A Physical Analysis of Changes in Australian Pan Evaporation

Transcription

1 A Physical Analysis of Changes in Australian Pan Evaporation Technical Report prepared as part of Land & Water Australia Project No. ANU49 titled Agro-ecological implications of change to the terrestrial water balance Michael L. Roderick & Graham D. Farquhar Research School of Biological Sciences Principal Investigator: Dr Michael L. Roderick Research School of Biological Sciences Canberra ACT 2 File: PhysicEpan_2.doc Date: 1 March 26

2 1 Summary Roderick and Farquhar (24) found that evaporative demand as measured by pan evaporation has, on average, declined throughout Australia since the 197s. In this study we used Bureau of Meteorology measurements of temperature, humidity, wind speed and solar radiation, and an existing model called the PenPan model to determine why pan evaporation had decreased. We follow a Penman-style approach and calculated the radiative and aerodynamic components of pan evaporation separately. This allowed us to attribute the observed trend to one or more contributing factors. Pan evaporation rate was calculated at 7 sites having long term solar radiation and aerodynamic measurements extending back 3 years. The linear trend in pan evaporation as determined by the model-based calculations agreed with the observed trends within acceptable limits. Using that as a basis we calculated the aerodynamic component at 41 sites having long-term measurements (wind, humidity, temperature) for The radiative component was estimated as the difference between the observed and aerodynamic trend. The results showed that in general, there was very little change over time in the overall humidity regime. There was some evidence for a decline in solar radiation in the north-west of Australia that contributed to the observed decline in pan evaporation in that region. Overall, the most important factor was a decline in the wind speed. Whether the stilling is a local phenomenon (e.g. local obstructions causing changes in air flow over the pans) or a regional (or larger scale) change remains unknown.

3 2 Introduction Roderick and Farquhar (24) reported that evaporative demand, as measured by pan evaporation rate had, on average, declined in Australia from the early 197s until 22. This came as a surprise to many in the climate and natural resource management community because, until that research, the dominant paradigm was that evaporative demand would increase with warming. One possibility to explain the decline was that a mistake had been made in the measurements. However, a special forum hosted by the Australian Academy of Science, involving leading Australian and international scientists, did not identify any problems of that nature (Gifford, 25). From physical principles we know that evaporative demand should increase slightly with increases in near-surface air temperature provided that all else is constant. Assuming that the pan evaporation measurements have been made correctly, then the above-noted observed decline in evaporative demand means that all else is not constant. In fact, it would have been a surprise to find that Australian pan evaporation had on average increased, because the dominant worldwide trend has been for declines. For example, declines have been reported in the US and former Soviet Union (Peterson et al., 1995; Golubev et al., 21), China (Liu et al., 24; Chen et al., 25), India (Chattopadhyay and Hulme, 1997), Thailand (Tebakari et al., 25), Canada (Hesch and Burn, 25) and New Zealand (Roderick and Farquhar, 25). The decline in Australian pan evaporation rate, and hence evaporative demand, is of fundamental importance for understanding changes in water availability. The results

4 3 raise two important questions; (i) is the decline happening all year around or is it specific to a particular season/s?, and (ii) what are the physical reasons for the decline? The first question has been addressed in a separate report (Roderick and Farquhar, 26). The results showed that pan evaporation rate was, on average, declining in all seasons. This report addresses the second question why? The approach is to compile existing meteorological data and to calculate how pan evaporation rate has changed as a function of changes in the radiative (e.g. solar radiation) and aerodynamic (e.g. humidity, wind speed) regimes. To do that we used data from the Bureau of Meteorology (BoM) and an existing model describing evaporation from a class A pan called the PenPan model (Linacre, 1994). The modelbased calculations are then compared to observations. Theory The PenPan Model Linacre (1994) used a Penman-style approach to formulate a combination equation describing the mass and energy balance of a class A pan. He called it the PenPan model. The PenPan model is based on a steady-state heat balance. For a class A pan this means that it can be applied for periods of a week or more. Linacre s formulation applies to a month. The derivation (along with a worked example) is described in Appendix A only the main results are listed here. The PenPan equation is (see Table 1 for definition of terms),

5 4 s λ E pan = ( RN, pan + 6 u F ( Ta Td )) (1) s + 2.4γ Note that Eqn (1) can be rewritten as the sum of radiative ( λ E pan, R ) and aerodynamic ( λ E pan, A ) terms, λ = + (2) E pan λe pan, R λe pan, A where the respective components are, s E pan, R = ( RN, pan λ ) (3a) s + 2.4γ and, s λ E pan, A = ( 6 uf ( Ta Td )) (3b) s + 2.4γ Symbol Units Comments λ J kg -1 Latent heat of vaporization of liquid water (~ 2.4 MJ kg -1 ) {Estimate in J kg -1 using λ = 1 6 (2.5.24T ) with T in deg C} E pan kg m -2 s -1 Evaporation rate from class A pan R N,pan W m -2 Net radiation of the class A pan s Pa K -1 Derivative of saturation vapour pressure with respect to temperature {Estimate in Pa K -1 2 using s = 1*(.5 +.1T +.19T ) with T in deg C} γ Pa K -1 Psychrometric constant (~ 67 Pa K -1 ) {Estimate in Pa K -1 using 5 γ = 1*(.67 z ) with z (elevation) in metres} T a K Air temperature T d K Dew point temperature of air F - Correction for change in air density with 5 altitude {Estimate using F = 1. z with z (elevation) in metres} u m s -1 Monthly mean wind speed Table 1 Definition of terms in the PenPan model

6 5 To calculate the aerodynamic component of pan evaporation requires estimates of monthly mean air temperature (T a, Eqn 3b, also used to estimate s, see Table 1), monthly mean dew point temperature of the air (T d, Eqn 3b), monthly wind run expressed as a monthly mean wind speed (u, Eqn 3b) and elevation (z, used to calculate γ and F). To calculate the radiative component, R N,pan is estimated using the global solar irradiance, the site latitude and the albedo of the ground surrounding the pan. See Appendix A for details. Two key points about the PenPan model (see Appendix A for details) need to considered when interpreting the results. First, the PenPan model assumes that the aerodynamic component varies linearly with wind speed. Second, the PenPan model as currently implemented assumes that the net long wave irradiance of a pan is constant over space and time. This appears to be a plausible first approximation for many climatological purposes. However, for use in studying the enhanced greenhouse effect over long periods (e.g. 1 years) the assumption may not be realistic. For the 3 year period ( ) considered here, we assume, in the absence of contrary evidence, that it is a reasonable approximation. Methods Data Sources & Site Selection As a basis for the project we used the 61 BoM sites identified previously as having near-continuous class A pan evaporation (E pan ) records since 1975 (Roderick and

7 6 Farquhar, 24). A further 9 potential sites were identified from the list compiled by the BoM (Jovanovic et al., 25). This gave 7 sites that were potentially suitable for analysis of changes in pan evaporation and the database was constructed for those sites. Database Construction Daily data for pan evaporation, precipitation, radiation, air temperature, dew point temperature, relative humidity and wind speed were purchased in a digital format from the BoM. These data were used to construct daily databases for each separate element. These daily databases were then summarised into monthly databases for the 7 sites over the period In doing that, we calculated monthly mean daily values of the relevant variables for all months having at least 25 daily observations with a Y quality control flag (i.e. quality controlled and considered acceptable ) in the daily BoM database. The final database record was left NULL (i.e. blank) for any month that did satisfy this criterion. The final database was constructed by combining all relevant monthly data (Database Name: LWA_1967_24_7stns) and contains 3192 records (38 years X 12 months X 7 stns = 3192 records). The database is available (as a text file, as a MS Excel spreadsheet and as a MS Access database) on the CD-ROM that accompanies this report. Details of the database are listed in Table 2.

8 7 Database Data Source Description Field STN_NUM BOM Site Number Year Month ndays Actual number of days in the month Epan_raw IDCJDCO5.256 (mm d-1) - Monthly mean daily Epan_raw (this are the data as they appear on the BOM CDs and are not adjusted for bird guards) Epan_nobs Actual number of obs used to calculate the mean Pre MADAM (mm mth-1) - Total monthly precipitation Solar_Num_Rs The number of the solar stn (BoM have different site numbers for climate and solar stns) should be the same as Solar_Num_Rl Rs NCCSOL Vers (J m-2 d-1) - Monthly mean daily global solar irradiance Rs_nobs Actual number of obs used to calculate the mean Solar_Num_Rl The number of the solar stn (BoM have different site numbers for climate and solar stns) should be the same as Solar_Num_Rs Rl NCCSOL Vers (W m-2) - Monthly mean daily incoming longwave irradiance Rl_nobs Actual number of obs used to calculate the mean Ta IDCJHCO2.256 (degc) - Monthly mean air temperature Ta_nobs Actual number of obs used to calculate the mean Td IDCJHCO2.256 (degc) - Monthly mean dew point temperature Td_nobs Actual number of obs used to calculate the mean Rh IDCJHCO2.256 (%) - Monthly mean relative humidity Rh_nobs Actual number of obs used to calculate the mean U IDCJDCO5.256 (m s-1) - Monthly mean wind speed U_nobs Actual number of obs used to calculate the mean Tw_max IDCJDCO5.256 (degc) - Monthly mean daily max T of water in the Class A Pan Tw_max_nobs Actual number of obs used to calculate the mean Tw_min IDCJDCO5.256 (degc) - Monthly mean daily min T of water in the Class A Pan Tw_min_nobs Actual number of obs used to calculate the mean Table 2 Details of the database. The data source column lists the BoM product code (CD-ROM) used for each data element. All CD-ROM s were dated June 25, except for the radiation data. The radiation database (CD-ROM titled NCCSOL Vers. 2.29, dated 21) is no longer being updated. The BoM provided an update CD (ASCII files, dated June 25).

9 8 Description of the Meteorological Data The pan evaporation, wind speed and pan water temperature data were all taken from the daily pan evaporation database (BoM product code: IDCJDCO5.256, see Table 2). Those data were already in a daily format. The air temperature (T a ), dew point temperature (T d ) and relative humidity data (Rh) data were taken from the so-called daily THP (Temperature, Humidity, Pressure) CD- ROM (BoM product code: IDCJHCO2.256, see Table 2). This CD-ROM contains temperature, humidity and pressure measurements taken at particular instants of time. At some sites over some time periods, there may be as few as 2 measurements per day, while at other sites/times, there are up to 8 measurements (i.e. one every 3 hours) per day. In all cases, whenever there is an air temperature measurement there is also a dew point estimate they come together. The database used here was constructed by averaging all of the available measurements each month. Thus some database elements (T a, T d, Rh) are averages of 6 measurements, while others are averages of 24 measurements. Further, this is not specific to individual stations, i.e. in a few cases some stations have 6 measurements per month for a period, then 24, then back to 6, and so on, as the local circumstances changed. These situations can be distinguished using the relevant nobs fields in the database which are counts of the number of measurements used to calculate the average (Ta_nobs, Td_nobs, Rh_nobs; see Table 2). Similarly, standard BoM protocol is to take measurements based on local standard time. Hence during periods of daylight saving, the local solar time of the observations will show a step change of 1 hour. Because of these issues, any

10 9 individual trends derived from the Ta and Td fields must be considered uncertain until the data are made more uniform with respect to observing practice. The BoM are currently working on the humidity database and future improvements are expected (Coughlan et al., 25). However, in the evaporation equations the key factor is the difference between T a and T d. The database estimates, while by no means perfect, should be a much better estimate of that difference, and are considered sufficient for this initial analysis. The quality of the solar radiation data is uncertain prior to c. 1993, and especially prior to c (Bruce Forgan, pers. comm.). Most measurements made post-1993 have used new and more precise instrumentation and the BoM expect an accuracy of better than c. 1 % for those data. Those data can be identified in the database by having a three digit identifier (in the Solar_Num_Rs field, see Table 2). Prior to 1993, the network used less accurate instrumentation and the BoM expect lower accuracy. An additional complication is that prior to 1988, all solar radiation measurements were calibrated using a statistical (instead of a physical) approach. The calibration was based on the assumption that the clear sky global solar irradiance on a particular day of the year should remain constant over time (see description in Frick et al., 1987) and that any observed variations were due to sensor drift. The measurements were subsequently adjusted by this assumed sensor drift. It is not possible to re-process the original observations using physically based calibration procedures because the original observations are no longer available (Bruce Forgan, pers. comm.). The solar calibration procedure is implicitly based on the assumption that there would be no trends in non-cloud atmospheric elements, of which the most important are

11 1 aerosols and water vapour. The aerosol assumption may be plausible in Australia but cannot be evaluated because the original measurements are no longer available (Bruce Forgan, pers. comm.). The water vapour assumption is most likely to be unreasonable because an increase in atmospheric water vapour is expected due to the enhanced greenhouse effect and should lead to increased absorption of solar radiation (Arking, 1999). Hence any changes in global solar irradiance due to changes in water vapour would have been inadvertently removed, although they should be small over a 3 year period. Any cloud-based effect on global solar irradiance should still be present in the data because the calibration procedure was based on clear-sky irradiance. The net effect is that the accuracy of solar radiation measurements made prior to 1993, and especially those made prior to 1988, are uncertain. Any downward (or upward) trend due to non-cloud effects (e.g. aerosols, water vapour) would have been removed. While not entirely satisfactory, this is the best that we can do at the moment. Bird Guard Corrections All current BoM evaporation pans are fitted with a standardised bird guard. In the early years, the BoM retro-fitted bird guards on some pans. The installation dates for bird guards were available in the BoM database. All pan evaporation measurements made prior to the bird guard installation were reduced by 7% in line with empirical findings (Hoy and Stephens, 1979; van Dijk, 1985). Calculated estimates of pan evaporation

12 11 For all months having estimates of global solar irradiance (R s ) and mean air temperature (T a ), the radiative component of pan evaporation was calculated at each site using the modified PenPan model. There were 5843 such estimates (out of a maximum possible 3192) from 27 sites. For all months having estimates of air temperature (T a ), dew point temperature (T d ) and wind speed (u), the aerodynamic component of pan evaporation was calculated. There were 2144 such estimates from 58 sites. Where the calculated radiative and aerodynamic components were both available in a given month at a given site, they were added to give a total calculated estimate of monthly pan evaporation. There were 5264 such monthly estimates that came from a total of 26 stations. Unfortunately, of those 26 sites, only 7 have a more or less continuous time series from the 197s until 24. The underlying reason for this is that many of the solar radiation measurement stations have been shut down. The calculated values (see Table 3) are stored in the final database (available on the CD-ROM). Field STN_NUM Year Month ndays Epan_adj Epan_rad Epan_aero Epan_calc Description BOM Site Number Actual number of days in the month (mm d -1 ) - OBSERVATION - observed monthly mean daily Epan that have been adjusted where necessary for the Bird Guard (reduce by 7%) (mm d -1 ) - CALCULATION - Radiative component of the calculated monthly mean daily Epan. All calculations per a modified PenPan Model. (mm d -1 ) - CALCULATION - Aerodynamic component of the calculated monthly mean daily Epan. All calculations per a modifed PenPan Model. (mm d -1 ) - CALCULATION - Epan_rad + Epan_aero when both are available. Table 3 Details of the pan evaporation calculations held in the database.

13 12 Trend Estimation Linear regression (ordinary least squares) was used to describe the changes over time. The slope of the linear regression is denoted the trend throughout this report. The regressions were calculated separately at each site for each month, and because a linear regression was used, the annual trend at the site could be calculated as the sum of the monthly trends. The principal advantage of using this procedure is that we avoided the need to estimate any missing data. Where appropriate we have listed the actual number of observations used to estimate the trend. This gives an indication of the amount of missing data. Results Evaluation of the modified PenPan model (26 sites) The modified PenPan model was evaluated at the 26 sites having at least one modelbased estimate of pan evaporation. In making the model-based estimate, the same parameters were used at all sites. In particular, the albedo of the pan surroundings was assumed to be.22 (typical value for short green grass) at all sites, although we recognise that this would in fact vary between sites, and over time. The subsequent comparisons are summarised in Table 4 and plots showing the comparison at each of the 26 sites are available in Fig. B1 (Appendix B). At some sites, there is evidence of consistent bias (i.e. slope not equal to unity, intercept not equal to zero, see Table 4). That bias could be easily removed by tuning the model parameters - the two main parameters that could be tuned are the albedo of the ground surrounding the pan (α,

14 13 see Eqn A1 in Appendix A) and the heat transfer coefficient (the numerical value 6 in Eqn 3b, also see Eqn A2 in Appendix A). While such tuning would have been physically realistic, no attempt was made to do that because improving the fit between calculations and observations was not the aim of the study. The RMS varied across the 26 sites from 12 to 49 mm mth -1 with a mean of about 26 mm mth -1. The RMS is a measure of disagreement between calculations and observations. In general, in the absence of gross measurement error, the observations should be much more precise than the model-based calculations. In that context, the RMS is a measure of the disagreement due to errors in the meteorological measurements (temperature, humidity, wind, solar irradiance) and also any errors in the model parameters and/or model formulation. The RMS errors reported here are in the same range as those reported by Linacre (1994) and are typical of results in the environmental physics field. For most of the 26 sites, the model-based calculations explained more than 9% of the variation in the observations but at three sites, the percentage was closer to 8% (see Table 4); Site 33 (Broome Airport, R 2 =.84), Site 1415 (Darwin Airport, R 2 =.81), Site 324 (Townsville Aero, R 2 =.84). There were no glaring problems with the meteorological data at these sites and we concluded that this was a reasonable representation of the results. In contrast, there were several sites where the model explained more than 98% of the variation in the observations. These were mostly in relatively arid environments.

15 14 Stn Slope Intercept R 2 N RMS mm mth -1 mm mth Table 4 Evaluation of the modified PenPan model at 26 BoM sites (see Fig. B1 for plots at each of the 26 sites). The slope and intercept are from a linear regression between Y (model-based calculation) and X (observed) pan evaporation rate. N denotes the number of months used in the comparison at each site. RMS is the rootmean-square of the difference between observed and calculated pan evaporation rate. Detailed inspection of the plots (Fig. B1, Appendix B) shows that at many sites there is a residual seasonal variation (e.g. Fig. B1, 611 Carnarvon Airport, 745 Meekatharra Airport, etc.). This demonstrates that there is a radiative process occurring that is not represented by the model. This is almost certainly due to the geometric calculations (see Appendix A). In particular, in the original formulation, Linacre calculated the irradiance of the pan walls relative to the water surface (the P parameter in Eqn A1) as a function of latitude. However, as Linacre noted in the discussion, this should also be a function of time (i.e. the apparent solar position

16 15 changes with latitude and time). Given that we are primarily interested in trends over more than one year, this will not have an impact on the results. A more important problem is that the residuals often show correlations through time (see lower right panels in Fig. B1). Ideally, the residuals should be uncorrelated, i.e. white noise. For example, at Darwin Airport (Site 1415, lower right panel in Fig. B1) there is a jump in c. 1987, followed by a trend in the residuals. This indicates either; (a) a problem with the measurements, and/or (b) that something in the surroundings of the pan is changing in a systematic way, e.g. changes in albedo, that is not accounted for in the model. For attribution purposes, it is important that the residuals are uncorrelated over the period being considered. At Darwin Airport, attribution is still possible over the period because a linear regression of the residuals (observed minus calculated) over that period would have a slope near zero. Further, at Darwin, the magnitude of the residual trend (i.e. c. 6 mm a -1 from , i.e. c. 5 mm a -2 ) is much smaller than the trend in the observations (c mm a -2 ). The situation is similar at Alice Springs (Site 1559, Fig. B1, lower right panel) where there is a step in c. 198 separating two different trends in the residuals. As for Darwin, the data at Alice Springs could be used for attribution over the period because the overall slope of the residuals over that period is near zero. However, in contrast to Darwin, this is not the case for other periods. For example, at Alice Springs, there is a systematic trend in the residuals of about + 1 mm a -1 from (i.e. c. + 5 mm a -2 ) that is of the same order as the observed trend in that period. Alternatively, at Mount Gambier (Site 2621, Fig. B1), the residuals are more or less uncorrelated through time and the data at this site can be used for attribution purposes. Future improvements in the model and the BoM data should remove some of these

17 16 residual trends. In the interim, it is prudent to check each station individually if attribution is being attempted. Trend Calculations at Sites with Long Term Records (7 sites) Site Name Period de obs /dt de calc /dt de R /dt de A /dt (mm a -2 ) (mm a -2 ) (mm a -2 ) (mm a -2 ) 851 GERALDTON AIRPORT 1415 DARWIN AIRPORT 1559 ALICE SPRINGS AIRPORT 2621 MOUNT GAMBIER AERO 3983 ROCKHAMPTON AERO 7215 WAGGA WAGGA AMO 7631 MILDURA AIRPORT (n = 432) (n = 336) (n=432) (n=384) (n=384) (n=396) (n=372) -5. (n=427) -17. (n=331) 1.9 (n=432) -5.4 (n=378) 1. (n=374) -.7 (n=394) -5.7 (n=37) -2. (± 2.3) -.4 (n=369) -16. (± 5.3) -6. (n=297) 14.1 (± 3.6) 1.4 (n=37) -7.6 (± 1.4) -.4 (n=344) 8.9 (± 3.3) 3.6 (n=37) 3.9 (± 1.8).6 (n=299) -9.1 (± 2.) 1.4 (n=363) -1.6 (n=429) -1. (n=334) 12.7 (n=428) -7.2 (n=383) 5.3 (n=382) 3.3 (n=394) -1.5 (n=37) Table 5 Comparison between observed (de obs /dt) and calculated (de calc /dt) trends in pan evaporation rate at seven sites having long term meteorological records. Note that the calculated trend is the sum of the radiative (de R /dt) and aerodynamic (de A /dt) components. The maximum number of possible monthly observations is shown in brackets under the period while the actual number of observations used in each calculation are listed under the trend estimates. The (1σ) error estimates (de calc /dt) are based on the RMS values (Table 4) at each site. The trends in the shaded columns should agree (within the error estimates). The calculations at Darwin Airport (Site 1415) were begun in 1977 to avoid a problem (discontinuity) in the wind speed measurements at that site. Of the 26 sites having suitable radiative and aerodynamic observation, there were 7 sites having long term observations. At these 7 elite sites, the trends in observed and calculated pan evaporation rates were determined using the longest possible period at each site (Table 5). Using the best example - at Darwin (Site 1415), the calculations for estimated the trends to be -6. mm a -2 and 1. mm a -2 for the radiative and aerodynamic component respectively, giving a total calculated trend of mm a -2. By comparison, the observed trend was -17 mm a -2 excellent

18 17 agreement. The agreement at the seven elite sites is summarised in Table 5. In all cases the observed and calculated trends are within the error estimates. While one can say little about regional trends from these 7 sites, this was still a very important result because it gives an independent confirmation that the results based on the BoM measurements and the modified PenPan model are generally reliable for the period considered. Estimates of the aerodynamic and radiative trends (41 sites) The major limitation to the attribution study is the lack of long term solar radiation measurements. However, of the 66 sites, there are 41 that have suitable nearcontinuous measurements to calculate the aerodynamic component. At each of the 41 sites, the trend in the observations, and the model-based calculations of the aerodynamic component were estimated. The trend in the radiative component was then estimated as the difference between the observed trend and the aerodynamic trend at the 41 sites (Fig. 1). One interesting feature (Fig. 1) in the trend maps is the two inland sites showing conspicuously large increasing trends. Those site locations are: Alice Springs Airport (133.89, -23.8, Site 1559) and Woomera Aerodrome (136.81, , Site 161). As noted previously (Roderick and Farquhar, 26), the large increase at Alice Springs is due to the very low E pan values recorded during a very wet period in the mid 197s around the starting year for the calculations. If the calculations at Alice Springs are begun at a different date (e.g. either 197 or 198) the sharp upward

19 18 trend is not nearly as strong. However, the trend at Woomera appears to be a realistic record of changes at that pan. Site Map Epan OBS + 1 mm a -2-1 mm a Epan AERO Epan RAD + 1 mm a -2-1 mm a mm a -2-1 mm a -2 Figure 1 Results of the attribution analysis for Locations of the 41 sites (top left) and the linear trends in: observed pan evaporation rate (top right), aerodynamic component of pan evaporation rate (lower left), radiative component of pan evaporation rate (lower right). Note that the radiative component is computed as the difference between the observed and aerodynamic trends. Black (grey) dots denote decreasing (increasing) trends with the dot diameter scaled per the legend in the bottom left.

20 19 The results show that at many sites, the observed trend is mostly due to changes in the aerodynamic component, although declines in the radiative component are prominent in the north-west region (Fig. 1). Segmenting the Aerodynamic trend into Wind and VPD components The decline in the aerodynamic component (Fig. 1) raises the question: is this due to changes in the humidity regime and/or the wind regime? To address that question we partitioned the aerodynamic trend into two components; one due to changes in wind (u) and a second due to changes in VPD (here represented as T a -T d ). This was estimated by differentiating Eqns 3a and 3b, λ de pan, A s du s d( Ta Td ) 6 F ( Ta Td ) + 6 F u dt s + 2.4γ dt s + 2.4γ dt (4) where the first term is an estimate of the trend due to changes in wind speed while the second term is that due to changes in the VPD. The linear trends were estimated from the trends in the BoM observations ( d( T T ) dt du dt ) (see Fig. 2) and the a d, calculations were completed separately for each month using appropriate monthly mean values ( Ta Td, u ) for the period. Note that in partitioning the trends, we have assumed that s ( s + 2.4γ ) (which is a function of temperature) has no trend as well as neglecting higher order terms (Eqn 4). Because of those approximations, the sum of the humidity and wind terms will not exactly equal the calculated aerodynamic component. However, the differences are small and do not alter the final interpretation (see Table C1, Appendix C). The results are summarised in Fig. 3. A full listing for the 41 sites is also available in Table C1.

21 Ta-Td U +.2 K a K a m s -1 a m s -1 a -1 Figure 2 Observed trends in humidity (T a -T d, left panel) and wind (u, right panel) regimes at 41 sites for Epan AERO + 1 mm a -2-1 mm a AERO: Ta-Td AERO: U + 1 mm a -2-1 mm a mm a -2-1 mm a -2 Figure 3 Partition of the aerodynamic trend (top panel) into VPD (lower left) and wind (lower right) components at 41 sites for

22 21 Summary and Synthesis of the Attribution Study According to the modified PenPan model used here, the changes (mostly declines) in pan evaporation rate reported over Australia since the 197s are mostly due to declines in the wind speed (Figs 1-3). At several sites, the trend in wind speed, according to the BoM observations can be as large as -.5 m s -1 a -1. Over a thirty year period, this is equivalent to a drop in mean annual wind speed of c. 1.5 m s -1. This is a relatively large decline given that a typical global mean wind speed is roughly 2 m s -1. The trend in the radiative component was generally smaller although a decline in the radiative component was evident in the north-west of Australia (Fig. 1). Changes in pan evaporation rate due to changes in the humidity regime were generally small (Fig. 3). Discussion & Conclusion The attribution reported here is dependent on the model-based calculations (i.e. model and data). The results at the 7 elite sites provide support for the attribution with an error margin of about 4 mm a -2 (see Table 5). With this context in mind, we calculated the trend in the aerodynamic component of pan evaporation using monthly observations of air temperature, humidity and wind speed that had been made by the BoM at 41 sites. The radiative component was estimated as the difference between the trend in the observed pan evaporation rate and the aerodynamic component. Note that any error made in the aerodynamic calculations is compensated for in the radiative component because we obtained that by difference. Ideally one should compute the

23 22 radiative trend from observations but there is a paucity of radiation measurements, both in Australia, and elsewhere. The encouraging results reported here suggest that evaporation pans might be useful surrogate radiometers. This is important because there are many more evaporation pans than radiometers, in Australia, and elsewhere. The results of the above-noted approach showed that a widespread (but not universal) decline in wind speed was the main reason for the widespread (but not universal) decline in pan evaporation. Trends in the radiative component were generally smaller, except in the north-west of Australia, where there is evidence of a decline in solar radiation. This is consistent with BoM observations showing a decline in solar radiation at Darwin (Table C1). Presumably this is due to increased cloud cover as might be expected to accompany the well known increase in rainfall in the north-west of Australia over the last 3 years (e.g. see & Trends in pan evaporation rate due to changes in the humidity were generally small. This was expected (Roderick and Farquhar, 22). A decline in wind speed at an individual site could be due to a change in local exposure (e.g. growing trees that are part of a wind break located upwind of the BoM class A pan). However, the fact that many sites show declines in wind speed (Fig. 2) suggests that it might be a more widespread climate-related phenomenon. If that is true, the reason for this stilling remains unknown.

24 23 Acknowledgements We thank Alan Beswick, John Carter, Greg McKeon and David Rayner from the Climate Impacts Group at the Queensland Department of Natural Resources and Mines (QDNRM) for their generous and helpful advice. We also thank Randall Donohue and Michael Hobbins for useful discussions and especially Alison Saunders for expert assistance in acquiring and processing the data.

25 24 References Arking A The influence of clouds and water vapour on atmospheric absorption. Geophysical Research Letters 26: Chattopadhyay N, Hulme M Evaporation and potential evapotranspiration in India under conditions of recent and future climate change. Agricultural and Forest Meteorology 87: Chen D, Gao G, Xu C-Y, Guo J, Ren G. 25. Comparison of the Thornthwaite method and pan data with the standard Penman-Monteith estimates of reference evapotranspiration in China. Climate Research 28: Coughlan M, Braganza K, Collins D, Jones D, Jovanovic B, Trewin B, 25: Observed climate change in Australia. In: Greenhouse 25, November 25, Melbourne, Victoria. Frick RA, Walsh PJ, Rice SP, Leadbeater M, 1987: Australian Solar radiation Data Handbook. Vol II. End of Grant Report No. 714, National Energy Research, Development and Demonstration Program, Canberra. Gifford RM (ed), 25: Pan evaporation: An example of the detection and attribution of trends in climate variables, Australian Academy of Science. Canberra. 86 pp. Golubev VS, Lawrimore JH, Groisman PY, Speranskaya NA, Zhuravin SA, Menne MJ, Peterson TC, Malone RW. 21. Evaporation changes over the contiguous United States and the former USSR: A reassessment. Geophysical Research Letters 28: Hesch NM, Burn DH, 25: Analysis of trends in evaporation - Phase I, Technical Report, Agriculture and Agri-Food Canada: Prairie Farm Rehabilitation Administration, Waterloo, Ontario, 127 pp. Hoy RD, Stephens SK, 1979: Field Study of Lake Evaporation - Analysis of Data from Phase 2 Storages and Summary of Phase 1 and 2, Technical Paper No. 41, Australian Water Resources Council, 177 pp. Jovanovic B, Jones DA, Nicholls N, 25: A historical monthly pan-evaporation dataset for Australia. In: Australian Institute of Physics 16th Biennial Congress, February 25, Canberra, ACT. Linacre ET Estimating U.S. class A pan evaporation from few climate data. Water International 19: Liu B, Xu M, Henderson M, Gong W. 24. A spatial analysis of pan evaporation trends in China, Journal of Geophysical Research 19: D1512, doi:1.129/24jd4511. Peterson TC, Golubev VS, Groisman PY Evaporation losing its strength. Nature 377:

26 25 Roderick ML Estimating the diffuse component from daily and monthly measurements of global radiation. Agricultural and Forest Meteorology 95: Roderick ML, Farquhar GD. 22. The cause of decreased pan evaporation over the past 5 years. Science 298: Roderick ML, Farquhar GD. 24. Changes in Australian pan evaporation from 197 to 22. International Journal of Climatology 24: Roderick ML, Farquhar GD. 25. Changes in New Zealand pan evaporation since the 197s. International Journal of Climatology 25: Roderick ML, Farquhar GD, 26: Seasonal changes in Australian pan evaporation. Land & Water Australia Technical Report, Canberra, February 26. Tebakari T, Yoshitani J, Suvanpimol C. 25. Time-space trend analysis in pan evaporation over Kingdom of Thailand. Journal of Hydrologic Engineering 1: van Dijk MH Reduction in evaporation due to the bird screen used in the Australian class A pan evaporation network. Australian Meteorological Magazine 33: Wallace BB, 1994: Modelling evaporation from a U.S. Weather Bureau class A pan, B.E. (Hons) Thesis. Centre for Water Research, University of Western Australia.

27 26 Appendix A Linacre s PenPan Equation with minor modifications Symbol Units Comments λ J kg -1 Latent heat of vaporization of liquid water (~ 2.4 MJ kg -1 ) {Estimate in J kg -1 using λ = 1 6 (2.5.24T ) with T in deg C} E pan kg m -2 s -1 Evaporation rate from class A pan R N,pan W m -2 Net radiation of the class A pan ρ kg m -3 Density of air (~ 1.2 kg m -3 ) C J kg -1 K -1 Specific heat of dry air (~ 1 J kg -1 K -1 ) D Pa Vapour pressure deficit s Pa K -1 Derivative of saturation vapour pressure with respect to temperature`{estimate in Pa K -1 using 2 s = 1*(.5 +.1T +.19T ) with T in deg C} r a s m -1 Resistance to sensible heat loss from water surface (~ 2/u with u {wind speed} in m s -1 ) γ Pa K -1 Psychrometric constant (~ 67 Pa K -1 ) {Estimate in Pa K -1 5 using γ = 1*(.67 z ) with z (elevation) in metres} r s s m -1 Additional resistance to sensible heat loss due to walls of pan (~ 28/u with u {wind speed} in m s -1 ) T a K Air temperature T d K Dew point temperature of air F - Density correction for change with altitude 5 {Estimate using F = 1. z with z (elevation) in metres} R S,pan W m -2 Solar irradiance of pan (i.e. water surface plus walls of the pan) R S W m -2 Global solar irradiance at surface (i.e. the quantity observed by the BoM) B - Fractional reduction in solar irradiance of the water surface due to the bird guard F - Ratio of direct to global solar irradiance (Eqn A11) P - A latitude dependent correction factor (Eqn A1) {Estimate using φ φ P = based on latitude (φ, decimal degrees). NB. φ is absolute value of the latitude} α - Albedo of surface surrounding the pan (.22 used here) Table A1 Definition of terms in the PenPan model

28 27 Theory Linacre (1994) formulated a Penman-type equation for the evaporation from a class A pan (without a bird guard) that is known as the PenPan model. The model is based on a steady-state heat balance. In practice, this means that the equation is applicable over time periods longer than a week or so, and Linacre s formulation was applied to monthly time scales. The basis of that formulation was a combination-type (i.e. Penman-type) equation as follows (see Table A1 for definitions); ρ c D ( RN, pan + ) s ra λ E pan = (A1) γ ra + rs 1+ ( ) s r a Linacre used typical heat transfer coefficients, i.e., r a ~ 2/u s m -1, r s ~ 28/u s m -1 where u is the wind speed. With these values, and keeping SI units throughout ( ρ ~ 1.2 kg m, c ~ 1 J kg K ) we have, ρ c (1.2)(1) u ~ = 6 u (A2) ra 2 Note that Linacre used 6uF (cf. Eqn A2) instead, where F is a (small) correction to account for the dependence of air density on elevation (z, metres), 5 F = 1. z (A3) Also, with the above-noted numerical values, we have, ra + rs 2/ u + 28/ u ~ = 48/ 2 = 2.4 (A4) ra 2/ u Linacre also noted that D ~ T a T d (A5) s Combining the above equations, we have ( RN, pan + 6uF( Ta Td )) λe pan = (A6) γ s which can be rewritten as s λ E pan = ( RN, pan + 6uF( Ta Td )) (A7) s + 2.4γ Note that Eqn (A7) can be interpreted as the sum of radiative and aerodynamic terms, λ = λe + E (A8a) E pan pan, R λ pan, A where the radiative component is s λ E pan, R = ( RN, pan ), s + 2.4γ (A8b) and the aerodynamic component is s λ E pan, A = ( 6uF( Ta Td )) s + 2.4γ. (A8c)

29 28 In this project, these two terms were calculated for each month having the appropriate meteorological data. The aerodynamic calculation is straightforward and not described further. The radiative calculation is described in more detail below. The Radiative Calculations Linacre used an empirical equation for monthly net irradiance of the pan, R.71R 4. (W m -2 ) (A9) N, pan = S, pan R S, pan where is the solar irradiance of the pan (i.e. solar irradiance of the water surface plus the pan walls). Note that Eqn A9 implies that the net long-wave irradiance is -4 W m -2 and is invariant over space and through time. (This could be modified with more research on the energy balance of a pan.) In turn, R is related to the global solar S, pan irradiance (Rs, i.e. the quantity measured by the BoM) by the following equation which Linacre derived based on the geometry of a Class A pan (4 ft diameter, 1 inches deep), RS, pan = RS (1.42 b + f ( P 1.42) +.42 α) (A1) The b term in Eqn A1 is a modification added here to account for the presence of a birdguard (see below), α is the albedo of the ground surrounding the pan (set as.22 for all the calculations in this report), P is a latitude dependent factor (see Table A1) and f is the ratio of direct solar irradiance to global solar irradiance. The calculation of f was based on previous work (Roderick, 1999), i.e., RS f = (A11) R O where RO is the solar irradiance at the top of the atmosphere (calculations for Ro are described by Roderick (1999)). The Birdguard Correction Linacre s original formulation did not account for birdguards. Wallace (1994) noted that the shade cast by the standard BoM birdguard reduced the solar irradiance at the water surface by about 5.5% and that this was (more or less) seasonally invariant. It is very close to the 7% reduction due to the BoM birdguard that has been found empirically. The Wallace result was implemented here by setting b (Eqn A1) equal to.55. (Note that in the absence of a bird guard, b is ). Linacre s augmented long-wave formulation for dry ground Linacre s original PenPan formulation included an adjustment that accounts for additional long-wave irradiance received by the pan walls when the ground around the pan is dry. The idea was that when the ground surrounding the pan is dry, evaporation from the ground is reduced, and the ground becomes warmer. However, the pan is never short of water, so when the ground is dry, the temperature of the ground is higher than the water in the pan, and presumably also higher than the metal walls of the pan. (NB. Presumably this only applies during daylight hours.) We originally implemented the formulation for an additional long-wave flux as given by Linacre. We found that at high pan evaporation rates (i.e. usually when the ground surrounding the pan is dry) the calculated pan evaporation rate was systematically larger than

30 29 observations. The deviation was about the amount of the augmented long-wave irradiance. Hence, the formulation of the augmented long-wave irradiance was not implemented. Possible problems are that while the dry ground might be warmer than the walls of the pan during the day light hours, it can also be cooler at night and over a full diurnal cycle the effect might be diminished (at least partly). Secondly, Linacre s formulation was based on relating the net long wave flux to the temperature difference between the surroundings and the pan walls and effectively assumed that both radiating surfaces were near black bodies (i.e. long-wave emissivity near unity). However, while the dry ground would be expected to have an emissivity near unity (e.g would be typical), the metal walls of the pan would have a much lower emissivity. A Worked Example Calculations using the modified PenPan SITE DETAILS Site Name: Halls Creek Airport Site Number: 212 (latitude decimal deg, elevation 422 m ASL) Birdguard installation: 1 November 1968 OBSERVATIONS Date: May 1969 (hence bird guard was installed at time of observations) E pan observed: Monthly mean daily average of 6.95 mm d -1 (per database) ( 31 d mth -1 = mm mth -1 ) R s observed: Monthly mean daily average of J m -2 d -1 (per database) (/ 864 s d -1 = W m -2 ) T a : C (Monthly mean air temperature) (per database) T d : 5.49 C (Monthly mean dew point temperature of the air) (per database) u: 1.23 m s -1 (Monthly mean wind speed) (per database) PARAMETERS α:.22 (assumed albedo of the surroundings, i.e. short grass surface) b:.55 (shade cast onto water surface by the birdguard, see main text) CALCULATIONS (a) Calculate s (T dependent); s = 1 (.5 +.1T +.19T with T = o C, s = Pa K 2 ) 1 (b) Calculate γ (elevation (z) dependent); 5 γ = 1 (.67 z ) with z = 422 metres, γ = 65 Pa K -1

31 3 (c) Calculate F (elevation (z) dependent); 5 F = 1. z with z = 422 metres, F =.963 (d) Calculate the aerodynamic component of pan evaporation: s λe pan, A = ( 6uF( Ta Td )) s + 2.4γ λe pan, A = ( ( )) λe = 77 W m pan, A (e) Now calculate radiative component. First, the top of atmosphere solar irradiance; -2 R O = W m (calc per Roderick (1999); also see computer program solarpos.pro on the CD-ROM available with this report). (f) Ratio of direct to global solar irradiance; RS f = R f = = O (g) The latitude factor, P; P = P = φ φ 2 with φ = (h) Solar irradiance of pan; R = R (1.42 b + f ( P 1.42) +.42 α) S, pan with b =.55, f R R S, pan S, pan S = = W m =.87, P = 1.354, α =.22 ( ( ) ) -2 (i) Net irradiance of pan; R.71R 4. = = W -2 N, pan = S, pan m (j) Calculate the radiative component of pan evaporation; s λe pan, R = ( RN, pan ) s + 2.4γ λe pan, R = ( 196.3) = 19 W m Calculations all finished.

32 31 (k) Unit conversions between energy-mass-depth; 6 λ = 1 (2.5.24T ) with T = o C, λ = J kg E pan, R = = kg m s The calculations are for a month so we need to express it over that period E = kg m s ( ) s mth E pan, R = kg m -2 and with the density of liquid water set as1 kg m E pan,r pan,r =.1196 m mth mth SUMMARY OF RESULTS = mm mth -1-3, we convert to a depth equivalent, For this worked example (Halls Creek Airport, Site 212, May 1969), the observed pan evaporation rate was mm mth -1 (= 6.95 mm d -1 averaged over the month) while the calculated estimate was slightly lower at 24.1 mm mth -1 (= 6.6 mm d -1 ). CALCULATION λe pan,a 77 W m -2 E pan,a 84.5 mm mth -1 λe pan,r 19 W m -2 E pan,r mm mth -1 λe pan 186 W m -2 E pan 24.1 mm mth -1 OBSERVATION λe pan W m -2 E pan mm mth -1 Table A2 Result summary for the worked example

33 32 Appendix B Evaluation of the modifed PenPan model at 26 sites Figure B1 (26 pages following) Comparison between observed and model-based calculations of pan evaporation rate at 26 sites. Each page shows: (top panel) observed (line) and calculated ( ) pan evaporation rate; (lower left panel) comparison between observed and calculated pan evaporation with dotted line showing linear regression (see Table 4 for statistics) and 1:1 line also shown (full line); (lower right panel) variations in observed minus calculated pan evaporation rate as a function of time.

34 HALLS CREEK AIRPORT 4 Epan (mm mth -1 ) Epan Residuals 5 5 CALC (mm mth -1 ) OBS - CALC (mm mth -1 ) OBS (mm mth -1 )

35 BROOME AIRPORT 3 Epan (mm mth -1 ) Epan Residuals 4 1 CALC (mm mth -1 ) 3 2 OBS - CALC (mm mth -1 ) OBS (mm mth -1 )

36 PORT HEDLAND AIRPORT 4 Epan (mm mth -1 ) Epan Residuals 5 6 CALC (mm mth -1 ) OBS - CALC (mm mth -1 ) OBS (mm mth -1 )

37 LEARMONTH AIRPORT 4 Epan (mm mth -1 ) Epan Residuals 5 1 CALC (mm mth -1 ) OBS - CALC (mm mth -1 ) OBS (mm mth -1 )