When this is done the correlation between inflow residuals and temperature (r = −0.02) effectively
disappears. From this analysis we conclude that the direct relationship CT99021 between inflows and temperature is misleading because (a) rainfall and temperature tend to be inversely related and (b) there exist long-term trends in the data sets. Once these have been accounted for, there is no evidence that SWWA temperature has any significant effect on total inflows to Perth dams. Estimates of SWWA annual rainfall from each model were made by averaging the results from grid squares representing the wider SWWA region and generating continuous time series over the period 1901–2100. For a variety of reasons (e.g. different model resolutions, physical parameterizations, and overall skill) model results for regional rainfall tend to differ (both in means and variability) from observations. Fig. 6 shows an example of a time series of raw values from one particular CMIP5 model (MPI-ESM-LR) which is characterized by a consistent underestimate
of both the mean and interannual variance. While it is tempting to discriminate amongst the model results depending on their see more skill at reproducing these fundamental characteristics of rainfall there is little evidence that this has much of an effect on projections (e.g. Smith and Chandler, 2009). Instead, we assume in the first instance that all model results are of equal value but transform them to remove any biases relative to observations. If Y denotes a model value for rainfall, O denotes an observed value, overbars denote averages over the 20th century (1901–2000) and σ denotes the associated interannual standard deviation, then the transformation equation(1) Y*=(Y−Y¯)σoσy+O¯provides
a bias correction and makes the projected values from the different models comparable ( Smith et al., 2013). Note that it is not necessary to use observations for the transformation since setting O¯=0 and σo = 1 yields time series with zero mean and unit variance. A potential problem with this type of linear transformation is that it can sometimes lead to small, physically unrealistic, Etoposide concentration negative values for rainfall. However, these situations are rare and replacing any such occurrences with zeroes has negligible impact on the findings presented in this study. While other techniques exist for transforming model time series to obtain a closer match with observed time series (e.g. quantile–quantile matching), this is usually done at the daily time scale (c.f. Bennett et al., 2012 and Kokic et al., 2013) where there can be relatively large discrepancies between model and observed values.