Wavelet analysis of rainfall–runoff variability isolating climatic from anthropogenic patterns

Environmental Modelling & Software 14 (1999) 283–295

Wavelet analysis of rainfall–runoff variability isolating climatic from anthropogenic patterns Margriet Nakken

*

Natural Hazards Research Centre, School of Earth Sciences, Macquarie University, North Ryde, NSW 2109, Australia Received 15 February 1998; received in revised form 15 June 1998; accepted 1 July 1998

Abstract Continuous wavelet transforms (CWTs) are used to identify the temporal variability of rainfall and runoff and their relationship. The wavelet analysis is applied to rainfall and runoff records from Peak Hill and Neurie Plains, in the upper Bogan River catchment in central western New South Wales, Australia, as well as to the large-scale circulation index SOI. A method utilising wavelet analysis is being developed to identify and isolate the ‘natural’ climatic components of the hydrological record, by using SOI correlations, as well as to distinguish the influence of other non-stationary trends, such as anthropogenic land use changes, on runoff records over time. Results using the Morlet wavelet show that the variability of both rainfall and runoff as well as their relationship has changed over time. A wavelet spectrum analysis shows a change in dominant frequency since the 1950s. Climate induced catchment response is at short time scales (27–32 months over the time period 1911–1996). The relationship between the SOI and rainfall is stronger from the 1950s onwards, with a dominant frequency of SOI at 27 months. The non-stationary, multiscale time series analysis could be important in floodplain management and development decisions, for the insurance industry, and in engineering, by identifying past changes, by detecting streamflow response to climate changes, and by aiding in future flood and drought predictability.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Wavelet analysis; Rainfall; Runoff; SOI

Software availability The software used for the analysis of the data is WaveLab Version 0.701, developed by Jonathan Buckheit, Shaobing Chen, David Donoho, Iain Johnstone (all of Stanford University) and Jeffrey Scargle (NASA– Amos Research Centre). WaveLab is a library of MATLAB routines for continuous and discrete wavelet analysis, and is available free of charge over the Internet (http://playfair.stanford.edu/~wavelab or ftp://playfair. stanford.edu/pub/wavelab), with versions provided for UNIX, Macintosh and Windows machines. An overview document and reference manual are available from the website. MATLAB is a registered trademark of The MathWorks, Inc. (http://www.mathworks.com/).

* Tel.: ⫹ 61-2-9850-9466; Fax: ⫹ 61-2-9850-8428; e-mail: [email protected]

1. Introduction In April 1990, widespread flooding occurred in inland New South Wales and Queensland, Australia. The town of Nyngan, in the central west of New South Wales, was inundated by the Bogan River and subsequently evacuated. Unfortunately for the residents of the town, both the height and timing of the peak were under-forecast. The devastating immediate effects of the flood, and subsequent long-term impacts upon the catchment, have brought into focus the need for a review of hydrologic modelling techniques used in the catchment. Although an investigation into the Nyngan flood and its impacts was undertaken by the Department of Water Resources (DWR, 1990), little or no work has been undertaken to relate rainfall and runoff as non-stationary series. The latter investigation ignores land use changes over time, with the questionable statement that “…although impossible to prove, it is thought that catchment clearing has not significantly affected the homogeneity of Bogan River flood data” (DWR, 1990).

1364-8152/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 4 - 8 1 5 2 ( 9 8 ) 0 0 0 8 0 - 2

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Rainfall and runoff in the central west of New South Wales are highly variable. Studies of seasonal cycles and long-term trends are important in floodplain management, for local communities, for the insurance industry, and to establish engineering design standards. Many studies have identified the relationship and trends of east Australian rainfall and the El Nin˜o Southern Oscillation (ENSO) (e.g. Kane, 1997; Suppiah and Hennessy, 1996; Nicholls and Kariko, 1993; Opoku-Ankomah and Cordery, 1993; Drosdowsky, 1993; Zhang and Casey, 1992; Stone and Auliciems, 1992). These studies, however, have not been linked to trends in runoff time series. Smith (1995) compared rainfall and discharges of the Avoca River catchment in northwestern Victoria, finding changes in both rainfall and discharge series since the early 1970s. Smith concludes that the change in discharge is not a direct result of increased rainfall but is due to a change in the rainfall–runoff relationship. The main purpose of the present paper is to investigate hydrological changes in the Bogan River catchment and to provide further insight to the nature of runoff changes over the last century due to changes in rainfall regime and/or human interference in the catchment. The Fourier spectral analysis has often been used in identifying trends, but its use is limited for non-stationary data such as precipitation and runoff records which show a periodic component. The continuous wavelet transform (CWT) provides a time scale representation of the signal and has recently been used for analysing climatic and oceanographic data (e.g. Wang and Wang, 1996; Gu and Philander, 1995; Lau and Weng, 1995; Meyers et al., 1993), as well as stream discharge data and flood levels (Fraedrich et al., 1997; Bradshaw and McIntosh, 1994). To distinguish climate induced patterns from human induced patterns in the runoff signal, a methodology utilising wavelet analysis is being developed. The method aims to detect and isolate patterns across temporal scales and is critical to identify the climatic and anthropogenic components of the hydrological record.

2. The Bogan River catchment 2.1. General physiography The Bogan River is part of the Macquarie River catchment. It rises in the low hills of the western slopes in central western New South Wales north of Parkes and is nearly 600 km long. The river level falls from an elevation of about 450 m near Peak Hill to 170 m at Nyngan. The total catchment area at Nyngan is 18 040 km2. Below Nyngan the river breaks into distributary streams flowing across the Bogan–Macquarie alluvial fan and eventually joins the Darling River just upstream of

Bourke. It is fairly typical of a low gradient inland stream on the margin of the semi-arid zone. The Bogan River catchment is mostly flat plains country, with slopes of less than 2%, except for some hilly areas near Peak Hill. The subcatchment analysed in this paper is the unregulated catchment upstream from Peak Hill (1036 km2), in the upper reaches of the Bogan River Basin, while results are checked with data from the catchment upstream from Neurie Plains (14 760 km2), which includes the Peak Hill catchment (see Fig. 1). The headwaters have a major influence on flooding downstream and are therefore of principal interest in flood studies. 2.2. Land use changes and other non-stationary trends Since European settlement in the 1840s, approximately 70% of the Bogan River catchment has been cleared to improve grazing, a management practice that was dominant until the 1950s after which substantial areas of grazing land were converted to cereal cropping. It would seem likely that these ongoing changes in land management practices have had, and will continue to have, profound impacts upon streamflow, flood heights and channel morphology, but none have yet been documented. Given that Australian rivers have such a huge range in flow conditions, catchments like the Bogan have been extensively modified; and that we have little more than 70 years of gauging record, the task of predicting recurrence intervals for larger and less frequent floods is little better than guesswork. Several attempts have been made to improve prediction reliability but all have their limitations and even one of the more widely adopted patterns of Flood Dominated Regimes (FDR) and Drought Dominated Regimes (DDR) (e.g. Erskine and Warner, 1988) has recently been shown to rest on a less than adequate statistical base (Kirkup, 1996; Brizga et al., 1993). In order to better appreciate flow variability in Australian streams, and thus make more reliable estimates of flood risks and costs, a fundamental analysis of raw hydrological data and land use changes is required. Wavelet analysis is an important means of determining the non-stationary trends and relationships and is invaluable to evaluate the impacts of future climate changes as well as the specific effects of land use changes and catchment characteristics on runoff.

3. Data 3.1. Hydrological data For the Bogan River catchment, a barrier to adequate floodplain management is the lack of hydrological data for determining flood risk, such as flood magnitude and

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Fig. 1.

285

Location of the upper Bogan River catchment, precipitation stations, and runoff gauging stations.

the frequency of occurrence. The first gauging station on the Bogan River was established in 1925, at the Peak Hill water supply weir. Flood records of between 20 and 40 years from only seven other gauging stations are available. Despite the limited data, a methodology to quantify and relate information about temporal and spatial patterns in runoff data utilising wavelet analysis is being developed. River flow records are represented here as time series of runoff expressed in millimetres of equivalent water depth over a catchment area for ease of comparison with precipitation. Average annual rainfall at Peak Hill is 564 mm, while the annual runoff through Peak Hill gauging station is approximately 35 mm (see Table 1). A fundamental tenet of any long-term trend analysis is that the data used in the analysis needs to be homogeneous. The aim of the present study is to detect inhomogeneous catchment characteristics over time due to land use changes. Therefore, discontinuities in rainfall and runoff time series due to changes in the location of stations need consideration. The Peak Hill gauging

station was moved downstream in September 1967. Therefore, Neurie Plains gauging station, with the second longest record and the only record before 1967 besides Peak Hill, is used to normalise Peak Hill runoff data using the parallel estimation technique and to provide additional evidence of change since the mid-1950s. Runoff data for 100 months before (May 1959–August 1967) and 100 months after the location change (September 1967–December 1975) at Peak Hill (Rph) are compared with those at Neurie Plains (Rnp) The hypothesis is made that simultaneous measurements at Peak Hill and Neurie Plains bear a constant, linear relationship (see Fig. 2), as there is little relief in the catchment between Peak Hill and Neurie Plains. The parallel estimation is used to normalise the runoff values at Peak Hill after September 1967. 3.2. Rainfall data To ensure homogeneity of precipitation data, only rainfall data from a high quality long-term rainfall

Table 1 List of precipitation and runoff gauging stations used in the analysis Station number

Station name

Variable

Annual mean (mm)

Period

050031 421010 421076 421039

Peak Hill Peak Hill no. 1 Peak Hill no. 2 Neurie Plains

Precipitation Runoff Runoff Runoff

563.9 34.65 37.21 7.50

1890–1996 1925–1967 1967–1996 1959–1996

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Fig. 2. Double mass analysis of runoff at Peak Hill (Rph) vs runoff at Neurie Plains (Rnp) from May 1959 to August 1967 (solid line) and September 1967 to December 1975 (dashed line).

station (Peak Hill) (Lavery et al., 1992, 1997) are used in the analysis. The Peak Hill rainfall station is used for flood forecasting and warning by the Bureau of Meteorology, Australia, who use a rainfall–runoff model to forecast peak water levels at Peak Hill and correlate between upstream and downstream river gauge heights for locations further downstream. The Peak Hill rainfall station has been identified by Nicholls and Lavery (1992) as a station suitable for long-term monitoring of rainfall trends. It was shown to be representative of the inland region of New South Wales. 3.3. Rainfall and runoff anomalies The standardised anomaly R⬘ij , which removes seasonal fluctuations and short-term biases, is utilised in the continuous wavelet transform and spectrum analysis according to R⬘ij ⫽

(Rij ⫺ Rj ) ␴j

(1)

where Rij represents monthly averaged observed data in the year i and the month j, and Rj and ␴j are the longterm mean and standard deviation of each successive month j, respectively. Fig. 3 shows accumulated anomalies for both precipitation and runoff, where the standardised anomalies are summed over each successive month j, in each successive year i, i.e.:

冘冘 n

aij ⫽

m

R⬘ij

(2)

i⫽1 j⫽1

where n is the total number of years and m the total number of months in the year. Months with missing data have been ignored. A negative slope in Fig. 3 indicates rainfall or runoff values smaller than the long-term average and a positive slope indicates values greater than

average. It can be seen that precipitation at Peak Hill decreased during the period 1920 through to about 1949. Thereafter, an increase in precipitation values relative to the long-term average is seen, similar to results found by Nicholls and Lavery (1992), Cornish (1977), and Kraus (1963). Nicholls and Kariko (1993) found an increase in rainfall for five stations in east Australia, including Peak Hill, which is mainly due to an increase in the number of rainfall events rather than mean rainfall intensity. A warm period coincided with the greater rainfall in the Southern Hemisphere (Yu and Neil, 1991). Runoff series at Peak Hill (solid line) mirror the decrease in rainfall until the 1950s. The trend is reversed after 1950. However, runoff values at both Peak Hill and Neurie Plains (dashed line) experience a negative trend from the early 1960s to mid-1970s and during the 1980s, which do not correspond to the rainfall trends in the same time periods. These results imply a change in the catchment’s rainfall–runoff relationship due to a change in catchment conditions, such as changes in land use (e.g. clearing or agricultural practices); drainage network extensions (through gullying processes); changes in channel geometry or roughness; or changes in the catchment water storage capacity. 3.4. Large-scale circulation systems and east Australian rainfall ENSO is an important control in the interannual and intraseasonal variability of rainfall in eastern Australia. Although the term southern oscillation (SO) was introduced by Walker (1924), the classical paper by Bjerkness (1969) was one of the first to describe a physical explanation for ocean–atmosphere interactions underlying the phenomenon and introduced teleconnections. Since then, the impact of ENSO on climatic variability in eastern Australia has been well documented and is summarised by Allan et al. (1996). ENSO influences both the number of rain events as well as the intensity

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Fig. 3. Accumulated anomalies of standardised (a) precipitation at Peak Hill, September 1911–December 1996, and (b) runoff at Peak Hill, January 1925–December 1996 (solid line) and runoff at Neurie Plains, May 1959–December 1996 (dashed line).

(Nicholls and Kariko, 1993). Ropelewski and Halpert (1987) found the strongest relationship between ENSO and rainfall for inland Australia, while the relationship for rainfall in the coastal region is not well defined. Opoku-Ankomah and Cordery (1993) determined rainfall correlations with ENSO for most areas in New South Wales in all seasons, with changes in the relationship in summer and autumn, while McBride and Nicholls (1983) showed the weakest correlation in summer. During strong El Nin˜o phases (negative southern oscillation index (SOI) values), eastern Australia receives less than average rainfall during the austral winter to early summer period, while during strong La Nin˜a events (positive SOI values) rainfall patterns are enhanced and extensive flooding occurs over eastern Australia. The role of climate and climatic variability as a control on flooding can, therefore, be distinguished from anthropogenic and other controls by incorporating a large-scale circulation index in the wavelet time series analysis. Several large-scale indices are recognised as indicators of the southern oscillation, such as the Troup Index, the Wright Index, mean sea level pressure indices, and sea surface temperature indices (e.g. Wright, 1989, 1984; Trenberth, 1984; McBride and Nicholls, 1983; Chen, 1982). Troup’s SOI (Troup, 1965) has been

chosen for this analysis, as it is the most widely used index (Allan et al., 1991). Troup’s SOI is the standardised anomaly of the mean sea level pressure difference (⌬Pij) between Tahiti and Darwin, i.e.: SOI ⫽

10 ⫻ (⌬Pij ⫺ ⌬Pj ) ␴j

(3)

where ⌬Pj is the longterm average SOI for the month in question and ␴j the respective standard deviation. Troup’s monthly SOI time series from September 1911 to December 1996 are given in Fig. 4.

4. Methods of time series analysis: wavelet vs Fourier transform 4.1. Fourier transform The transformation of a signal s(t) is a mathematical operation that results in a different representation of the signal. Joseph Fourier (1768–1830) introduced the concept that an arbitrary function, even a function which exhibits discontinuities, could be expressed by a single

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Fig. 4.

Time series of Troup’s monthly SOI for September 1911 to December 1996.

analytical expression. The well known Fourier transform gives the spectrum of any periodic signal as a unique representation of a continuous sum of sinusoids of different amplitudes, frequencies and phases. Despite the functionality of the Fourier transform, especially in regard to obtaining the spectral analysis of a signal, it is not sufficient for representing non-stationary signals. This is due to the Fourier transform being based on the assumption that the signal to be transformed is periodic in nature and of infinite length. If the signal is well localised in one domain (e.g. the spatial domain) by using the Fourier transform, then it is badly localised in the other domain (i.e. frequency domain) and vice versa.

4.3. Continuous wavelet transform

4.2. Wavelet transform

C(a,b) ⫽

A wavelet analysis is performed in a similar way to the short time Fourier transform (STFT), in the sense that the signal is multiplied by a function, the wavelet, similar to the window function in the STFT, and the transform is computed separately for different segments of the time domain signal. Both time series transformations break a signal down into its constituent parts for analysis. Whereas the Fourier transform breaks the signal into a series of sine waves of different frequencies, the wavelet transform breaks the signal into its ‘wavelets’: scaled and shifted versions of the ‘mother wavelet’. The term wavelet, or small wave, refers to the fact that the window function is of finite length and is oscillatory. The window in the STFT is the same for all frequencies. However, the width of the wavelet is changed as the transform is computed for every single spectral component. The use of Fourier spectral analysis is limited for non-stationary data as it only reveals what frequency (spectral) components exist in the signal. Wavelet analysis provides a time scale representation of the signal. Thus, wavelets can perform a local analysis, revealing aspects of data that other signal analysis techniques miss, such as trends, abrupt changes, breakdown points and discontinuities.

The continuous wavelet transform (CWT) is defined as the sum over all time of the real signal s(t) multiplied by the scaled (stretched or compressed), shifted versions of the wavelet function ␺, i.e.:

冕 ⬁

C (scale, position) ⫽

s(t)␺ (scale, position, t)dt

(4)

⫺⬁

or

冉 冊

1 t⫺b dt 兰s(t)␺ √a a

(5)

(e.g. Ogden, 1997; Daubechies, 1992; Chui, 1992) where the wavelet coefficients C are the result of the CWT of signal s(t). The scale or dilation parameter, a, scales a function by compressing or stretching it, while b is the translation of the wavelet function along the time axis. The parameters a and b vary continuously over ᑬ (a⫽0). For a small scale (兩a兩¿1), the wavelet is a very highly concentrated, shrunken version of the mother wavelet with frequency contents mostly in high frequency range. Conversely, for 兩a兩À1, the wavelet is stretched and has mostly low frequencies. Thus, a small scale (兩a兩 ⬍ 1) implies detailed view or higher resolution, and a large scale (兩a兩 > 1) implies global view of the image or lower resolution. By varying a, CWT can zoom in on very short-lived high frequency phenomena. Changing the translation parameter b as well moves the time localisation centre. The CWT, therefore, is continuous in that it can operate at every scale and is also continuous in terms of shifting over the full domain of the analysed signal. The appropriate wavelet should have a similar pattern to the signal. For this reason, the wavelet function used in the present analysis is the Morlet (1983) wavelet (see

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Fig. 5), as it reveals peaks and troughs in wavelike signals such as rainfall and runoff records. The complex valued Morlet function (a modulated Gaussian) can be approximated by −1/4 −ict −t2/2

␺(t) ⫽ ␲

e

e

(6)

with c ⫽ ␲√2/ln2 (after Daubechies, 1992). A property of any wavelet is that the integral of the wavelet ␺ is zero (兰␺(t)dt ⫽ 0). Rainfall and runoff series require, due to the temporal nature of the signals, time–frequency analyses to reveal their spectral characteristics as a function of time. Continuous wavelet analysis is, therefore, a better signal transformation than the Fourier transform in analysing rainfall–runoff trends. Wavelets can be used for data characterisation and measuring local maxima and minima as a function of time and duration. As the wavelet is moved stretched and compressed along the time axis, the shape of the signal is compared to that of the wavelet. Transform coefficients are calculated for the match between signal and wavelet. This process is repeated with a wavelet of similar shape, but of shorter or longer duration. Therefore, some spectral resolution can be achieved by selection of the wavelet size, and some temporal resolution follows from the location of the wavelet relative to the signal. The largest values of the transform are obtained when the wavelet duration matches the period of the signal. Transform coefficients can be shown graphically for the various scales, with the time axis common to the raw data. Individual peaks and troughs of the signal as well as its frequency can be identified. It is this compromise between the temporal domain and the spectral domain that makes wavelet transforms superior over Fourier transforms for studying nonstationary, multiscale signals such as rainfall, runoff and large-scale circulation indices.

Fig. 5.

The real part of the Morlet wavelet.

289

5. Trends and relationships utilising CWT 5.1. Rainfall–runoff analysis The wavelet analysis is applied to the standardised anomalies of rainfall and runoff records from Peak Hill. The raw signal for continuous wavelet analysis is dyadic, i.e. to the power 2, which in this case encompasses 1024 (210) months from September 1911 to December 1996. The runoff signal is extended with the long-term anomaly from 1911 to 1925. The trend component is assumed to be caused by long-term climatic changes and gradual changes in the catchment’s response owing to land use changes. The wavelet maps (Figs. 6 and 7) show the real part of the CWT for both rainfall and runoff at Peak Hill. A wavelet map is a graphical representation of the continuous wavelet coefficients C, which represent how closely related the wavelet is with each section of the signal. The continuous wavelet coefficients of the signals have been computed at real, positive scales (32 voices), using the Morlet wavelet. The higher the voice used in the analysis, the more stretched the wavelet, the longer the part of the signal with which it is being compared, and thus the coarser the signal features being measured by the wavelet coefficients. That is, a high voice is used to reveal long-term changes in the signal rather than rapidly changing details and vice versa. The intensity at each x– y point represents the magnitude of the wavelet coefficients C. A high correlation between the Morlet wavelet and the signal combined with a large fluctuation of the signal returns large values of the wavelet transform coefficients; in Figs. 6 and 7 this is reflected in the light colours. Dark colours relate to troughs or low values of the transform coefficients, where the signal and the wavelet are out of phase. The colours are scaled between zero and the maximum absolute value of the coefficients. The Morlet wavelet isolates local minima and maxima of the signal. The fine granularity in the bottom part of the scale reflects seasonal peaks in the precipitation and runoff data. For rainfall, the interannual periodicity changes from 4 to 2.5 years from 1911 to 1935 (feature I in Fig. 6). After that time, there is a distinct change to a 2 year cycle from 1945 to 1960 and from 1970 to 1985. In the 1990s, the rainfall periodicity moves again to 2.5 years. The runoff signal shows apparent 2 to 2.5 year periodicities in the time periods 1925 to 1935, 1945 to 1965, in the 1970s and 1990s (feature I in Fig. 7). The major flood events in the Bogan River catchment in 1925, 1950, 1955, 1976 and 1990 are readily discernible in the CWT for runoff at the seasonal scale (highlighted by the circles in part I of Fig. 7). Interannual (2 to 3.5 and 8 to 10 years), and interdecadal (10 to 20 years) frequencies are also recognisable. The variability over time of interannual and interdecadal periodicities changes dramatically for both rainfall and runoff at around 1950

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Fig. 6. Real part of CWT for standardised precipitation anomaly at Peak Hill using Morlet 32 voices. The small figures highlight frequency changes of dominant periodicities.

Fig. 7. Real part of CWT for standardised runoff anomaly at Peak Hill using Morlet 32 voices. The small figures highlight frequency changes of dominant periodicities.

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and 1960, respectively. The 8 to 10 year periodicity (feature II in Figs. 6 and 7) becomes less apparent around the 1950s and changes to lower scales. The 10 to 20 year interdecadal periodicity (feature III) becomes more prominent, with the highest intensity changing from 19 years in the 1940s to 10 years in the late 1990s.

Fig. 9. Wavelet spectrum for standardised runoff anomaly at Peak Hill using Morlet four voices: (a) 1911–1996, (b) 1911–1949, and (c) 1950–1996. The dashed line indicates the Markov 95% confidence limit.

Fig. 8. Wavelet spectrum for standardised precipitation anomaly at Peak Hill using Morlet four voices: (a) 1911–1996, (b) 1911–1949, and (c) 1950–1996. The dashed line indicates the Markov 95% confidence limit.

CWT can analyse both high and low frequency signals in the original data. Where the CWT analysis identifies patterns in the temporal domain, the dominant climatic component in the hydrological record can be specified using the wavelet variance. The wavelet variance is the integration of the wavelet transform over the temporal

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Fig. 10. Real part of CWT for Troup’s SOI, using Morlet 32 voices. The small figures highlight frequency changes of dominant periodicities.

record. To identify dominant components, wavelet spectrums for precipitation and runoff are analysed for the complete period 1911–1996, as well as for 1911–1949 and 1950–1996 (see Figs. 8 and 9), to provide further insight into the change in hydrologic regime at around 1950. Results using the Morlet wavelet (four voices) are shown. The smaller voice is used to improve the visualisation of dominant frequencies at monthly intervals. The 95% confidence limit shown (dashed line) is based on the Markov ‘red noise’ null hypothesis continuum, and indicates which peaks in the power spectrum are statistically significant. Similarities as well as differences between the rainfall and the runoff wavelet spectrum are apparent. The dominant, significant, frequency for both precipitation and runoff is 27 to 32 months for the complete time period 1911 to 1996 (Fig. 8(a) and Fig. 9(a)). During that time period, the runoff spectrum also shows a 45–54 month peak. From 1911 to 1949, the significant peak for rainfall is between 45 and 54 months (Fig. 8(b)). The peak in the runoff spectrum remains at 27 to 45 months (Fig. 9(b)). A change occurs after the 1950s, when the peak for rainfall is between 27 and 32 months (Fig. 8(c)), while the dominant frequency for runoff is 45– 64 months (Fig. 9(c)). These features indicate a change in the hydrologic regime.

5.2. SOI analysis Preliminary results for the real part of the CWT for Troup’s SOI (Fig. 10) show some similarities with the CWT for rainfall and runoff (Figs. 6 and 7, respectively) in the strengthening of the interdecadal signal after the 1950s (feature III). Before the 1950s the 2.5 to 5.5 year cycle is dominant in the SOI series, whereas after 1950 there is a shift to a 9 to 20 year periodicity. The quasibiennial oscillation (QBO) (1.5 to 3 year) time scales are dominant throughout the time period 1925 to 1996 (feature I). The ENSO (3 to 7 year) time scales, however, intensify from 1935 to 1960 and again from 1960 to 1996, compared with the period 1911–1935. Similar results have been found for the Australian tropics, where relationships between Troup’s SOI and rainfall in the months between September and April were stronger during the period from 1950–1989 relative to 1910–1949, suggesting a change in large-scale atmospheric circulation patterns (Suppiah and Hennessy, 1996). The SOI wavelet spectrum (Fig. 11) displays a broad peak. The dominant frequencies in the SOI spectrum over the complete period 1911–1996 (Fig. 11(a)) are 27 months and 45 to 64 months, corresponding to periodicities described by Rasmusson and Carpenter (1982). In the time period from 1911 to 1949 (Fig.

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Nicholls and Kariko (1993), while Rasmusson et al. (1990) identified a biennial mode with periods near 24 months and a lower frequency concentration of variance in periods of four to five years. QBOs in rainfall over Australia have been identified (e.g. Trenberth, 1975; Wright, 1974a,b) and the interannual variability of the QBO is expected to have a dominant frequency close to those frequencies seen in the rainfall–runoff analysis. The relationship between SOI and rainfall–runoff events will be evaluated further in additional analyses utilising the wavelet cross-covariance, to determine whether the dominant spectra of rainfall, runoff and SOI are in phase with each other and to determine lag times.

6. Conclusions and future work

Fig. 11. Wavelet spectrum for Troup’s SOI using Morlet four voices: (a) 1911–1996, (b) 1911–1949, and (e) 1950–1996. The dashed line indicates the Markov 95% confidence limit.

11(b)), 27 and 64 month spectrums are dominant, whereas from 1950 to 1996 (Fig. 11(c)) the 27 month spectrum is more pronounced. From the wavelet spectrum it can be concluded that the southern oscillation has an influence on rainfall–runoff events (with a dominant spectrum of 27 to 32 months) at short (QBO) time scales only. These findings are in agreement with those of

Rainfall, runoff and SOI show a change in dominant interannual scales (8 to 10 and 5 to 10 years) to interdecadal time scales (10 to 20 years) around 1950. The interdecadal scales seem to be moving towards smaller scales in the late 1990s. This suggests that the frequency of extreme events, such as floods and droughts, is increasing in the Bogan River catchment. If SOI indeed influences the number and intensity of rain events (Nicholls and Kariko, 1993) and is thus inversely correlated to eastern Australian rainfall (e.g. Zhang and Casey, 1992; Stone and Auliciems, 1992), increased occurrences of wet and dry periods over eastern Australia can be expected. The latter generalisation will be investigated for different seasons using data from representative high quality precipitation stations identified by Lavery et al. (1992, 1997). The frequencies where rainfall, runoff and SOI are strongly correlated at a monthly time scale in the spectrum analysis are assumed to be a measure of climate induced catchment response. These scales (27– 32 months) will be removed from the runoff signal and the signal reconstructed. Dominant scales in the reassembled filtered signal may be related to other factors controlling runoff—the most important of which is believed to be land use. Land use, riparian vegetation and channel condition changes are currently being evaluated using historical records (from explorers and surveyors, portion plans, etc.) and aerial photographs. Wavelet analysis can be used to isolate the climatic component of the hydrological cycle from other trends such as land use changes. It is, therefore, a first step in the detection of streamflow response to climate change, especially detecting impacts of large-scale circulation phenomena. Although precipitation, linked to the southern oscillation, is the only climatic component examined in the present analysis, future work may include temperature records as an available surrogate for evaporation. Having established a set of relationships, the likely effects of past, present and future climate and land use

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variations will be presented for gauged subcatchments. It is hoped that these relationships will be robust enough to be applicable to ungauged subcatchments. As most practical procedures in hydrologic design and analysis assume stationary conditions, the wavelet analysis presented here may decrease the uncertainty in design and analysis, thereby aiding in floodplain management, in estimating flood heights for design standards for engineering, and in planning for the costs and impacts of future flood events for insurance industries, businesses and communities.

Acknowledgements I would like to thank Drs Peter Mitchell, Neil Holbrook, Ivan Khu¨nel and Christopher Wooldridge for their ideas, assistance in the analysis of the data and comments on the paper. The data used in the analysis were supplied by the NSW Bureau of Meteorology.

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