Benjamin Vivès 1 and Roger N. Jones

Transcription

1 Detecton of abrupt changes n Australan decadal ranfall ( ) Benjamn Vvès 1 and Roger N. Jones CSIRO Atmospherc Research Techncal Paper 73

2 The Natonal Lbrary of Australa Catalogung-n-Publcaton Entry Vvès, Benjamn. Detecton of abrupt changes n Australan decadal ranfall ( ). ISBN Ran and ranfall - Australa - Measurement - Mathematcal models. 2. Tme-seres analyss. I. Jones, Roger N. II. CSIRO Atmospherc Research. III. Ttle. (Seres : CSIRO Atmospherc Research techncal paper ; no. 73) Address and contact detals: CSIRO Atmospherc Research PMB 1 Aspendale, Vctora 3195 Australa Ph: (+61 3) ; Fax(+61 3) Emal: ar-enqures@csro.au A complete lst of CSIRO Atmospherc Research Techncal Papers can be found at Acknowledgment: Jance Bathols for the IDL contourng and the Bureau of Meteorology data extracton. Cher Page for the UNIX ntaton and her help wth the dfferent FORTRAN programs. Jule Sedses for the drawng of the cluster dstrct map. Bob Cechet, Ramasamy Suppah and Dew Krono for ther useful comments. CSIRO Atmospherc Research Techncal Papers may be ssued out of sequence. From July 2000, all new Techncal Papers appeared on the web ste of CSIRO Atmospherc Research. Some Techncal Papers are stll avalable n paper form. CSIRO Australa Electronc edton 2005

3 Abstract The bvarate test s used to dentfy abrupt changes n Australa s ranfall record for the perod Ths statstcal test s appled to the extended hstorcal hgh-qualty dataset and all other ranfall records longer than 60 years. Clmatc step-lke changes have been dentfed n the mean value on an annual and half-yearly bass. The detecton of such shfts n mean n an ndependent tme seres has been carred out comparng a random seres versus the observed tme seres. Results are successfully compared to the outputs of the more specfcally desgned Lepage test and the relevant lterature on hstorcal ranfall change. The results from the bvarate test and hstorcal analyses dsplay a greater coherence than the Lepage test results. Together, they provde evdence of three clmatc (ranfall-domnated) shfts occurrng durng the past 100 years. The most notceable s the well-known shft toward greater precptaton n eastern Australa n the late 1940s. The two others correspond to a global decrease n the md-1890s and a regonal downward shft n Western Australa n the end of the 1960s. An assessment of the resultng hydrologcal mpacts suggests that knowledge of the dynamcs and statstcs of changes n ranfall regme wll be of beneft n adaptng to future clmate.

4 Contents Abstract 1 Contents 1 1 Introducton 1 2 Australan precptaton data Prevous studes on Australan ranfall and ts varablty Ranfall datasets and basc analyss Clusterng 6 3 The bvarate test Presentaton Applcaton of the test 12 4 Results of the bvarate test Australa-wde results shfts events events Concluson of the bvarate test results 26 5 The Lepage test Presentaton of the test Applcablty of the Lepage test Results Concluson for the Lepage test 33 6 Decadal clmate varablty Decadal ranfall varablty n the perod Regonal studes of decadal clmate varablty Hydrologcal mpacts of shfts n decadal ranfall regmes 41 7 Concluson 43 8 References 44 Appendx 1 Bvarate computer program: descrpton and achevements 48 A1.1 The computer program 48 A1.2 Program achevements 48 A1.3 Program control 49 Appendx 2 Bvarate results: shfts n the 1920 s 50 Appendx 3 Bvarate results: shfts n the 1980s 51 Appendx 4 Bvarate results: random tme seres 52 Appendx 5 Lepage test adaptablty 54

5 1 Introducton The sustanable management of water-relant systems n Australa requres the understandng of ranfall varablty n all ts forms. Ranfall vares on a wde range of tme scales, from ndvdual events to decades and centures: 1. Event varablty 2. Daly ranfall varablty 3. Intra-annual, seasonal and nstraseasonal ranfall varablty 4. Interannual ranfall varablty 5. Century and decadal-scale ranfall varablty 6. Clmate change (Natural and human-nduced) Because short-term varablty has the most vsble mpact on human affars, much effort has been spent on understandng ts statstcal and dynamc propertes. For example, Australan nterannual ranfall varablty s amongst the hghest n the world, leadng to sgnfcant research largely focussed on the El Nño Southern Oscllaton (ENSO) phenomenon and related teleconnectons. Longer term varablty n ranfall s less well understood. Despte many efforts over the years to defne predctve elements of long-term varablty from observatons of the ranfall record, these efforts have largely been unsuccessful. Proposals have not stood up to rgorous statstcal analyss, often falng to satsfy the null hypothess sgnfcance test (NHST; Ncholls, 2000), or have not shown suffcent skll to survve as forecastng systems. More recently, the development of clmate models has offered the possblty of understandng the underlyng dynamcs of long-term varablty, but the relatvely bref hstorcal record makes valdaton of smulated long-term dynamcs dffcult. Descrbng the mean ranfall and accompanyng short-term statstcal propertes of a place requres an assumpton of statonarty. Ths assumpton requres that there are no trends or phase shfts that wll lead to an nadequate descrpton beng made. Often the NHST has been used to suggest that because a partcular trend s below a gven level of probablty (that level tself arbtrarly chosen), t cannot be attrbuted to a non-random cause,.e. t resdes n the nose of chaos. Ths s despte the evdence of long-term persstence n ranfall records that appear to nfluence the mean and/or modulate shorter-term varablty. Often, napproprate statstcal tests are used. For example, tme seres are often analysed usng tests that quantfy the sgnfcance of lnear trends. Such tests are napproprate for analysng step changes n tme seres. Where nterannual clmate varablty s very hgh, such as Australa, a change needs to exceed most or all of that varablty to regster as statstcally sgnfcant, so all phenomena below that threshold are overlooked. We take a much more practcal approach to the dentfcaton of long-term ranfall varablty. The practcal questons that mght arse are has there been a change n clmate that s statstcally sgnfcant, or f there has been a change n varablty, what type of change was t and how may t affect the management of water-relant systems? Because decadal varablty can produce large varatons n mean ranfall and shorter-term ranfall varables (e.g. daly ranfall ntensty) averaged over several decades, t wll nfluence the outcomes of such an nvestgaton. In a changng clmate, the attrbuton of trends to decadal varablty or a longer term secular change becomes problematc. Wth decadal ranfall varablty occurrng ndependently of possble trends due to greenhouse nduced clmate change, t may take many decades before possble ranfall changes can be properly attrbuted (Hulme et al., 1999). 1

6 Ths paper nvestgates abrupt changes n decadal mean ranfall n the Australan record usng a statstcal test normally used for testng for nhomogenetes n clmate records. The bvarate test has been used for testng nhomogenetes for ranfall (Potter, 1981) and temperature (Bücher and Dessens, 1991). The hypothess explored here s that f large numbers of ranfall statons change smultaneously and ths change s not an artefact of largescale changes n the observng system, that change must have a clmatc orgn. Ths follows on from the applcaton by Jones (1995) of the bvarate test to ranfall statons n southwestern Vctora where about half of all long-term statons n dsplayed a statstcally sgnfcant upward shft n Jones (1995) speculated that these changes had a smlar orgn to decadal ranfall regmes dentfed n eastern New South Wales by Warner (1987). Lkewse, n south-western Western Australa, a decrease n ranfall from the md-1970s has resulted n sgnfcant water shortages, requrng substantal nvestment n nfrastructure to secure water supply and the consequent establshment of the Indan Ocean Clmate Intatve to explore the cause of the change and ts possble longevty (IOCI, 2002). Here, we analyse all the Australan ranfall records of over 60 years n length from to determne when and where abrupt changes n ranfall have occurred n the nstrumental record. Fnally, the mplcatons for managng long-term rsks arsng from such changes are dscussed. 2

7 2 Australan precptaton data 2.1 Prevous studes on Australan ranfall and ts varablty General characterstcs Australan ranfall records began n the md 19 th century. The earlest readngs commenced wth the am of assessng the average condton of the new country. However, t was soon realsed that hgh nterannual ranfall varablty separated Australa from recollected condtons of Europe. As records became longer, fluctuatons n the ranfall record were analysed. Deacon (1953), Kraus (1954) and Gentll (1971) all noted a wetter perod n the late 19 th early 20 th century then a drer perod n the frst half of the 20 th century. Pttock (1975) analysed 20 th century ranfall records, examnng the nfluence of the hgh pressure belt and the Southern Oscllaton Index on nterannual ranfall patterns, locatng a sgnfcant ranfall ncrease n the late 1940s. Later, Pttock (1983) speculated whether ths change was due to global warmng. Utlsng both 19 th and 20 th century Australan ranfall records Srkanthan and Stewart (1991) nterpreted ths shft as part of longer term varablty. Lavery et al. (1992, 1997) produced a hgh qualty hstorcal ranfall data set for Australa analysed from 1910 by Ncholls and Lavery (1992). They detected no sgnfcant changes n mean ranfall, although the nfluence of ENSO and a changed relatonshp between ranfall and temperature n El Nño perods snce 1976 has been noted (Ncholls et al., 1996). Usng the same data set, Suppah and Hennessy (1998) and Hennessy et al. (1999) showed sgnfcant ncreases n extreme ranfall (based on annual values of 95 th and 99 th percentle daly falls) over the century for most of the contnent except n south-west Western Australa (SW WA). Usng records of rver floods and flow dscharge (Warner, 1987) parttoned eastern Australan ranfall nto flood-domnated (FDR) and drought-domnated regmes (DDR) coverng the 19 th and 20 th centures. Ths hypothess was rejected by Krkup et al. (1998) on both statstcal and conceptual grounds. On the other hand, Whetton et al. (1990) noted an abrupt change n rver flows from the Darlng Rver n the Murray Darlng Basn n the early 1890s that concded wth changes n the Nle and n Northern Chna. Franks (2002) and Franks and Kucszera (2002) have also nvestgated the effect of decadal ranfall varablty usng flood gauge data from New South Wales, that supports Warner s hypothess and confrms the abrupt nature of changes noted by Whetton et al. (1990). A more recent decrease n ranfall n SW WA (Allan and Haylock, 1993) has lead to sgnfcant decreases n longterm water storage n that state (IOCI, 2001). More recent research has concentrated on the relatonshp between Australan ranfall and other clmatc varables and ndces to better understand clmate varablty. Ncholls et al., 1996 and Power et al. (1998) examned relatonshps wth the El Nño Southern Oscllaton, whereas Power et al. (1999a and b) examned recent aspects of decadal clmate varablty. Other studes wll be rased n the dscusson. 2.2 Ranfall datasets and basc analyss Two dfferent datasets of Australan precptaton were used n the analyss. The hgh-qualty hstorcal ranfall dataset for Australa provded a baselne dataset largely free of artefacts for 3

8 the study. The other major dataset used was Australa s complete daly ranfall record, descrbed n secton Hgh-qualty hstorcal ranfall data set for Australa After an exhaustve search of documentaton on measurement stes, coupled wth statstcal tests, Lavery et al. (1992) compled a 191 staton hgh-qualty long-term ranfall data set. Some records of shorter duraton were later used to buld composte records, extendng ths dataset to 379 records (Lavery et al., 1997). The selecton process vetted changes n observng practces, exposure of the ran gauge (or the ran-gauge type) and staton locaton. Statons wth dscontnutes were mmedately rejected those dscontnutes could not be explaned clmatologcally. Trends were closely examned and, f there was any suspcon that an observed trend was non-clmatc, the staton was rejected. The fnal testng was based on the method outlned n Craddock (1981) to compute a cumulatve devaton term referred to as a bas statstc. Ths bas statstc tests a tme seres for a staton and flags any excessve drft from the expected clmate. Data from 363 ranfall statons out of the 379 descrbed by Lavery et al. (1997) n the artcle were avalable to us. These records are referred as the Hgh-Qualty Dataset (HQD). Because the complete daly ranfall dataset dscussed n the next secton set only extended to 1990 at the tme of analyss, the HQD was utlsed for the perod The dstrbuton of frst and last years of these records are presented n Fgure 2.1 and record length n Fgure 2.2. Only statons wth a record length greater or equal to 60 years durng ths 100-year perod have been selected. Ths restrcton reduces the number of statons to 348. More than 30% of the statons (wth a record length greater or equal to 60 years n between ) have data pror to 1890 and almost all (98%) have records untl at least More than 90% of the statons have at least 80 years of record durng the perod (30% cover the whole 100 years). 100 Percent of statons Year Frst year Fnal year Fgure 2.1 Cumulatve percentage of record start and end years of the hgh qualty ranfall data set. 4

9 100 Percent of statons Length (years) Fgure 2.2 Percent of statons wth a gven record length from the hgh qualty ranfall data set Daly ranfall dataset These fles cover 15,425 statons across Australa, comprsng the entre daly data record from the Australan Bureau of Meteorology, and nclude the hgh-qualty statons presented above. Many contan only a few years of record or have numerous gaps. Only 3,539 statons provded years of 60 years or greater n length. Ther data homogenety has not been tested so may contan unrepresentatve shfts related to staton relocaton, changes n observng schedules and practces, changes n nstrument exposure, etc. The assumpton made here s that these shfts should be spread randomly among the perod studed (snce no globally unrepresentatve shft has been descrbed for the Australan ranfall data, ncludng the change from the Brtsh Unts to the Internatonal System of Unts n 1974, Lavery et al., 1992). Lkewse, these unrelable shfts should be randomly spatally dstrbuted. Both assumptons are used to dstngush changes wth a clmatc orgn from artefacts of measurement. 100 Percent of statons Year Frst year Fnal year Fgure 2.3 Cumulatve percent of record start and end years for all Australan ranfall statons >60 years n length. 5

10 100 Percent of statons Length (years) Fgure 2.4 Percent of all Australan ranfall statons wth a gven record length of >60 years. Almost 40% of the statons wth a record length greater or equal to 60 years durng the perod have data pror to 1890 (Fgure 2.3) and more than 56% have records untl Year 1989 s the last year avalable from ths database. Only 53% of the statons have at least 80 years of records durng the perod (7% cover the whole 100 years; Fgure 2.4). 2.3 Clusterng To meet the bvarate test requrements and buld homogeneous and statonary regonal seres, the records were clustered nto groups of closely related statons, based on analyses carred out by Ncholls and Lavery (1992). They clustered the data of Lavery et al. (1992) nto 10 groups based on smlar varatons of annual ranfall over the perod , usng the VARCLUS algorthm (SAS, 1985). For convenence, we have set the cluster lmts of the larger HQD by followng the meteorologcal dstrcts used by the Australan Bureau of Meteorology (ths allowed the computer program to straghtforwardly sort out the dfferent statons by usng ther dentfcaton number). See Fgure 2.5 and Table 2.1 below. 6

11 Fgure 2.5 Clmatologcal workng chart, Australan ranfall dstrcts (1 99) and the derved clusters (1 10). 7

12 Table 2.1 Summary of the clusters and the number of statons selected. Cluster number 1 Cluster name Eastern New South Wales Dstrcts ncluded 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 84 Number of statons HQD Natonal ranfall dataset Western Australa 5, 6, 7, 11, South-east 39, 40, 41, 42, 54, 56, Queensland 57, 58, South Australa 18, 19, 20, 21, 22, 23, 24, Tasmana 26, 85, 90, 91, 92, 93, 94, 95, 96, 97, 98, , 2, 3, 4, 13, 14, 15, North-east 16, 17, 27, 28, 29, 30, Australa 31, 32, 33, 34, 36, South-west Western Australa 8, 9, South coast Western Australa 9A, 10A Vctora 76, 77, 78, 79, 80, 81, 82, 83, 86, 87, 88, , 43, 44, 46, 47, 48, Inland New South 49, 50, 51, 52, 53, 55, Wales 64, 65, 73, TOTAL Note that because cluster 7 and 8 have two common ranfall dstrcts (9 and 10), they were merged whle processng the natonal ranfall dataset for easer management. 8

13 3 The bvarate test 3.1 Presentaton General background Maronna and Yoha (1978) developed the bvarate test to detect a sngle systematc change n mean n an ndependent tme seres, based on a second correlated seres whch s assumed to be unchanged. It not only ndcates whether or not a change has occurred, but also gves the maxmum lkelhood estmates and the tme and magntude of change. In clmatology, the most common applcaton of the bvarate test s to determne whether there s a shft n the mean of one staton relatve to a reference seres, neghbourng statons or a regonally representatve seres, that mght be evdence of an artefact n measurement or staton characterstcs. Potter (1981) tested annual precptaton seres from the northeast Unted States for homogenety usng the bvarate test. Results were excellent, even n cases where there was more than one shft n the precptaton mean. Bücher and Dessens (1991) successfully used the test to check nhomogenetes n tme seres of surface temperature from an elevated observatory n the Pyrenees n France. The bvarate test has also been used to demonstrate abrupt shfts n clmatologcal varables that have a clmatc orgn. Lettenmaer et al. (1994) used the bvarate test to evaluate the relatve changes n streamflow relatve to precptaton, streamflow relatve to temperature, and precptaton relatve to temperature across the Unted States. Gan (1995) computed smlar analyss comparng precptaton versus maxmum temperature for Canada and North-eastern USA Step by step descrpton The test should deally be appled to a serally ndependent sequence {x,y } of n twodmensonal random vectors, each of them dstrbuted normally. It s also assumed that the sequence s statonary, wth the excepton of a possble shft n the mean n {y }. Hypothess H 0 : {x,y } have the same bvarate normal dstrbuton, N(µ x,µ y,σ x 2,σ y 2,ρ), wth all parameters unknown. H 1 : For some 0 < 0 < n and d 0, the dstrbuton of {x,y } s N(µ x,µ y,σ x 2,σ y 2,ρ), for 0 and s N(µ x,µ y +d,σ x 2,σ y 2,ρ) for > 0. The lkelhood rato test of H 0 aganst H 1 s based on the followng statstcs. Seres standardsaton Let {x j } be the regonal seres of length n and {y j } be the test seres of length n. It s necessary to standardse {x j } and {y j } by ther mean and standard devaton to be able to use the crtcal values of the statstc T 0, computed by Maronna and Yoha (1978), under the null hypothess N (0,0,1,1,ρ). 9

14 10 j S Y y y S X x x Y y n S X x n S y n Y x n X y j j x j n j j y n j j x n j j n j j all for ) (, ) ( ) ( 1 ) ( 1 1, 1 Let ' ' 2 1 / 1 2 ' 2 1 / 1 2 ' 1 ' 1 ' = = = = = = = = = = Compute test statstcs [ ] [ ] maxmum a s for whch T value of the s and T max T n for all ) ( F )D - ( T n for all ) ( ) (S D n for all ) ( S n for all 1 and 1 Let o n xy 2 1 xy 1 1 S n n F n n ny X n n X n F y x y Y x X xy n j j j j j j j < = = = = < = < = < = = < = = Conduct test Maronna and Yoha (1978) computed, under the null hypothess, T crtcal values by smulaton for n=10, 15, 20, 30 and 70 and Potter (1981) extended the results to n=100. These are gven n Table 3.1. T 0 has to be compared to the crtcal value for the approprate n and the desred sgnfcance level. If T 0 exceeds the crtcal value, one has to reject the null hypothess. That s assumed that the mean of y has changed n the year after 0 by an amount equal to (D o S y ). Table 3.1 Crtcal values of T 0 (Potter, 1981). Sgnfcance level n (years)

15 3.1.3 Applcablty for ranfall analyss Potter (1981) showed that for annual precptaton seres, the assumpton of normalty does not pose a problem. However, ths can be dfferent n regons of low ranfall. The assumpton of ndependence may not be strctly satsfed, but t s probable that the seral dependence s not strong enough to substantally alter the concluson of the test (Potter 1981). Lkewse, the assumpton of statonary s generally satsfed. Most annual precptaton seres are assumed to be statonary. A flow dagram of the applcaton of the test on an Excel spreadsheet s shown n Fgure / Inputs 2/ Outputs Year X Y Standardzaton Bvarate test Year D T Measure of the dfference Composte seres Staton seres Y Average Std devaton Dfference between the regresson estmator of Y and the actual value Statstcs of the staton seres 3/ Results T s max for year (so called To) Year precedng the shft Sgnfcance level Sy Do Sy Do Amount of the change n mean Fgure 3.1 Flow dagram of the applcaton of the bvarate test on an Excel spreadsheet. 11

16 3.2 Applcaton of the test CSIRO Atmospherc Research Techncal Paper No. 73 To apply the bvarate test to Australan ranfall, we tred several combnatons of reference staton and subject seres. Ths secton brefly descrbes some of those trals and outlnes the successful analytcal desgn. To create cluster and natonal reference records, we converted ndvdual statons nto anomales based on the ranfall and averaged those anomales. For each staton, T 0 s chosen and tested for sgnfcance. Even f there may be several jumps n a record for ths study we chose only the most sgnfcant Cluster reference seres The frst tral used as the reference seres the average HQD ranfall anomaly for each cluster. Note that the level of sgnfcance (SL) shown s >10% (P>0.1) and wll reman so for all the results presented. Hgh-Qualty Dataset Tral 1 tested each of the 348 HQD staton aganst ts mean cluster anomaly for all clusters. Of those, 140 statons (40%) show a sgnfcant change n ther ranfall mean durng the (Fgure 3.2). They are randomly spread, the most mportant peak beng 1965 wth only 2.2% of all statons showng a sgnfcant change. Ths confrms that the HQD s, by and large, homogeneous. Number of statons Year Total Postve Fgure 3.2 Temporal dstrbuton of shfts n annual ranfall from the HQD compared to each cluster average, SL >0.1 (Tral 1). Natonal ranfall dataset Tral 2 tested the full data set for each cluster aganst each mean cluster anomaly of the HQD (as above). Ths tme, 1,191 statons (33%) show a peak n the perod of nterest (Fgure 3.3). As for the HQD, results are spread relatvely evenly, wth lttle evdence of a change of clmatc orgn. Events n 1972, the largest peak, accounts for less than 1.5% of the total number of statons. 12

17 Number of statons Year Total Postve Fgure 3.3 Temporal dstrbuton of shfts n annual ranfall from all Australan records >60 years compared to each cluster average, SL > 0.1 (Tral 2) Natonal reference seres In Trals 3 and 4 we used an Australa-wde reference seres created from the average annual anomaly of the HQD. From the results of Trals 1 and 2, we concluded that there was lttle evdence of clmate changes when statons wthn clusters were tested aganst the mean anomaly for each cluster. In Fgure 3.2 and Fgure 3.3, most nhomogenetes appeared to be random, consstent wth the lkely spread of measurement artefacts. Therefore, we hypotheszed that f any regonal changes had occurred they would have affected the whole cluster as part of regonal homogenety (e.g. the recent downturn n ranfall n SW WA). Trals 3 and 4 tested every precptaton seres >60 years aganst the reference seres. Hgh-Qualty Dataset Tral 3 for the HQD aganst the natonal average anomaly showed lttle dfference to Tral 1 (Fgure 3.4). One thrd (32%) of the statons tested showed a sgnfcant shft n the mean wth the most mportant peak representng 2% of all 348 statons occurrng n Indvdual cluster results (not shown) also dd not ndcate any partcular pattern of shfts. The most mportant peak was n cluster 3 (South-east Queensland) wth 3.2% of the statons showng a shft n

18 Number of statons Year Total Postve Fgure 3.4 Temporal dstrbuton of shfts n annual ranfall from the HQD compared to a natonal average from the HQD, SL >0.1 (Tral 3). Natonal ranfall dataset Tral 4, testng all statons >60 years n length aganst the HQD natonal anomaly shows 1,067 statons (30%) wth an abrupt change n the precptaton seres (Fgure 3.5). The dstrbuton of shfts s now much more dstnct, wth peaks n the early 1890s, n the late 1940s and n the late 1960s/early 1970s. The two most mportant peaks, 1891 and 1948, comprse 2.2% and 2.3% of the total number of statons, respectvely. The spatal dstrbuton and relatve mportance of these shfts are shown n Table 3.2, where the results are presented for each cluster. The relatve mportance refers to the percentage of statons for whch a shft has been detected compared to the total number of statons of the natonal ranfall dataset. The drecton of change corresponds to a shft to hgher precptaton (postve shft) or lower precptaton (negatve shft). Number of statons Year Total Postve Fgure 3.5 Temporal dstrbuton of shfts n annual ranfall from all Australan records >60 years compared to a natonal average from the HQD, SL >0.1 (Tral 4). 14

19 Table 3.2 Proporton of the shfts and drecton of change for each cluster (natonal ranfall dataset). Cluster Year Number of Proporton of Drecton of statons total change % 100% negatve % 100% postve 2 No peak wth more than 5% of the statons nvolved % 100% negatve % 100% negatve 6 No peak wth more than 5% of the statons nvolved 7& % 100% negatve % 100% negatve % 100% negatve 9 No peak wth more than 5% of the statons nvolved % 100% negatve The peaks n Fgure 3.4 exceed 5% of the total number of statons n several clusters (Table 3.2). The early 1890s are sgnfcant n clusters 1, 3 and 10 (New South Wales and Queensland) wth negatve shfts. The late 1940s are sgnfcant n cluster 1, 4, and 7&8 (New South Wales, South Australa and Western Australa). The shfts are negatve n South and Western Australa and postve n New South Wales. Another downward shft n occurs Western Australa n the late 1960s. We conclude that ths s the decrease noted by a number of other authors (e.g. Allan and Haylock, 1993) Random number reference seres For Trals 5 and 6, we used a random number reference seres. We nterpret the results from Trals 3 and 4 as shown n Fgure 3.4 and Fgure 3.5, as representng shfts of both artfcal and clmatc orgn. The larger peaks appear to be due to abrupt shfts (step-lke changes) of a clmatc orgn. However, due to the range of dfferent clmates and the poor spatal coverage of some regons (especally central Australa), ths seres s not deal. Moreover, for the cluster seres and perhaps the natonal seres, f there s any clmatc shft represented n the seres average, the bvarate test may not properly detect t. We hypothessed that the detecton of abrupt clmatc shfts wthn a tme seres caused by complex system responses would be best usng a random seres wth smlar statstcal propertes that shows no such shfts tself. We therefore created an ndependent, statonary seres usng generated random numbers (µ x =0, σ x 2 =1). Two seres wth no obvous trends or shfts were selected (tme seres have been plotted wth a dfferent runnng average) and tested wth the bvarate test aganst one another. The bvarate test dd not detect any sgnfcant shft, so one of the seres has been used as a reference seres. Tral 5 and 6 used the HQD and natonal ranfall dataset wth ths seres. Hgh-Qualty Dataset For Tral 5 the percentage of statons showng a sgnfcant shft s smlar to the natonal seres (31%) but the results dsplay much more temporal coherence. Sgnfcant peaks are consstent wth a clmatc orgn. The percentage of statons nvolved n each peak s stll low but larger than prevously (2% of the total number of statons n 1890 and 1893, 3% n 1946 and 4% n 1972; Fgure 3.6). 15

20 Number of statons Year Total Postve Fgure 3.6 Temporal dstrbuton of shfts n annual ranfall from the HQD compared to a random seres, SL >0.1 (Tral 5). Natonal ranfall dataset For Tral 6, 29% (1,034) of all statons show sgnfcant shfts, a smlar number to Tral 4. But the temporal dstrbuton of these changes s much more precse, wth three major groups ( , , ) accountng for more than 70% of the total number of shfts detected, and occurrng n only 16% of the length of the tme seres (Fgure 3.7). The agreement between Trals 5 and 6 s also mportant, snce t ndcates that these events cannot be attrbuted to the record qualty n Trals 1 and 3 the HQD was shown to be largely homogenous wth the mean regonal and natonal average anomales as Lavery et al. (1992, 1997) ntended. Therefore, ths method, usng an ndependent random seres as requred by the bvarate test, s the best method for testng abrupt shfts of clmatc orgn. We present the results of these tests n the next chapter. Number of statons Year Total Postve Fgure 3.7 Temporal dstrbuton of shfts n annual ranfall from all Australan records >60 years compared to a random seres, SL > 0.1 (Tral 6). 16

21 3.2.4 Selected results wth dfferent reference seres In ths secton we show how the bvarate test works for ndvdual tme seres. Annual precptaton and the results of the bvarate test on a gven staton from the HQD, Canary Island (Vctora, Cluster 9) are shown n Fgure 3.8. The results are shown usng the Cluster 9 mean anomales, the natonal HQD average anomales and the randomly generated seres as a reference. Fgure 3.8 (lower) shows the annual precptaton seres and ts fve-year runnng mean durng the 100-year perod from 1890 to The mean for the entre perod s 364 mm. It s evdent that a relatvely dry perod before 1950 was followed by a relatvely wet perod (Table 3.3). Ths s partcularly notceable for the 5-year runnng mean. After 1950, annual average precptaton ncreased by 25% compared to the pre-1950 average, wth an even more mportant varaton n nterannual varablty (standard devaton ncreased by 30%). Ths staton was selected by Ncholls and Lavery (1992) as one of the ten representatve statons for Australa (one for each cluster). They have also descrbed an ncrease n ranfall after Fgure 3.8 (upper) shows the tme seres of the bvarate statstc (T) for the three tests. The advantage of usng the random seres s t gves more accurate results than the other two (Measured by comparng the magntude of ncrease n Table 3.4 wth that n Table 3.3). Ths confrms the use of a random seres as an absolute reference aganst whch to test clmatcallydrven step changes as contrasted wth a regonal or natonal seres. The latter two wll be preferred for testng nhomogenetes wth an artfcal orgn. Although usng the cluster seres as a reference n Fgure 3.8 gves the hghest value of T 0, f the complete sequence of T s carefully studed, the bvarate test detects another sgnfcant shft n 1907 (wth a sgnfcant level >0.1). But the comparson of the perod and the followng one ( ) does not reveal any sgnfcant dfference between them. The average value remans n the same order (respectvely 321mm and 334mm) and the standard devaton s almost the same (95mm and 98 mm). The use of a random seres as a reference has proved to be the best seres to use to detect shfts whch have a clmatc orgnal (charactersed by a coherent spatal and temporal dstrbuton) because t elmnates regonal clmatc nfluences of averaged tme seres (cluster or naton-wde) and provdes a realstc estmate of the magntude of the shft. Therefore, n the rest of ths study, the bvarate test s conducted usng the random seres as a reference. Further tests, shown n Appendx 4, nvestgatng the behavour of the bvarate test usng known departures from a random seres, further demonstrate ts sutablty for the task n queston. 17

22 Statstc T T cluster T natonal T random 1949 P=0.01 P=0.05 P= Precptaton (mm) xz P Annual precptaton seres Average 0 P = 364mm Year Fgure 3.8 Annual ranfall wth 5-year runnng mean for Canary Island (lower panel), wth bvarate test results usng three dfferent reference seres (upper panel). Table 3.3 Means and standard devaton for annual precptaton for two successve perods at Canary Island, showng change n mean. Perod Mean (plus change) 332 mm 412 mm (+80mm) Standard devaton 97 mm 127 mm Coeffcent of varance 29% 31% Table 3.4 Results of the bvarate test. Years of occurrence of T 0 at Canary Island, wth three dfferent reference seres. Reference seres Cluster average Natonal average Random Year wth max. T (T 0 ) Value (sgnfcance level) 13.6 (>0.01) 11.4 (>0.05) 11.3 (>0.05) Change (mm)

23 4 Results of the bvarate test Ths chapter presents the results of the bvarate test on an annual and seasonal bass, and for selected perods between 1890 and 1989, addressng the locaton, regonal mportance and order of magntude of changes. Independently, two smple parameters (mean and standard devaton) are computed from the data to confrm the valdty of the bvarate test outcomes. 4.1 Australa-wde results Major peaks Natonal results for the statons of the natonal ranfall dataset were presented n Fgure 3.6. Results for the summer half of the year (November Aprl) and the wnter half of the year (May October) are shown n Fgure 4.1 and Fgure 4.2, respectvely. Fgure 4.1 shows that abrupt changes n the summer half of the year after 1900 are domnated by ncreases, wth the largest changes occurrng n the late 1940s. Earler studes of ranfall trends by Deacon (1953), Kraus (1954), Cornsh (1977), Russell (1981) and Pttock (1983) found that summer ranfall had ncreased over much of south-eastern Australa snce the start of the 20 th century. Compared to the annual shfts shown n Fgure 3.6, the 1890s s less pronounced, a seres of mnor peaks occur n the 1920s, the 1940s reman sgnfcant, the late 1960s/early 1970s less so and the md 1980s, nsgnfcant n the annual set, becomes the second-most promnent. From the results shown n Appendx 4, ths latter promnence may be overstated by the senstvty of the bvarate test to changes close to the begnnng and end of tme seres. Wnter changes show some dfferences wth the annual results. The 1890s are domnated by decreases and nvolve a large number of statons. The 1920s show a small downward shft, compared to the upward shft n summer seen n summer (wth lttle movement seen annually, Fgure 3.7, nferrng a change n varablty but not n mean). The late 1940s are domnated by ncreases, 1968 by decreases and 1972 by ncreases. Slght ncreases are also apparent n Number of statons Year Total Postve Fgure 4.1 Temporal dstrbuton of shfts n summer (November to Aprl) ranfall from all Australan records >60 years compared to a random seres, SL >

24 Number of statons Year Total Postve Fgure 4.2 Temporal dstrbuton of shfts n wnter (May to October) ranfall from all Australan records >60 years compared to a random seres, SL >0.1. From the two last fgures, t becomes obvous that the shfts are manly due to a decrease n the wnter precptaton as are the ones n 1968 and The perod s domnated by ncreases n both seasons Other shfts Changes n the 1920s appear to have a clmatc orgn wth summer ncreases and wnter decreases havng lttle effect on the change n mean (Fgure 3.7). The wnter decreases are manly located n South Australa (cluster 4) and n a less mportant extent n Western Australa (clusters 7 and 8). The summer varatons are manly located n Vctora, Tasmana and south-east Queensland (respectvely clusters 9, 5 and 3). Maps are presented n Appendx 2. Shfts n annual precptaton nvolve fewer statons. Ths s due to these regons also beng subjected to the more mportant and shfts. These shfts could be nvestgated by truncatng seres to avod the largest shfts,.e. nvestgatng the perod In the 1980s, as maps n Appendx 3 show, the majorty of May to October shfts are located n tropcal and sub-tropcal regons (southeast Queensland) where most of ranfall occurs durng the summer. Ths could explan why these changes are not mportant enough to nfluence the overall annual seres. However, as shown n Appendx 4, sgnfcant shfts at the end of a seres may have less statstcal sgnfcance than those n ts mdst. 20

25 shfts Results summary Table 4.1 presents a summary of the bvarate test results for ths perod. The bvarate results are on the left part of the table and the raw data from the same statons are on the rght. The mean value and the standard devaton before and after the year of the change are computed but are not sgnfcant due to the avalable sample sze for In the deal case, the change n mean should correspond to the bvarate estmate most of these values are very close. Changes where the proporton of statons showng shfts n each cluster exceeds 20% are outlned n blue f the shft s towards hgher ranfall or red n the case of a decrease. Table 4.1 Bvarate test results obtaned for the shfts (natonal ranfall dataset). Cluster Dataset & Total Shfts detected by the bvarate test (SL > 0.1) Number of statons Percentage of statons Percentage of all shfts Nature of change Change n mm Precptaton data for / Mean ranfall n mm Standard devaton n mm Annual 38 12% 24% negatve Summer 12 4% 7% negatve Wnter 19 6% 33% negatve Annual 0 0% 0% Summer 0 0% 0% Wnter 0 0% 0% Annual 95 22% 54% negatve Summer 24 5% 16% negatve Wnter 11 2% 48% negatve Annual 19 4% 22% negatve Summer 0 0% 0% Wnter 10 2% 10% negatve Annual 7 2% 11% negatve Summer 0 0% 0% Wnter 11 4% 15% negatve Annual 38 8% 33% negatve Summer 18 4% 20% negatve Wnter 43 9% 43% negatve Annual 3 1% 3% negatve Summer 0 0% 0% Wnter 4 1% 3% negatve Annual 7 1% 6% negatve Summer 1 0% 2% negatve Wnter 12 2% 13% negatve Annual % 52% negatve Summer 12 2% 1% negatve Wnter % 65% negatve Annual % negatve Summer % negatve Wnter % negatve

26 Ths decrease n precptaton (almost one thrd of the total shfts detected n the annual seres happen durng ths fve-year perod) requres supportng evdence to be nterpreted as a clmatc event. Because t appears at the very begnnng of the record, one can argue that ths shft s overestmated n sgnfcance and may only be due to a short-lved wet perod beng exaggerated by ts presence near the begnnng of the seres (see Appendx 4). However, the mean ranfall value for these statons falls from 1,138 mm a -1 to 662 mm a -1, a smlar amount to that ndcated by the bvarate test. Ths decrease s confrmed by other evdence that wll be presented later. Comparson of the change n mean calculated by the bvarate test agrees wth that calculated by the dfference n the averages ether sde of the date of change. The change gven by the bvarate estmate s -488 mm compared to -476 mm (1,138 decreasng to 662 mm a -1 ). The large ncreases n standard devaton and decreases n mean n Table 4.1 wll be affected by the short length of the perod before the shft; therefore wll not accurately represent the magntude of change n the clmate regme Locaton Fgure 4.3 shows the locaton of the shfts n annual ranfall lsted n Table 4.1 whch are domnated by decreases. Each staton was plotted as occupyng one square n a 0.5 grd; f two or more statons are plotted n the same locaton they are averaged. Few statons were n operaton outsde the area shown to be affected. Northern Terrtory Western Australa Queensland South Australa New South Wales Vctora Tasmana Fgure 4.3 Locaton and ampltude (n mm) of the shfts (natonal ranfall dataset). 22

27 events Results summary Shfts occurrng n the perod are almost as numerous as those n Most statons show an abrupt ncrease n precptaton n both seasons. The estmated average change by the bvarate test s +161mm for the annual precptaton seres compared to a +150 mm dfference n averages ( ). Because ths change occurs at the halfway pont of most of the records, sample length s unlkely to nfluence the sgnfcance of the result. In clusters 7 and 8 the lower value can be explaned by the mean ranfall decrease (Table 4.2). Table 4.2 Bvarate test results obtaned for the shfts (natonal ranfall dataset). Cluster Dataset & Total Shfts detected by the bvarate test (SL > 0.1) Number of statons Percentage of statons Percentage of all shfts Nature of change Change n mm Precptaton data for / Mean ranfall n mm Standard devaton n mm Annual % 70% postve Summer 73 23% 44% postve Wnter 16 5% 28% postve Annual 0 0% 0% Summer 0 0% 0% Wnter 0 0% 0% Annual 21 5% 12% postve Summer 1 1% 1% postve Wnter 19 4% 33% postve Annual 3 1% 5% pos. (80%) Summer 1 1% 4% negatve Wnter 2 1% 2% postve Annual 20 7% 11% postve Summer 1 1% 2% postve Wnter 29 9% 39% postve Annual 5 1% 4% postve Summer 3 1% 3% postve Wnter 2 1% 2% postve Annual 5 2% 6% negatve Summer 2 1% 6% postve Wnter 16 5% 12% negatve Annual 58 11% 53% postve Summer 0 0% 0% Wnter 46 8% 50% postve Annual 71 12% 31% postve Summer 58 10% 46% postve Wnter 11 2% 7% postve Annual 294 8% 28% pos. (99%) Summer 139 4% 20% pos. (99%) Wnter 141 4% 18% pos. (88%)

28 4.3.2 Locaton Fgure 4.4 shows the domnance of the postve shft n precptaton n the eastern part of the contnent. Interestngly, the south-west part of Western Australa experenced decreases durng the same perod; 16 (5%) of statons from clusters 7 and 8 show decreases n wnter. Fgure 4.4 Locaton and ampltude (n mm) of the shfts (natonal ranfall dataset). 24

29 events Results summary The perod can be dvded n two. All the decreases detected n south-west Western Australa occur durng In south-west Western Australa (clusters 7 and 8), 26% of the shfts (22 statons) n the annual seres are detected durng these years and severe decreases n standard devaton are notceable. The decrease n mean ranfall s more than 18% compared to prevous mean (from 798 mm a -1 to 653 mm a -1 ). Ths declne occurs manly n wnter. In contrast, parts of South Australa (cluster 4) undergo a 24% ncrease n annual precptaton (from 310 mm a -1 to 407 mm a -1 ). Ths ncrease s wdespread across the contnent durng , except n south-west Western Australa (Table 4.3). Table 4.3 Bvarate test results obtaned for the shfts (natonal ranfall dataset). Due to low numbers, shfts >20% n Cluster 2 are not shaded. Cluster Dataset & Total Shfts detected by the bvarate test (SL > 0.1) Number of statons Percentage of statons Percentage of all shfts 25 Nature of change Change n mm Precptaton data for Standard devaton n Mean ranfall n mm mm Annual 0 0% 0% Summer 6 2% 5% postve Wnter 0 0% 0% Annual 1 1% 11% postve Summer 2 1% 25% postve Wnter 9 2% 40% postve Annual 3 1% 2% postve Summer 7 2% 5% postve Wnter 2 1% 3% postve Annual 26 5% 30% postve Summer 3 1% 13% pos. (66%) Wnter 20 4% 20% postve Annual 7 5% 11% postve Summer 2 1% 5% pos. (50%) Wnter 6 2% 7% postve Annual 31 7% 27% postve Summer 23 5% 25% postve Wnter 15 3% 15% postve Annual 22 3% 26% negatve Summer 0 0% 0% Wnter 49 14% 30% negatve Annual 17 3% 15% postve Summer 14 2% 23% postve Wnter 9 2% 10% postve Annual 22 4% 10% postve Summer 13 1% 1% postve Wnter 19 3% 12% postve Annual 129 4% 12% pos. (83%) Summer 70 2% 10% pos. (97%) Wnter 129 4% 16% pos. (62%)

30 4.4.2 Locaton Fgure 4.5 shows the decreases n ranfall over south-west Western Australa, contrastng wth ncreases n ranfall occurrng over a large part of the contnent. The patchy response n central Australa s due to the low densty of the nput data. There are only fve statons nvolved, but the area covered s wde because of the lack of neghbourng statons n ths desert-lke regon. Fgure 4.5 Locaton and ampltude (n mm) of the shfts (natonal ranfall dataset). 4.5 Concluson of the bvarate test results A large number of statons show a shft durng three major tme perods, clustered around , and The changes n mean from the bvarate test correspond closely wth means calculated by the dfference of the two tme perods n queston. More evdence of a clmatc orgn of these step-lke ncreases or decreases n the ranfall regme comes from analysng the locaton of these events. In the followng part of ths study the relevance of these shfts wll be compared wth the results of the Lepage test and wth prevous scentfc work analysng hstorcal records of Australan ranfall and related phenomena. 26

31 5 The Lepage test 5.1 Presentaton of the test General background Another test that has been used to detect step-lke changes n ranfall s the Lepage test. Ths statstcal test s a non-parametrc, two-sample test for locaton and dsperson (Lepage, 1971). The Lepage test has been used to detect changes such as long-term trends, cyclc varatons and step-lke changes for ranfall (Yonetan, 1993). Ths latter characterstc allows comparson wth the bvarate test. Moreover, the Lepage test does not rely upon a reference seres. Ths major dfference wth the bvarate test allows us to check the valdty of the prevous results Step by step descrpton The test statstc, HK (whch plays the same role as T n the bvarate test), s a sum of the squares of the standardsed Wlcoxon s and Ansar-Bradley s statstcs. Ths approxmates to the ch-squared dstrbuton wth two degrees of freedom f a sample sze s suffcently large. Therefore when HK exceeds / / 9.210, a dfference s judged wth a 10% / 5% / 1% sgnfcance level between the two samples. 2 { W-E(W) } ( W ) + { A E ( A )} V ( A ) HK = 2 V The HK s calculated as follows: Let {x } and {y } be two ndependent samples of sze n 1 and n 2, respectvely. It s assumed that u =1 f the -th smallest observaton n a combned sample of sze 2n=(n 1 +n 2 ) belongs to {x } and u =0 f t belongs to {y }. Then each term of the above equaton can be expressed as: For the Wlcoxon statstcs W 2 n = = 1 u 1 E ( W ) = n1(n 1 + n ) 2 1 V ( W ) = n1n 2(n 1 + n ) 12 For the Ansar-Bradley statstcs n 2 n A = u + = 1 = n + 1 (2 n 1 + 1) u E ( A ) = 1 n 1(n 1 + n ) 4 V ( A ) = n 1n 2(n 1 + n 2 2 )( n 1 + n 48 ( n + n 1) ) 27

32 5.1.3 Procedure Changes are detected n the followng way: Note a certan year Y (n the example 1895), and take the tme seres for n years (here n=5 years for both samples) after the year Y (sample {x } ncludng Y) and those before the year Y-1 (sample {y }, ncludng Y-1). If the Lepage test shows a dfference between the two samples {x } and {y } wth 1%, 5% or 10% of the sgnfcance level, then the change s judged to occur n the year Y. 1/ Inputs 2/ Process Year Precptaton (mm) Rankng of the data Staton seres The year Y s moved so as to cover the tme seres data at each staton. () Precptaton ranked u() Wlcoxon s and Ansar- Bradley s statstcs are computed. Value of HK(Y) u I =1 f orgnally the data belongs to the {x } seres and u I =0 f t belongs {y } 3/ Results HK s max for year y Year of the shft Sgnfcance level Fgure 5.1 Flow dagram of the applcaton of the Lepage test. 28

33 5.2 Applcablty of the Lepage test The Lepage test has an optmal sample sze for detectng step-lke changes for any seres (Yonetan, 1993). On the one hand, large samples tend to detect less notceable changes; on the other hand, pnpontng the tme at whch a change occurs becomes vague when the sample sze s too large. In Yonetan s paper, the duraton n s the same for both samples ({x } and {y }). The same scheme s retaned here. The Lepage s carred out wth dfferent values of n to determne whch s the most sutable. The frst range of values tested was n= 10, 20, 30 and 40 years (Appendx 5). When n=10, all the changes detected wth the other values of n were detected and peaks were the largest obtaned. Thus the ranges of n are reduced to 5, 10 and 15 years. The results Australa-wde are shown below (Fgure 5.2). Number of statons n=5 years n=10 years n=15 years Year Fgure 5.2 Results of the Lepage test on the natonal ranfall dataset (annual seres) wth dfferent sample szes. Where n=5, the test detects many changes but the largest response s obtaned when n=10 years wth the excepton of the md-1890s peak. In ths latter case, the calculaton of HK can only begn n years after the begnnng of the record. The same ranfall records used prevously are used here, but to best cover ths perod, the entre record length was used (.e. ncludng records before 1890). One quarter of all records >60 years n length began before 1885 (so HK can be calculated from 1890 f n=5years) but only one eghth began before Ths explans why the run wth n=5 years produces the hghest peaks for the early 1890 changes. 29

34 5.3 Results Natonal results for the statons of the natonal ranfall dataset are presented below. They are smlar to the outcomes for the hgh-qualty statons. The pattern n Fgure 5.3, showng a majorty of negatve shfts at the end of the 19 th century and early the 20 th century, resembles that from the bvarate test (Fgure 3.6). However, the Lepage test reveals a larger number of shfts nvolvng a greater number of statons. The most mportant annual shft detected wth the bvarate test durng s 99 statons n 1946; the Lepage test detects up to 319 statons n Ths s due to ts greater senstvty (90% of the statons tested show a sgnfcant shft compared to 29% usng the bvarate test) and ts dependence upon the samplng nterval. We compared the results of the Lepage test wth those for the bvarate test durng the key events of , and Snce the Lepage test does not estmate the nature (postve or negatve) or the magntude of the change, the dfference (n mm) between the average value of the ranfalls before and after the year of the shft was computed from the records. Fgure 5.4 shows the mportance of the change n the south-eastern part of the country. Results are smlar to the bvarate test outputs both for the locaton and the nature of the shft detected but the areas covered are much smaller. Both south-west South Australa and Queensland show no response whereas the bvarate test showed mportant negatve shfts. Ths may an artefact of the record length. As noted earler, the shfts occurrng n 1890 can only be computed by the Lepage test f the record begns n Only 8.8% of cluster 6 data (whch nclude most of north and west Queensland) begn n 1880 (compared to 35% n 1890). Although n South Australa (cluster 4), 25% of the statons have data avalable from 1880, the Lepage test does not reveal any downward shft. The postve shfts detected n central Australa concern only three statons. Number of statons Total Year Postve Fgure 5.3 Results of the Lepage test on the Australan annual precptaton seres of the same natonal ranfall dataset used wth the bvarate test. Sample sze s 10 years, level of sgnfcance s 10%. 30

35 Fgure 5.4 Results of the Lepage test for shfts (changes n mm). Despte the results of the Lepage test showng a more complex pattern of shfts occurrng n , the man characterstcs of ths perod reman smlar (Fgure 5.5). Major ncreases n the precptaton seres occur n the eastern part of Australa wth a largely negatve shft occurrng n Western Australa. Postve shfts cover a larger area than revealed by the bvarate test. The Lepage test also ndcates sgnfcance wth changes at a lower magntude than the bvarate test. For nstance, most of the regons wth lght blue (change of less than 50mm) were not represented n the bvarate test results. Whle the results obtaned for the perod largely agree wth the bvarate test (mportant decreases n the south-west part of Western Australa) durng the perod there are spatal dfferences. Negatve shfts domnate n south-western Western Australa whle the rest of the contnent s covered by a patchy network of ncreases (Fgure 5.6). 31

36 Fgure 5.5 Results of the Lepage test for (changes n mm). Fgure 5.6 Results of the Lepage test for (changes n mm). 32

37 5.4 Concluson for the Lepage test The use of a test wth a completely dfferent mathematcal structure from the bvarate test produces smlar patterns for the key perods of , and but locates a larger number of step-lke changes wthn the ranfall record at other tmes. The Lepage test s much more senstve to short-term varatons (~10 years) n clmate and therefore detects shfts n staton records wth changes below the threshold of statstcal sgnfcance for the bvarate test, especally when n s low. The man dsadvantages of the Lepage test are ts dependence on the sample sze (see Fgure 5.2) and ts senstvty to short-term perturbatons n a tme seres where the perturbaton s n. Here, we are nterested n abrupt changes n mean ranfall on a decadal scale, rather than short-term departures of several wet years. Due to these dsadvantages, the Lepage test s less sutable for assessng step changes n clmatc records than the bvarate test. Further tests on the bvarate test shown n Appendx 4 demonstrate ts superorty for determnng step-lke changes n mean, whle beng able to dstngush these from the short-term fluctuatons n nterannual varablty. 33

38 6 Decadal clmate varablty The bvarate and Lepage tests have been used to detect large scale abrupt shfts n mean decadal ranfall n ranfall over Australa between 1890 and In ths chapter, we attempt to reconcle these results wth aspects of decadal clmate varablty nvestgated by other authors. Power et al. (1998) characterse decadal varablty as: 1. Chaotc varablty extendng to decadal tmescales, 2. Interdecadal modes that demonstrate a level of predctablty, and 3. Evolvng responses to greenhouse-nduced clmate change. Settng asde c) for the present; to manage water-relant systems, we need to understand the statstcs behnd mode 1 and the statstcs and dynamcs behnd mode 2. When a rapd shft that ntates a clmate regme lastng for several decades or more s dentfed, how much of that regme s chaotc and how much s predctable? At least two forms of decadal varablty may be mplcated n the answer: a. The modulaton of nterannual varablty on a decadal scale, and b. Step-lke changes n decadal ranfall regmes, affectng average ranfall and ranfall ntensty at the decadal scale. Longer-term clmatc nfluences may modulate shorter-term varablty; for example, decadal scale modulatons of nterannual varablty comprse 10 40% of the total varance of Australan ranfall (Power et al., 1999a). The supportng evdence for step changes n clmatc regmes s more dffcult to locate whle there s wdespread evdence n hydrologcal systems, palaeoclmatc proxes and wthn ranfall statstcs, a clmatc understandng of such phenomena s harder to fnd. In ths chapter, we revew the evdence for decadal ranfall varablty to try and dstngush between these modes. We also brefly explore the mpacts of decadal ranfall regmes and outlne possble benefts that may be obtaned va rsk management and predcton. Fnally, some of the lmtatons of ths analyss and how mprovements may nform future studes of ranfall are dscussed. 6.1 Decadal ranfall varablty n the perod Tmng In ths paper, the bvarate test has been used to dentfy and analyse the evdence for step changes n hstorcal Australan ranfall records. Usng ths test on all Australan ranfall seres >60 years n length from wth an ndependent, random reference seres, we have shown that Australan ranfall has experenced three abrupt shfts n mean over that perod. These shfts cannot be explaned as artefacts of measurement, and n ths secton we revew the evdence from other sources. The frst shft occurred n the early 1890s and affected most of Australa, especally eastern Australa. Both summer and wnter ranfall was affected. Although ths shft took part n the early part of the record when the bvarate test wll react more senstvely to changes, extensve evdence from rver flows both n Australa and overseas (Nle, Yangtze etc) ndcates that a large-scale clmate shft occurred at ths tme (Fgure 6.1; Whetton et al., 1990). 34

39 Fgure 6.1 Tme seres representaton of the Darlng Rver stream flow at Wlcanna (32ºS, 143ºE; Whetton et al., 1990). Red shows the decrease and blue shows the and ncreases. Gentll (1971) showed that mean yearly ranfall decreased over most of the northern and eastern Australa from the perod compared to the perod , and ncreased over south western Western Australa over the same perod. Kraus (1950a, b) dentfed ths feature n a number of tropcal and subtropcal ranfall records n both hemspheres. Supportng evdence n the form of good rans n the 1880s followed by drought n the 1890s has been cted as nfluencng grazng success and stock numbers n Western New South Wales (Wllams and Oxley, 1979) and croppng n northern South Australa, later coned as the famous Goyder s lne, whch moved south at about that tme (Ncholls, submtted). The next major shft occurred n the late 1940s, and was concentrated over eastern Australa, sgnallng the end of a dry perod of just over ffty years duraton. Ths shft was almost overwhelmngly postve, except for a downward shft n wnter n south-west Western Australa. Dfferent mathematcal tools rangng from the smple change n mean (Pttock, 1975) to contnuous wavelet transforms (Nakken, 1999) have been used to descrbe the ncrease n precptaton n eastern Australa over ths perod, centred on changes n Fgure 6.2 s consstent wth the shfts dentfed n Fgure 4.4. Pttock (1975) reported that a major ncrease n annual ranfall occurred n the mddle to late 1940s over much eastern Australa. The negatve changes n south-west Western Australa are also ndcated n Fgure 6.2. Pttock (1975) correlated the change seen n Fgure 6.2 wth an L ndex, whch essentally measures the lattude of the hgh pressure belt over eastern Australa. The second most mportant pattern he produced (the frst was related to ENSO) s very smlar to the wnter patterns of change from the bvarate test n (the latter not shown) that shows ncreases n eastern Australa and decreases n SW WA. Ths suggests that the shfts n ranfall may be related to the lattude of md-lattude and sub-tropcal weather systems, but subsequent work has not confrmed ths lnk. Later analyses have tended to concentrate on post 1950 clmate data for reasons of qualty. Correlatons and emprcal orthogonal functon analyss usng ths data tend to dentfy ENSO as the largest contrbutor to nterannual varablty and Pacfc and Indan decadal oscllatons (that modulate nterannual varablty) 35

40 as the second most mportant (see Smth et al., 2000; p. 1914). However, long-term decreases n sea level pressure consstent wth the lattudnal movement of weather systems have occurred n concert wth decreases n ranfall n SW WA (Smth et al., 2000). Fgure 6.2 Dstrbuton of changes n mean annual ranfall (mm) between the ntervals and (Pttock, 1975). The thrd shft occurred over the nterval , manfestng as a decrease n SW WA n the late 1960s and an ncrease n eastern Australa n the early 1970s. It s not clear whether these events are connected. The bvarate test s a statstcal test, so may not correctly dentfy the year of a change. A decrease may not be regstered n the exact year t happened. For example, a decrease may be assocated wth a nearby drought year and an ncrease wth a nearby flood year. Ths may be the case durng where was a drought year and assocated wth a downward shft and 1973, a flood year assocated wth an upward shft (Fgure 3.7 and Fgure 4.5). The ranfall decrease n south west Western Australa has attracted a great deal of recent attenton (Allan and Haylock, 1993; Yu and Nel, 1993; Ansell et al., 2000; IOCI, 2002) n partcular, as to whether t s part of natural clmate varablty or clmate change. The analyss presented here ndcates that the latest shft follows a seres of quas-perodc shfts n ranfall. Ths vew s complcated by the possblty that f there s long-term warmng n the Australan regon, and greenhouse clmate change has accelerated ths warmng how s one to tell the dfference n terms of changes n ranfall varablty (IOCI, 2002) who conclude that both natural varablty and greenhouse-nduced clmate change may be mplcated n the recent observed ranfall decreases. Whether the ncrease n eastern and central Australa n the early 1970s qualfes as a step change smlar to those n the 1890s and 1940s s not clear. Ths ncrease followed a seres of dry years n the 1960s (Gbbs, 1975). As mentoned earler, the rapd onset of a seres of wet years of one or two decades duraton followng a gradual declne may be suffcent to produce a statstcally sgnfcant response. Ths possblty s tested usng artfcally perturbed seres n Appendx 4. 36

41 6.1.2 Magntude Estmatng the magntude of step changes n ranfall from the bvarate test s not easy for the followng reasons: 1. Only one result (T 0 ) from each tme seres was chosen, despte the fact that several sgnfcant changes may have occurred wthn a partcular record. Selecton by sgnfcance also means that the hghest values of change n mean (D 0 S y ) are sampled. 2. It was not possble to screen ndvdual statons for documented evdence of potental nhomogenetes caused by measurement artefacts. Although random nhomogenetes occur at a relatvely low frequency, they have a slght nfluence on the results. 3. Staton records are of dfferent length, due to closures and mssng data, makng average changes n shft for a perod of consstent length dffcult to calculate. 4. Statons of dfferent exposure wll not respond unformly to the same clmatc shft due to dfferent rates of aerodynamc gauge loss, whch are a functon of wnd speed at gauge heght. Hgh wnd speeds lead to a greater proporton of gauge loss, but ncreasng ranfall ntensty reduces gauge loss. If a step change n ranfall occurs ths change wll be greater at an exposed and wndy ste compared to a sheltered ste (Jones, 1995). Therefore, t s not possble to estmate mean ranfall change from a regon where sgnfcant losses are regstered n gauges wth a range of exposures. A spatal approach usng ranfall records corrected for aerodynamc gauge loss would be requred to estmate the magntude of changes wth any accuracy. Tables 4.1, 4.2 and 4.3 lst average changes n mean for the three perods. The changes suggest a decrease of 40% annually, 50% n summer and 45% n wnter (the changes for the two seasons wll average 40% because of the dfferent number of statons affected). The changes are lkely to be over-estmated because they are comparng the average of 5year wth >55 year perods. In , the ncrease for all clusters except SW WA was 25%, 30% and 25% for annual, summer and wnter perods, respectvely. In SW WA, the decrease was 15% annually and n wnter. In , the ncrease for all statons except SW WA was 35%, 55% and 40% for annual, summer and wnter perods, respectvely. The large changes n percentage terms are largely due to many of these occurrng across the ard nteror of Australa. In SW WA, the decrease was 20% annually and n wnter. These must be consdered maxmum changes Hydrologcal evdence Several assessments have dagnosed changes n ranfall regmes through observatons of change n streamflow and/or rverne morphology. Based on long-term flood stage records, Warner (1987, 1995) nomnated perods of DDR and FDR for the Nepean Hawkesbury catchment west of Sydney. He nomnated the perod as flood domnated, as drought domnated, as flood domnated, as drought domnated and as flood domnated. The 1899 and 1948 dates broadly agree wth those dagnosed here (1988 marks the end of the data rather avalable to Warner than a regme change). In a study of ranfall and rver flow varablty lnked wth El Nño, Whetton et al. (1990) llustrate seven tme seres of streamflow from major rvers n Afrca, Chna, Inda and Australa, ncludng the Darlng Rver n Australa. Major varatons n the total annual flow for the Darlng are smlar to those of the other man rvers of nland eastern and north-east Australa over the perod Flohn (1986) notes a 25% fall n streamflow on the Nle after referenced to the perod Ths suggests that the change n regme n 37

42 eastern Australa at the end of the 19 th century may have part of a global or hemspherc phenomenon. Franks (2002) and Franks and Kucszera (2002) also nvestgated the effect of decadal ranfall varablty usng flood gauge data from New South Wales. Franks (2002) used the Mann- Whtney test to analyse changes n annual maxmum flood for 40 gauges n New South Wales and from a regonal ndex compled from those records. The results showed a change occurrng n 1945, ndcatng that flood behavour before and after that date were sgnfcantly dfferent. 6.2 Regonal studes of decadal clmate varablty The studes descrbed above have assembled a sgnfcant body of evdence showng that abrupt changes n ranfall have affected large proportons of Australa at least three tmes over the century spannng 1890 and Such large changes would be expected to manfest n other aspects of clmate varablty. In the followng sectons we examne some of that evdence Australan studes Power et al. (1999b) examned hgh qualty Australan ranfall (Lavery et al., 1997) and temperature (Torok and Ncholls, 1996) datasets to assess clmate varablty over the 20 th century. Total annual ranfall was fltered to remove <8 year varablty and detrended (removng a small postve trend over ). They found that the rato of decadal to total varance of Australan ranfall (nterannual and greater) ranged from 10 to 40% of total varance. As mentoned earler, there are at least two possble modes of decadal varablty: step-lke changes n varables and the modulaton of nterannual varablty. The bvarate test dagnoses shfts n decadal mean clmate that persst for several decades. Further trals wth the bvarate test show that other varables whch also shft wth the mean nclude standard devaton, number of randays and annual daly ranfall extremes markng the 95 th and 99 th percentle. For example, step changes n randays and ranfall extremes consstent wth changes n average pre- and post-1946 ranfall have been dentfed for New South Wales and Queensland ranfall (unpublshed data). Ths suggests that aspects of both ranfall quantty and varablty are ted to these regmes. Decadal oscllatons n ENSO modulatng ts mpact on nterannual clmate varablty s the other mode of decadal varablty. Power et al. (1999a) nvestgated ths relatonshp, descrbng how the Interdecadal Pacfc Oscllaton (IPO) alters the relatonshp between ENSO and Australan ranfall. When the IPO s postve ths relatonshp has low predctablty and when t s negatve, predctablty s hgh. The IPO phases dscussed by Power et al. (1999a; Fgure 6.3) shows a dfferent perodcty to the shfts detected here n ths paper (15 25 years compared wth years). The droughtdomnated perod durng contans two postve phases of the IPO and one mnor negatve phase; the next postve phase s from the md 1970s to the late 1990s, clearly not a drought-domnated perod. The perod from the late 1940s to the md 1970s has a negatve IPO, as does the perod snce However, major excursons of the IPO from one sgn to the other, occur at about 1895 and the late 1940s so there may be a lnk, though not a drect one. The next major excurson of the IPO occurred n 1976 but ths s not lnked to a sgnfcant date wthn the bvarate test results. Therefore, we do not thnk rapd changes n 38

43 clmatc regmes and the modulaton of nterannual varablty are the same phenomena. They appear to be dfferent, operatng on dfferent tmescales, although they may be respondng n part to the same root cause. Fgure 6.3 Correlaton coeffcents between the Southern Oscllaton Index and varous Australan compared to the Interdecadal Pacfc Oscllaton (IPO) Index. The correlatons between temperature and the SOI have been multpled by 1 to facltate comparson (from Power et al., 1999a). Franks (2002) has nvestgated the late 1940s shft usng flood data n eastern New South Wales and ascrbes the FDR and DDR to phase reversal n the IPO, predctng that wth ts reversal n 1999/2000, eastern Australa wll soon be returnng to a flood-domnated regme. For the above reasons we do not thnk ths s the case; phase changes n the IPO are mplcated but are not the root cause. Kadonaga et al. (1999) also found dfferences between the Pacfc Decadal Oscllaton (a related ndex) and flood/drought regmes for the Pacfc north-west of the USA. Studes centred on SW WA have attempted to determne the nature and cause of decreases n wnter ranfall durng the 20 th century. Our analyss suggests successve step-lke changes occurred n 1948 and agan n Allan and Haylock (1993) dentfed a strong negatve correlaton between mean sea level pressure and wnter ranfall n the regon. They dentfed both decadal-multdecadal pulses and a long term trend n the relatonshp assocated wth ncreasng MSLP/decreasng ranfall. Ansell et al. (2000) narrowed the frequency of these pulses to 8 9 years and showed that MSLP was much more relevant to varatons n regonal ranfall than sea surface temperatures n the Indan Ocean. They also confrmed that relatonshps between local ranfall and regonal MSLP and SST were dfferent to those elsewhere n southern Australa. Smth et al. (2000) analysed tme seres of Indan Ocean sea surface temperatures and SW WA wnter ranfall and found that the frst two emprcal orthogonal functons (EOFs) appeared to reflect much of the longer term varablty. Both 39