1 Supplementary Material to paper ‘Estimating actual, potential, reference crop and pan evaporation using standard meteorological data: A pragmatic synthesis’ Thomas A McMahon, Murray C Peel, Lisa Lowe, R Srikanthan, Tim R McVicar This supplementary material consists of a list of symbols and variables used in the paper and in the following 21 sections. Section S1 discusses data used or referred to in the sections. Section S2 addresses the computation of some common meteorological variables and Section S3 outlines the computation of net solar radiation. The application of the evaporation models, Penman and Penman-Monteith, is discussed in Sections S4 and S5. Computation of Class-A pan evaporation by the PenPan model is outlined in Section S6. Actual evaporation estimates using Morton, and Advection-Aridity and like models are discussed in Sections S7 and S8. Section S9 describes the computation of potential evaporation by several other models. Two methods to estimate deep lake evaporation where advected energy and heat storage should be accounted for are outlined in Section S10 and Section S11 describes the application of four methods to estimate shallow lake evaporation. The next four sections deal with evaporation from lakes covered by vegetation (Section S12), estimating potential evaporation in rainfall-runoff modelling (Section S13), estimating evaporation from intercepted rainfall (Section S14) and estimating bare soil evaporation (Section S15). In Section S16 there is a discussion of Class-A pan evaporation equations and pan coefficients. Section S17 includes a summary of published evaporation estimates. Section S18 is a summary of a comparison of evaporation estimates by 14 models for six sites across Australia. Detailed worked examples for most models are carried out in Section S19. Section S20 is a Fortran 90 listing of Morton’s WREVAP program and Section S21 is a worked example of Morton’s CRAE, CRWE and CRLE models within the WREVAP framework. List of Supplementary Material List of variables and symbols in the paper and supplementary sections excluding Sections 20 and 21 Section S1 Data Section S2 Computation of some common variables Section S3 Estimating net solar radiation Section S4 Penman model Section S5 Penman-Monteith and FAO-56 Reference Crop models Section S6 PenPan model Section S7 Morton models Section S8 Advection-Aridity and like models Section S9 Additional evaporation equations Section S10 Estimating deep lake evaporation Section S11 Estimating shallow lake evaporation 2 Section S12 Estimating evaporation from lakes covered by vegetation Section S13 Estimating potential evaporation in rainfall-runoff modelling Section S14 Estimating evaporation of intercepted rainfall Section S15 Estimating bare soil evaporation Section S16 Class-A pan evaporation equations and pan coefficients Section S17 Comparing published evaporation estimates Section S18 Comparing evaporation estimates based on measured climate data for six Australian automatic weather stations Section S19 Worked examples Section S20 Listing of Fortran 90 version of Morton’s WREVAP program Section S21 Worked example of Morton’s CRAE, CRWE and CRLE models within the WREVAP framework References for Supplementary Material Table S1 Values of specific constants Table S2 Roughness height, aerodynamic and surface resistance of typical surfaces Table S3 Albedo values Table S4 Median, 10th and 90th percentile monthly evaporation based on data recorded at the 68 Australian AWSs for three Penman wind functions, and for FAO-56 Reference Crop and Priestley-Taylor algorithms expressed as a percentage of the Penman (1948) median estimate Table S5 Guideline for defining shallow and deep lakes and the methods to estimate lake evaporation Table S6 Mean monthly guarded Class-A evaporation pan coefficients for 68 Australian locations Table S7 Comparison of equations to estimate evaporation from a lake covered with vegetation Table S8 Measured values of Priestley-Taylor coefficient ( ) Table S9 Effect of type and length fetch, wind speed and humidity on Class-A pan 훼푃푇 coefficients without bird-guard Table S10 Published references listing annual Class-A pan coefficients based on the Penman equation with wind functions of Penman (1948) and Penman (1956), Reference Crop equation and Priestley-Taylor equation Table S11 Monthly Class-A evaporation pan coefficients for selected Australian lakes Table S12 Annual Class-A evaporation pan coefficients for selected Australian lakes Table S13 Comparison of annual estimates of evaporation (mm day-1) at six Australian locations by 13 daily and monthly models plus Class-A pan and mean annual rainfall for period January 1979 to March 2010 Figure S1 Location of the 68 Automatic Weather Stations and Class-A evaporation pans (of which 39 pans are high quality) used in the analyses 3 Figure S2 Plot showing Priestley-Taylor pan coefficients against mean annual unscreened Class-A pan evaporation based on six years of climate station data in Jordon (Weiβ and Menzel, 2008) Figure S3 Comparison of monthly PenPan evaporation and Class-A pan evaporation for 68 Australian climate stations 4 List of variables and symbols in the paper and supplementary sections excluding Sections S20 and S21 Variable/symbol Description Units* Symbols AA Advection-Aridity model symbol AWBM Rainfall-runoff model symbol AWS Automatic Weather Station symbol BC Blaney-Criddle evapotranspiration model symbol BS Brutsaert-Stricker evaporation model symbol CR Complementary Relationship symbol CRAE Complementary Relationship Areal Evapotranspiration symbol CRLE Complementary Relationship Lake Evaporation symbol CRWE Complementary Relationship Wet-surface Evaporation symbol Evapotranspiration symbol 퐸푇FAO56 RC FAO-56 Reference Crop model symbol GG Granger-Gray evaporation model symbol HS Hargreaves-Samani evapotranspiration model symbol M Month symbol Mo Morton evaporation model symbol Ma Makkink evaporation equation symbol modH Modified Hargreaves evaporation model symbol PM Penman-Monteith evapotranspiration model symbol Potential evapotranspiration symbol 푃퐸푇PT Priestley-Taylor evaporation model symbol P48 Penman equation with 1948 wind function symbol P56 Penman equation with 1956 wind function symbol SILO An enhanced Australian climate database symbol SW Shuttleworth-Wallace model symbol SHE Système Hydrologique Européen rainfall-runoff model symbol SIMHYD Rainfall-runoff model symbol SWAT Soil and Water Assessment Tool symbol Th Thornthwaite evapotranspiration model symbol TIN Triangular irregular networks symbol 5 Tu Turc evaporation model symbol Program combining three Morton models CRAE, CRWE and WREVAP symbol CRLE Variables 2 Evaporating area m 2 2 퐴 Lake area (in Kohler and Parmele (1967) procedure) km , (m ) Net water advected energy during (net inflow from inflows -1 퐿 mm day 퐴 and outflows of water) ∆푡 퐴푊 Available energy (sensible and latent heat) above canopy MJ m-2 day-1 푒 Gradient in Equation (S13.1) undefined 퐴 -1 퐴푝 Net water advected energy during mm day 푤 2 퐴 Surface area of the lake ∆푡 m 푠 퐴 Available energy at sub-strate MJ m-2 day-1 , 2 퐴푠푠 Area of adjacent layers m 퐴 푖 +1 퐴푖 Coefficient undefined 푎 Exponent in Thornthwaite 1948 procedure undefined 푎푇ℎ Constant in PenPan equation dimensionless 푎푝 Constant for Ǻngström –Prescott formula dimensionless 푎푠 Constant dimensionless 표 Bowen Ratio dimensionless 푎 퐵 Intercept in Equation (S13.1) undefined 퐵 푝 Coefficient or slope of the regression between two variables undefined Constant , or constant in CRAE and CRWE models dimensionless 푏 푏0 Constant for Ǻngström –Prescott formula dimensionless 푠 Working variable undefined 푏 -2 푏푣푎푟, Empirical coefficients for Morton’s procedure W m 푏C1 푏2 Constant = 13 m m Hargreaves-Samani working coefficient undefined 퐶퐻푆 Cloud cover oktas 표 Fraction of cloud cover dimensionless 퐶 퐶푓 Wind function coefficient undefined 푢 Number of tenths of the sky covered by cloud dimensionless 퐶 -1 퐶퐷 Atmospheric conductance m s 퐶푎푡푚 6 Canopy conductance m s-1 퐶푐푎푛 Empirical coefficient undefined 퐶푒푚푝 , Working variables undefined 퐶푐푎 퐶푠푢 Amount of water retained on the canopy mm 퐶 푟푒푡 Parameter in linear Budyko-type relationship undefined -1° -1 푐 Specific heat of air MJ kg C 푐푎 Constant dimensionless 표 Volumetric heat capacity of soil -3 ° -1 푐 MJ m C -1 ° -1 푐푠 Specific heat of water MJ kg C 푐푤 Constant = 0.61 dimensionless -1 푐1 Constant = 0.12 mm day 푐2 Day or dimensionless relative drying power dimensionless Day of Year dimensionless 퐷 퐷표푌 Dimensionless relative drying power dimensionless 퐷 푝 Zero plane displacement height m 푑 Number of days in month day 푑푎푦푚표푛 Relative distance between the earth and the sun undefined 푟 Effective soil depth m 푑 푑푠 Constant dimensionless -1 표 Surface evaporation mm day 푑 퐸 Elevation above sea level m -1 퐸푙푒푣 Actual evaporation rate mm day -1 퐸퐴푐푡 Equilibrium evaporation rate mm day -1 퐸퐸푄 Makkink potential evaporation mm day -1 퐸푀푎푘 Modelled Class-A (unscreened) pan evaporation mm day -1 퐸푃푒푛푃푎푛 Lake evaporation on day mm day 푖 Working variable undefined 퐸 푖 퐸EP푝푎2, EP3, EP5 Various definitions of potential evaporation undefined Shuttleworth-Wallace combined evaporation from vegetation mm day-1 and soil 푆푊 Wet-environment evaporation estimated by Priestley-Taylor 퐸 ( ) mm day-1 at 푃푇 푒 퐸 ,푇 Penman estimate of evaporation for specific period mm/unit time 푇푒 -1 퐸푃푒푛 푗 Evaporation from a deep lake mm day -1 퐷퐿 Lake evaporation large enough to be unaffected by the upwind mm day 퐸 퐸퐿 7 transition Evaporation from a water body using McJannet