Comparison of results from this study with those from other studies

The relatively strong relationships found between discharge and catchment area in this study across all average recurrence intervals and using both annual and partial series flood

frequency estimates (Table 4.2) reflect the strong relationships previously found in this region. In a study using data from north-eastern Tasmanian streamflow data, Knighton (1987) found that more than 97% of the variation in flood discharges was explained by catchment area. The weaker association found in this study (61 – 82% for annual series flood frequency estimates) may be explained by a number of factors. Firstly, this study used a dataset which was larger and with a wider range of catchment areas than those used by Knighton. Secondly, changes in the strength of the relationship may be a result of the different flood frequency estimation techniques that were used in the two studies. Finally, the hydrology of the region is likely to have altered due to a changed climate, with an estimated 12% reduction in mean annual rainfall occurring in the Pipers-Ringarooma region of north-eastern Tasmania in the period 1997 to 2007, relative to historical climate (1924 to 2007) (CSIRO, 2009).

The values of the power-law relationship coefficient a and exponent b from this study (Figure 4.5) fall within the range of values found in other studies (Table 4.4), both globally and in Australia. However the comparison of regional regression coefficients between different studies is problematic and should be undertaken with caution. Data quantity, quality and type, flood frequency estimation techniques and regression methods vary between studies, and there is frequently a lack of detail on which methods have been employed. In addition, difficulties exist in comparing values of a across different studies due to the use of different units (Galster, 2007). However, if these limitations are acknowledged, comparison of the results from different regions is valid.

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Table 4.4.Selected summary of coefficients and exponents for discharge-catchment area relationships for small floods following the general form of QT =aAdb, where QT = discharge with an average recurrence interval of T

years, Ad = discharge, a is the power-law coefficient representing base discharge (m3s-1) and b is a scaling

exponent (n = number of stations, bf = bankfull discharge).

Source Location n T a b

(Leopold et al., 1964) US 0.65-0.8

McKerchar and Pearson (1989) quoted in (McKerchar and Pearson, 1990)

New Zealand 2.33a 0.8

(Leclerc and Lapointe, 1994) Southern Quebec 26 2.33 a 0.03 0.96

bf 1.64 0.71

(Galster, 2007) US 2.33a 0.49-0.97

(Stacey and Rutherford, 2007) Virginia, USA 9 1.5 0.56b 0.80

(Rachol and Boley-Morse, 2009) Michigan, USA 43 2 4.05 b 0.95

Australia

(Alexander, 1972) Australia 0.7

(Gippel, 1985) Hunter Valley, NSW 36 bf 1.51 0.91

(Loebis, 2002) Australia 6 2.33 a 1.58 0.81

(Reinfelds et al., 2004) Bellinger, NSW 2 0.89 0.80

(Worthy, 2005) Cotter River, ACT 2 0.12 0.98

(Jain et al., 2006) Upper Hunter, NSW 19 2 1.21 0.72

Tasmania

Watson (1975) quoted in (Knighton, 1987)

Western Tasmania 7 2 4.70 b 0.74

Watson and Williams (1983) quoted in (Knighton, 1987)

Western Tasmania 10 2 5.19 b 0.75

(Hughes, 1987) Tasmania 77 2.33 a 0.88 0.87

(Knighton, 1987) North-eastern Tasmania 9 1.11 0.23 0.84

2 0.32 0.93

5 0.40 0.98

10 0.45 1.01

This study North-eastern Tasmania 13 1.1 0.34 0.89

1.5C 0.40 0.90 2 C 0.45 0.90 2.33 C 0.47 0.91 3 C 0.51 0.91 5 C 0.58 0.92 10 C 0.67 0.94

(a Results are for mean annual flood, which is generally thought to be equivalent to T = 2.33 years (Knighton, 1999); b results are in miles; c results are from partial series flood frequency estimates)

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While common values of the coefficients from Equation 4.1 are around 1 for a and 0·7 for b

(Dunne and Leopold, 1978, Jain et al., 2006, Pérez-Peña et al., 2009), a relatively large range of values have been found worldwide (Table 4.4). Values of partial series coefficient b from this study were larger than those found in the US (Leopold et al., 1964, Stacey and

Rutherford, 2007) (Table 4.4), and slightly less than those found in Quebec (Leclerc and Lapointe, 1994), which is at a similar latitude to the sites in this study. Where the scaling factor b = 1, the relationship between catchment area and discharge is linear. Linear scaling occurs in basins with uniform hydrology, including precipitation and runoff; although the scaling may depend on the exact discharge (T) chosen for the analysis. When b < 1 than less discharge is being added by the downstream catchment area than the upstream area (Galster, 2007). In a study of the relationship between mean annual flow (commonly considered to be

T = 2.33 years) and catchment area using weighted least squares regression and data from more than a thousand global rivers, McMahon et al. (2007), found Australian and South African streams had values of a = 1.013 and b = 0.727, while streams from the rest of the world had values of 1.526 and 0.818 for a and b respectively. These results are not necessarily reflected in the selected data in Table 4.4 where values for b for Australian studies ranged from 0.81 to 0.91 at T = 2.33 years, compared to a range of 0.49 to 0.96 for studies from the rest of the world. This study has low values of a and high values of b in comparison to those derived from the amalgamated Australian and South African data set of McMahon et al. (2007), and the same pattern exists between the results of this study and the other Australian studies shown in Table 4.4.

There may be a number of explanations of these results. Galster (2007) suggested that in larger catchments the time taken for water to travel to the mouth of a watershed complicates the scaling of discharge with catchment area. River regulation and water usage is generally higher in the lower parts of catchments, particularly in Australia where human settlements are clustered along the coast. Australian rivers may have lower values of b then those from other parts of the world as a result of these lower parts of the catchments contributing less

discharge than upper catchment areas which are often much less impacted. North-eastern Tasmanian rivers are largely unregulated, and human habitation and water usage is higher in inland areas away from the coast. This may result in more discharge being added in

downstream catchment areas in north-eastern Tasmania then elsewhere and account, at least in part, for the high b values. Galster (2007) suggested smaller catchments, particularly those

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that are undisturbed, have c values near 1 as a result of the short time required for discharge to travel through the catchment.

This study from north-eastern Tasmanian catchments found higher values of exponent b

relative to those using data from western Tasmania (Table 4.4), which may be expected as these two regions experience differences in rainfall, topography and geology. The results from this study suggest that discharge in north-eastern Tasmanian rivers has a much more linear relationship with catchment area than western Tasmanian rivers, which may be expected as western Tasmanian rivers rise on the slopes of the west coast ranges and generally travel only a short distance to the west coast to discharge. Western Tasmania also generally experiences higher frequency and longer duration storms than eastern Tasmania (McConachy et al., 2003), largely concentrated in upper catchment areas. The values of exponent b at T = 2.33 years using annual series flood frequency estimates in this study was similar to that found by Hughes (1987), who used annual series data from 77 Tasmanian streamflow stations to undertake hydrological analyses. The value of coefficient a in this study was lower than that found by Hughes, but as Hughes included sites located across Tasmania differences are expected. Using annual series data from north-eastern Tasmania, Knighton (1987) found a range of values of coefficients in the discharge-catchment area power law relationship similar to those found in this study. The values of coefficient a from this study estimated using annual series flood frequency estimates were lower than those found by Knighton at T = 1.1 years, but were equivalent at T = 2 years. The values of coefficient a from this study at T = 5 years and T = 10 years were progressively larger than those found by Knighton. The values of coefficient b found in this study was equal to that found by Knighton at T = 1.1 years, but were progressively smaller at T = 2, 5 and 10 years. While these differences may reflect actual temporal changes in precipitation, it is equally possible they reflect the different datasets and techniques used. Knighton used a smaller dataset than this study, which is likely to increase both the statistical error on the scaling parameter and the bias from finite size effects (Clauset et al., 2009). Catchment area (Ad) values used in this study may also be significantly different to those used by Knighton, due to the different methods used.

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