Temporal scaling function for simultaneous determination of trend in frequency parameters (location, scale and shape respectively) for selleck compound time in years (t) for varying growth functions (i = 0 is no growth, i = 1 is linear and i = 2 is power). equation(3) μˆ(t)=μ0+∑0i=2μi⋅tiσˆ(t)=σ0+∑0i=2σi⋅tiξˆ(t)=ξ0+∑0i=2ξi⋅ti Frequency re-analysis of both the NMIA and SIA datasets confirm the original results of the UWA (1995), and this was used as the control experiment (PWM-Gumbel). Both the correlation and SRC are high with a CC of 0.98 for NMIA and 0.96 for SIA (see Fig. 2 columns labelled PWM-Gumbel). Along with the low biases
this confirms the ability of the Gumbel PDF with PWM and Hosking PPF to fit the data for the two stations. Goodness of fit was visually inspected, and the quantile of the PDF describes the AMS data accurately (see Fig. 3 top panel). Frequency analysis was not sensitive to PPF. All three PPFs performed credibly with CC ranging from 0.93 to 1.0 and biases ranging from −0.36 to 0.7 mm selleck inhibitor in Experiment 1 (Fig. 2 middle and bottom panels). Neither the CC nor bias suggested an improvement for the NMIA
dataset. For the SIA station, CC reduced from 0.96 (control) to 0.93 with the Weibull PPF and the biases increased from 0.39 to 0.7 mm. It should be kept in mind that CC is not a robust estimator of the variance and is sensitive to fringeliers. PPF by Hazen performed best with a lower absolute bias for both NMIA and SIA of 0.22 and 0.26 mm respectively in comparison to the Hosking or Weibull (−0.36 and 0.39 mm respectively). Frequency analysis was similarly not sensitive to PEM, in Experiment 2 (see Fig. 2). L-Moments and standard statistics estimation methods produced similar performances
for NMIA but reduced performance for SIA. For SIA, the CC reduced from 0.96 (control) to 0.93 for both L-Moments and standard statistics estimation methods; however the SRC remained at 1.0. The biases for NMIA increased significantly from −0.36 (control) to 0.73 mm for NMIA and affirm the importance of using multiple GOF. Parameter estimation using either L-Moments or standard statistics did not provide any significant improvement over the PWM method in the analysis of this dataset. The Weibull PDF and L-Moments parameter Inositol monophosphatase 1 estimation are frequently used in hydrological frequency analysis because of their purported benefits relative to other distributions and parameter estimation techniques (Gaál and Kysely, 2009, García-Marín et al., 2013, Sarkar et al., 2010, Yang et al., 2010, Kharin and Zwiers, 2005, Fowler et al., 2007 and Leander et al., 2014). However, the benefits were not consistently observed throughout this analysis as Weibull outperformed the Gumbel in terms of CC and SRC, but underperformed in terms of the bias as shown in the results of Experiment 3 (see Fig. 2). The Weibull configured analysis had CC of 0.983 and 0.963 for NMIA and SIA respectively versus a CC in the control of 0.981 and 0.963.