Evaluation of log-log linear model performance (clustering group A2)

Model development

The model is developed considering the same determinants as before which are R2, SEE and p-statistics. The model statistics for log-log linear model for A2 is found from Table 5.4 below. From the R2 values, it is observed that the values range showing large variations from 0.69 to 0.27 respectively for Q2 to Q100. The large variations from lower to higher ARIs for

this model indicate toward larger uncertainty associated with higher ARIs for this model. Moreover, particularly small R2 values for higher ARIs (e.g., Q50 and Q100) indicate towards

the larger variance of prediction in estimation of higher ARI flows. Most of the R2 values seem to be relatively low except for Q2 and Q5 which indicates towards poor prediction

77 The SEE values vary from 0.19 to 0.34 respectively for Q2 to Q100. The lowest value of

residual standard error was found for Q2 and highest was found for Q100 which indicates

towards the higher percentage of prediction error associated with higher ARIs.

The most important predictor variable found for the model is area, which is common in every prediction model. The second most important independent variable is found as sden, which is present in every model except for Q20. Only for Q2, rainis found as a functioning predictor

variable in final model. Overall the prediction models are found to be consistent in selection of predictor variables.

Table 5.4 Model statistics for log-log linear model of clustering group A2 Equation Predictor variables Regression Coefficient (β) Standard Error Standard Error of Estimate (SEE) R2 p value D.F

log Q2 (constant) -4.77 1.01 0.19 0.69 5.00E-05 31

log (area) 0.80 0.10 5.47E-09 log (rain) 1.47 0.34 1.39E-04 log (sden) 0.74 0.16 4.35E-05

log Q5 (constant) -0.07 0.29 0.22 0.55 8.16E-01 32

log (area) 0.74 0.11 2.90E-07 log (sden) 0.62 0.18 1.32E-03

log Q10 (constant) 0.14 0.33 0.24 0.48 6.74E-01 32

log (area) 0.72 0.13 2.58E-06 log (sden) 0.58 0.20 5.77E-03

log Q20 (constant) -3.44 1.06 0.31 0.43 2.08E-03 32

log (area) 0.68 0.08 4.17E-11 log (I6,2) 2.66 0.67 1.85E-04

log Q50 (constant) 0.47 0.42 0.31 0.32 2.77E-01 32

log (area) 0.70 0.16 1.66E-04 log (sden) 0.48 0.26 6.80E-02

log Q100 (constant) 0.58 0.47 0.34 0.27 2.26E-01 32

log (area) 0.70 0.18 5.46E-04 log (sden) 0.44 0.28 1.27E-01

Overall, the model equations can be written as;

log 𝑄2 = −4.77 + 0.80 log(𝑎𝑟𝑒𝑎) + 1.47 log(𝑟𝑎𝑖𝑛) + .74log (𝑠𝑑𝑒𝑛) …(5.13)

78

log 𝑄10= 0.14 + 0.72 log(𝑎𝑟𝑒𝑎) + .58log (𝑠𝑑𝑒𝑛) …(5.15)

log 𝑄₂₀ = −3.44 + 0.68 log(𝑎𝑟𝑒𝑎) + 2.66 log(𝐼_6,2) …(5.16)

log 𝑄₅₀ = .47 + 0.70 log(𝑎𝑟𝑒𝑎) + .48log (𝑠𝑑𝑒𝑛) …(5.17)

log 𝑄₁₀₀= .58 + 0.70 log(𝑎𝑟𝑒𝑎) + .44log (𝑠𝑑𝑒𝑛) …(5.18)

Adequacy checking of model

To assess the model performance, the plot of Qobs and Qpred, Qpred/Qobs ratio and median RE

values are computed for clustering group A2 (Figures 5.11, 5.12 and 5.13).

Figure 5.11 shows a reasonable scatter between the observed and predicted flood quantiles for clustering group A2 for Q20. Overall, the scatter around the 45-degree line in this figure is

deemed to be reasonable for most of the catchments. The plots of observed and predicted flood quantiles for all the six return periods can be seen in Appendix C (Figures C.11 to C.15). Results for ARIs of 2 and 5 years (Figures C.11 to C.12, respectively) are relatively better as compared with other ARIs.

79 Figure 5.11 Comparison of observed and predicted flood quantiles for log-log linear model of

clustering group A2 for Q20,

Figure 5.12 shows the boxplots of RE values for the log-log linear model for clustering group A2. The median RE values match with the 0 – 0 line very well for ARI of 2, 5, 10 and 20 years and reasonably well for ARIs of 50 and 100 years. For ARIs of 50 and 100 years, slight overestimations are noticed. In terms of the RE band, ARI of 2 years shows the lowest spread. The spread of RE increases with increasing ARI. The RE band for 100 years ARI is more than double to that of 2 and 5 years ARIs. These results show that in terms of RE, the overall best result is achieved for 2 years ARI. The results for higher ARIs (20, 50 and 100 years) are relatively poor, i.e. too high spread in RE values, indicating a higher model error.

0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 lo g Qpr ed (m 3/s ec )

80 Figure 5.12 Boxplots of RE for log-log linear model of clustering group A2

Figure 5.13 presents the boxplots of the Qpred/Qobs ratio values for clustering group A2 for

different ARIs. It is found that the median Qpred/Qobs ratio values are located closer to 1 – 1

line, in particular for ARIs of 2, 5 and 20 years. However, for ARIs of 10, 50 and 100 years, the median Qpred/Qobs ratio value is located a short distance below the 1 – 1 line, indicating a

negative bias. Also, most of the Qpred/Qobs ratio values for ARIs of 20, 50 and 100 years are

located above the 1 – 1 line, indicating overestimation by the log-log model for many catchments. In terms of the spread of the Qpred/Qobs ratio values, ARI of 2 years exhibits the

lowest spread, followed by ARIs of 5, 10, 20, 50 and 100 years. Furthermore, the spreads of the Qpred/Qobs ratio values for 50 and 100 years are very similar, which are remarkably larger

than 2, 5 and 10 years. It indicates a comparatively higher range of overestimation of flood quantiles for larger ARI values for clustering group A2.

81 Figure 5.13 Boxplots of Qpred/Qobs ratio values for log-log linear model of clustering group A2