Random Modeling of Daily Rainfall and Runoff Using a Seasonal Model and Wavelet Denoising

Table 2

The probability distribution of the percentage coefficients obtained from calibrated daily rainfall and runoff data using Fourier smoothing and wavelet denoising.

Rainfall data using Fourier smoothing
M	Range of k	−1.0<𝑘≦−0.5	−0.5<𝑘≦−0.3	−0.3<𝑘≦0.0	0.0<𝑘≦0.5	0.5<𝑘≦1.0	1.0<𝑘≦3.0
0	Probability	0.139726	0.158904	0.252055	0.306849	0.104110	0.038356
	Cumulative probability	0.139726	0.298630	0.550685	0.857534	0.961644	1
Runoff data using Fourier smoothing
M	Range of k	−1.0<𝑘≦−0.5	−0.5<𝑘≦−0.3	−0.3<𝑘≦0.0	0.0<𝑘≦0.5	0.5<𝑘≦1.0	1.0<𝑘≦5.0
0	Probability	0.098630	0.147945	0.323288	0.315069	0.068493	0.046575
	Cumulative probability	0.098630	0.246575	0.569863	0.884932	0.953425	1
Rainfall data using wavelet denoising
M	Range of k	−1.0<𝑘≦−0.5	−0.5<𝑘≦−0.3	−0.3<𝑘≦0.0	0.0<𝑘≦0.5	0.5<𝑘≦1.0	1.0<𝑘≦3.0
1	Probability	0.035616	0.063014	0.380822	0.490411	0.024658	0.005479
	Cumulative probability	0.035616	0.098630	0.479452	0.969863	0.994521	1
2	Probability	0.071233	0.090411	0.347945	0.405479	0.068494	0.016438
	Cumulative probability	0.071233	0.161644	0.509589	0.915068	0.983562	1
3	Probability	0.104110	0.131506	0.298630	0.364384	0.087671	0.013699
	Cumulative probability	0.104110	0.235616	0.534246	0.898630	0.986301	1
4	Probability	0.109589	0.134247	0.279452	0.356164	0.093151	0.027397
	Cumulative probability	0.109589	0.243836	0.523288	0.879452	0.972603	1
Runoff data using wavelet denoising
M	Range of k	−1.0<𝑘≦−0.5	−0.5<𝑘≦−0.3	−0.3<𝑘≦0.0	0.0<𝑘≦0.5	0.5<𝑘≦1.0	1.0<𝑘≦2.1
1	Probability	0.002740	0.032877	0.468493	0.476712	0.016438	0.002740
	Cumulative probability	0.002740	0.035617	0.504110	0.980822	0.997260	1
2	Probability	0.019178	0.046575	0.468494	0.435616	0.021918	0.008219
	Cumulative probability	0.019178	0.065753	0.534247	0.969863	0.991781	1
3	Probability	0.027397	0.079452	0.449315	0.402740	0.030137	0.010959
	Cumulative probability	0.027397	0.106849	0.556164	0.958904	0.989041	1
4	Probability	0.049315	0.112329	0.383561	0.378082	0.063014	0.013699
	Cumulative probability	0.049315	0.161644	0.545205	0.923287	0.986301	1