead. The factor of 0.42 appears because, for a Class A pan, the water surface area is 1.15 m2, the wall area is 0.97 m2, and the vertical walls are effectively exposed to half of the diffuse and reflected irradiance; then 0.42 = 0.5 × 0.97/1.15 [Linacre, 1994]. The three terms in square brackets thus represent the direct, diffuse and reflected components respectively. The implied increase of SW irradiance relative to that at the ground is substantial; over Australia, the ratio Rsp/Rs ranges from 1.46 in the far north to 1.54 over Tasmania. We set As = 0.22, a value appropriate for short, green grass. In arid regions, the albedo of the bare ground around a pan can be as high as 0.30 [Linacre, 1994], so this is a possible source of error in the model. In annual-mean terms, Linacre  derived Prad = 1.32 + 4 × 10−4 ϕ + 8 × 10−5 ϕ2, where ϕ is the absolute value of latitude in degrees. We adopt Ap = 0.14 as a typical value for the albedo of a Class A pan [Linacre, 1992]. Then
where Rl is the net longwave (LW) irradiance of the pan. Note that using an annual-mean expression for Prad underestimates Rsp for larger solar zenith angles, but this is offset by the use of a fixed albedo for the pan, since in reality the pan's albedo is larger when the sun is lower in the sky. Accurate calculation of Rl is a complex problem, since it is affected by the geometry of the pan, and the different temperature and emissivity of the water surface relative to the sides of the pan. Linacre  assumed a fixed value of −40 W m−2 for the net LW irradiance, but this seems too inflexible for climate-change studies. For simplicity, we assume that the downward component of Rl at the pan water surface is the same as the downward LW irradiance at the ground, and that the pan water surface radiates as a black body with temperature Ta. We currently ignore any LW interactions between the air and the sides of the pan. Linacre  proposed an additional longwave irradiance from the ground into the sides of the pan in “dry” months, but when we included this correction, PenPan tended to overestimate Ep. For this reason, and because Linacre unrealistically assumed that the pan wall radiates as a black body, we omitted his aridity correction from PenPan.
 The evaporation rate given by equation 2 should be reduced when a bird guard is fitted to the pan. For the Class A pan network of the Australian Bureau of Meteorology, this reduction was found empirically to be about 7% [van Dijk, 1985], so we multiply equation 2 by 0.93.
2.2. Climate Model and Observations
 An earlier version of the CSIRO Mk3 Atmospheric GCM was described by Gordon et al. . It has horizontal resolution of spectral T63 (roughly 1.9° by 1.9°) and 18 vertical levels. Recent improvements to the GCM are described by Rotstayn et al. (Have Australian rainfall and cloudiness increased due to the remote effects of Asian anthropogenic aerosols?, submitted to Journal of Geophysical Research, 2006). These include treatments of sulfate, carbonaceous, dust, volcanic and sea-salt aerosols, and an updated radiation scheme. After a one-year spinup, we ran the GCM for five years using climatological sea-surface temperatures, and forcing for the year 2000. The fields needed to run PenPan were saved as monthly means, namely air temperature, wind speed and VPD at two meters, surface pressure, and downward LW and SW (total and diffuse) irradiance at the surface. For comparison of GCM-derived output with the point observations described below, we used linear interpolation in space to ensure that the output from the GCM (and PenPan) had the correct geographic coordinates. Note that GCMs are generally unable to resolve steep topography, which could cause errors if the altitude of the measurement site differs substantially from that of the GCM grid box. Since Australia does not have much steep topography, this is unlikely to cause serious errors in this study, but it may be important if PenPan is applied to GCM output in other regions.
 We used an observational data set supplied by the Australian Bureau of Meteorology, comprising monthly pan evaporation measurements at 70 sites for the period 1967–2004. The locations of these sites are shown in Figure 1. We averaged the monthly evaporation data over the 25-year period 1980–2004, to avoid the problem of the introduction of bird guards, since all Australian pans had bird guards fitted by 1978. Evaporation measurements commenced at some sites after 1980, but all sites have at least nine complete years of monthly data. Air temperature and rainfall measurements are available for all 70 sites, but other measurements that are useful for reconciling modeled and observed pan evaporation are available at smaller numbers of sites: downwelling SW irradiance, wind speed and humidity (26 sites) and downwelling LW irradiance (11 sites). The temporal coverage of the radiation data is the most limited, with sites generally having from five to 23 complete years of SW data and five to 10 complete years of LW data. The 11 sites with LW data provide all the inputs needed to force PenPan purely by observations, except that the direct fraction of Rs must be parameterized. We use fdir = −0.11 + 1.31*Rs/Rst, where Rst is the downwelling SW irradiance at the top of the atmosphere [Roderick, 1999]. Also, in the absence of surface pressure observations, the psychrometric constant (in Pa K−1) is estimated as γ = 67 − 7.2 × 10−3z, where z is elevation in meters [Linacre, 1994]. In the following figures, we show the 11 “elite” sites as blue points, the remaining 15 sites with SW irradiance, wind speed and humidity measurements as green points, and the other 44 sites as red points.
Figure 1. Locations of the 70 measurement sites. Blue points show the 11 sites for which pan evaporation can be calculated purely from observations; green points show the other 15 sites for which SW radiation and humidity observations exist; red points show the remaining 46 sites.
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