Boulariah O; Mikhailov PA; Longobardi A; Elizariev AN; Aksenov SG

doi:10.19637/j.cnki.2305-7068.2021.02.008

doi: 10.19637/j.cnki.2305-7068.2021.02.008

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出版历程
- 收稿日期: 2020-11-02
- 录用日期: 2021-04-20
- 网络出版日期: 2021-08-04
- 刊出日期: 2021-06-28

Assessment of prediction performances of stochastic models: Monthly groundwater level prediction in Southern Italy

1.
Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II, 123, 84084, Italy
2.
Ufa State Aviation Technical University, 450000, Russian Federation

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Corresponding author: oboulariah@unisa.it

摘要

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Abstract: Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills. In this paper, we proposed a method for searching the seasonal autoregressive integrated moving average (SARIMA) model parameters to predict the behavior of groundwater time series affected by the issues mentioned. Based on the analysis of statistical indices, 8 stations among 44 available within the Campania region (Italy) have been selected as the highest quality measurements. Different SARIMA models, with different autoregressive, moving average and differentiation orders had been used. By reviewing the criteria used to determine the consistency and goodness-of-fit of the model, it is revealed that the model with specific combination of parameters, SARIMA (0,1,3) (0,1,2) ₁₂, has a high R² value, larger than 92%, for each of the 8 selected stations. The same model has also good performances for what concern the forecasting skills, with an average NSE of about 96%. Therefore, this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.
- Groundwater level forecast /
- Stochastic modelling /
- Southern Italy /
- Seasonality /
- Homogeneity

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Figure 1. Flowchart of applied methodology for forecasting time series

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Figure 2. ARIMA model prediction method (Chatfield et al.1973)

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Figure 3. Digital elevation model with location of water wells (right panel) and mean annual precipitation (left panel) in the study area

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Figure 4. Predicted and observed values of the ground water level.

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Figure 5. Autocorrelation function graph for the residues of the SARIMA model (1,1,2) (0,1,1)₁₂

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Figure 6. Forecasting using SARIMA(0,1,3)(0,1,2)₁₂; (a) Acera Capomazzo, (b) Casamicciola, (c) Cassano di Sessa Aurunca, (d) Forio(Calitto), (e) Forio(Pontone), (f) Forio(Umberto I), (g) Nocelleto di Carinola, (h) Parete(tre ponti) scrivi cosa sono le fasce colorate.

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Table 1. Forecasting models Results based on AIC and BIC criteria

Name of station	Parameters of model	AIC	BIC
Acera Capomazzo	(1,1,2)(0,1,2)₁₂	514.44	542.39
Casamicciola	(1,1,2)(0,1,1)₁₂	−1228.75	−1209.5
Cassano di Sessa Aurunca	(0,1,3)(0,1,2)₁₂	914.41	942.54
Forio(Calitto)	(1,1,2)(0,1,1)₁₂	607.55	630.75
Forio(Pontone)	(0,1,3)(0,1,2)₁₂	−571.39	−547.92
Forio(Umberto I)	(1,1,1)(0,1,1)₁₂	−39.8	−24.01
Nocelleto di Carinola	(1,1,1)(0,1,1)₁₂	−377.44	−309.26
Parete(tre ponti)	(1,1,2)(0,1,1)₁₂	−702.58	−682.21

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Table 2. The comparison of different SARIMA models based on accuracy measures

	Parete (tre ponti)	Nocelleto di carinola	Forio (Umberto I)	Forio (Pontone)	Forio (Calitto)	Cassano di Sessa Aurunca	Casamicciola	Accera Copmazzo
SARIMA (0,1,3)(0,1,2)₁₂
NSE	0.944	0.996	0.920	0.949	0.985	0.999	0.932	0.984
MAE	0.065	0.110	0.131	0.067	0.217	0.255	0.026	0.214
RMSE	0.107	0.183	0.218	0.108	0.363	0.420	0.037	0.331
Pearson cоr.	0.971	0.935	0.960	0.974	0.962	0.930	0.965	0.983
MSE	0.011	0.032	0.047	0.011	0.121	0.176	0,001	0.109
d	0.999	0.999	0.999	0.999	0.999	0.999	0.999	0.999
BIAS$	−0.026	0.027	−0.006	−0.012	−0.046	−0.045	0.036	0.003
MSDE	4.7E-04	4.3E-06	1.5E-05	3.1E-09	0.006	0.101	2.2E-06	0.016
R²	0.944	0.874	0.922	0.949	0.9257	0.865	0.932	0.967
AIC	−678.64	−321.22	−36.87	−571.61	625.55	914.41	−1203.63	532.08
BIC	−654.2	−294.18	−13.18	−547.92	652.85	941.39	−1180.55	559.97
SARIMA (1,1,2)(0,1,1)₁₂
NSE	0.943	0.996	0.920	0.947	0.689	0.999	0.930	0.984
MAE	0.064	0.109	0.129	0.068	0.529	0.255	0.026	0.211
RMSE	0.108	0.182	0.218	0.110	1625774	0.422	0.037	0.329
Pearson cor.	0.971	0.934	0.960	0.973	0.553	0.929	0.964	0.983
MSE	0.012	0.032	0.047	0.012	0.419	0.178	0.001	0.107
d	0.999	0.999	0.999	0.999	0.999	0.999	0.999	0.999
BIAS$	−0.018	0.032	−0.0088	−0.013	−2.340	−0.046	−0.117	0.057
MSDE	0.0001	2.6E-06	1.3E-05	3.1E-09	0.198	0.106	2.2E-06	0017
R²	0.943	0.873	0.921	0.948	0.306	0.863	0.931	0.967
AIC	−702.58	−327.03	−37.95	−562.72	607.55	920.63	−1226.74	519.45
BIC	−682.21	−304.5	−18.2	−542.97	630.3	943.12	−1207.5	542.69
SARIMA (1,1,2)(0,1,1)₁₂
NSE	0.943	0.996	0.920	0.946	0.985	0.999	0.940	0.984
MAE	0.063	0.110	0.129	0.069	0.219	0.257	0.024	0.212
RMSE	0.108	0.183	0.218	0.111	0.365	0.424	0.034	0.330
Pearson cor.	0.971	0.934	0.960	0.973	0.962	0.928	0.970	0.983
MSE	0,011	0.032	0.047	0.012	0.122	0.180	0.001	0.107
d	0.999	0.999	0.999	0.999	0.999	0.999	0.999	0.999
BIAS$	−0.018	0.033	−0.008	−0.013	−0.042	−0.047	0.048	0.061
MSDE	0,0001	2.4E-06	1.3E-05	3.1E-09	0.005	0.109	2.2E-06	0017
R²	0.943	0.873	0.921	0.947	0.862	0.862	0.941	0.967
AIC	−672.01	−327.44	−39.8	−561.6	629.36	924.5	−1194.32	518.6
BIC	−655.71	−309.41	−24	−545.8	647.56	942.491	−1178.931	537.19

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Table 3. Statistical index values for the selected SARIMA model (0,1,3) (0,1,2)₁₂

	NSE	BIAS%	R²	d	r
Accera Copmazzo	0.98	0.003	0.96	0.99	0.98
Casamicciola	0.93	0.03	0.93	0.99	0.96
Cassano di Sessa Aurunca	0.99	−0.04	0.86	0.99	0.93
Forio Calitto	0.98	−0.04	0.92	0.99	0.96
Forio Pontone	0.94	−0.012	0.94	0.99	0.97
Forio Umberto I	0.92	−0.006	0.92	0.99	0.96
Nocelleto di carinola	0.99	0.02	0.87	0.99	0.93
Parete tre ponti	0.94	−0.02	0.94	0.99	0.97
Model Quality (Very good)	0.75< NSE<1.00	PBIAS<±10	0.75 < R²≤ 1.0	1	r > 0.7

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