Results

4.1 Regression Analysis in the Calibration Periods

Rainfall-runoff relationships in the calibration and testing periods were examined before developing the regression relationships. For example, in severely burnt catchments such as Flowerdale, Taggerty and Koornalla (with burnt percentages of 96.6%, 89.7% and 83.1% respectively), there are obvious changes in the rainfall-runoff relationship in the testing period compared with that in the calibration period (see Figure 3). Similar results were obtained in the majority of the selected catchments and the extent of the relationship change is related to the burnt percentage as well as the burnt severity. The results illustrate that there is more streamflow after the vegetation loss caused by bushfire, which is consistent with our knowledge of how bushfire affects streamflow in a catchment. This provides confidence in our further analysis of bushfire impacts on streamflow.
Then, the regression relationships between rainfall and streamflow were constructed before quantifying the bushfire and climate change impacts on mean annual streamflow. The rainfall-streamflow relationship varies largely from catchment to catchment in different time periods. In this study, relationship between rainfall and streamflow in almost every catchment impacted by bushfire can be fitted by linear regression model in both calibration period and testing period (see Figure 3) and the evaluation results of the regression model are listed in Table 2.
<Figure 3 Here Please>
Figure 3 shows the regression relationships obtained for each catchment in the calibration and test periods and Table 2 summarizes the statistical metrics of the linear regressions. There exist good linear relationships between annual rainfall and annual streamflow in most catchments in the calibration periods (Figure 3). The coefficient of determination (\(R^{2}\)) result varying from 0.56 to 0.85 indicates annual rainfall explains 56% - 85% variation of annual streamflow in the calibration periods (Table 2). The modified coefficient of efficiency (\(E_{1}\)) ranges from 0.26-0.65 and the modified index of agreement (\(d_{1}\)) ranges from 0.62 to 0.82. The mean absolute error (MAE) is in the range of 16.3-101.8. These results indicate that the linear regressions are satisfactory in most of burnt catchments, and can be used for estimating the streamflow under a given precipitation during the testing period (i.e. the post-bushfire period).
<Table 2 Here Please>

4.2 Bushfire and Climate Variability Impacts on Mean Annual Streamflow

To evaluate the total mean annual streamflow changes in the testing period, the total annual streamflow change (ΔQtot) were calculated based on Equation 10 and the results are summarized in Table 3. The total mean annual streamflow of all the catchments increases in the testing period (post-bushfire period), compared with the calibration period (pre-bushfire period) except for Jamieson (with decline of 22.3 mm). The increase in mean annual streamflow ranges from 5.9 to 141.4 mm. 12 out of the 15 selected catchments have increasing average runoff ratio in the testing period, which varies from 0.002 to 0.106. In contrast, the average runoff ratio of Running Creek and Tallarook decreases by 0.009 and 0.03 respectively while Frenchman Creek Junction’s average runoff ratio remains stable.
To quantify the contribution of bushfire effects to the mean annual streamflow change, streamflow changes due to vegetation change caused by bushfire (ΔQveg) were determined from time trend analysis method (see 3.1). As shown in Table 3, the calculated streamflow increase due to vegetation change caused by bushfire (ΔQveg) ranges from 1.6 (Frenchman Creek Junction) to 125.9 mm (Traralgon South) or -45% (Jamieson) to 98% (Murrindindi above) of the observed total streamflow change (ΔQtot). The results indicate that the bushfire caused streamflow increases during the testing period in each burnt catchment.
Changes in rainfall and potential evaporation (PET) also contribute to streamflow variations. Thus, the streamflow changes due to climate variability (ΔQclim) were determined from sensitivity-based method (see 3.3). The choice of w value in sensitivity-based method was based on climate condition and agreement in the calibration period between measured and estimated annual runoff ratio (Zhang et al., 2011). The w value remained constant in testing period to ensure equation 11 only represents the effect of climate variability. Table 3 shows that climate variability in the testing period increases annual streamflow in the majority of catchments such as Running Creek and Rosewhite, but decreases annual streamflow in the rest (e.g., Jamieson and Koornalla). The proportion of streamflow change due to climate variability in total streamflow change ranges from -7% to 157%.
<Table 3 Here Please>
In this study, percentage changes in mean annual streamflow caused by bushfire and climate variability were calculated independently. When the sum of the two percentage changes approaches 100%, it means that the independent simulated streamflow changes are close to the actual streamflow changes. Figure 4 summarizes the sum of the two proportions. For most catchments except for Frenchman Creek Junction, the sum is close to 100%, which means the sum of streamflow change due to bushfire (ΔQveg) and climate variability (ΔQclim) approaches the total streamflow change (ΔQtot). This indicates that the two independent methods are reliable for most of the bushfire impacted catchments. The reason why Frenchman Creek Junction only has 28% total streamflow change is because the absolute streamflow change before and after bushfire is only 5.9 mm. Such a small change may amplify the error of the actual total change of streamflow and the sum of estimated streamflow change from bushfire and climate variability. As shown in Figure 4, streamflow change between the two periods (pre- and post- bushfire periods) is mainly contributed by bushfire impact in 11 catchments, but by climate variability in the other 3. It is worth noting that among all the burnt catchments, only Jamieson has a decrease in streamflow after bushfire. This occurs because the streamflow change caused by bushfire increased but the climate variability induced a greater decrease in streamflow, which is consistent with the fact that Jamieson only has 36.3% burnt area with less burnt severity (see Figure 2) and the rainfall in the testing period is lower compared with the calibration period (see Figure 1).
<Figure 4 Here Please>
To further investigate if the bushfire impacts on streamflow are related to the burnt area, Figure 5 shows the relationship between burnt percentage (fire scars area within a catchment as a proportion of the total area of a catchment) and percentage of mean annual streamflow increase due to bushfire. It is shown that the percentage of mean annual streamflow increase due to bushfire is strongly related to the percentage area burnt. The linear relationship between the two indicate the burnt percentage can explain 68% of the percentage of mean annual streamflow increase due to bushfire. This result can be used to estimate or predict the annual streamflow changes due to bushfire if the burnt percentage for a small to medium sized catchment is available. It is worth noting that the relationship is suitable at annual time scale and may be not appropriate at sub-annual time steps.
<Figure 5 Here Please>