Hydrograph Analysis using HARTT

SEA Working Paper 00/12

Explaining groundwater hydrographs: separating atypical rainfall events from time trends

Ruhi Ferdowsian^A, David J. Pannell^B , Clare McCarron^A, Arjen Ryder^A and Lisa Crossing^A

^AAgriculture Western Australia, Albany WA 6330, Australia.
^BFaculty of Agriculture, University of Western Australia, Perth, WA 6907, Australia.

Tables

Table 1. Results of OLS estimations

				Rainfall (m/mm)		Month (m/month)
Bore no	Rainfall variable	Lag (L) (months)	Constant (K₀) (m)**	Parameter estimate (K₁)	P	Parameter estimate (K₂)	P	R²
1	AMRR	28	-18.7	0.0024	0.000	0.018	0.000	0.93
2*	AMRR	28	-18.2	0.0007	0.000	0.018	0.000	0.99
3*	AMRR	10	-18.3	0.0004	0.042	0.012	0.000	0.95
4	AARR	7	-17.1	0.0013	0.181	0.017	0.000	0.63
5	AMRR	46	-15.6	0.0033	0.007	0.028	0.000	0.87
6	AMRR	14	-13.8	0.0016	0.000	0.025	0.000	0.91
7	AMRR	17	-12.8	0.0022	0.000	0.022	0.000	0.97
8	AARR	1	-13.5	0.0016	0.000	0.013	0.000	0.90
9*	AMRR	27	-12.5	0.0005	0.000	0.011	0.000	0.97
10	AMRR	11	-11.4	0.0019	0.000	0.027	0.000	0.98
11	AMRR	7	-8.2	0.0040	0.000	0.007	0.000	0.79
12	AMRR	6	-7.8	0.0036	0.000	0.016	0.000	0.95
13	AMRR	1	-6.4	0.0033	0.008	0.015	0.000	0.73
14	AMRR	17	-5.9	0.0005	0.357	0.017	0.000	0.90
15	AMRR	3	-5.7	0.0031	0.000	0.001	0.248	0.91
16	AMRR	6	-4.9	0.0035	0.000	0.005	0.006	0.62
17	AMRR	3	-5.5	0.0034	0.000	0.023	0.000	0.91
18	AMRR	2	-5.2	0.0019	0.000	0.008	0.000	0.80
19	AMRR	4	-5.0	0.0007	0.033	0.015	0.000	0.92
20	AMRR	0	-3.2	0.0020	0.066	0.015	0.000	0.48
21*	AMRR	3	-4.1	0.0032	0.000	-0.005	0.001	0.72
22	AMRR	0	-3.5	0.0053	0.000	-0.007	0.000	0.80
23	AMRR	1	-3.5	0.0041	0.000	-0.014	0.000	0.86
24	AMRR	0	-3.3	0.0061	0.000	-0.001	0.683	0.84
25	AMRR	6	-2.8	0.0048	0.000	0.020	0.000	0.96
26	AMRR	0	-3.7	0.0060	0.000	-0.016	0.000	0.82
27	AMRR	5	-3.2	0.0008	0.000	0.002	0.000	0.54
28	AMRR	0	-2.8	0.0024	0.000	0.012	0.000	0.79
29	AMRR	1	-2.6	0.0014	0.001	0.005	0.000	0.54
30	AARR	0	-2.2	0.0015	0.096	0.011	0.000	0.45
31*	AMRR	3	-2.3	0.0036	0.000	-0.005	0.002	0.77
32	AMRR	1	-1.4	0.0015	0.014	0.007	0.001	0.36
33	AARR	0	-2.0	0.0010	0.098	0.001	0.390	0.09
34	AMRR	0	-1.9	0.0011	0.035	0.000	0.843	0.20
35	AMRR	0	-1.5	0.0021	0.030	0.000	0.844	0.17
36	AMRR	0	-0.5	0.0008	0.277	-0.001	0.525	0.11
37	AARR	0	-1.4	0.0006	0.015	0.003	0.000	0.46
38	AMRR	1	-1.0	0.0016	0.009	0.001	0.505	0.34
39	AMRR	1	-1.0	0.0028	0.000	0.003	0.024	0.78
40*	AARR	1	-1.1	0.0024	0.000	-0.003	0.002	0.71
41	AARR	0	-0.8	0.0024	0.011	-0.006	0.045	0.41
42	AMRR	0	-1.4	0.0020	0.000	0.003	0.089	0.40
43	AMRR	0	-0.2	0.0035	0.005	-0.012	0.010	0.61
44	AMRR	0	-0.4	0.0018	0.000	0.005	0.016	0.58
45	AARR	0	-1.2	0.0026	0.024	-0.003	0.542	0.36
46	AARR	0	-0.9	0.0016	0.170	-0.009	0.093	0.34
47	AMRR	0	-0.6	0.0005	0.272	-0.002	0.127	0.15
48	AARR	0	-0.2	0.0018	0.000	-0.004	0.006	0.55
49	AMRR	0	-0.3	0.0007	0.006	0.000	0.663	0.25

*, Bores in Tertiary sand plain;

**, constant is approximately equal to initial depth to groundwater.

Table 2. Diagnostic test results for OLS models

Bore no	Omitted variable test		Heteroskedasticity test		Durbin-Watson statistic
1	0.021	*	0.091		1.13	++
2	0.052		0.021	*	1.07	++
3	0.792		0.104		1.47	+
4	0.799		0.054		2.14
5	0.000	*	0.082		0.53	++
6	0.466		0.000	*	1.37	++
7	0.001	*	0.645		0.88	++
8	0.003	*	0.022	*	1.02	++
9	0.222		0.562		1.57	+
10	0.000	*	0.550		0.54	++
11	0.438		0.947		1.09	++
12	0.001	*	0.001	*	1.44	+
13	0.000	*	0.789		0.39	++
14	0.336		0.001	*	0.17	++
15	0.282		0.011	*	1.23	++
16	0.556		0.289		1.53	+
17	0.288		0.676		1.71
18	0.173		0.740		0.81	++
19	0.743		0.752		1.83
20	0.059		0.039	*	1.13	++
21	0.577		0.997		0.79	++
22	0.152		0.400		0.72	++
23	0.115		0.001	*	0.33	++
24	0.823		0.448		1.58	+
25	0.963		0.707		1.19	++
26	0.003	*	0.831		0.89	++
27	0.261		0.457		1.16	++
28	0.011	*	0.304		0.80	++
29	0.116		0.959		0.83	++
30	0.170		0.450		0.79	++
31	0.175		0.965		1.44	+
32	0.303		0.001	*	1.33	++
33	0.755		0.020	*	1.96
34	0.400		0.418		0.58	++
35	0.325		0.849		0.74	++
36	0.515		0.011	*	0.41	++
37	0.790		0.213		0.75	++
38	0.029	*	0.334		1.66
39	0.432		0.827		0.40	++
40	0.809		0.880		0.55	++
41	0.410		0.139		0.29	++
42	0.576		0.758		1.00	++
43	0.542		0.803		0.49	++
44	0.208		0.609		1.87
45	0.600		0.615		0.81	++
46	0.000	*	0.552		0.34	++
47	0.041	*	0.402		1.06	++
48	0.184		0.141		1.46
49	0.974		0.794		1.20	++

*, Below critical value of 0.05;

+, below upper critical value of 1.62 (i.e. rejection of H₀ of no serial correlation is not clear);

++, below lower critical value of 1.44 (i.e. reject H₀ of no serial correlation, with P = 0.05).

Table 3. Results of PRAIS estimations

		Rainfall variable (m/mm)		Month (m/month)
Bore no	Constant (K₀) (m)	Parameter estimate (K₁)	p	Parameter estimate (K₂)	p	R²	Durbin-Watson statistic
1	-18.7	0.0026	0.000	0.052	0.000	0.99	1.63
2	-18.2	0.0007	0.000	0.053	0.000	1.00	1.67
3	-18.3	0.0004	0.051	0.036	0.000	0.99	1.52	+
4	-17.1	0.0007	0.374	0.049	0.000	0.97	1.79
5	-15.7	0.0033	0.003	0.082	0.000	0.99	1.15	++
6	-13.9	0.0017	0.000	0.078	0.000	1.00	1.29	++
7	-12.8	0.0021	0.000	0.066	0.000	1.00	1.80
8	-13.5	0.0015	0.000	0.036	0.000	0.99	1.44	+
9	-12.5	0.0005	0.001	0.032	0.000	0.99	1.84
10	-11.5	0.0020	0.000	0.079	0.000