Climate filter

To identify decadal streamflow trends, a climate filter needs to distinguish random climatic fluctuations that lie within the natural variability range of streamflow from decadal trends as a result of vegetation disturbance and subsequent growth. Filtering out the effects of natural variation in climate on streamflow is a fundamental problem in detecting long-term trends in streamflow (Kuczera, 1985). For example, Langford (1976) used streamflow records of Melbourne’s water catchments subject to the 1939 fire to perform a regression against climatic indices derived from neighbouring catchment streamflow data and rainfall records. The regression procedure involved formulating a climate filter by calibrating the pre-disturbance catchment conditions and then applying it to the post-disturbance data to quantify the residual assumed to be a result of the post-fire vegetation dynamic. For the climate filter to be effective,

93 the methodology required the assumption that the pre-disturbed catchment was in a state of quasi-hydrological equilibrium, hence consisted of mature or over-mature forest with negligible vegetation growth. This requirement meant that significant pre- 1939 bush fire events at the O’Shannassy catchment confounded the results and hence erroneously showed there was no significant streamflow trend. The methodology was also limited in that, to reduce the uncertainty in the parameter estimates during calibration, the climate filter required the pre-disturbance runoff record to be at least 15 years long, which is rarely available, as is the case in this study.

To relax these restrictive assumptions, Kuczera (1985) developed a general climate- bushfire yield response model that simultaneously estimated the parameters for both the annual climate filter and forest water use trend response function. The climate filter used Langford’s (1976) generalised linear model to define the mean residence time of seasonal rainfall from the source area to the outlet, and hence implicitly represents the rainfall-runoff transformation with the following equation:

t t i i i t a bP

Q

= +

∑

+ε = , 3 1 [4.1] where Qtis observed runoff for a May-April water year, P1,t is May-December

rainfall for water year t, P2,tis December-April rainfall of antecedent water year t-1,

P3,tis January-April rainfall for water year t, ε tis a random error and a, b1, b2, b3

are parameters to be estimated from pre-1939 data (Kuczera, 1987).

In theory, the climate filter aimed to capture the fast and slow flowing runoff

processes in the transfer function. This study builds on the climate filter presented by Kuczera (1985) by not assuming that the rainfall data is aggregated in the same way as Langford (1976). Instead, a large array of independent variables derived from aggregated rainfall data are used to identify the most effective linear regression for explaining the rainfall induced streamflow variance. The overall objective is to reduce the residual standard error of the model in order to extract the streamflow trend with the greatest level of confidence.

In the proposed climate filter, the water year was not assumed to begin in May, as suggested by Langford (1976), and instead the optimal water year was identified by

94 evaluating each month as a potential starting month for a water year. For each water year, T, explanatory variables were constructed by aggregating monthly rainfall records for water year, T, as well as the antecedent water year, T-1. Rainfall records for water year T were aggregated to represent either two or three explanatory variables, with each explanatory variable having a minimum of two months of data. This is illustrated in figure 4.2(a) with each of the bars representing a candidate method for aggregating the monthly rainfall data. Figure 4.2(b) shows that the antecedent year was aggregated into either one or two explanatory variables where each explanatory variable had a minimum of two months, and some of the candidate methods had only a portion of the antecedent year with explanatory power. Each of the 37 possible combinations of explanatory variables developed using water year T

were separately coupled to each of the 55 combinations of explanatory variables developed using the antecedent water year, T-1. In mathematical form, the proposed climate filter may be defined as:

T T j n j j T i m i i T a BP Ant P

Q

= +

∑

+

∑

+

ε

= = , 1 , 1 [4.2]

where QTis observed runoff in year T, Pi,T is rainfall for water year T aggregated into m explanatory variables, Pj,Tis rainfall of antecedent water year T-1 aggregated into n explanatory variables, εTis a random error and a, Bi, Antj, are parameters to be

estimated from streamflow data.

Figure 4.2: (a) Aggregation of monthly rainfall data for water year, T, where B1, B2, and B3, are explanatory variables, and month 1 and 12 respectively represent the first and last month of water year, T, (b) Aggregation of monthly rainfall data for antecedent water year, T-1, where Ant1 and Ant2 are explanatory variables, and month 1 and 12 respectively represent the last and first month of the antecedent year.

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In document Modelling the effects of forest regeneration on streamflow using forest growth models (Page 113-116)