Flood variability east of Australia’s Great Dividing Range

Journal of Hydrology 374 (2009) 196–208

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Flood variability east of Australia’s Great Dividing Range Paul Rustomji *, Neil Bennett, Francis Chiew CSIRO Land and Water, GPO Box 1666, Canberra, 2601 ACT, Australia

a r t i c l e

i n f o

Article history: Received 21 December 2007 Received in revised form 11 April 2009 Accepted 1 June 2009

This manuscript was handled by K. Georgakakos, Editor-in-Chief, with the assistance of Andreas Bardossy, Associate Editor Keywords: Flood variability Australia Bootstrap Flood frequency L-moments Power law scaling

s u m m a r y The variability of flow in river channels influences the spatial and temporal variability of many biophysical processes including the transport of sediment and waterborne pollutants and the recruitment of aquatic animals and plants. In this study, inter- and intra-basin patterns of flood variability are examined for catchments east of Australia’s Great Dividing Range. Three measures of flood variability are explored with uncertainty quantified using bootstrap resampling. The two preferred measures of flood variability (namely a flood quantile ratio and a power law scaling coefficient) produced similar results. Catchments in the wet tropics of far north Queensland experience low flood variability. Flood variability increased southwards through Queensland, reaching a maximum in the vicinity of the Fitzroy and Burnett River basins. The small near-coast catchments of southern Queensland and northern New Wales experience low flood variability. Flood variability is also high in the southern Hunter River and Hawkesbury–Nepean basins. Using L-moment ratio diagrams with data from 424 streamflow stations, we also conclude that the Generalised Pareto distribution is preferable for modelling flood frequency curves for this region. These results provide a regional perspective that can be used to develop new hypotheses about the effects of hydrologic variability on the biophysical characteristics of these Australian rivers. Crown Copyright Ó 2009 Published by Elsevier B.V. All rights reserved.

Introduction The flow of water in river channels influences many biophysical processes including the transport of sediment and waterborne pollutants, recruitment of aquatic animals and plants and the opening regime of estuaries. It follows that variability in river flow will be an important control upon the variability of these related processes, particularly where non-linear responses to streamflow occur. Characterising the variability of flow in a river can, in some senses, be more important than characterising the mean or modal state. The importance of hydrologic variability as a distinct phenomena has long been recognised in the field of fluvial geomorphology. Wolman and Miller (1960) noted that as flow variability increases because of climate or decreasing catchment area, a larger percentage of a stream’s total sediment load tends to be transported by less frequent flows. Baker (1977) highlighted the importance of process thresholds for increasing the importance of large magnitude, infrequent events relative to more commonly occurring, smaller flows. Baker (1977) also suggested that the high hydrologic variability experienced by many small streams in the semi-arid areas of Texas that he studied meant that they had higher potential for ‘catastrophic’ (i.e. large magnitude) channel change. Similar arguments implicating hydrologic variability with dramatic channel change * Corresponding author. Tel.: +61 2 6246 5810. E-mail address: [email protected] (P. Rustomji).

have been made in the Australian context, particularly for the sand bed streams common to the coastal valleys of south eastern Australia by Erskine and Melville (1983), Erskine (1993, 1994) and Rutherfurd (2000). Nanson and Erskine (1988) and Rustomji (2008) have suggested that, rather than being adjusted to some long term mean hydrologic condition, a more widespread mode of behaviour of many south eastern Australian streams is a cyclic evolutionary model characterised by periodic channel enlargement in response to large magnitude, infrequent flows, followed by gradual channel contraction driven by smaller, more frequent events. The role of flow variability in the field of lotic ecology is also well documented. Poff and Allan (1995) show fish assemblage in eastern United States is related to hydrologic variability, with hydrologically variable environments supporting resource generalists while less variable hydrologic habitats supported a higher proportion of specialist species. Jowett and Duncan (1990) show flow variability affects periphyton and aquatic invertebrate communities in New Zealand. Jassby et al. (1993) found flow variability in the Sacramento and San Joaquin Rivers to exert a strong control on the rate of organic carbon delivery to San Francisco Bay in the United States. Understanding hydrologic variability is particularly important in the Australian context, given Australia’s high hydrologic variability relative to the rest of the world (Finlayson and McMahon, 1988; Peel et al., 2004). Given the importance of hydrologic variability, it is important to be able to characterise it in a sound

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P. Rustomji et al. / Journal of Hydrology 374 (2009) 196–208

manner. In this paper we focus on the variability of flood peaks (as distinct from a more general analysis of flow variability which would encompass a greater broader portion of the flow spectrum) and seek to achieve three objectives. Firstly, to evaluate three published measures of flood variability. Secondly, to examine whether uncertainty in these flood variability measures can be usefully quantified using bootstrap resampling techniques. This is particularly important given that flood variability analyses (such as those undertaken here) commonly utilise only a small subset of flow peaks (such as the annual maximum or a peaks-over-threshold flood series) from the full flow spectrum. Thus, in dealing with the extremes of a dataset, it is important to evaluate the robustness of a flood variability statistic to the inclusion or exclusion of different events from the sampled period. Thirdly, we present a regional, inter-basin assessment of flood variability for catchments east of Australia’s Great Dividing Range. This regional perspective, apart from contributing to objectives one and two, provides a basis for hypothesis generation for other studies where flood variability is considered of relevance. This regional perspective also provides a context within which the findings of other research can placed. Study region We examine catchments east of Australia’s Great Dividing Range, from northern Queensland to eastern Victoria (Fig. 1). The Great Dividing Range runs along Australia’s east coast and rises to maximum elevation of 2228 m, though large areas are less that 500 m above sea level. The Range generally constitutes the western (or northern in the case of some Victorian catchments) catchment boundary of the study region. Landscape relief is variable, ranging from over 1000 m along parts of the Range in New South Wales and northern Queensland, to much lower levels in some of the larger catchments such as the Burdekin and Fitzroy basins. The gauging stations selected here range in latitude from 12° to 38° south, and consequently experience large climatic differences. Drainage basins north of the Fitzroy River (basin 130) experience a strongly summer dominant rainfall pattern and tropical cyclone activity. Between the Fitzroy basin and the central New South Wales coast, a less intense summer precipitation dominance prevails, whilst southern New South Wales and Victoria experience a relatively uniform (though variable) seasonal precipitation regime (Bureau of Meteorology, 2007) though runoff in Victoria predominantly occurs in winter. East-coast cyclones represent important flood-generating weather systems for coastal eastern Australia from southern Queensland through to eastern Victoria (Holland et al., 1987; Hopkins and Holland, 1997). Mean annual rainfall varies from 400 mm/ year in the inland regions of the Fitzroy and Burdekin Rivers to greater than 3200 mm/year in the wetter parts of northern Queensland. Southern Queensland and New South Wales typically receive mean annual rainfall of 600–1200 mm/year. Catchment vegetation and geology are obviously variable across such a large study region. Gauging stations have been grouped by Australian Water Resources Commission (AWRC) drainage basin. Note that AWRC DrainageDivision 1 (the North East Coast Division with gauge numbers starting with 1) extends north of the Queensland border with Division 2 (the South East Coast Division, with gauge numbers commencing with 2) extending southwards. Within each AWRC drainage-division, basin numbers increase southwards.

Data and methods Station selection In this study we are concerned with characterising the variability in the magnitude of peak flood discharge for (largely)

197

unregulated gauging stations (generally) of at least 20 years record from catchments east of Australia’s Great Dividing Range. In a synoptic study such as this it is desirable to be as inclusive as possible with regards to data selection. Hence there is a need for some pragmatic flexibility in the station selection criteria. The phrase ‘largely unregulated’ has been used as in the case 46 stations (just over 10% of the total number of 424 stations), some upstream flow regulation structures (such as dams and reservoirs) are present. A subjective assessment was made that for these stations any flow regulation was unlikely to exert a major influence on the flood record. This could be due to the period of regulation covering a relatively short period of the discharge record and/or small upstream storage volumes relative to flood discharges at a downstream gauging station. With regards to the record length, some stations in far northern Queensland have less than 20 years data. In order to capture information about this region the 20 year record length criteria was waived. One of these Queensland stations has 14 years of data and seven have either 18 or 19 years. The flow data supplied by the various stage agencies has been taken at face value. It is likely that discharge estimates for some of the largest floods in particular may be considerably in error due to either extrapolation of a gauge’s rating curve substantially beyond the maximum gauged stage or to complex and ungauged overbank flow patterns at a gauging station. As our variability metrics are calculated on aggregated flood data, extreme points, even if erroneous, would generally only represent a minority of the data and are unlikely to dominate the calculated metrics. Additionally, the use of bootstrap resampling to quantify uncertainty in the variability measures appears to cover what would be the likely uncertainty estimate (perhaps ±100–200% of the nominal value) for large floods at locations where there may be little constraint on the upper end of the station’s rating curve. By way of summary, the median start year was 1965 (with 25% of records commencing before 1949), the median (mean) record length was 38 (42) years and in total, 17,811 station-years of data have been analysed across the 424 stations. Fig. 2 shows the period of record for each station within each AWRC basin. Selection of flood peaks Discharge data (m3 s1) were obtained from the hydrographic agencies of New South Wales, Queensland and Victoria, each of which has its own data collection and archival methods. It is important to point out that the nature of stream gauging has changed over time. What are now automatically recorded ‘instantaneous’ (i.e. 15 min interval) discharge records were preceded in the pre-electronic era by discharge values calculated from manually read stage height observations. To derive a subset of flood peaks from these mixed records of streamflow two major issues were considered: (1) theoretical concerns about how to extract flood peaks from a mixed time series of river flow, and (2) practical concerns related to the characteristics of data collection and storage by independent hydrographic agencies, each with their own data handling protocols. The annual maximum flood series is one flood series commonly used in analysing streamflow data. It comprises the largest instantaneous discharge observation of each water year and has the advantage of being relatively easy to compute. However, the annual maximum series has the drawback that it will exclude secondary flood events in a given year despite them potentially being larger in size than smaller events in another water year. However, its ease of computation has made it a widely used flood series and has been adopted here for the calculation of the Flash Flood Magnitude Index (FFMI) proposed by Baker (1977), as described below.

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A

B

AWRC Basin Name

102 104 105

116

120

130

Queensland 136 143

145 203

204 206

New South Wales 210

209 212 215 222

Victoria 226

224

219 221

Fig. 1. Location of gauging stations used to characterise flood variability in eastern Australia, shown along with Australian Water Resources Commission drainage division boundaries and names.

A hydrologically sounder approach is to conduct a peaks-overthreshold analysis to identify statistically independent flood peaks (Lang et al., 1999). In a peaks-over-threshold approach, a threshold discharge is selected and discharge observations exceeding this threshold are classified as ‘‘floods”. As a single flood (or a single wet season) may have multiple peaks, the second step in a peaks-over-threshold approach is to specify a minimum time period for which discharge must be below the threshold value for a sequence of floods to be considered independent. The two critical issues are thus selecting the value of the threshold and selecting a suitable time period either side of a peak (the ‘inter-flood period’) to maximise independence of flood peaks. We followed the recommendation of Lang et al. (1999) that a range of threshold values be

explored and for each station have conducted a peaks-over-threshold analysis using a stepped sequence of thresholds. Lang et al. (1999) recommend that the exact value of the threshold be chosen such that the distribution of the mean exceedence of flood peaks above the threshold range is a linear function of threshold magnitude and, secondly, the selection of the largest threshold within this range that gives a mean number of floods per year greater than two. The thresholds adopted for this study scale positively with catchment area, though they can vary by a factor of 100 for any given catchment area, reflecting different rainfall and runoff characteristics across the study region. In general and due to historic variations in stage height recording methodology, instantaneous monthly maximum data

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P. Rustomji et al. / Journal of Hydrology 374 (2009) 196–208 2010

2000

1990

1980

1970

Year

1960

1950

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1900

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111

106 107 108 110

102 104 105

1890

AWRC Basin Number Fig. 2. Start and finish year of each gauging station record shown as vertical bars. The shaded grey bars show alternate AWRC drainage basins.

were available for longer periods of record than were daily maximum data. Hence we have used monthly maximums to characterise flood peaks using a peaks-over-threshold approach and stipulated a minimum inter-flood period of one calendar month between floods. Note that the inter-flood period pertains to the period between the time of the falling limb of the previous flood crossing the threshold and the time when the rising limb of the next flood crosses the threshold, not the time between flood peaks. Using this approach, the mean maximum number of floods per year per station was 1.8 for the 424 stations (interquartile range: 1.6–2.0). The peaks-over-threshold analysis was conducted using R (R Development Core Team, 2005) using the ‘‘pot” (peaks over threshold) and ‘‘decluster” algorithms in the Extreme Values in R package (McNeil, 2007). We also conducted a peaks over threshold analysis with a 30 day interflood period for stations in New South Wales and Queensland for which daily maximum discharge observations (as opposed to monthly maximum observations) were available. The resulting flood series was essentially indistinguishable for events with a recurrence interval greater than one year to that derived using monthly maximum data with a one calendar month inter-flood period. This indicates that the use of the monthly maximum observations did not lead to a significant loss of information relative to using daily data. Plotting positions For two of the flood variability measures the data are examined within a magnitude–frequency framework which requires ‘plotting positions’ (or estimates of the average return period) to be defined for the observational data. Discharge estimates are ranked in descending order and an average recurrence interval t (years) for each event is estimated according to:

t¼

n þ 0:2 r  0:4

ð1Þ

where n is the number of years of record and r is the sample rank (Cunnane, 1978). The flood with a recurrence interval of t years is denoted Q t and T denotes the estimated average recurrence interval of the largest observed flood.

Measures of flood variability Three measures of flow variability identified from the literature are considered in this study: 1. A flood quantile ratio calculated from a fitted probability density function 2. Power law scaling coefficient 3. The Flash Flood Magnitude Index For each statistic, bootstrap resampling techniques (Efron and Tibshirani, 1993; Davison and Hinkley, 1997) have been used to quantify uncertainty in each flood variability statistic. The flood variability statistic calculated from the original data is denoted the ‘primary’ value. Bootstrap resampling involves randomly drawing observations with replacement from the sample population, recalculating the statistic of interest and repeating this process multiple times (in this case 1000). In each case, the number of resampled values was equivalent to the number of original data points. An empirical probability density function can be defined from the distribution of the bootstrapped statistic and its modal value taken as the bootstrapped statistic estimate. The uncertainty in each flood variability statistic is represented using bootstrap percentile confidence intervals (as described by Efron and Tibshirani, 1993). This involves taking the 5th and 95th percentiles of this empirical probability distribution to provide the bounds for a 90% confidence interval. Note in this manuscript we use the following notation: Q ½i represents a time series ði ¼ 1; 2; . . . ; NÞ of discharge ðQ Þ, where N is the number of years of record of an annual maximum series, though it will likely differ when using a peaks-overthreshold derived flood series. Flood quantile ratio A flood quantile ratio is the ratio of the magnitude of a relatively infrequently occurring flood quantile (such as the 1 in 50 year recurrence interval event, Q 50 ), to that of a more frequent event. Pickup (1984), contrasted the Q20:Q2 ratio of 62 of Papua New Guinean Rivers with Q20:Q2 ratios of 4–8 for a number of Australian

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Rivers. Kemp (2004) also noted that the normalised (i.e. Qt,. . .,T:Q2.33) flood frequency curve for the Lachlan River, which drains the western slopes of the Great Dividing Range in southern New South Wales was notably steeper than curves from many other regions of the world. Whilst the choice of the specific quantiles adopted for comparison is somewhat arbitrary (though as is shown below of limited importance), a more critical issue is the selection of an appropriate probability density function to represent the flood record. Both in Australia and north America, the Pearson Type III distribution fitted to the log-transformed flood series (referred to as the log PearsonIII distribution) has traditionally been recommended for flood frequency modelling (see for example Pilgrim and Doran, 1987). However, Vogel et al. (1993) observed that other statistical distributions may potentially be more appropriate for Australian data. Here, L-moment ratio diagrams (Hosking, 1990; Vogel and Fennessey, 1993) have been used to select an appropriate probability density function for calculation of flood quantiles. A sample of flood peaks can be characterised by four statistical moments: the first and second moments are the mean value and standard deviation, which essentially indicate the magnitude and variability of the distribution, yet provide little information about which particular theoretical distribution is closest to the data. The third and fourth moments, being the skewness and kurtosis, are the principal discriminants of the differing shapes of different probability density functions, hence they can be used to select a probability density function that most closely resembles the shape of the data. L-moments, being linear combinations of the sample data (as opposed to the exponentiated combinations of traditional moments) have also been argued to be more robust estimators of a distribution’s shape as they are less sensitive to extreme events (Vogel and Fennessey, 1993). Power law scaling coefficient Power–law relationships have been found to be suitable for modelling magnitude–frequency distributions for a number of natural hazards, including floods (see and references therein Malamud and Turcotte, 2006). Malamud et al. (1996) and Malamud and Turcotte (2006) suggest that power law distributions may be preferable to other probability density functions for predicting the magnitude of large, infrequent floods. These two studies plus Kidson and Richards (2005) show good agreement between the predicted magnitude of floods with recurrence intervals derived from dating of palaeoflood sediments and corresponding discharge estimates derived using hydraulic modelling. One characteristic noted by Malamud and Turcotte (2006) is that power– law relationships typically fit partial duration series flood records better than annual maximum flood records, suggesting that the former are better statistical sample of the population of flood peaks. Malamud and Turcotte (2006) also show that the power– law distribution of a partial-duration flood series is related to that of the distribution of daily streamflow values. Power law scaling assumes the following formula describes the distribution of flood peaks:

Qt ¼ C  t

a

ð2Þ

where C and a are regression coefficients, calculated in this case by least squares regression of the base ten logarithms of the peaksover-threshold (monthly) flood series with the empirical recurrence interval estimates. Malamud and Turcotte (2006) introduce a ‘floodfrequency factor’ F, defined to be the ratio of the peak discharge over a 10-year interval to the peak discharge over a 1-year interval. Because of the scale-invariance of the power–law distribution (at least for a certain range of discharge magnitudes), F should theoretically also be the ratio of the 100-year peak discharge to the 10-year peak discharge:

F¼

Q 10 Q 100 ¼ ¼ constant Q1 Q 10

ð3Þ

The parameters F and a are related by

F ¼ 10a

ð4Þ

Hence a and F capture the magnitude of infrequently occurring floods relative to those occurring on a more common basis. However, it is often observed that distinct power–law scaling relationships are observed over different ranges of recurrence intervals, which is argued to be related to the different physical process responsible for generating the different magnitude events (Kidson and Richards, 2005). This is observed in much of the data examined here, with distinct a values apparent for events either side of a recurrence interval of approximately 3–5 years (see Fig. 3). Here, the power law scaling parameter a is calculated on floods with a recurrence interval greater than 3 years and Eq. (3) should in this case be more correctly written as:

F¼

Q 30 Q 300 ¼ ¼ constant Q3 Q 30

ð5Þ

Flash Flood Magnitude Index The Flash Flood Magnitude Index (FFMI), first proposed by Baker (1977), comprises the standard deviation of the base 10 logarithms of the annual maximum flood series, Q ½1; 2; . . . ; n, where n is the number of years of record. The FFMI is calculated as:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðlog Q ½i  log Q Þ FFMI ¼ n1

ð6Þ

where Q is the mean of the annual maximum flood series. The FFMI has been used to characterise flood variability in Australian streams by Erskine and Melville (1983); Erskine (1993, 1994). One characteristic of this measure is that low magnitude floods contribute relatively strongly to this index, yet the geomorphic significance of very low magnitude ‘‘floods” is much less than for high magnitude floods and in principle there is no lower limit to river discharge. This characteristic is particularly important in the Australian context where a large number of ephemeral rivers or rivers that experience multi-year periods of low or zero flow exist. Methods summary Fig. 3 illustrates the three methods used and the variability identified by the bootstrap sampling (represented by the results of the first 100 bootstrap simulations). For each flood variability statistic, the empirical probability density function based on the 1000 bootstrap simulations is presented. The parts of the empirical probability density functions beyond the 5th and 95th percentiles have been shaded. These distribution quantiles constitute a 90% bootstrap percentile confidence interval for each statistic.

Results Flood quantile ratios L-moment ratio diagrams Fig. 4 shows L-moment ratio diagrams for the annual maximum flood series, the base 10 logarithms of the annual maximum series and the peaks-over-threshold (monthly) flood series. Of the six potential distributions examined for flood frequency modelling, the Generalised Pareto Distribution clearly fits both the annual maximum and peaks-over-threshold (monthly) data the best. Consequently it was used to estimate the selected distribution quantiles for calculation of flood quantile ratios.

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P. Rustomji et al. / Journal of Hydrology 374 (2009) 196–208 104

105

203005

) Q (m s

10

3 −1

) 3 −1

)

103 102

observed floods primary curve fit bootstrapped curve fit

1

100 101 Average Recurrence Interval (Years)

101

1

10 10−1

102

2

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6 Q50 : Q2

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0 10

203005 N = 20

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) 3 −1

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103 102

observed floods primary power law fit bootstrapped power law fit

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100 101 Average Recurrence Interval (Years)

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Fig. 3. Illustration of methods. The top two rows show fitted flood frequency curves and empirical probability density functions for Q50:Q2. The middle two rows show the same but for the power law scaling coefficient whilst bottom two rows illustrate bootstrapped flood peak selection used to calculate FFMI. For the power law scaling graph, N represents the number of data points used to fit the curve.

Internal consistency of flood quantile ratios The Q50:Q2 flood quantile ratio, derived from fitting a Generalised Pareto distribution to the monthly peaks-over-threshold flood series has been used to quantify flood variability. The flood variability results appear relatively insensitive to the choice of specific quantile ratio, with strongly positive Kendall (rank-based) correlation coefficients between the Q20:Q2, Q50:Q2 and Q100:Q2 ratios, as listed in Table 1 and shown in Fig. 5. When the distributions of Q50:Q2 and Q100:Q2 are linearised with respect to Q20:Q2 (through square-root transformation), Pearson correlation coefficients between these ratios all exceeded 0.96. Results obtained from using the annual maximum flood series are also comparable to those derived from the peaks-over-threshold (monthly) series, with the Kendall correlation coefficient between the above three flood quantile ratios derived from the two flood series all >0.82. Pearson correlation coefficients between the modal bootstrap flood

quantile ratios and the primary values exceeded 0.96 for the peaks-over-threshold flood series for all flood quantile ratios and all correlations were highly significant. Regional patterns of Q50:Q2 flood quantile ratio Fig. 6 (top panel) shows the distribution of the Q50:Q2 flood quantile ratio calculated from the peaks-over-threshold (monthly) flood series and grouped by AWRC basin, whilst Fig. 7 shows the spatial distribution of this statistic. Low flood variability is observed in far north Queensland (AWRC basins 6 114) and along the small drainage basins in close proximity to the coast north of the Burdekin River (basin 120). Q50:Q2 flood variability at a basin scale rises southwards, reaching a maximum in central and southern Queensland, with the main stem of the Burnett River (basin 136) showing consistently high flood variability. Flood variability is lower in the southern most Queensland basin (145) and in

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0.6 0.5

0.7

Generalised Logarithmic Generalised Extreme Value Generalised Pareto Log Normal Pearson Type III Annual Maximum Series

L−Kurtosis

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Log Pearson III Annual Maximum Series

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Fig. 4. L-moment ratio diagrams for the annual maximum series (left), log annual maximum series (centre) and peaks-over-threshold (monthly) flood series.

nearby basins of northern New South Wales (basins 201–203). The Hunter River basin (number 210) shows a wide range of flood var-

iability with some particularly high Q50:Q2 values found along the main stem of the Hunter River. Q50:Q2 flood variability generally decreases southwards of the Hunter valley, though is moderately high for some New South Wales stations of the Snowy River catchment (basin 222).

Table 1 Kendall correlation coefficients for three flood quantile ratios derived from the peaksover-threshold (monthly) flood series. Note that the Pearson correlation coefficients pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi between the Q 50 : Q 2 Q 100 : Q 2 and Q20:Q2 measures all exceed 0.96. Q50:Q2

Q100:Q2

1.00 0.90 0.85

0.90 1.00 0.93

0.85 0.93 1.00

10

15

20

25

8

10

12

5

Internal consistency of power law alpha coefficient The value of the a coefficient is relatively insensitive to the selection of flood series, with the Kendall correlation coefficient between primary alpha values calculated using the monthly peaks over threshold and primary a values from annual maximum flood

15

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0

Q20:Q2 Q50:Q2 Q100:Q2

Q20:Q2

Power law scaling coefficient

2

4

6

8

10

12

0

10

20

30

40

Fig. 5. Pairs plot of flood quantile ratios Q20:Q2, Q50:Q2 and Q100:Q2 derived from the peaks-over-threshold (monthly) flood series.

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30

Q50 : Q2

25

20

15

10

5

215

216 217 218

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226 227

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223 224

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226 227

210 210

216 217 218

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AWRC Basin Number Fig. 6. Flood variability statistics grouped first by AWRC drainage-division then by decreasing latitude within each drainage division. Top: Q50:Q2 flood quantile ratio calculated from monthly peaks-over-threshold flood series, power law alpha coefficient calculated using monthly peaks-over-threshold flood series (centre) and Flash Flood Magnitude Index calculated using the annual maximum flood series (bottom). Vertical bars show a 90% bootstrap percentile confidence interval.

series equal to 0.92 ðp  0:001Þ. The Pearson correlation between the primary and modal bootstrapped alpha values exceeded 0.97

for both the annual maximum and peaks-over-threshold monthly flood series, with p  0:001 in both cases.

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Fig. 7. Spatial distribution of flood the Q50:Q2, a and FFMI flood variability measures.

Regional patterns of a values The regional pattern of flood variability as measured by a using the peaks-over-threshold monthly flood series is shown in the centre panel of Fig. 6 and the spatial distribution in Fig. 7. The main features are broadly similar to those of the Q50:Q2 flood quantile ratio, with a southwards increase in a from far northern Queensland to a maximum amidst the central-southern Queensland coast. Moderate a values are observed in northern New South Wales, with a secondary peak associated with the Hunter and Hawkesbury–Nepean River drainage basins. Low to moderate a values are generally observed along the southern NSW coast, though again the Snowy River basin (222) has moderately high flood variability as measured by a.

Flash Flood Magnitude Index Internal consistency of FFMI values The correlation between the primary FFMI values and the modal bootstrap value is 0.96 ðp  0:001Þ, indicating that the modal bootstrapped FFMI values are a reliable reflection of the original data. Regional FFMI patterns The distribution of FFMI values grouped by AWRC basin is shown in the bottom panel of Fig. 6 and differs moderately from the generally consistent inter-basin patterns observed between the power law and flood quantile flood variability measures. Low

P. Rustomji et al. / Journal of Hydrology 374 (2009) 196–208

FFMI values are observed in the northernmost catchments (with the exception of the single station in basin 104). Relatively high FFMI values occur southwards to drainage division 143. From southeast Queensland (basin 145) through to the northern margin of the Hunter Valley (those data points plotted on the left hand side of basin 210), low to moderate FFMI values are observed. Higher FFMI values are observed in the southern half of the Hunter River basin and along the main stem of the Hunter River. Flood variability (as measured by the FFMI) declines southwards and reaches a minimum in basin 226 in Gippsland, Victoria. Comparison of flood variability measures Fig. 8 shows the inter-relationships between the Q50:Q2, a and FFMI flood variability measures calculated using the annual maximum flood series, and the peaks-over-threshold (monthly, POTM) a and Q50:Q2 variability measures. Strong positive (though not in all cases linear) correlations are evident between all flood variability measures except for the FFMI (which is only calculated on the annual maximum flood series). The reason for the poor correlations between the FFMI and the other measures can be attributed to two characteristics. Firstly, it is based on the full length of the annual maximum flood series. This flood series almost always includes a number of annual maxima that are smaller (often considerably so) than would be obtained by selecting the n largest independent flood events where n is the number of years data (this type of flood series is commonly referred to as the partial-duration flood series). Secondly, as the FFMI is essentially a calculation of the average deviation from the mean calculated in log units, these (arguably ‘‘non-flood”) small events in an annual maximum series contribute heavily to this index. There is in principle no lower limit to how small an annual maximum discharge observation can be. To illustrate this further, we noted that the hypothetical annual maximum flood series X = 10, 1, 0.1, 0.01 and 0.001 m3 s1 has a corresponding FFMI of 1.58. This is an identical value to an alternate annual maximum series of Y = 10, 100, 1000, 10,000 and 100, 000 m3 s1. The hydrologic, geomorphic and ecologic significance of the latter series would be considered by most a more meaningfully variable flow regime, though the FFMI fails to distinguish this. For this reason, we recommend against the use of the FFMI as a measure of flood variability. Given this, the data presented in Fig. 8 suggests that the ranking of flood variability amongst the stations selected here is relatively insensitive to the choice between the alpha and Q50:Q2 variability measures, or alternatively whether the flood series is represented by an annual maximum or peaks-over-threshold flood series. This is not surprising as both these statistics are calculated from a similar region of the flood frequency distribution. Furthermore, we note that the alpha parameter is calculated using events with a recurrence interval greater than or equal to 3 years. That is, in most environments it is likely to exclude many of the non-flood events that may be present within an annual maximum series. A similar observation obviously pertains to the Q50:Q2 variability measure. Using bootstrap resampling to quantify uncertainty in flood variability Bootstrap resampling has been used in this study to quantify uncertainty (via the bootstrap percentile confidence intervals). One key question in analyses of this kind is how much data is required to reduce the uncertainty in a given statistic to a particular level. We address this question by examining how the size of the 90% bootstrap percentile confidence interval (normalised by the modal bootstrap statistic) varies with record length. Assuming symmetrical upper and lower confidence intervals (an assumption that is, in most cases, sufficiently robust for this excercise) and using the following formula:

205

   95th bootstrap percentile  5th bootstrap percentile 2 modal bootstrap statistic  100 ð7Þ The bootstrap percentile confidence intervals can be expressed as a ‘plus or minus’ percentage uncertainty. Fig. 9 shows how this measure of uncertainty relates to the length of record for the three flood variability statistics. Records of less than 40–60 years are generally associated with higher uncertainty. With 60 years or more of data, uncertainty is much lower, though the rate of reduction in uncertainty with increasing record length is less, with little additional benefit obtained from using more than 80 years of data. The solid line in Fig. 9 shows a smoothed running 90th percentile calculated from the data. This curve indicates for a given length of record the uncertainty below which 90% of stations lie. For example for the Q50:Q2 statistic, 90% of stations with 40 years of data have a 90% bootstrap percentile confidence interval equivalent to approximately ±65% of the modal value, and this decreases to ±40% with 80 years of data.

Discussion As noted in the introduction, flood variability has been implicated with large magnitude, episodic changes to river channel morphology. This study’s regional perspective of flood variability provides important context for the work of Erskine (1986, 1994, 1996) and Erskine and Livingston (1999) from the Hunter Valley and adjacent Macdonald River. These studies provide some of the best documented examples of large magnitude changes to river morphology in response to floods and whilst it has been suggested that the Hunter Valley region experienced particularly high flood variability, to date there has not been a comprehensive regional study to robustly demonstrate this. However, this can now be seen to genuinely be the case. Having provided a broader regional perspective, the question also arises of how the channels of other rivers with either similar or different degrees of flood variability have evolved over time. One river of note that may well be worthy of further study in this regard is the Burnett River in Queensland (basin number 136), which has similarly high flood variability to that of the Hunter River. To the best of our knowledge, there has been no detailed examination of how this river has evolved and responded to this hydrologic variability either in historical or prehistorical times. One of the notable regional contrasts in flood variability appears to be between the near-coast and inland areas in the vicinity of the Burdekin River in northern Queensland. In particular, the relatively small rivers located in close proximity to the coast which experience a wet ‘‘tropical” climatic (as defined by Stern et al., 2000, http://www.bom.gov.au/climate/environ/other/koppen_explain. shtml) have low flood variability, due to the persistently wet conditions. Large rainfall totals are common in this region on a regular basis, leading to relatively uniform runoff generation rates and low flood variability. Only a short distance inland, associated with a change in climate classification to a ‘‘sub-tropical” (locally described as ‘‘dry tropical”) regime, flood variability increases markedly. Interannual rainfall variability in this area is strongly influenced by the nature of the Australian monsoon. This region experiences the strongest spatial gradient in annual rainfall variability of the entire eastern Australian coast (see http:// www.bom.gov.au/climate/averages/climatology/variability/IDCJCM0009_rainfall_variability.shtml) and this difference clearly manifests in the spatial pattern of flood variability. Interestingly, flood variability declines towards the western margin of the Burdekin basin, which is the driest area of the entire study region. Despite

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Fig. 8. Interrelationships between the FFMI, Q50:Q2 and alpha measures of flood variability calculated using the annual maximum flood series (AMS), and the peaks-overthreshold (monthly, POTM) alpha and Q50:Q2 variability measures.

the high rainfall variability, the low overall precipitation and a low gradient landscape appears to be limiting the magnitude of any flood peaks that may be generated and consequently limiting the flood variability. The El Niño-Southern Oscillation (ENSO) phenomena exerts a strong influence on both inter-annual rainfall (McBride and Nicholls, 1983) and streamflow (Chiew et al., 1998; Chiew and McMahon, 2002; Verdon et al., 2005) variability in many parts of eastern Australia. However ENSO’s influence is not spatially uniform and this spatial heterogeneity could be another factor influencing flood variability. Coastal catchments in eastern Victoria and a number in southern New South Wales tend to have lower variation in total streamflow between El Niño and La Niña years (Verdon et al., 2005). By contrast, the north coast of New South

Wales and the Queensland coast (south of the Burdekin River) experience larger variations in total streamflow between ENSO phases. Whilst streamflow totals are not the same as flood peaks, (Kiem et al., 2003) have shown a strong ENSO signal in the New South Wales flood record, which probably extends into southern Queensland. This ENSO related variability in rainfall arguably contributes to the pattern of flood variability in that a wider range of hydro-climatic conditions may exist at some sites relative to others. Inter-decadal modulation of the hydro-meteorologic effects of ENSO driven by the Inter-decadal Pacific Oscillation (IPO) provides another lower-frequency source of rainfall (Power et al., 1999), streamflow (Verdon et al., 2005) and flood variability (Kiem et al., 2003). Again, spatial patterns of IPO modulation of ENSO

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exist. Micevski et al. (2006) found that during IPO negative phases, flood quantiles for New South Wales and Southern Queensland increased by a factor of approximately 1.7, though there is a large amount of variation around this value. By contrast, the IPO negative phases appear to exert minimal influence on flood quantiles in the north of Queensland, particularly for the stations in the ‘wet tropics’ located to the north of the Burdekin River’s outlet that we have demonstrated experience relatively low flood variability. As IPO modulation of ENSO effects (including flood magnitude) occurs on an inter-decadal timescale, it is likely that differing record lengths and periods of observation (which variously sample IPO negative and positive phases) are contributing to some of the intra-regional and intra-basin variation in flood variability that we observe.

The New South Wales, Victorian and Queensland hydrographic agencies are thanked for providing the required flow data. Statistical analyses were undertaken using the ‘lmomco’ package (Asquith, 2007) in R (R Development Core Team, 2005). Tim Ellis and two anonymous reviewers are thanked for comments on the manuscript.

Conclusions

References

We have sought to identify regional and inter-basin patterns of flood variability amongst catchments east of Australia’s Great Dividing Range in this study. Three measures of flood variability were explored: (1) a selection of flood quantile ratios, (2) a power law scaling coefficient and (3) the ‘Flash Flood Magnitude Index’ (FFMI). The FFMI (when utilising annual maximum flow data) was rejected as a measure of flood variability because of its sensitivity to low flow values that would be excluded from a flood frequency analysis if a more hydrologically sound, peaks-overthreshold approach were adopted. The flood quantile ratio and power law scaling coefficient methods produced similar results and are recommended as measures of flood variability. Catchments in the wet tropics of far north Queensland experience low flood variability. Flood variability rises southwards through Queensland and reaches a maximum in the vicinity of the Fitzroy and Burnett Rivers. The small near-coast catchments of southern Queensland and northern New Wales are regions of low flood variability, though the southern Hunter River and Hawkesbury–Nepean basins along the central New South Wales coast also experience high flood variability, as do parts of the Snowy River basin. Flood variability along the southern New South Wales coast is moderate, with some high exceptions. Bootstrap resampling was used to quantify uncertainty in the flood variability statistics. Analysis of these uncertainties indicated that large reductions in uncertainty in the measures of flood variability were obtained after approximately 50 years of monitoring. Finally, our results regarding an appropriate probability density function for modelling flood frequency distributions were consistent with previous research indicating the Generalised Pareto dis-

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