Diseño Universal de Aprendizaje.

Little difference was found between the discharge-catchment area relationships produced using annual series flood frequency estimates and those based on partial series estimates (Table 4.3 and Figure 4.2). However log(a) determined using flood frequency estimates based on annual series data was significantly less than log(a) determined using partial series data at the lowest average recurrence intervals (T = 1.1, 1.5 and 2 years) (Table 4.3). There was also a strong trend across other average recurrence intervals for both the coefficient and

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the exponent of the power-law relationship developed using annual series flood frequency estimates to be smaller, although not significantly so, than that developed using partial series estimates, with the difference largest at the lowest average recurrence interval and decreasing as average recurrence interval increased (Table 4.2 and Figure 4.2).

The larger values of the coefficient a obtained from partial series estimates in comparison to those from annual series estimates at low average recurrence intervals (Table 4.2 and Figure 4.2a, 4.2b and 4.2c) can be explained by the larger magnitude flood frequency estimates of small floods provided by the partial series (Appendix 4.2). The coefficient a indicates the flow at a unit area, and if discharge increases while the unit area remains the same, a will increase. The trend for the difference in a between the two series to decrease as T increases (Figure 4.5a) may be explained by the differences in flood frequency estimates between the annual and partial series decreasing as T increases, with annual series flood frequency estimates becoming roughly equivalent to partial series estimates at around T = 5 years, and becoming larger than partial series values at T = 10 years (Appendix 4.2). Figure 4.5.a also illustrates the larger range of values in coefficient a determined using the partial series in comparison to annual series.

The relationship between values of the power-law exponent b obtained from annual series estimates and those from partial series estimates was quite different to that of the coefficient

a (Figure 4.5.b). Annual series estimates of the power-law exponent b were smaller than partial series estimates across all values of T, and the range of annual series values of b (0.09) over the range of T examined was smaller than that of partial series values (0.05).

The power-law coefficient (a) and the power-law exponent (b) determined using both annual and partial series flood frequency estimates became progressively larger with increasing average recurrence interval. The increase in the values of the power-law coefficient a as T

increases (Table 4.2) is expected given that increases in T results in progressively larger flood discharges and coefficient a indicates the flow at a unit area. Knighton (1987) suggested that

b ordinarily decreases as T increases because greater channel and valley storage attenuate the flood wave at higher flows. He suggested that the reverse occurred in north-eastern

Tasmanian streams due to the low levels of storage available so that translation rather than reservoir effects dominate the downstream transmission of flood. The increase in b as T

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The stronger relationships (larger R2 values) between discharge and catchment area using annual series flood frequency values in comparison to those using partial series estimates suggests that it may be better described by the linear relationship between the log transformed variables than the partial series relationship. This is supported by the lower RSE values for annual series estimates in comparison to partial series estimates (Table 4.2). Conversely, the relationship between discharge and catchment area using partial series flood frequency values may be better described by a non-linear relationship between the variables. This is supported by the fits of the log transformed data series to the normal distribution (Appendix 4.3). However it should be remembered that in practice, few empirical phenomena obey power laws across the full range of values (Clauset et al., 2009), and while examination of the error distribution of the different relationships would provide further insight into models that could better describe the relationship (Xiao et al., 2011), that was not the purpose of this study.

A large range of catchment areas was used in this study (largest site > 100 times the

catchment area of the smallest site) (Table 4.1) in an attempt to reduce the estimated variance of the slope estimate and reduce the standard error of points on the fitted line (Maindonald and Braun, 2010), as well as to ensure the developed relationships are valid over an extended range. However as extreme values tend to have extremely large residuals (Griffith et al., 1991), a number of techniques was used to assess the influence of the smallest and largest catchment areas on the values of exponent b. In addition to normal regression diagnostic tools (leverage and Cook’s distance plots), both jackknife resampling (Figure 4.3) and plots of the regression lines (Figure 4.4) were used, with all assessments indicating that the relationships developed were not unduly influenced by the presence of these catchment area outliers.

It is interesting to note the difference in behaviour of the plotted regression lines of both annual series and partial series estimates of the coefficient a and the exponent b as they approach the origin (Figure 4.5). The partial series provides intuitively better results as discharge approaches 0 as average recurrence interval approaches 0. Overall, while the discharge-catchment area relationships produced using annual series flood frequency estimates were similar to those based on partial series estimates, the results of this study suggest that partial series relationships will provide better estimates of the power-law coefficient and exponent at low average recurrence intervals (T ≤ 2 years).

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