Generating Australian potential evaporation data suitable for assessing the dynamics in evaporative demand within a changing climate

Transcription

1 Hve thg Generting Austrlin potentil evportion dt suitble for ssessing the dynmics in evportive demnd within chnging climte Rndll J. Donohue, Tim R. McVicr nd Michel L. Roderick December 2009

2 Wter for Helthy Country Flgship Report series ISSN: X Austrli is founding its future on science nd innovtion. Its ntionl science gency, CSIRO, is powerhouse of ides, technologies nd skills. CSIRO initited the Ntionl Reserch Flgships to ddress Austrli s mjor reserch chllenges nd opportunities. They pply lrge scle, long term, multidisciplinry science nd im for widespred doption of solutions. The Flgship Collbortion Fund supports the best nd brightest reserchers to ddress these complex chllenges through prtnerships between CSIRO, universities, reserch gencies nd industry. The Wter for Helthy Country Flgship ims to chieve tenfold increse in the economic, socil nd environmentl benefits from wter by For more informtion bout Wter for Helthy Country Flgship or the Ntionl Reserch Flgship Inititive visit Cittion: Donohue, R.J., McVicr, T.R. nd Roderick, M.L., Generting Austrlin potentil evportion dt suitble for ssessing the dynmics in evportive demnd within chnging climte, December 2009.CSIRO: Wter for Helthy Country Ntionl Reserch Flgship, 50 pp. Enquiries should be ddressed to: Rndll Donohue CSIRO Lnd nd Wter GPO Box 1666, CANBERRA ACT 2601, Austrli Rndll.donohue@csiro.u Copyright nd Disclimer 2009 CSIRO To the extent permitted by lw, ll rights re reserved nd no prt of this publiction covered by copyright my be reproduced or copied in ny form or by ny mens except with the written permission of CSIRO. Importnt Disclimer: CSIRO dvises tht the informtion contined in this publiction comprises generl sttements bsed on scientific reserch. The reder is dvised nd needs to be wre tht such informtion my be incomplete or unble to be used in ny specific sitution. No relince or ctions must therefore be mde on tht informtion without seeking prior expert professionl, scientific nd technicl dvice. To the extent permitted by lw, CSIRO (including its employees nd consultnts) excludes ll libility to ny person for ny consequences, including but not limited to ll losses, dmges, costs, expenses nd ny other compenstion, rising directly or indirectly from using this publiction (in prt or in whole) nd ny informtion or mteril contined in it. Cover Photogrph: Photogrpher: Rndll Donohue Description: The Tsmn Flx Lily (Dinell tsmnic), ntive to south-estern Austrli. iii

3 Contents SUMMARY Introduction Mterils nd Methods Input dt description nd vlidtion Modelling net rdition Potentil evportion formultions Penmn potentil evportion Priestley-Tylor potentil evportion Morton s point nd rel potentil evportions Thornthwite potentil evportion Pn coefficients Anlysis of trends Attribution of trends Results Input dt vlidtion Net rdition vlidtion Potentil evportion formultions Pn coefficients Anlysis of trends Attribution of trends Discussion The vilbility nd qulity of pproprite input dt Difficulties in prmeterising surfce conditions in potentil evportion formultions Findings nd recommendtions Summry nd Conclusions Acknowledgements REFERENCES APPENDIX A Derivtion of incoming longwve rdition... 43

4 List of Figures Figure 1. Distribution of sttions with long-term rdition nd pn evportion observtions Figure 2. Comprison of observed nd interpolted monthly meteorologicl dt Figure 3. Comprison of observed nd interpolted nnul trends in meteorologicl dt Figure 4. Comprison of observed pn evportion nd modelled Penpn evportion t 102 sites cross Austrli Figure 5. Comprison of observed nd modelled monthly incoming rdition Figure 6. Austrlin-verge monthly potentil evportion estimted using five formultions of potentil evportion Figure 7. An exmple of Austrli-wide, dily pn coefficient vlues Figure 8. Annul trends ( ) in the vribles used to clculte net rdition Figure 9. Annul trends ( ) in rdition Figure 10. Annul trends in the vribles used to clculte potentil evportion ( ) Figure 11. Annul trends in potentil evportion ( ) Figure 12. Monthly trends in Austrli-wide potentil evportion ( ) Figure 13. Comprison of nnul trends of precipittion nd potentil evportion ( ) t the 102 loctions Figure 14. Attribution of the chnges in Penmn potentil evportion ( ) Figure 15. Attribution of the Austrli-wide, monthly trends in Penmn potentil evportion ( ) Figure 16. Attribution of the nnul trends in Priestley-Tylor potentil evportion ( ) Figure 17. Attribution of the Austrli-wide, monthly trends in Priestley-Tylor potentil evportion from v

5 List of Tbles Tble 1. Input dtset specifictions nd sources for (A) grid-bsed dt nd (B) point-bsed dt...5 Tble 2. Austrli-wide nnul verge vlues nd trends (first derivtives) for selected input vribles Tble 3. Pn coefficient vlues for ech of the five potentil evportion formultions Tble 4. Austrlin-verge nnul trends ( ) in the vribles used to clculte net rdition nd the trends in the rdition components...23 Tble 5. Austrlin-verge nnul trends in potentil evportion ( ) Tble 6. Correltion between Austrlin-verge per-month trends in precipittion nd potentil evportion ( ) Tble 7. Attribution of the chnges in nnul, Austrli-wide Penmn potentil evportion ( )...31 Tble 8. Attribution of the chnges in Austrli-wide Priestley-Tylor potentil evportion ( ) due to chnges in Δ nd net rdition...33 vi

6 SUMMARY SUMMARY Evportive demnd cn be modelled using one of numerous formultions of potentil evportion. Physiclly, evportive demnd is driven by four key vribles net rdition, vpour pressure, wind speed, nd ir temperture ech of which hve been chnging cross the globe over the pst few decdes. Anlyses of long-term chnges in potentil evportion require fully dynmic formultion where the effects of chnges in ech of the driving vribles re ccounted for. Often, however, dequte input dt describing ll four vribles re unvilble. In this reserch we sought to produce potentil evportion dt set suitble for the nlysis of long-term dynmics in evportive demnd. Prior to the clcultion of potentil evportion, we tested the temporl ccurcy of the surfce-bsed input dt, by compring trends derived from the input surfces with equivlent trends from the underlying observtion dt. Another test of the input dt compred trends in modelled US Clss A pn evportion, generted using the input surfces, with observed trends in pn evportion. Results indicted tht the input dt were suitble for looking t long-term temporl dynmics in evportive demnd. We generted five different dily potentil evportion dtsets for Austrli, spnning , using the: (i) Penmn; (ii) Priestley-Tylor; (iii) Morton point; (iv) Morton rel; nd (v) Thornthwite formultions. A novel spect of this process ws the use of dynmic net rdition model tht utilised sptilly nd temporlly vrying remotely sensed mesures of surfce lbedo. We ssessed how well ech potentil evportion formultion cptured dynmics in evportive demnd by nlysing the sptil, nnul, nd sesonl trends in ech ginst chnges in ctul evportion, ssuming tht they should vry in n pproximtely inverse mnner. Results show tht only potentil evportion modelled with fully physicl formultion (i.e., Penmn), or with Morton s point formultion, displyed such chrcteristics. An ttribution nlysis ws performed to quntify the contribution ech input vrible mde to the overll trends in fully physicl formultion (in this cse, Penmn). Even though chnges in ir temperture plyed n importnt role in the overll mgnitude of trends in potentil evportion, it ws the contribution of vpour pressure, net rdition (primrily due to lbedo) nd wind speed tht produced the complementry behviour, which is in greement with previous findings. For the conditions tested, we found tht only the Penmn formultion displyed relistic vlues of potentil evportion rtes nd trends, nd we conclude tht this is the model of choice for exmining evportive demnd dynmics when ll input dt re vilble. This highlights the need for ll inputs to be treted s vribles nd, consequently, the need for dynmic input dt. Few formultions dynmiclly include wind speed nd conclusions bout chnges in evportive demnd from such formultions re likely to be misleding. Of the formultions tht omit wind speed dynmics, the Priestley-Tylor nd Morton rel formultions produced resonble estimtes of potentil evportion rtes. Whilst neither should be relied upon to reproduce temporl dynmics, the simplicity of the Priestley-Tylor model mkes it the better model for estimting potentil evportion rtes when wind speed dt re bsent. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

7 INTRODUCTION 1. INTRODUCTION Anlyses of ctchment hydrologicl dynmics require estimtes of the supply of wter nd of the evportive demnd for wter. Estimtes of potentil evportion re generlly used to represent evportive demnd. Conceptully, potentil evportion represents the mximum possible evportion rte (e.g., Grnger 1989; Lhomme 1999) nd is the rte tht would occur under given meteorologicl conditions from continuously sturted surfce (Thornthwite 1948). Notionlly, the concept of potentil evportion is simple. However the prcticl implementtion of the concept is problemtic nd mbiguous due to the mny wys potentil evportion cn be, nd hs been, formulted. Here our focus is on how input vribles re treted within severl common formultions. Even though potentil evportion is primrily driven by four meteorologicl vribles (net rdition, vpor pressure, wind speed nd temperture) it is conceptul entity tht cn not be mesured directly (Thornthwite 1948). Mny different methods of estimting potentil evportion from one or more of these four vribles hve been developed ccording to locl climtic conditions nd the vilbility of suitble dt (see Shuttleworth 1993; Singh nd Xu 1997; Xu nd Singh 2000, 2001). Some formultions, such s Thornthwite's (1948), use single vrible (i.e., ir temperture) tht is relted to potentil evportion rtes vi empiricl reltionships. These typiclly need to be reclibrted to mintin ccurcy when pplied outside the originl sptil nd temporl contexts (Xu nd Singh 2001). Other formultions, by ssuming the surfce is extensive nd continully sturted, omit the effects of the dvective vribles (i.e., wind speed nd vpor pressure), nd ccount only for the verticl het nd mss fluxes. Such formultions re often referred to s rel or wet re potentils nd re best suited to energy-limited environments. Alterntively, fully physicl models, such s the Penmn nd the Penmn-Monteith equtions (Penmn 1948; Monteith 1981), re physiclly derived (except for ny resistnce terms) nd explicitly incorporte ll the driving vribles. Although these formultions re dt intensive they re universlly pplicble. The reltionship between potentil evportion nd ctul evportion differs depending on wht process is the dominnt limit to evportion. In wter-limited lndscpes, where the vilble energy exceeds the vilble wter, the ctul evportion rte is less thn the potentil rte nd is lrgely determined by the supply of wter. Alterntively, in energy-limited environments where the supply of wter exceeds tht of energy, ctul evportion rtes closely follow those of potentil (McIllroy nd Angus 1964; Budyko 1974; Thornthwite 1948; Lincre 2004). This reserch ws prompted by the need for sptilly explicit potentil evportion dt tht re suitble for the nlysis of long-term dynmics in evportive demnd. Widespred chnges in climtic conditions hve been reported, with long-term trends observed in globl verge ir temperture (e.g., IPCC 2007), in vpour pressure (e.g., Durre et l. 2009), precipittion (e.g., New et l. 2001), net rdition (e.g., Wild 2009), nd wind speed (e.g., McVicr et l. 2008). This is no less true for Austrli, where temperture nd precipittion hve been incresing on verge over the pst 3 or so decdes (Bureu of Meteorology, 2007) s hs vpour pressure (this study), whilst wind (Roderick et l. 2007; Ryner 2007; McVicr et l. 2008) nd net rdition (this study) hve been decresing. All these chnges will hve inevitbly led to chnges in evportive demnd. Given the extremely vrible nture of the drivers of potentil 2 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

8 INTRODUCTION evportion, ny methods used to exmine long-term nlyses of evportive demnd need to be cpble of ccounting for the observed, nd expected, chnges in ll relevnt input vribles (McKenney nd Rosenberg 1993) nd should idelly be pplicble in both wter- nd energy-limited environments. Our im is to produce, nd chrcterise, n Austrlin potentil evportion dt set suitble for the nlysis of long-term dynmics in evportive demnd. Towrds this end, we creted dynmic representtion of net rdition tht utilised remotely sensed dt. For Austrli, from 1981 to 2006, dtsets of dily potentil evportion were generted using vriety of formultions, nmely the: (i) Penmn (1948); (ii) Priestley- Tylor (1972); (iii) Morton (1983) point; (iv) Morton (1983) rel; nd (v) Thornthwite (1948) potentil evportion formultions. We nlysed the nnul, sesonl nd sptil trends of ech formultion s well s ttributing, for two of the formultions, how ech input vrible contributed to the overll trends. This llowed us to mke n ssessment of the suitbility of ech potentil evportion formultion for representing long-term dynmics in evportive demnd. Potentil evportion cn not be mesured directly nd so no mens exists by which modelled potentil evportion dt cn be directly vlidted either sptilly or temporlly. However, the qulity of the input dt used to generte potentil evportion estimtes cn be tested. Sptil surfces of meteorologicl vribles re incresingly being used in hydro-meteorologicl nlyses. Little ttention hs been given to ssessing the temporl ccurcy of such surfces. Here, prior to conducting nlyses of potentil evportion dynmics, we undertke two rigorous tests of the temporl ccurcy of the input surfce dt. Firstly, we compre surfce-derived trends in the input vribles with trends present in the underlying point dt from which the surfces were generted. Secondly, we use the input dt nd the Penpn model (Rotstyn et l. 2006) to estimte US Clss A pn evportion rtes nd trends, nd compre these with rtes nd trends of observed pn evportion. This pper is orgnised s follows. In the next Section Dt nd Methods we describe: (i) the dt used in these nlyses nd the vlidtions performed to test their temporl ccurcy; (ii) the genertion of Austrli-wide dily net rdition surfces; (iii) the five different potentil evportion formultions used; (iv) the determintion of pn coefficients ; (v) the clcultion of trends in potentil evportion; nd (iv) n ttribution nlysis to quntify the contribution of ech input vrible to potentil evportion trends. Results re presented using this sme structure, followed by discussion of results. We then provide conclusions nd recommendtions. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

9 MATERIALS AND METHODS 2. MATERIALS AND METHODS 2.1 Input dt description nd vlidtion Dt in the form of dily grids were used for these nlyses, spnning Jnury 1981 through to December 2006 (see Tble 1). This time spn ws chosen to mtch tht of the remotely sensed vegettion cover dt of Donohue et l. (2008) from which estimtes of lbedo nd surfce emissivity were derived. Elevtion ws derived from the DEM-9S dtset of Geoscience Austrli (2007). Meteorologicl dt describing precipittion, ir temperture nd vpour pressure were sourced from the Jones et l. (2006 ) nd wind speed dt McVicr et l. (2008). For comprison, n lterntive sptil dtset of dily wind speed ws generted using the sme input dt s used by McVicr et l. (2008), but here the dt were sptilly interpolted using Tringulr Irregulr Networks (TINs). All input sptil dt were converted to the sme sptil resolution (0.05 ), the sme extent ( E nd S ) nd to SI units prior to nlyses. Before generting the surfces of potentil evportion, we undertook two tests of the temporl ccurcy of the input surfces. Firstly, the temporl ccurcy of the input dt ws compred to the trends present in the underlying point dt. This is essentilly test of the ccurcy of the interpoltion technique. Monthly trends in totl precipittion (P, mm.mth -1 ), nd in dily mximum nd minimum ir temperture (T n nd T x, respectively, in K), dily ctul vpour pressure (e, P) nd dily verge wind speed (u 2, m.s -1 ) were clculted using the input dily surfces described bove (see section 2.5 for detils on the clcultion of trends). Point-bsed dt were extrcted from the Monthly Austrlin Dt Archive for Meteorology dtbse (Bureu of Meteorology 2006). For T x, T n, dew point temperture (used to clculte e ), nd u 2, dt were extrcted using simple completeness-of-record criteri for the period : (i) ech month needed t lest 25 dys of dt to be considered complete; (ii) ech yer needed t lest 9 complete months of dt; nd (iii) ech sttion hd to hve t lest 20 complete yers of dt. This procedure determined how mny sttions were used for the vlidtion of ech input vrible. For P dt, the number of observtion sttions ws restricted, purely for resons of efficiency, to the sttions tht hd n djcent complete pn evportion record (see below). The point-bsed monthly vlues nd nnul trends were compred to the equivlent vlues extrcted from the monthly grids t the corresponding loctions. 4 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

10 MATERIALS AND METHODS Tble 1. Input dtset specifictions nd sources for (A) grid-bsed dt nd (B) point-bsed dt. Vpour pressure (e ) Wind speed t 2m height (u 2 ) Wind speed t 2m height (u 2 ) fpar (F t ) Red nd NIR reflectnce(ρ R, ρ N ) Elevtion (z) TIN-interpolted point dt AVHRR* observtions AVHRR* observtions A Input vrible Dt origin Units Timestep Cell Reference size Precipittion (P) Splineinterpolted mm.d -1 Dy 0.05 Jones et l. (2009) point dt Air temperture (mx, T x ; min, T n ) Splineinterpolted point dt K Dy 0.05 Jones et l. (2009) Splineinterpolted point dt Splineinterpolted point dt Splineinterpolted point dt P Dy 0.05 Jones et l. (2009) m.s -1 Dy 0.01 McVicr et l. (2008) m.s -1 Dy 0.05 This study Month 0.08 Donohue et l. (2007) % Month 0.08 Donohue et l. (2007) m 9 Geoscience Austrli (2007) B Input vrible Dt origin Units Timestep Reference Precipittion (P) Meteorologicl observtions mm.mth -1 Month Bureu of Meteorology (2006) Pn evportion Meteorologicl observtions mm.mth -1 Month Bureu of Meteorology (2006) Air temperture (T x ; T n ; dew point) Meteorologicl observtions K Month Bureu of Meteorology (2006) Wind speed t 2m height (u 2 ) Meteorologicl observtions * Advnced Very High-Resolution Rdiometer m.s -1 Month Bureu of Meteorology (2006) The second test of the input dt ws to use the input surfces nd the Penpn model (Rotstyn et l. 2006) to estimte US Clss A pn evportion rtes nd trends nd to compre these with observed pn evportion rtes nd trends. This provides rigorous test of the dt nd gives good indiction of the ccurcy of subsequently modelled potentil evportion dt for two resons: (i) Roderick et l. (2007) hve shown tht the Penpn model cn ccurtely reproduce both rtes nd trends in US Clss A pn evportion with high qulity point-bsed input dt; nd (ii) pn evporimeters integrte the effects of rdition, humidity, wind nd temperture on wet-surfce evportion rtes (Stnhill 2002), nd so provide mesurements of evportion tht re conceptully similr to potentil evportion rtes (e.g., McVicr et l. 2007). We modelled Penpn evportion using the sptil input grids (using the TIN-bsed wind speed). Point-bsed pn evportion observtions were extrcted Cpturing evportive demnd dynmics with potentil evportion dt 1 December

11 MATERIALS AND METHODS from the originl dtbse (Bureu of Meteorology 2006) using the completeness procedure outlined bove, resulting in 102 sites (Figure 1). Penpn evportion (E pp, mm.d -1 ) is Penmn-bsed model of US Clss A pn evportion rtes nd ws clculted ccording to: E pp 8 ( ( 2 )) Δ Rp + γ D u =. (1) Δ+ γ Here R p (in wter-equivlent units, mm.d -1 ) is the net rdition of the pn (see Rotstyn et l. 2006). Deriving R p requires estimtes of the diffuse frction of incoming rdition which were derived following Roderick (1999). Δ is the slope of the sturtion vpour pressure curve (P.K -1 t ir temperture), is dimensionless constnt (2.4), γ is the psychrometric constnt (P.K -1 ), D is the vpour pressure deficit (P), nd u 2 is dily verge wind speed t 2m height (m.s -1 ). Δ is clculted s function of sturted vpour pressure (e s, P) nd men ir temperture (T, K): Δ= 4098 e ( T 35.86) 2 s. (2) T ws clculted s the dily verge of T x nd T n. e s ws clculted s the dily verge of the sturted vpour pressure determined for tht dy s T x nd T n, ccording to: 17.27( T ) es T = e. (3) Note tht in this nd ll equtions temperture hs been converted to K. The psychrometric constnt (γ, P.K -1 ) vries with tmospheric pressure (P, P), γ =, (4) P where λ is the ltent het of vporistion of wter (2.45 x 10 6 J.kg -1 ). P is estimted here s function of elevtion (z, m): P z = (5) 6 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

12 MATERIALS AND METHODS 2.2 Modelling net rdition Net rdition (R n, W.m -2 ) is defined s the sum of the component longwve nd shortwve fluxes: Rn = Rsi Rso + Rli Rlo (6) where R si is the incoming shortwve rdition, R so is outgoing shortwve rdition, R li incoming longwve rdition, nd R lo outgoing longwve rdition (ll in units of W.m - 2 ). Incoming shortwve rdition ws clculted s the top-of-tmosphere incoming rdition (R o, W.m -2 ) modified by n estimte of tmospheric trnsmissivity (τ ). R = R τ (7) si o R o ws clculted using the method of Iqbl (1983) nd Roderick (1999). A loclly clibrted (McVicr nd Jupp 1999) version of the Bristow-Cmpbell (1984) reltionship ws used to derive τ, Tr ( ) ( 1 ) τ = + z e (8) with T r representing the dily temperture rnge (clculted s T x T n, K). Following Bristow nd Cmpbell (1984), T n ws determined s the verge of the current dy s nd the following dy s minimum vlues. Outgoing shortwve rdition ws clculted s: R so = α R (9) si where α is the surfce lbedo, which ws estimted using clibrted Advnced Very High Resolution Rdiometer red (ρ R, %) nd ner-infrred (ρ N, %) monthly reflectnces (Donohue et l. 2008), following Sunders (1990): ρr + ρn α =. (10) 2 There were occsionl gps in the monthly α dt due to cloud cover or high stellite viewing ngles (Donohue et l. 2008). Wherever pixel contined gp in its time series, liner regressions were performed on tht pixel s time series for ech month-ofyer (i.e., ll Jnuries, ll Februries, etc.). Gps were then filled with the vlues derived from the pproprite month s regression model. Ech month's lbedo vlue ws used to represent dily vlues for tht month. Outgoing longwve rdition ws clculted s: R = ε σt (11) 4 lo s s Cpturing evportive demnd dynmics with potentil evportion dt 1 December

13 MATERIALS AND METHODS where ε s is the surfce emissivity, σ the Stefn-Boltzmnn constnt (5.67 x10-8 W.m - 2.K -4 ), nd T s the surfce temperture (K). Here T ws used to pproximte T s. Dily T 4 ws clculted s the verge of the fourth power of both tht dy s T x nd T n. Surfce emissivity ws estimted s function of monthly vegettion frctionl cover (f v ), scled between 0.97 nd 0.92 for fully vegetted nd bre surfces, respectively (Monteith nd Unsworth 1990): ε = 0.97 f (1 f ). (12) s v v Frctionl cover (F v ) ws derived from AVHRR frction of Photosyntheticlly Active Rdition bsorbed by vegettion (F) dt (Donohue et l. 2008): F f v =. (13) 0.95 The frctionl cover dt were gp-filled using the sme method s used for lbedo. An dpted version of the FAO56 method (Allen et l. 1998) ws used for clculting incoming longwve rdition. The dpttion included the incorportion of surfce emissivity nd the use of Austrlin coefficients (McVicr nd Jupp 1999) in estimting cler-sky rdition (see Appendix 1) R si Rli = εσ S T 1 ( e 1000 ) ( z) R + o (14) The monthly time series of modelled R si nd R li were vlidted using ground-bsed mesurements. Monthly observtions of R si nd R li (W.m -2 ) originte from the dily rdition observtions collected nd published by the BOM (which were subsequently summrised by Roderick nd Frquhr (2006)). The R so dt cme from 25 sttions cross Austrli nd the R lo from 10 sttions (Figure 1). 8 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

14 MATERIALS AND METHODS Figure 1. Distribution of sttions with long-term rdition nd pn evportion observtions. Also shown res tht re wter/energy-limited on n nnul verge bsis. Of the 102 pn evportion sttions, 96 lie within wter-limited lndscpes. 2.3 Potentil evportion formultions Penmn potentil evportion Potentil evportion (E p, mm.d -1 ) ws clculted using Penmn's (1948) formultion s given in Shuttleworth (1993): ( + u ) Δ γ Ep = EpR + EpA = Rn + Δ+ γ Δ+ γ λ 2 D (15) where E pr nd E pa represent the rditive nd erodynmic components of the Penmn eqution, respectively. R n is dily net rdition (mm.d -1 ) s clculted previously Priestley-Tylor potentil evportion Priestley-Tylor potentil evportion (E pt, mm.d -1 ) is rdition-bsed model nd ws formulted s function of rdition nd, vi Δ, of ir temperture (Priestley nd Tylor 1972): Cpturing evportive demnd dynmics with potentil evportion dt 1 December

15 MATERIALS AND METHODS E pt Δ = 1.26 Rn. (16) Δ+ γ Morton s point nd rel potentil evportions Morton (1983) formulted point potentil evportion (E mp, mm.d -1 ) nd n rel or wet environment potentil evportion (E m, mm.d -1 ) where the equilibrium temperture is itertively determined by simultneously solving the vpour trnsfer nd energy blnce equtions. Potentil evportion is then clculted for the equilibrium temperture. The Morton formultions include three of the four driving vribles: R n, e, nd T. The first step ws to clculte three coefficients. The stbility fctor (ξ) is: 1 e ΔRn = ξ e γ P P f e e 0.5 ( ) ( ) s s z s. (17) Here R n is in W.m -2, P s is men se level pressure ( P) nd f z is W.m - 2.P -1 for T t or bove K nd for T below K. The vpour trnsfer coefficient (C, W.m -2.P -1 ) is C 0.5 Ps = P fz, (18) ξ nd the het trnsfer coefficient (H, P.K -1 ) is H ( T ) = γ +. (19) C The second step is to itertively clculte the equilibrium temperture, T p (K). This is done by initilly setting T p to T, setting the equilibrium vpour pressure, e p, to e, nd setting the equilibrium sturtion vpour pressure slope, Δ p, to Δ. A temperture increment (δt) is clculted ccording to: ( ) R C+ H T T + e e δt = Δ + H n p p p. (20) Estimtes of equilibrium temperture (T p ), vpour pressure (e p ) nd sturtion vpour pressure slope (Δ p ) re derived in ech itertion: T = δt + T, (21) p p 10 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

16 MATERIALS AND METHODS ( T p ) T p e = e, (22) p nd Δ = p 4098e p ( T 35.86) 2 p. (23) However, if T p is below K, then ( T p ) T p 7.66 e = e (24) p nd Δ = p 5809e p ( T 7.66) 2 p. (25) T p is then set to T p, e p to e p nd Δ p to Δ p nd the itertion [Eqs. (20)-(25)] is repeted until the bsolute vlue of δt is less thn 0.01 K. Morton s point potentil evportion (E mp, mm.d -1 ) is clculted prior to clculting R np (W.m -2 ), the net rdition tht would occur t the equilibrium temperture. Finlly E m is clculted: ( ( )) E = R HC T T, (26) mp n p R = E + γ C( T T ), (27) np mp p E m 1.2Δ pr np = (28) Δ p + γ Thornthwite potentil evportion Thornthwite (1948) potentil evportion (E th, mm.mth -1 ) uses ir temperture s the sole input nd is clculted t monthly time-step. Following Xu nd Singh (2001), the nnul het index, I, is clculted s the sum of the 12 monthly het indices, i, ech of which is function of the men monthly ir temperture, T m (K): T m i = (29) Cpturing evportive demnd dynmics with potentil evportion dt 1 December

17 MATERIALS AND METHODS For ech month, potentil evportion is then estimted s E th ( T ) 16d 10 m = 360 I (30) where is equl to I I I 3, nd d is the monthly verge dy-length (hours). 2.4 Pn coefficients Surfces of dily pn coefficients (K pn ) were derived for ech of the five potentil evportion formultions. K pn vlues were determined s: K pn E E x = (31) pp where E x represents one of the five potentil evportion formultions. 2.5 Anlysis of trends Long-term dynmics in potentil evportion were exmined in terms of liner trends clculted using ordinry lest squres regressions on month-of-yer bsis (i.e., clculte the trend for ll Jnuries, then for ll Februries, etc.). Annul trends were clculted s the sum of the twelve monthly trends. For the sptil dt, regressions were performed for every pixel cross Austrli nd Austrli-wide trends were clculted s the sptil verges of ll the pixel trends. Trends in point-bsed dt were clculted in the sme month-of-yer mnner. In this wy, long-term chnges in the rdition blnce nd in the five formultions of potentil evportion including trends in the inputs vribles used in ech of the models were clculted. Here we present trends in flux vribles in units of x.yr -2 (i.e., the chnge over time [.yr -1 ] in the rte [x.yr -1 ]), nd in units of x.mth -1.yr -1 (i.e., the chnge over time [.yr -1 ] in the rte [x.mth -1 ]). One wy of testing the bility of ech formultion of potentil evportion to relisticlly cpture chnges in evportive demnd in wter limited environments is to compre the trends in potentil evportion with trends in precipittion. The pttern generlly expected is n inverse reltionship due to the feedbcks between evportive demnd nd precipittion (e.g., Yng et l. 2006). Tht is, in wter limited environments, n increse in precipittion should be ssocited with incresed ltent het flux becuse of increses in surfce moisture vilbility, nd should be ssocited with decresed incoming shortwve rdition due to incresed cloudiness nd humidity. It hs recently been shown tht the role of chnges in wind speed in these feedbcks does not produce simple inverse reltion (Shuttleworth et l. 2009). Given this cvet, this test of inverse proportionlity though pproximte constitutes useful mens of exmining potentil evportion dynmics. 12 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

18 MATERIALS AND METHODS 2.6 Attribution of trends Another mens of exmining the modelled trends in potentil evportion is to ttribute the chnges in potentil evportion to chnges in the component input vribles. This llows the effects of the ssumptions in formultions (tht is, which vribles re held constnt) to be quntified on the overll dynmics in potentil evportion. The ttribution of trends ws undertken by performing prtil differentitions on the input vribles of both the Penmn (Eq. (15)) nd the Priestley-Tylor (Eq. (16)) formultions. These two formultions were chosen s representtives of the Penmnbsed equtions nd the rdition-bsed equtions, respectively. Attribution of the temperture-bsed Thornthwite formultion is not needed, s ny chnges in E th re directly ttributed to dt /dt. As per Roderick et l. (2007), the chnge in E p cn be ttributed to chnges in the rditive nd erodynmic components, dep depr depa = +. (32) dt dt dt Dynmics in the rditive component re due to chnges in Δ (which itself is function solely of T ) nd R n : depr E pr dδ dt E pr dr = + dt Δ dt dt R dt n n ; (33) where E dδ dt R γ dδ dt = Δ dt dt Δ+ dt dt pr n ( γ ) 2 ; nd (34) E dr Δ dr = R dt Δ+ γ dt p n n n, respectively. (35) Given tht D is the difference between e s nd e, chnges in the erodynmic component re de E dδ dt E du E de dt E de = dt Δ dt dt u dt e dt dt e dt pa pa pa 2 pa s pa 2 s, (36) with the contributions from Δ, u 2, e s, nd e estimted s: γ ( u ) ( γ) 2 λ E pa dδ dt 6430 D u dδ dt = ; (37) Δ dt dt Δ+ dt dt Cpturing evportive demnd dynmics with potentil evportion dt 1 December

19 MATERIALS AND METHODS E pa du γ D du = u dt Δ+ γ λ dt ( ) ; (38) E de dt 6430 γ ( u ) de dt = e dt dt Δ+ γ λ dt dt pa s 2 s ( ) s ; nd (39) E de 6430 γ ( u ) de = e dt Δ+ γ λ dt pa 2 ( ). (40) For Priestley-Tylor, the chnge in E pt nd its prtil differentils cn be similrly expressed: dept E p dδ dt E p dr = + dt Δ dt dt R dt n n. (41) Agin, ignoring the ffect of dt /dt on dr n /dt nd ssuming Δ is function solely of T, the ttribution of T nd R n cn be expressed, respectively, s: E dδ dt 1.26R γ dδ dt = Δ dt dt Δ+ dt dt pt n ( γ ) 2 ; nd (42) E dr 1.26Δ dr = R dt Δ+ γ dt pt n n n. (43) In quntifying these prtil differentils, the Austrlin verge trend is used to represent the derivtive (i.e., dx/dt) nd the Austrlin, long-term nnul verge vlue is used to represent the coefficients. For exmple, to ttribute the chnges in E p to chnges in T, Equtions (37), (39), (42) nd (44) cn be combined s E dt E dδ dt E dδ dt E de dt = + + T dt Δ dt dt Δ dt dt e dt dt p pr pa pa s s (44) or more fully s ( ) γ ( u ) dδ γ ( ) ( ) E dt R γ dδ dt 6430 D u dt 6430 ( u ) de dt = + + T dt dt dt dt dt Δ+ dt dt p n 2 s 2 2 Δ+ γ Δ+ γ λ γ λ (45) Inserting the vlues within Tble 2 into Eqution (45) gives: 14 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

20 MATERIALS AND METHODS E T p dt dt = = 1.5 mm. yr 2 (46) Tble 2. Austrli-wide nnul verge vlues nd trends (first derivtives) for selected input vribles. Vrible Annul verge Differentil Trend T 295 K dt K.yr -1 dt e s 3071 P de dt s 3.08 P.yr -1 dt dt D 1730 P dd 2.2 P.yr -1 dt U m.s -1 du m.s -1.yr -1 dt γ 65.3 P.K -1 Δ P.K -1 dδ dt 0.17 P.K -1.yr -1 dt dt R n 153 W.m -2 drn dt W.m -2.yr -1 Cpturing evportive demnd dynmics with potentil evportion dt 1 December

21 RESULTS 3. RESULTS 3.1 Input dt vlidtion Monthly observtions in P, T x, T n, e nd u 2 re compred, in Figure 2, with their equivlent vlues obtined from the input grid dt. Although P ws not used in the clcultion of potentil evportion, it is included here: (i) to illustrte the reltionship between the ccurcy of spline interpoltion nd the density of input dt points; nd (ii) s it is subsequently used s surrogte for ctul evportion. The monthly vlues from spline-derived BAWAP dt mtch the observtions well for ll vribles (Figure 2 d). The spline-derived u 2 dt do not compre well with observed trends wheres those from the TIN-derived u 2 do ccurtely mtch the observtions (Figure 2e f). From the comprison of nnul spline-derived trends in these sme vribles (Figure 3-e), it cn be seen tht spline-interpolted P dt cpture underlying trends well, T x nd T n dt less so, e less gin, nd with u 2 being generlly unble to cpture underlying trends. The verge number of sttions cross Austrli used to crete the P grids ws 5760, for the temperture grids there were 721 sttions, for e 670 (Jones et l. 2007) nd for u sttions (McVicr et l. 2008). As intuitively expected, the greter the density of input dt used in spline-bsed sptil interpoltions, the greter the ccurcy with which the splines cpture the underlying temporl trends in the observed dt. Even though TINs produce less relistic sptil ptterns, they more ccurtely cpture the temporl trends present in the input dt (Figure 3f) when the density of dt points is low. It ws for this reson tht the TIN-bsed u 2 dtset ws produced. The comprison of vlues nd trends in modelled Penpn evportion (E pp ) with vlues nd trends in pn observtions (E pn ) provides robust test of the input dt (Figure 4); these comprisons re quntified by liner regression. Modelled E pp derived using the spline-bsed u 2 dtset (Figure 4) is well relted to E pn vlues, with slope of 0.90, n r 2 of 0.90 nd 29 mm.mth -1 RMSE (Root Men Squre Error). Figure 4c shows tht, when using E pp derived using the TIN-bsed u 2 dtset, these sttistics improve to be 0.99, 0.92, nd 27 mm.mth -1, respectively. A similr level of ccurcy between modelled nd observed vlues ws ttined by Roderick et l. (2007) using solely point-bsed dt. The reltion between trends in the spline-bsed E pp nd trends in E pn hs slope of 0.26 nd r 2 of 0.29 (Figure 4b); these vlues chnged to 0.43 nd 0.31, respectively, when using the TIN-derived E pp. Trends in E pp only modertely mtch those of pn observtions (Figure 4b), presumbly due to the compounding effect of the input vribles inbility to perfectly cpture temporl trends (see Figure 3). However, the verge Austrlin trend in E pp from the grid is 0.0 mm.yr -2 (with stndrd error of 2.3 mm.yr -2 ) nd is comprble to the verge of the observed trends t the 102 points of Figure 4d, which is -1.5 mm.yr -2 (with stndrd error of 4.0 mm.yr -2 ). Given tht the modelled E pp vlues reproduced E pn vlues extremely well (Figure 4c) nd reproduced temporl trends modertely well (Figure 4d), the input dtsets cn be used with resonble confidence to clculte the five formultions of potentil evportion which re subsequently ssessed for their dynmics. In the reminder of this work, only the TIN-bsed u 2 dtset is used. 16 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

22 RESULTS b c d e f Figure 2. Comprison of observed nd interpolted monthly meteorologicl dt. Plot: () precipittion; (b) mximum ir temperture; (c) minimum ir temperture; (d) dew-point temperture; (e) wind speed derived from spline-interpolted dt; nd (f) wind speed derived from TINinterpolted dt. The dotted line is the 1:1 line, the dshed line is the eqution of best fit (given on ech plot), n is the number of observtions, the offset nd RMSE sttistics re in ordinte units. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

23 RESULTS b c d e f Figure 3. Comprison of observed nd interpolted nnul trends in meteorologicl dt. Plot: () precipittion; (b) mximum ir temperture; (c) minimum ir temperture; (d) dew-point temperture; (e) wind speed derived from spline-interpolted dt; nd (f) wind speed derived from TINinterpolted dt. The dotted line is the 1:1 line, the dshed line is the eqution of best fit (given on ech plot), n is the number of observtions, the offset nd RMSE sttistics re in ordinte units. 18 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

24 RESULTS b c d Figure 4. Comprison of observed pn evportion nd modelled Penpn evportion t 102 sites cross Austrli. Plot () the monthly verges nd (b) the nnul trends when using the spline-derived wind speed, with (c) being the monthly verges nd (d) the nnul trends when using the TIN-derived wind speed. The dotted line is the 1:1 line, the dshed line is the eqution of best fit (given on ech plot), n is the number of observtions, the offset nd RMSE sttistics re in ordinte units. 3.2 Net rdition vlidtion The use of McVicr nd Jupp s (1999) loclly clibrted coefficients within the Bristow- Cmpbell (1984) reltion improved the ccurcy of modelled R si when compred to using the stndrd Bristow-Cmpbell formultion from r 2 nd RMSE vlues of 0.72 nd 43 W.m -2 to 0.93 nd 18 W.m -2, respectively (Figure 5 nd b). Likewise, the ddition of the locl clibrtions nd the remotely sensed estimtes of ε s improved R li estimtes from r 2 nd RMSE vlues of 0.91 nd 11 W.m -2 to 0.92 nd 9 W.m -2, respectively (Figure 5c nd d). Cpturing evportive demnd dynmics with potentil evportion dt 1 December

25 RESULTS b c d Figure 5. Comprison of observed nd modelled monthly incoming rdition. Plot () shows incoming shortwve rdition (R si ) using the originl Bristow-Cmpbell model; nd (b) R si using the Bristow-Cmpbell model clibrted with coefficients derived by McVicr nd Jupp (1999). Plot (c) is the incoming longwve rdition (R li ) modelled using the stndrd FAO56 formultion (Allen et l. 1998); nd (d) R li modelled using the FAO56 formultion dpted to include the McVicr nd Jupp (1999) coefficients nd remotely sensed estimtes of surfce emissivity (ε s ). The dotted line is the 1:1 line, the dshed line is the eqution of best fit (given on ech plot), n is the number of observtions, the offset nd RMSE sttistics re in ordinte units. 3.3 Potentil evportion formultions Estimtes of potentil evportion rtes using the five formultions vry substntilly in their mgnitudes nd rnges (Figure 6). Austrlin-verge nnul potentil evportion vries between 1765 nd 3670 mm.yr -1, whilst the smllest sesonl vrition is pproximtely 80 mm nd the gretest is 300 mm.mth -1. E mp hs the highest rte, nd rnge, followed by E p nd E m. Pn evporimeters, due to their 3- dimensionl, bove-ground geometry, re cpble of bsorbing more energy thn cn flt surfce (Lincre 1994; McVicr et l. 2007; Rotstyn et l. 2006). Hence, E pn should be higher thn ny rtes of potentil evportion. Given this, nd tht the verge E pp vlue for Austrli is 2894 mm.yr -1, the vlues of E mp seem unrelisticlly high, over-estimting potentil rtes by s much s 25%. 20 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

26 RESULTS The vlues of E p re estimtes of open-wter evportion nd the Penmn formultion effectively hs surfce resistnce (r s ) of zero. E pt nd E m hve similr verge vlues nd temporl ptterns, ech being less thn E p. The temperture-bsed E th bers the lest resemblnce to ny other formultion, both in terms of the sesonl rnge nd the temporl pttern in vlues. Figure 6. Austrlin-verge monthly potentil evportion estimted using five formultions of potentil evportion. Ordinte units re mm.mth -1. Annul verges re in mm.yr -1. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

27 RESULTS 3.4 Pn coefficients Long-term Austrlin verge K pn vlues, clculted using the Austrlin grids of E pp nd ech of the five potentil formultions, re shown in Tble 3. As rtes of potentil evportion should be lower thn rtes of E pn, so K pn should be < 1. Hence, the nnul verge K pn for E mp is unrelisticlly high. K pn for E p is pproximtely the sme s the widely used nnul verge vlue for converting E pn to evportion rtes from open wter bodies (0.7, Lincre 1994; Stnhill 2002). The remining potentil evportion formultions hve K pn vlues of round , except for E th which shows lmost no reltionship with E pp. Figure 7 gives two exmples of grids of dily K pn vlues which demonstrte tht K pn vries both sptilly nd temporlly. Longterm, sptilly verged K pn vlues hve trditionlly been used to convert pn rtes to potentil rtes; now sptilly nd temporlly explicit estimtes of K pn re vilble. Tble 3. Pn coefficient vlues for ech of the five potentil evportion formultions. Formultion Penmn potentil (E p ) Priestley-Tylor potentil (E pt ) Morton point potentil (E mp ) Morton rel potentil (E m ) Thornthwite potentil (E th ) Pn coefficient Jnury 1981 b 1 July 1981 Figure 7. An exmple of Austrli-wide, dily pn coefficient vlues. Here the pn coefficient is for Penmn potentil evportion for () the first of Jnury 1981 nd (b) the first of July Anlysis of trends The Austrli-wide trends in the inputs to the rdition modelling, s well s the modelled rdition components themselves, re shown in Tble 4. Ech component of the rdition blnce hs incresed over the study period, with similr mgnitude trends being experienced for both the two incoming components nd for both the two outgoing components (see Tble 4). As the combined trend in outgoing rdition is greter thn tht of incoming rdition (lmost 1.5 times greter), net rdition hs 22 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

28 RESULTS decresed overll (down pproximtely 1% over the 26-yer period). Differentition of Equtions (6) nd (9) indicte tht 90% of the increse in R so is due to the increse in α. If α ws held constnt in the modelling, the chnge in R so would hve been 0.01 W.m -2.yr -1 nd R n would hve incresed by n verge of W.m -2.yr -1. This result demonstrtes the importnce of understnding the role tht even subtle chnges in lbedo cn ply in dynmics in the surfce energy blnce. Figure 8 shows the sptil distributions of trends in the inputs used in the rdition modelling, nd Figure 9 shows those of R si, R li, nd R n. The sptil ptterns in the trends of R si nd R li reflect the ptterns in T r nd T trends, respectively. Across most of estern Austrli, nd cross the fr north, R n hs decresed over the study period. Conversely, throughout the western interior R n hs incresed. In generl, R n hs incresed where α hs decresed, which in mny res hs occurred where P hs incresed, nd vice vers (see Figure 9). The incorportion of remotely sensed α hs mrked effect on R n, s it hs produced fine scle ptterning within the R n trends governed by observed chnges in lnd-surfce properties. Tble 4. Austrlin-verge nnul trends ( ) in the vribles used to clculte net rdition nd the trends in the rdition components. Here the trend in Rn is clculted s the sum of the trends in incoming rdition minus the sum of those in outgoing rdition. P-vlues re determined using two-sided Kendll tu test (Kendll nd Gibbons 1990) performed on Austrlin-verge nnul vlues. Attribute Trend Stndrd error of trend P-vlue Albedo (α) yr Minimum temperture (T n ) K.yr K 0.98 Mximum temperture (T x ) K.yr K 0.30 Air temperture (T ) K.yr K 0.47 Diurnl temperture rnge K.yr K 0.58 (T r ) Actul vpour pressure (e ) 0.88 P.yr P 0.30 Sturted vpour pressure 3.08 P.yr P 0.55 (e s ) Incoming shortwve (R si ) W.m -2.yr W.m Incoming longwve (R li ) W.m -2.yr W.m Outgoing shortwve (R so ) W.m -2.yr W.m Outgoing longwve (R lo ) W.m -2.yr W.m Net rdition (R n ) W.m -2.yr W.m Cpturing evportive demnd dynmics with potentil evportion dt 1 December

29 RESULTS Minimum ir temperture (T n ) b Mximum ir temperture (T x ) c Men ir temperture (T ) d Diurnl temperture rnge (T r ) e Actul vpour pressure (e ) f Sturted vpour pressure (e s ) g Vpour pressure deficit (D) h Albedo (α) Figure 8. Annul trends ( ) in the vribles used to clculte net rdition. () minimum ir temperture; (b) mximum ir temperture; (c) men ir temperture; (d) diurnl ir temperture rnge; (e) ctul vpour pressure; (f) sturted vpour pressure; (g) vpour pressure deficit; nd (h) lbedo. 24 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

30 RESULTS Incoming shortwve rdition (R si ) b Incoming longwve rdition (R li ) c Net rdition (R n ) d Precipittion (P) Figure 9. Annul trends ( ) in rdition. () incoming shortwve rdition; (b) incoming longwve rdition; nd (c) net rdition; nd (d) precipittion, shown for reference (Donohue et l. 2009). Annul Austrli-verge trends in potentil evportion (Tble 5) show tht E th nd E mp hve incresed over the study period, E m hs chnged little nd the trends for the remining formultions hve decresed over time. Despite the lrge error bounds of these trend estimtes, the seemingly smll chnges in rtes of potentil evportion cn hve importnt implictions on the wter blnce in energy-limited ctchments nd in the more humid wter-limited ctchments (which re where the mjority Austrli s wter supplies originte) over severl decdes. For comprison, the nnul Austrliverge ( ) trends in P nd E pp re 1.3 nd 0.0 mm.yr -2, respectively (Tble 5). Trends in the vribles used to clculte potentil evportion re presented in Figure 10. The effects of T on potentil evportion re expressed through R n, e s nd Δ. Overll, T hs incresed cross the mjority of Austrli, especilly in the centrl-est (Figure 10), the nnul Austrli-verge trend is K.yr -1 (Tble 4). As previously indicted, R n hs decresed by W.m -2.yr -1 (down 1%). Actul vpour pressure hs incresed by bout 1.7% overll, t rte of 0.88 P.yr -1 (Tble 4). The lrgest increses in e hve occurred in the centrl-west of the country (Figure 10c), region which hs lso experienced some of the lrgest increses in P (Figure 9d). The verge trend in u 2 is m.s -1.yr -1 (down 13% over 26 yers). A disdvntge of using TIN-bsed u 2 interpoltions is the tringulr sptil structure in the dt s cn be seen in Figure 10d. Tble 5. Austrlin-verge nnul trends in potentil evportion ( ). Cpturing evportive demnd dynmics with potentil evportion dt 1 December

31 RESULTS The equivlent trends in precipittion nd Penpn evportion re shown for reference. P-vlues re determined using two-sided Kendll tu test (Kendll nd Gibbons 1990) performed on Austrlinverge nnul vlues. Formultion Trend Stndrd error of P-vlue Thornthwite potentil (E th ) Morton point potentil (E mp ) Morton rel potentil (E m ) Priestley-Tylor potentil (E pt ) Penmn potentil (E p ) (mm.yr -2 ) trend (mm.yr -1 ) Precipittion (P) Penpn potentil (E pp ) Long-term trends in potentil evportion clculted using the five formultions cn be seen in Figure 11-e, with trends in P lso being provided for context (Figure 11f). The sptil ptterns in the trends of the Penmn-bsed potentil (Figure 11) re dominted by chnges in u 2, with decreses occurring cross much of the north of Austrli nd increses in regions in the centre nd the est (prtilly corresponding to where P hs decresed). Morton point potentil (Figure 11c) hs less distinct pttern nd lrgely follows chnges in R n (nd therefore in α). As with the Penmn-bsed potentils, E mp is lso decresing cross the north, however this time it is primrily due to decreses in e s. Ptterns in E pt nd E m trends (Figure 11b nd d) re very similr, generlly following R n trends, nd the pttern in E th trends (Figure 11e) re entirely product of those in T. 26 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

32 RESULTS Men ir temperture (T ) b Net rdition (R n ) c Actul vpour pressure (e ) d Wind speed (u 2 ) Figure 10. Annul trends in the vribles used to clculte potentil evportion ( ). () ir temperture; (b) net rdition; (c) vpour pressure; nd (d) wind speed. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

33 RESULTS Penmn (E p ) b Priestley-Tylor (E pt ) c Morton point (E mp ) d Morton rel (E m ) e Thornthwite (E th ) f Precipittion (P) Figure 11. Annul trends in potentil evportion ( ). () Penmn; (b) Priestley-Tylor; (c) Morton point; (d) Morton rel; nd (e) Thornthwite formultions. Annul precipittion trends re lso shown for reference (Donohue et l. 2009) note the reversed legend for precipittion. Given tht Austrli is predominntly wter-limited (Figure 1), nd tking chnges in P s useful surrogte for chnges in ctul evportion, we ssess trends in potentil evportion s to whether they disply n pproximte complementry reltion to trends in P. Figure 12 shows the per-month trends in potentil evportion nd in P. In Figure 12, two formultions (E p nd E mp ) hve distinct sesonl pttern with trends showing shrp decrese in summer (DJF) nd slight increse in winter (JJA), nd, for E mp, lrge increses in spring (SON) vlues. Chnges in E pt nd E m re similr nd resonbly uniform cross ll months (Figure 12). Correltions between the per- 28 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

34 RESULTS month potentil evportion trends (Figure 12) nd the per-month P trends (Figure 12b) show complementry reltionship for the Penmn formultion nd, to lesser extent, for E mp (Tble 4). Note tht the sesonl pttern in P trends is present in the trends of Austrlin vegettion cover over the study period (Donohue et l. 2009) nd is mirrored by trends in α (Figure 12b). This sesonl ssessment of complementrity provides stronger test of the potentil evportion trends thn does n ssessment done purely on Austrli-verge nnul trends. Figure 12. Monthly trends in Austrli-wide potentil evportion ( ). Plot () shows the monthly trends in potentil evportion nd (b) the monthly trends in Austrli-wide precipittion (blck) nd lbedo (grey). Tble 6. Correltion between Austrlin-verge per-month trends in precipittion nd potentil evportion ( ). P-vlues re determined using two-sided Kendll tu test (Kendll nd Gibbons 1990) performed on Austrlin-verge nnul vlues; n = 12 in ll cses. Formultion r P-vlue Penmn potentil (E p ) Priestley-Tylor potentil (E pt ) Morton point potentil (E mp ) Morton rel potentil (E m ) Thornthwite potentil (E th ) Figure 13 exmines which formultions of potentil hve trends tht re complementry with P trends t the 102 long-term pn evporimeter loctions cross Austrli. Only E p nd E mp (Figure 13 nd b) show substntil negtive reltionship with chnges in P (lthough ech hs resonble degree of sctter). E pt nd E m disply little complementrity with P trends (Figure 13b nd d) nd E th essentilly displys none t ll (Figure 13e). Cpturing evportive demnd dynmics with potentil evportion dt 1 December

35 RESULTS b c d e Figure 13. Comprison of nnul trends of precipittion nd potentil evportion ( ) t the 102 loctions. () Penmn; (b) Priestley-Tylor; (c) Morton point; (d) Morton rel; nd (e) Thornthwite formultions of potentil evportion, respectively. The dshed line is the eqution of best fit (given on ech plot), n is the number of observtions, the offset nd RMSE sttistics re in ordinte units. 30 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

36 RESULTS 3.6 Attribution of trends The Austrli-wide trend in Penmn potentil evportion over is -0.8 mm.yr -2 (see Tble 5). Tble 7 shows tht the results of ttributing the chnges in E p were, in order of mgnitude, due to: (i) dt /dt (1.5 mm.yr -2 ); (ii) du 2 /dt (-1.3 mm.yr -2 ); (iii) dr n /dt (-0.6 mm.yr -2 ); nd (iv) de /dt (-0.4 mm.yr -2 ). The sptil distributions of the effects of ech governing meteorologicl vrible on de p /dt re shown in Figure 14. If u 2 ws held constnt (i.e., in the bsence of vilble wind speed dt), de p /dt would hve been pproximtely 0.5 mm.yr -2. Further, if both u 2 nd α were held constnt, de p /dt would hve been round 1.0 mm.yr -2. Albedo nd wind speed both substntilly influence potentil evportion trends nd these results demonstrte the importnce of treting these vribles dynmiclly. Attribution of de p /dt on per-month bsis (Figure 15) indictes tht the distinct sesonlity in de p /dt is due to the combined effects of du 2 /dt, de /dt, nd dr n /dt, s the monthly chnges in dt /dt hve little impct on the monthly vribility of de p /dt. Tble 7. Attribution of the chnges in nnul, Austrli-wide Penmn potentil evportion ( ). All units re mm.yr -2. Rditive component de pr dt Sturtion vpour pressure slope E Δ pr dδ dt dt dt Chnge in Penmn potentil evportion Net rdition E pr R n dr dt n Sturtion vpour pressure slope E Δ pa dδ dt dt dt de p dt Aerodynmic component Wind speed E u pa 2 du dt de pa dt Vpour pressure deficit EpA des dt E pa de e dt dt e dt s Sturted vpour pressure E de dt e dt dt pa s s Actul vpour pressure E pa de e dt Cpturing evportive demnd dynmics with potentil evportion dt 1 December

37 RESULTS Men ir temperture (T ) b Net rdition (R n ) c Actul vpour pressure (e ) d Wind speed (u 2 ) Figure 14. Attribution of the chnges in Penmn potentil evportion ( ). () ir temperture; (b) net rdition; (c) vpour pressure; nd (d) wind speed. Figure 15. Attribution of the Austrli-wide, monthly trends in Penmn potentil evportion ( ). The Austrli-wide Priestley-Tylor potentil evportion trend over is -0.3 mm.yr -2 (see Tble 6). Tble 8 shows tht chnges in R n ccount for -0.8 mm.yr -2 of the overll chnge, whilst dt /dt ccounts for 0.5 mm.yr -2. The sptil distributions of δe pt /δt dt /dt nd δe pt /δr n dr n /dt re shown in Figure 16. The sesonl ptterns in de pt /dt re indistinct (Figure 17) compred to those in de p /dt (Figure 15), but re most influenced by dr n /dt. Given tht 90% of the trend in R so is due to chnges in α, if the 32 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

38 RESULTS formultion of R n ssumed α ws constnt, then de pt /dt would be hve been positive (~0.4 mm.yr -2 ) nd the sptil nd monthly ptterns would resemble those of the temperture-bsed potentil evportion formultions. Tble 8. Attribution of the chnges in Austrli-wide Priestley-Tylor potentil evportion ( ) due to chnges in Δ nd net rdition. All units re mm.yr -2. Chnge in Priestley-Tylor potentil evportion E pt dδ dt Temperture Δ dt dt Net rdition E de pt pt R n dt dr dt n Men ir temperture (T ) b Net rdition (R n ) Figure 16. Attribution of the nnul trends in Priestley-Tylor potentil evportion ( ). () ir temperture; nd (b) net rdition. Figure 17. Attribution of the Austrli-wide, monthly trends in Priestley-Tylor potentil evportion from Cpturing evportive demnd dynmics with potentil evportion dt 1 December

39 DISCUSSION 4. DISCUSSION 4.1 The vilbility nd qulity of pproprite input dt Recently Roderick et l. (2007) nd McVicr et l. (2008) demonstrted tht wind speed cross Austrli hs been declining over the pst three decdes, nd tht this decline hs been the min cuse of the observed declines in pn evportion (Roderick et l. 2007; Ryner 2007). Donohue et l. (2009) hve found tht, onverge, Austrlin vegettion cover hs been incresing since the erly 1980s. This chnge hs been incorported into the potentil evportion modelling through the dynmics in lbedo. In the work presented here, the dynmics of these two vribles (u 2 nd α) hve been explicitly included in the clcultion of potentil evportion (s pproprite ccording to ech formultion). Xu et l. (2006) exmined the temporl dynmics in FAO56 reference evportion (Allen et l. 1998) however this formultion prescribes constnt α. As fr s we re wre, the work presented here is the first time the effect of observed sptil nd temporl dynmics in these two vribles on vriety of potentil evportion formultions hs been reported. Until recently, Austrli-wide, dily wind speed dt did not exist nd McVicr et l. s (2008) reserch is n importnt step in the bility to undertke such nlyses s those presented here. Explortion of the chrcteristics of the McVicr et l. s (2008) wind dt reveled need to implement n lterntive interpoltion technique to the 3D smoothing splines becuse of the pucity of wind observtion dt. The TINinterpolted wind speed dt more ccurtely represented the underlying observtions both sptilly nd temporlly. The use of TIN-bsed u 2 dt improved the ccurcy of the modelled pn evportion dt, when compred to the spline-bsed results (Figure 4). There is limit to how ccurtely corse resolution grids cn replicte point-bsed dt; nonetheless, the reltionship between trends in modelled nd observed pn evportion could be further improved. Given the tightness of fit between the TINbsed nd point-bsed u 2 dt (Figure 3f), nd the loose fit between the grid-bsed nd point-bsed T x, T n nd e dt (Figure 3b-d), first step in improving the ccurcy of trends in modelled pn evportion would be to improve these ltter input dt sets. The clculted trends in e nd e s need to be interpreted crefully s both hve been clculted from mesurements mde t different times during the dy. Trends in e re trends in 9m (locl time) vpour pressure, not in dily integrls of vpour pressure. e s hs been clculted using dily T x nd T n, the times of which re unknown nd will differ from dy-to-dy (McVicr nd Jupp 1999). This mens tht e nd e s re not concurrent mesurements nd consequently the effects of chnges in the diurnl cycle of T nd/or e my not necessrily be reflected in the clculted trends in D or e s. 4.2 Difficulties in prmeterising surfce conditions in potentil evportion formultions Conceptully, potentil evportion is the evportion rte tht occurs from loction where energy is the dominnt limit to evportion. This is widely interpreted s being the evportion tht would occur from lrge, sturted surfce. Techniclly, this should men the surfce is prmeterised s ctully being sturted (e.g., 34 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

40 DISCUSSION Shuttleworth 1993), mening α 0.1 (Oke 1987). Here we choose to prmeterise the surfce with ctul α vlues insted (McVicr et l. 2007), s enforcing hypotheticl sturted-surfce α: (i) divorces the surfce from the meteorologicl mesurements mde bove the surfce; nd (ii) removes both temporl nd sptil dynmics in surfce conditions which is counter-intuitive when exmining surfce energy dynmics. Thus, our concept of potentil evportion does not enforce n ctul sturted surfce; it estimtes evportion from surfce s if ll (most) vilble energy t tht surfce ws to be converted into the ltent het flux under the extnt surfce nd erodynmic conditions. The ddition of mesured α in the clcultion of R n is n importnt component of the net rdition model presented here. Austrlin-verge α incresed by pproximtely 6% over the pst 26 yers. On per-pixel bsis both increses nd decreses in α hve been observed. Previously Donohue et l. (2009) found tht vegettion cover cross Austrli chnged considerbly over the sme period, generlly incresing but with positive nd negtive trends cross lrge res of Austrli. While the link between trends in α nd vegettion cover re not strightforwrd (it is complicted by soil colour vritions), it is resonble tht α hs been, nd is, chnging. Although the mgnitude of chnges in R n formulted with, nd without, dynmic α vries modertely ( versus W.m -2.yr -1 ), the sptil nd sesonl ptterns introduced by mesured α re importnt chrcteristics in dynmic R n model. 4.3 Findings nd recommendtions The hypothesis in undertking this reserch ws tht the fully physicl formultions of potentil evportion, clculted using sptilly nd temporlly dynmic input dt, would yield the most relistic estimtes of chnges in potentil evportion. The results generlly support this premise, s the greter the number of the four key vribles used within formultion, the more relistic the trends from tht formultion becme. E p, which includes dynmic estimtes of T, R n, e, nd u 2, hs the most relistic temporl dynmics s it showed the gretest degree of complementrity with ctul evportion trends (s represented by dp/dt) when considering: (i) Austrliwide nnul verge trends (Tble 5); (ii) sptil trends (Figure 11); (iii) sesonl trends (Figure 12); nd (iv) trends t selected long-term meteorologicl sttions (Figure 13). The E p ttribution nlysis showed tht, even though T nd u 2 were the biggest contributors to the overll E p trends (hving similr but opposite mgnitudes), it ws R n (due to dα/dt), e, nd u 2 tht produced the sesonl complementrity in trends. Morton point potentil is rdition-vpour pressure-temperture-bsed formultion it does not explicitly include u 2 s vrible. Its rtes of potentil re extremely high (see Figure 6 nd Tble 3), over-estimting potentil by up to one qurter of wht seems resonble (ssuming potentil evportion rtes should be no higher thn E pn ). Despite this, E mp still displys similr ptterns in trends in potentil s does the Penmn model. The Morton formultions re complex. Why the Morton point formultion cptures trends but not ctul vlues is uncler nd, becuse of this, should be voided s mens of estimting potentil evportion generlly. The rdition-temperture-bsed Priestley-Tylor formultion displys very wek complementrity with trends in ctul evportion (i.e., dp/dt) both sptilly (Figure 11) nd sesonlly (Figure 12 nd Tble 6). The monthly pttern in E pt trends (Figure 17) is minly cused by dr n /dt, which itself is primrily product of dα/dt. If E pt ws Cpturing evportive demnd dynmics with potentil evportion dt 1 December

41 DISCUSSION formulted with sttic α, it would effectively mimic temperture-bsed formultion under the climtic conditions of this study. However, considering the pproximte similrity in modelled vlues between E pt nd E p, for the ppliction considered here E pt is probbly the optiml formultion in the bsence of either e or u 2 dt. E pt should not be used for exmining trends in wter-limited environments, however. The temperture-bsed Thornthwite estimtes of potentil did not produce relistic vlues in either rtes or trends of potentil evportion, nd should not be used (Hobbins et l. 2008). Overll our results indicte tht the more vribles tht re held constnt when estimting potentil evportion, the less relistic the results become. This concurs with previous findings globlly (e.g., McKenney nd Rosenberg 1993; Chen et l. 2005; Shenbin et l. 2006; Grci et l. 2004). We rgue tht Penmn-bsed potentil formultions should be the preferred mens of exmining long-term dynmics in potentil evportion. This ssessment of potentil evportion dynmics hs been done only with respect to the inherent chrcteristics of the potentil evportion dt itself. No nlysis hs been performed of the effects of the potentil evportion on the long-term dynmics of ctul evportion. The choice of which formultion to use nd how it is prmeterised cn be crucil, for exmple: (i) in energy-limited ctchments where ctul evportion is minly determined by potentil evportion; (ii) in ctchments tht sesonlly switch between energy- nd wter-limited sttes where ctul evportion follows potentil for prts of the yer (such ctchments re crucil in Austrli s these yield the mjority of Austrli s wter supplies); or (iii) when ctul evportion is clculted s frction of potentil regrdless of the climte type (e.g., McVicr nd Jupp 2002; Guerschmn et l. 2009). The work presented here emphsises the fct tht increses in men ir temperture over the pst few decdes does not necessrily men tht potentil evportion rtes hve lso incresed. Considertion of ll the fctors driving potentil evportion is criticl, nd will continue to be so s climte chnge continues. An importnt impliction of this is tht, to predict future potentil evportion rtes, Generlised Circultion Models need the cpcity to predict the dynmics in ll the relevnt vribles with resonble ccurcy (Johnson nd Shrm 2009), including those in wind speed nd lbedo. 36 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

42 SUMMARY AND CONCLUSIONS 5. SUMMARY AND CONCLUSIONS Evportive demnd is driven by four vribles net rdition, vpour pressure, wind speed, nd ir temperture. Anlyses of long-term dynmics in potentil evportion, therefore, should idelly use fully dynmic formultion where the effects of the vribility in ech of the driving vribles re ccounted for. In Austrli chnges in wind speed, lbedo (nd net rdition), ir temperture nd vpour pressure hve been observed since the erly 1980s. To dte, no Austrli-wide, long-term potentil evportion dtsets hve been vilble tht dynmiclly incorporte ll these vribles. Two key inputs used in the genertion of potentil evportion dt reported here re sptilly nd temporlly dynmic representtions of lbedo (llowing for fully dynmic representtion of net rdition) nd wind speed. The vilbility of these two dtsets llowed the contribution of ech of these vribles on trends in potentil evportion to be quntified. We show tht both these vribles ply n importnt role in evportive demnd dynmics. Inputs to these nlyses were dily surfces interpolted from networks of observtionl dt. A significnt component of this work ws the testing of the temporl ccurcy of these input dtsets. This ws first done by compring surfcederived trends in the input vribles with the equivlent trends derived from the underlying observtionl point dt. We found for wind speed dt tht the Tringulr Irregulr Network (TIN) interpoltion method more ccurtely cptured the underlying site dt chrcteristics thn the spline-bsed interpoltion method. Another test undertken compred trends in modelled US Clss A pn evportion clculted using the input surfce dtsets with observed trends in pn evportion. Results from these tests provided resonble confidence in the temporl ccurcy of the input dt nd therefore in the modelled potentil evportion dt. This ccurcy is currently limited by the temporl ccurcy of the ir temperture nd vpour pressure dtsets. In order to ssess which formultions of potentil evportion re the most suitble for use in nlyses of long-term dynmics, we generted dily potentil evportion dtsets using five different formultions: (i) Penmn; (ii) Priestley-Tylor; (ii) Morton point; (iv) Morton rel; nd (v) Thornthwite potentil evportion formultions. Sptil, nnul, nd sesonl trends in ech were ssessed in terms of whether they displyed pproximte complementry chrcteristics with trends in ctul evportion (using precipittion s proxy for ctul evportion). We lso exmined the contribution tht trends in ech input vrible mde to the overll trends in fully physicl formultion (Penmn) nd in rdition-bsed formultion (Priestley-Tylor) of potentil evportion. Attribution of the Penmn formultion showed tht, the complementry nture of trends in Penmn potentil were due to the dynmics in rdition (nd prticulrly lbedo), vpour pressure nd wind speed. From first principles, fully physicl formultions, such s Penmn, re expected to best cpture trends in potentil evportion, nd our results confirmed this. Only the Penmn formultion displyed relistic vlues of both potentil evportion rtes nd trends for the conditions tested, nd these should be the models of choice when ll input dt re vilble. The trends in Morton point potentil, formultion which uses ll vribles except wind speed, were similr to those in the Penmn model. However, Cpturing evportive demnd dynmics with potentil evportion dt 1 December

43 SUMMARY AND CONCLUSIONS its estimted rtes of potentil were unrelisticlly high consequently, its use is not recommended. Both Priestly-Tylor nd Morton rel formultions produced similr rtes of potentil, which were pproximtely similr to those from the Penmn model. This, long with the simplicity of the Priestley-Tylor formultion, presents strong rgument for Priestley-Tylor being the best mens of estimting potentil evportion rtes when wind speed dt re bsent. Neither Priestley-Tylor nor Morton rel should be relied upon to reproduce temporl dynmics. Finlly, Thornthwite potentil evportion ws shown to be unsuitble for use. 38 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

44 ACKNOWLEDGEMENTS 6. ACKNOWLEDGEMENTS We would like to thnk Dvid McJnnet, Tom Vn Niel nd severl nonymous reviewers for helpful comments tht improved the mnuscript. We re grteful to Michel Hutchinson of the Austrlin Ntionl University nd to Dvid Jones nd Andrew Frost, both of the Bureu of Meteorology, for useful discussions on the ccurcy of spline-interpolted dt. Cpturing evportive demnd dynmics with potentil evportion dt 1 December

45 REFERENCES REFERENCES Allen RG, Pereir LS, Res D, Smith M (1998) Crop evpotrnspirtion: guidelines for computing crop wter requirements. FAO Irrigtion nd Dringe Pper 56. Food nd Agriculture Orgnistion of the United Ntions, Rome. Budyko MI (1974) Climte nd life. (eds Vn Mieghem J, Hles AL). Acdemic, New York, 508 pp. Bureu of Meteorology (2006) Climte Dt: Austrli CD-ROM, Version 2.2 December Austrlin Government Bureu of Meteorology Chen D, Go G, Xu CY, Guo J, Ren G (2005) Comprison of the Thornthwite method nd pn dt with the stndrd Penmn-Monteith estimtes of reference evpotrnspirtion in Chin. Climte Reserch, 28, Donohue RJ, McVicr TR, Roderick ML (2009) Climte-relted trends in Austrlin vegettion cover s inferred from stellite observtions, Globl Chnge Biology, 15, DOI: /j x Donohue RJ, Roderick ML, McVicr TR (2007) Correcting long-term AVHRR reflectnce dt using the vegettion cover tringle. CSIRO Lnd nd Wter Science Report 26/07. CSIRO Lnd nd Wter, Cnberr, 73 pp. Donohue RJ, Roderick ML, McVicr TR (2008) Deriving consistent long-term vegettion informtion from AVHRR reflectnce dt using cover-tringlebsed frmework. Remote Sensing of Environment, 112, DOI: /j.rse Durre I, Willims Jr CN, Yin X, Vose RS (2009) Rdiosonde-bsed trends in precipitble wter over the Northern Hemisphere: An updte. Journl of Geophysicl Reserch - Atmospheres, 114. D05112, doi: /2008jd Grci M, Res D, Allen R, Herbs C (2004) Dynmics of reference evpotrnspirtion in the Bolivin highlnds (Altiplno). Agriculturl nd Forest Meteorology, 125, Geoscience Austrli (2007) GEODATA 9 Second Digitl Elevtion Model (DEM-9S) Version 2 ccessed My Grnger RJ (1989) An exmintion of the concept of potentil evportion. Journl of Hydrology, 111, Guerschmn JP, Hill MJ, Renzullo LJ, Brrett DJ, Mrks AS, Both EJ (2009) Estimting frctionl cover of photosynthetic vegettion, non-photosynthetic vegettion nd bre soil in the Austrlin tropicl svnn region upscling the EO-1 Hyperion nd MODIS sensors. Remote Sensing of Environment, 113, Hobbins MT, Di AG, Roderick ML, Frquhr GD (2008) Revisiting the prmeteriztion of potentil evportion s driver of long-term wter blnce trends. Geophysicl Reserch Letters, 35, L DOI: /2008GL IPCC (2007) Summry for Policymkers. In Climte chnge 2007: the physicl science bsis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmentl Pnel on Climte Chnge (eds Solomon S, Qin D, Mnning M, et l.). Cmbridge University Press, Cmbridge. Iqbl M (1983) An Introduction to Solr Rdition. Acdemic Press, Ontrio, 390 pp. 40 Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

46 REFERENCES Johnson F, Shrm A (2009) Mesurement of GCM skill in predicting vribles relevnt for hydroclimtologicl ssessments. Journl of Climte, In Press. DOI: /2009JCLI Jones D, Wng W, Fwcett R (2007) Climte dt for the Austrlin Wter Avilbility Project. Finl Milestone Report. Austrlin Government Bureu of Meteorology. Jones D, Wng W, Fwcett R, Grnt I (2006) The genertion nd delivery of level-1 historicl climte dt sets. Austrlin Wter Avilbility Project. Finl Report. Austrlin Government Bureu of Meteorology. Jones DA, Wng W, Fwcett R (2009) High-qulity Sptil Climte Dt Sets for Austrli. Austrlin Meteorologicl nd Ocenogrphic Journl, In press. Kendll M, Gibbons JD (1990) Rnk correltion methods. 5th edition. Oxford University Press, Oxford. Lhomme JP (1999) Towrds rtionl definition of potentil evportion. Hydrology nd Erth System Sciences, 1, Lincre ET (1994) Estimting U.S. Clss A pn evportion from few climte dt. Wter Interntionl, 19, Lincre ET (2004) Evportion trends. Theoreticl nd Applied Climtology, 79, McIllroy IC, Angus DE (1964) Grss, wter nd soil evportion t Aspendle. Agriculturl Meteorology, 1, McKenney MS, Rosenberg NJ (1993) Sensitivity of some potentil evpotrnspirtion estimtion methods to climte chnge. Agriculturl nd Forest Meteorology, 64, McVicr TR, Jupp DLB (1999) Estimting one-time-of-dy meteorologicl dt from stndrd dily dt s inputs to therml remote sensing bsed energy blnce models. Agriculturl nd Forest Meteorology, 96, McVicr TR, Jupp DLB (2002) Using covrites to sptilly interpolte moisture vilbility in the Murry-Drling Bsin - A novel use of remotely sensed dt. Remote Sensing of Environment, 79, McVicr TR, Vn Niel TG, Li LT, Hutchinson MF, Mu XM, Liu ZH (2007) Sptilly distributing monthly reference evpotrnspirtion nd pn evportion considering topogrphic influences. Journl of Hydrology, 338, McVicr TR, Vn Niel TG, Li LT, Roderick ML, Ryner DP, Riccirdulli L, Donohue RJ (2008) Wind speed climtology nd trends for Austrli, : cpturing the stilling phenomenon nd comprison with ner-surfce renlysis output. Geophysicl Reserch Letters, 35, L DOI: /2008GL Monteith JL (1981) Evportion nd surfce temperture. Qurterly Journl of the Royl Meteorologicl Society, 107, Monteith JL, Unsworth MH (1990) Principles of environmentl physics. Second edition. Edwrd Arnold, London. Morton FI (1983) Opertionl estimtes of rel evpo-trnspirtion nd their significnce to the science nd prctice of hydrology. Journl of Hydrology, 66, New M, Todd M, Hulme M, Jones P (2001) Precipittion mesurements nd trends in the twentieth century. Interntionl Journl of Climtology, 21. Oke TR (1987) Boundry lyer climtes. Second edition. Routledge, London. Penmn HL (1948) Nturl evportion from open wter, bre soil nd grss. Proceedings of the Royl Society of London A, 193, Priestley CHB, Tylor RJ (1972) On the ssessment of surfce het flux nd evportion using lrge-scle prmeters. Monthly Wether Review, 100, Ryner DP (2007) Wind run chnges: the dominnt fctor ffecting pn evportion trends in Austrli. Journl of Climte, 20, Cpturing evportive demnd dynmics with potentil evportion dt 1 December

47 REFERENCES Roderick ML (1999) Estimting the diffuse component from dily nd monthly mesurements of globl rdition. Agriculturl nd Forest Meteorology, 95, Roderick ML, Frquhr G (2006) A physicl nlysis of chnges in Austrlin pn evportion. Lnd & Wter Austrli Project No. ANU49. CRC for Greenhouse Accounting, Reserch School of Biologicl Sciences, The Austrlin Ntionl University, Cnberr. Roderick ML, Rotstyn LD, Frquhr GD, Hobbins MT (2007) On the ttribution of chnging pn evportion. Geophysicl Reserch Letters, 34, L17403, doi: /12007gl Rotstyn LD, Roderick ML, Frquhr GD (2006) A simple pn-evportion model for nlysis of climte simultions: evlution over Austrli. Geophysicl Reserch Letters, 33, L17715, doi: /12006gl Sunders RW (1990) The determintion of brod-bnd surfce lbedo from AVHRR visible nd ner-infrred rdinces. Interntionl Journl of Remote Sensing, 11, Shenbin C, Yunfeng L, Thoms A (2006) Climtic chnge on the Tibetn Plteu: potentil evpotrnspirtion trends from Climtic Chnge, 76, DOI: /s z. Shuttleworth WJ (1993) Evportion. In Hndbook of Hydrology (ed Midment DR). McGrw-Hill, Sydney. Shuttleworth WJ, Serrt-Cpdevil A, Roderick ML, Scott RL (2009) On the theory relting chnges in re-verge nd pn evportion. Qurterly Journl of the Royl Meteorologicl Society, 135, DOI: /qj.434 Singh VP, Xu CY (1997) Evlution nd generliztion of 13 mss-trnsfer equtions for determining free wter evportion. Hydrologicl Processes, 11, Specht RL (1984) The Mediterrnen climte of Austrli nd its impct on the structure nd distribution of vegettion. Bulletin De L Societe Botnique De Frnce-Actulites Botniques, 131, Stnhill G (2002) Is the Clss A evportion pn still the most prcticl nd ccurte meteorologicl method for determining irrigtion wter requirements? Agriculturl nd Forest Meteorology, 112, Thornthwite CW (1948) An pproch towrd rtionl clssifiction of climte. Geogrphicl Review, 38, Wild M (2009) Globl dimming nd brightening: A review. Journl of Geophysicl Reserch - Atmospheres, 114. D00D16, doi: /2008jd Xu CY, Gong LB, Jing T, Chen DL, Singh VP (2006) Anlysis of sptil distribution nd temporl trend of reference evpotrnspirtion nd pn evportion in Chngjing (Yngtze River) ctchment. Journl of Hydrology, 327, Xu CY, Singh VP (2000) Evlution nd generliztion of rdition-bsed methods for clculting evportion. Hydrologicl Processes, 14, Xu CY, Singh VP (2001) Evlution nd generliztion of temperture-bsed methods for clculting evportion. Hydrologicl Processes, 15, Yng DW, Sun FB, Liu ZT, Cong ZT, Lei ZD (2006) Interpreting the complementry reltionship in non-humid environments bsed on the Budyko nd Penmn hypotheses. Geophysicl Reserch Letters, 33, L18402, doi: /12006gl Cpturing evportive demnd dynmics with potentil evportion dt 1 December 2009

48 APPENDIX A DERIVATION OF INCOMING LONGWAVE RADIATION APPENDIX A Derivtion of incoming longwve rdition Allen et l. (1998) present formultion of net longwve rdition (R ln ) which Roderick et l. (1999) re-rrnged to obtin incoming longwve rdition. Here the sme rerrngement is presented except tht we hve included surfce emissivity in the formul of outgoing longwve, hve converted e to P, nd hve used Austrlin coefficients in estimting cler sky shortwve rdition. The rerrngement follows. Let R = R R, (A1) ln li lo (in which it is implied tht R ln is negtive flux due to R lo being lrger thn R li ) nd R = ε σt. (A2) 4 lo S s Here T is used to pproximte T s. In Allen et l. s (1998) definition of net longwve rdition, R ln is positive flux: ( ) R si Rln = σt e 0.35 Rcs (A3) where R cs is cler sky incoming shortwve rdition. To render (A1) nd (A3) equivlent, R ln in (A3) needs to become negtive flux. Further, we hve dpted this to include surfce emissivity, to be in SI units, nd to incorporte the Austrlin coefficients for the Bristow-Cmpbell reltion. Hence R si Rlnet = εσ s T ( e 1000 ) ( z) R + o (A4) Combining Equtions (A1), (A2) nd (A4) nd rerrnging for R li gives R si Rli = εσ s T εσ s T ( e 1000 ) ( z) R + o or R si Rli = εσ s T 1 ( e 1000 ) ( z) R + o which is formultion for R li s presented in the mnuscript in Eq 14. (A5) (A6) Cpturing evportive demnd dynmics with potentil evportion dt 1 December

49