Hybrid wavelet transform – MLR and ANN models for river flow prediction: Case study of Brahmaputra river (Pancharatna station)

Khandekar, Sachin Dadu; Aswar, Dinesh Shrikrishna; Sabale, Pandurang Digamber; Khandekar, Varsha Sachin; Bajad, Mohankumar Namdeorao; Khaple, Shivakumar

Hybrid wavelet transform – MLR and ANN models for river flow prediction: Case study of Brahmaputra river (Pancharatna station)

Scientific Review Engineering and Environmental Sciences

Volume 33 (2024): Issue 1 (March 2024)

By: Sachin Dadu Khandekar

, Dinesh Shrikrishna Aswar, Pandurang Digamber Sabale, Varsha Sachin Khandekar, Mohankumar Namdeorao Bajad and Shivakumar Khaple

Open Access

|Feb 2024

Figures & Tables

Location of the gauging sitesSource: Khandekar (2014)

Observed flow seriesSource: Khandekar (2014)

Wavelet decomposition treeSource: Khandekar (2014).

Flow chart of model developmentSource: own elaboration.

Daubechies waveletsSource: Khandekar (2014).

Effect of Daubechies wavelet order on RMSE (four-day lead time)Source: own elaboration.

Scatter plot for lead time during different testing periodSource: own elaboration.

Time series plot for lead time during different testing period influence of decomposition level on model performanceSource: own elaboration.

Effect of decomposition level on determination coefficient (R2) for WMLR(db10) modelSource: own elaboration.

Flow series comparison between observed, WMLR(db10) and WANN(db10) modelled flow for monsoon seasonSource: own elaboration.

Correlation coefficients for the flow series

Output^* (Q_t+n)	Input (Q_t−j)^*
Output^* (Q_t+n)	Q_t	Q_t−1	Q_t−2	Q_t−3	Q_t−4	Q_t−5	Q_t−6	Q_t−7	Q_t−8	Q_t−9
Q_t+2	0.983	0.971	0.957	0.942	0.929	0.915	0.903	0.891	0.880	0.871
Q_t+4	0.957	0.942	0.928	0.915	0.902	0.891	0.880	0.870	0.862	0.854
Q_t+7	0.915	0.902	0.891	0.880	0.870	0.862	0.854	0.846	0.839	0.832
Q_t+14	0.846	0.839	0.832	0.825	0.818	0.812	0.805	0.799	0.792	0.784

Values of statistical parameters for 14-day lead time

Model type	Training period					Testing period					Optimum ANN structure
Model type	RMSE	R²	MAE	BIAS	SI	RMSE	R²	MAE	BIAS	SI	Optimum ANN structure
ANN	5 704.97	0.765	4 035.67	1.014	0.353	7 084.21	0.673	5 116.37	1.068	0.433	4-2-1
MLR	4 584.37	0.848	3 204.37	1.000	0.283	5 415.77	0.809	3 630.94	0.999	0.333	–
WANN-db1l5	4 173.09	0.874	2 765.27	1.007	0.258	4 913.55	0.843	3 425.92	1.036	0.300	24-4-1
WMLR-db1l5	4 761.19	0.836	3 215.26	1.000	0.294	6 050.48	0.762	3 886.88	0.999	0.371	–
WANN-db2l5	3 071.96	0.932	2 062.78	1.004	0.190	4 716.30	0.855	3 017.38	1.038	0.288	24-3-1
WMLR-db2l5	4 037.44	0.882	2 571.67	1.000	0.249	4 876.84	0.845	3 109.41	0.999	0.299	–
WANN-db3l5	2 420.95	0.958	1 737.07	1.014	0.149	3 848.56	0.904	2 663.88	1.031	0.235	24-2-1
WMLR-db3l5	3 172.17	0.927	2 083.46	1.000	0.196	4 770.31	0.852	2 694.26	0.999	0.292	––
WANN-db8l5	1 922.74	0.973	1 353.08	1.012	0.119	3 746.15	0.908	2 190.53	1.020	0.229	24-2-1
WMLR-db8l5	1 985.33	0.971	1 325.19	1.000	0.123	2 612.09	0.955	1 731.46	0.999	0.160	–
WANN-db10l5	2 225.74	0.964	1 600.63	0.995	0.138	3 539.60	0.918	2 287.83	0.986	0.217	24-3-1
WMLR-db10l5	1 670.31	0.979	1 137.67	1.000	0.103	2 196.46	0.968	1 435.57	1.000	0.134	–

Values of statistical parameters for seven-day lead time

Model type	Training period					Testing period					Optimum ANN structure
Model type	RMSE	R²	MAE	BIAS	SI	RMSE	R²	MAE	BIAS	SI	Optimum ANN structure
ANN	4 308.72	0.866	2 801.05	1.002	0.266	5 185.33	0.825	3 441.99	1.032	0.318	4-3-1
MLR	4 490.92	0.854	2 986.84	1.000	0.277	5 376.87	0.811	3 429.75	0.999	0.331	–
WANN-db1l5	2 830.19	0.942	1 961.30	1.004	0.175	4 131.69	0.889	2 942.38	1.016	0.254	24-3-1
WMLR-db1l5	3 122.62	0.929	1 942.73	1.000	0.193	4 123.65	0.889	2 415.44	0.999	0.254	–
WANNdb2l5	2 038.56	0.970	1 408.02	1.004	0.126	2 894.02	0.945	1 927.13	1.024	0.178	24-2-1
WMLR-db2l5	2 623.55	0.950	1 617.63	1.000	0.162	3 193.40	0.933	1 937.76	0.999	0.196	–
WANN-db3l5	1 683.52	0.979	1 151.42	1.003	0.104	2 525.32	0.958	1 639.74	1.013	0.155	24-3-1
WMLR-db3l5	2 129.55	0.967	1 336.34	1.000	0.132	2 987.57	0.942	1 640.06	0.999	0.184	–
WANN-db8l5	1 313.63	0.987	871.91	0.999	0.081	2 038.33	0.973	1 233.97	0.997	0.125	24-2-1
WMLR-db8l5	1 318.74	0.987	837.08	1.000	0.082	1 702.96	0.981	1 042.41	0.999	0.105	–
WANN-db10l5	1 187.51	0.989	792.06	0.999	0.073	1 929.58	0.975	1 060.01	1.005	0.119	24-2-1
WMLR-db10l5	1 167.65	0.990	733.49	1.000	0.072	1 585.02	0.984	881.76	1.000	0.097	–

Values of statistical parameters for two-day lead time

Model type	Training period					Testing period					Optimum ANN structure
Model type	RMSE	R²	MAE	BIAS	SI	RMSE	R²	MAE	BIAS	SI	–
ANN	1 764.66	0.977	1 044.28	1.002	0.109	2 463.33	0.960	1 401.83	1.014	0.152	2-8-1
MLR	1 828.26	0.976	1 058.12	1.000	0.113	2 535.96	0.958	1 293.19	1.000	0.156	–
WANN-db1l5	1 199.43	0.989	757.47	1.008	0.074	1 795.99	0.979	1 144.51	1.018	0.110	12-2-1
WMLR-db1l5	1 228.25	0.989	680.19	1.000	0.076	1 758.64	0.980	913.41	1.000	0.109	–
WANN-db2l4	960.30	0.993	540.14	1.001	0.059	1 415.36	0.987	796.43	1.007	0.087	10-2-1
WMLR-db2l5	1 093.66	0.991	595.74	1.000	0.068	1 478.74	0.986	769.43	0.999	0.091	–
WANN-db3l4	813.84	0.995	469.56	1.001	0.050	1 202.33	0.990	698.70	1.007	0.074	10-3-1
WMLR-db3l5	909.81	0.994	510.23	1.000	0.056	1 311.38	0.989	629.76	0.999	0.081	–
WANN-db8l5	553.07	0.998	368.93	1.000	0.034	1 054.10	0.992	543.92	1.000	0.065	12-2-1
WMLR-db8l5	526.83	0.998	296.78	1.000	0.033	775.11	0.996	406.20	0.999	0.048	–
WANN-db10l5	481.40	0.998	298.51	0.999	0.030	933.06	0.994	436.49	0.999	0.057	12-2-1
WMLR-db10l5	471.99	0.998	261.79	1.000	0.029	751.87	0.996	369.69	1.000	0.046	–

Statistical properties of flow data

Statistical parameter	Training	Testing	All
Q_mean [m³·s⁻¹]	16 159	16 236	16 161
Q_max [m³·s⁻¹]	59 832	76 236	76 236
Q_min [m³·s⁻¹]	2 628	1 723	1 723
S_d [m³·s⁻¹]	11 783	12 388	11 965
C_x	0.726	0.968	0.809

Optimal input combination

Lead time [day]	Input parameter^*	Output parameter^** Q_(t+n)
2	Q_t, Q_(t−1)	Q_(t+2)
4	Q_t, Q_(t−1), Q_(t−2), Q_(t−3)	Q_(t+4)
7	Q_t, Q_(t−1), Q_(t−2), Q_(t−3)	Q_(t+7)
14	Q_t, Q_(t−1), Q_(t−2), Q_(t−3)	Q_(t+14)

Effect of decomposition level on determination coefficient (R2) for WMLR-db10 model (testing period)

Two-day lead time		Four-day lead time		Seven-day lead time		14-day lead time
Model type	R²	Model type	R²	Model type	R²	Model type	R²
WMLR-db10l1	0.976	WMLR-db10l1	0.914	WMLR-db10l1	0.824	WMLR-db10l1	0.656
WMLR-db10l2	0.995	WMLR-db10l2	0.966	WMLR-db10l2	0.861	WMLR-db10l2	0.684
WMLR-db10l3	0.996	WMLR-db10l3	0.990	WMLR-db10l3	0.967	WMLR-db10l3	0.760
WMLR-db10l4	0.996	WMLR-db10l4	0.991	WMLR-db10l4	0.983	WMLR-db10l4	0.953
WMLR-db10l5	0.996	WMLR-db10l5	0.991	WMLR-db10l5	0.984	WMLR-db10l5	0.968

Values of statistical parameters for four-day lead time

Model type	Training period					Testing period					Optimum ANN structure
Model type	RMSE	R²	MAE	BIAS	SI	RMSE	R²	MAE	BIAS	SI	Optimum ANN structure
ANN	3 133.09	0.929	2 067.41	1.005	0.194	3 890.35	0.901	2 566.07	1.031	0.239	4-8-1
MLR	3 136.83	0.929	1 988.84	1.000	0.194	3 932.06	0.899	2 274.72	1.000	0.243	–
WANN-db1l5	1 918.22	0.973	1 229.16	1.008	0.118	2 590.84	0.956	1 717.58	1.018	0.159	24-3-1
WMLR-db1l5	2 088.67	0.968	1 268.59	1.000	0.129	2 909.44	0.945	1 618.86	1.000	0.179	–
WANN-db2l5	1 431.04	0.985	868.66	1.001	0.088	1 986.38	0.974	1 137.20	1.009	0.122	24-2-1
WMLR-db2l4	1 922.49	0.973	1 160.03	1.000	0.119	2 342.13	0.964	1 354.14	0.999	0.144	–
WANN-db3l5	1 280.06	0.988	790.25	1.001	0.079	1 683.59	0.982	1 034.97	1.004	0.104	24-2-1
WMLR-db3l5	1 528.75	0.983	924.38	1.000	0.094	2 067.67	0.972	1 084.63	0.999	0.127	–
WANN-db8l4	962.64	0.993	601.76	1.001	0.059	1 465.35	0.986	774.11	1.000	0.090	20-2-1
WMLR-db8l5	940.03	0.994	556.62	1.000	0.058	1 213.32	0.990	664.47	0.999	0.075	–
WANN-db10l5	822.67	0.995	527.85	1.003	0.051	1 477.12	0.986	755.19	1.004	0.091	24-2-1
WMLR-db10l5	785.37	0.995	460.22	1.000	0.048	1 174.80	0.991	612.69	1.000	0.072	–

Values of statistical parameters for WMLR(db10) model for monsoon season (June to September) in testing period

Year	RMSE	R²	MAE	BIAS	S.I.
Two-day lead time
1997	890.55	0.995	596.966	1.000	0.034
1998	1 448.88	0.995	767.802	0.999	0.042
1999	1 070.20	0.996	629.899	0.999	0.034
Four-day lead time
1997	1 572.65	0.984	1 072.41	1.000	0.059
1998	2 188.39	0.989	1 153.71	0.999	0.063
1999	1514.68	0.992	968.89	0.998	0.048
Seven-day lead time
1997	2 243.79	0.967	1 667.90	0.998	0.084
1998	2 971.27	0.980	1 677.60	1.001	0.086
1999	1 797.46	0.989	1 209.73	0.999	0.058
14-day lead time
1997	3 035.86	0.938	2 292.43	1.002	0.115
1998	3 722.21	0.967	2 295.27	1.006	0.111
1999	2 588.93	0.976	1 972.25	0.998	0.084

Percent improvement in RMSE with increase in wavelet order from db1 to db10

Lead time [day]	Improvement in RMSE [%]
2	57.25
4	54.66
7	61.56
14	55.30

DOI: https://doi.org/10.22630/srees.5258 | Journal eISSN: 2543-7496 | Journal ISSN: 1732-9353

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Language: English

Page range: 69 - 94

Submitted on: Sep 2, 2023

Accepted on: Jan 19, 2024

Published on: Feb 28, 2024

Published by: Warsaw University of Life Sciences - SGGW Press

In partnership with: Paradigm Publishing Services

Keywords:

wavelet transform,

artificial neural network,

multiple linear regression,

streamflow,

Daubechies wavelet,

time series

Related subjects:

Architecture and design,

Architecture,

Architects, buildings,

Geosciences,

Geosciences, other,

Engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Geosciences,

Geology and mineralogy

© 2024 Sachin Dadu Khandekar, Dinesh Shrikrishna Aswar, Pandurang Digamber Sabale, Varsha Sachin Khandekar, Mohankumar Namdeorao Bajad, Shivakumar Khaple, published by Warsaw University of Life Sciences - SGGW Press
This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 License.

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Hybrid wavelet transform – MLR and ANN models for river flow prediction: Case study of Brahmaputra river (Pancharatna station)

Figures & Tables

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FIGURE 9.

FIGURE 10.

Correlation coefficients for the flow series

Values of statistical parameters for 14-day lead time

Values of statistical parameters for seven-day lead time

Values of statistical parameters for two-day lead time

Statistical properties of flow data

Optimal input combination

Effect of decomposition level on determination coefficient (R2) for WMLR-db10 model (testing period)

Values of statistical parameters for four-day lead time

Values of statistical parameters for WMLR(db10) model for monsoon season (June to September) in testing period

Percent improvement in RMSE with increase in wavelet order from db1 to db10

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