IWA Publishing

The dependence of

on A can be generalized by generating an exponential fit model that has the following form:

where a, b, c and d are the coefficients of the fit equation varying with the value of the integration window,

⁠. The fit parameters together with the fit statistics are tabulated in Table 1.

Table 1

The coefficient of fit form and statistical properties in Equation (12)

	Parameters				Statistics
Δ	a	b	c	d	SSE	R²	R² Adj.	RMSE
0.1	−1955.34	2.628738	0.001667	−2.36566	0.000438	1	1	0.002032
0.2	−350.522	2.559461	0.006826	−2.36966	0.000444	1	1	0.002057
0.3	−128.262	2.49452	0.015523	−2.37359	0.000448	1	1	0.002075
0.4	−63.3889	2.433597	0.027759	−2.37747	0.000449	1	1	0.002087
0.5	−37.0788	2.37642	0.043526	−2.38131	0.000448	1	1	0.002095
0.6	−24.175	2.322705	0.062815	−2.3851	0.000445	1	1	0.002098
0.7	−17.0047	2.272198	0.085613	−2.38887	0.00044	1	1	0.002098
0.8	−12.6507	2.224659	0.111912	−2.39262	0.000434	1	1	0.002094
0.9	−9.82577	2.179913	0.1417	−2.39635	0.000427	1	1	0.002088
1	−7.89589	2.137756	0.174969	−2.40007	0.000419	1	0.999999	0.002079
1.1	−6.52199	2.098013	0.21171	−2.40378	0.000411	1	0.999999	0.002068
1.2	−5.51039	2.060518	0.251916	−2.4075	0.000401	1	0.999999	0.002055
1.3	−4.74444	2.025144	0.29558	−2.41122	0.000391	1	0.999999	0.002041
1.4	−4.15061	1.991764	0.342694	−2.41495	0.000381	0.999999	0.999999	0.002025
1.5	−3.68076	1.960239	0.393254	−2.4187	0.000371	0.999999	0.999999	0.002008
1.6	−3.30244	1.930456	0.447254	−2.42247	0.00036	0.999999	0.999999	0.001989
1.7	−2.99315	1.902338	0.504688	−2.42627	0.000349	0.999999	0.999999	0.00197
1.8	−2.73685	1.875786	0.565552	−2.43009	0.000338	0.999999	0.999999	0.00195
1.9	−2.52189	1.850709	0.629843	−2.43395	0.000327	0.999999	0.999999	0.001929
2	−2.33966	1.827029	0.697556	−2.43785	0.000316	0.999999	0.999999	0.001907
2.1	−2.18368	1.804697	0.768686	−2.44178	0.000305	0.999999	0.999999	0.001884
2.2	−2.04898	1.783623	0.843234	−2.44576	0.000294	0.999999	0.999999	0.001861
2.3	−1.93172	1.763771	0.921195	−2.44979	0.000283	1	0.999999	0.001837
2.4	−1.82889	1.745063	1.002569	−2.45387	0.000273	1	0.999999	0.001813
2.5	−1.7381	1.727479	1.087352	−2.45801	0.000262	1	0.999999	0.001787

	Parameters				Statistics
Δ	a	b	c	d	SSE	R²	R² Adj.	RMSE
0.1	−1955.34	2.628738	0.001667	−2.36566	0.000438	1	1	0.002032
0.2	−350.522	2.559461	0.006826	−2.36966	0.000444	1	1	0.002057
0.3	−128.262	2.49452	0.015523	−2.37359	0.000448	1	1	0.002075
0.4	−63.3889	2.433597	0.027759	−2.37747	0.000449	1	1	0.002087
0.5	−37.0788	2.37642	0.043526	−2.38131	0.000448	1	1	0.002095
0.6	−24.175	2.322705	0.062815	−2.3851	0.000445	1	1	0.002098
0.7	−17.0047	2.272198	0.085613	−2.38887	0.00044	1	1	0.002098
0.8	−12.6507	2.224659	0.111912	−2.39262	0.000434	1	1	0.002094
0.9	−9.82577	2.179913	0.1417	−2.39635	0.000427	1	1	0.002088
1	−7.89589	2.137756	0.174969	−2.40007	0.000419	1	0.999999	0.002079
1.1	−6.52199	2.098013	0.21171	−2.40378	0.000411	1	0.999999	0.002068
1.2	−5.51039	2.060518	0.251916	−2.4075	0.000401	1	0.999999	0.002055
1.3	−4.74444	2.025144	0.29558	−2.41122	0.000391	1	0.999999	0.002041
1.4	−4.15061	1.991764	0.342694	−2.41495	0.000381	0.999999	0.999999	0.002025
1.5	−3.68076	1.960239	0.393254	−2.4187	0.000371	0.999999	0.999999	0.002008
1.6	−3.30244	1.930456	0.447254	−2.42247	0.00036	0.999999	0.999999	0.001989
1.7	−2.99315	1.902338	0.504688	−2.42627	0.000349	0.999999	0.999999	0.00197
1.8	−2.73685	1.875786	0.565552	−2.43009	0.000338	0.999999	0.999999	0.00195
1.9	−2.52189	1.850709	0.629843	−2.43395	0.000327	0.999999	0.999999	0.001929
2	−2.33966	1.827029	0.697556	−2.43785	0.000316	0.999999	0.999999	0.001907
2.1	−2.18368	1.804697	0.768686	−2.44178	0.000305	0.999999	0.999999	0.001884
2.2	−2.04898	1.783623	0.843234	−2.44576	0.000294	0.999999	0.999999	0.001861
2.3	−1.93172	1.763771	0.921195	−2.44979	0.000283	1	0.999999	0.001837
2.4	−1.82889	1.745063	1.002569	−2.45387	0.000273	1	0.999999	0.001813
2.5	−1.7381	1.727479	1.087352	−2.45801	0.000262	1	0.999999	0.001787

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