For example, Table 2 represents calibration setting and optimisation results for the FSM for the summer period from 1961 to 1990. First, the Parameter l is set as a fixed value for all the calibration period in Step 1 since l in the calibration stage has the highest P-value among the other parameters. The other seven parameters are set free and optimisation has been done. Next, Steps 2–5 have been carried out in the same way. In Step 5, optimisation result shows that all three optimised parameters show significant trends along time, among which f shows the lowest P-value. Hence, in Step 6, the trend of f along time is fixed, i.e. f value of each calibration period is calculated from a linear regression equation. Then optimisation has been done for the rest two parameters, c and βq. Step 7 has been done in the same way. Finally, for this nonstationary model, five parameters are set as fixed values and three parameters are set to have trends along time. This nonstationary model is compared with the other models described in the following sections.

Table 2

Parameter setting for calibration and optimisation results for the FSM for summer period from 1961 to 1990

Calibration setting
Optimisation result
Constant (fix)Trend (fix)FreeNo trendTrend
Calibration     c, τw, f, αs, αq, βq, l, p c, τw, βq, l, p f, αs, αq
Step 1 l  c, τw, f, αs, αq, βq, p c, αs, β τw, f, αq, p
Step 2 l, αs  c, τw, f, αq, βq, p c, τw, αq, p f, βq
Step 3 l, αs, αq  c, τw, f, βq, p c, τw, βq, p f
Step 4 l, αs, αq, τw  c, f, βq, p c, βq, p f
Step 5 l, αs, αq, τw, p  c, f, βq  c, f, βq
Step 6 l, αs, αq, τw, p f c, βq  c, βq
Step 7 l, αs, αq, τw, p f, c βq  βq
Calibration setting
Optimisation result
Constant (fix)Trend (fix)FreeNo trendTrend
Calibration     c, τw, f, αs, αq, βq, l, p c, τw, βq, l, p f, αs, αq
Step 1 l  c, τw, f, αs, αq, βq, p c, αs, β τw, f, αq, p
Step 2 l, αs  c, τw, f, αq, βq, p c, τw, αq, p f, βq
Step 3 l, αs, αq  c, τw, f, βq, p c, τw, βq, p f
Step 4 l, αs, αq, τw  c, f, βq, p c, βq, p f
Step 5 l, αs, αq, τw, p  c, f, βq  c, f, βq
Step 6 l, αs, αq, τw, p f c, βq  c, βq
Step 7 l, αs, αq, τw, p f, c βq  βq

Close Modal