Forecasting of saline intrusion in Ham Luong river, Ben Tre province (Southern Vietnam) using Box-Jenkins ARIMA models

Science & Technology Development Journal, 23(1):446-453 Open Access Full Text Article Research Article 1Institute of Tropical Biology, Vietnam Academy of Science and Technology, 85 Tran Quoc Toan Str., District 3, Ho Chi Minh City, Vietnam 2Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Str., Cau Giay District, Ha Noi City, Vietnam 3Department of Science and Technology of Ben Tre Province, 280 Str. 3/2, Ward 3, Ben Tre City, Ben Tre, Vietnam Correspondence Thai Thanh Tran, Institute of Tropical Biology, Vietnam Academy of Science and Technology, 85 Tran Quoc Toan Str., District 3, Ho Chi Minh City, Vietnam Email: thanhthai.bentrect@gmail.com History  Received: 2020-01-03  Accepted: 2020-02-17  Published: 2020-03-01 DOI : 10.32508/stdj.v23i1.1747 Forecasting of saline intrusion in Ham Luong river, Ben Tre province (Southern Vietnam) using Box-Jenkins ARIMAmodels Thai Thanh Tran1,*, Luong Duc Thien1, Ngo Xuan Quang1,2, Lam Van Tan3 Use your smartphone to scan this QR code and download this article ABSTRACT Introduction: HamLuong River is a branch ofMekong River located in Ben Tre Province, which has played a crucial role in supporting livelihoods of local residents and the province's economic de- velopment. However, the saline intrusion has been expanding in Ham Luong River, which seriously affects the productive agriculture, aquaculture, and further causes tremendous difficulties for local people's lives. Thus, it is crucial to have research for forecast the saline intrusion in Ham Luong River. Our aimwas to developmathematicalmodels in order to forecast the saline intrusion inHamLuong River, Ben Tre Province. Methods: The Auto regressive integrated moving average (ARIMA) model was built to forecast the weekly saline intrusion in Ham Luong River, which has been obtained from Ben Tre Province's Hydro-Meteorological Forecasting Center over eight years (from 2012 to 2019). Results: The saline concentration increased from January to March and then decreased from April to June. The highest salinity occurred in February andMarchwhile the lowest salinity was observed in early June. Moreover, the ARIMA technique provided an adequate predictivemodel for a forecast of the saline intrusion in An Thuan, Son Doc, and An Hiep station. However, the ARIMA model in My Hoa and Vam Mon might be improved upon by other forecasting methods. Conclusion: Our study suggested that the nonseasonal/seasonal ARIMA is an easy-to-use modeling tool for a quick forecast of the saline intrusion. Key words: ARIMA model, climate change, Mekong Delta, saline intrusion, time-series forecasts INTRODUCTION Ham Luong River (HLR) (in Vietnamese: Sông Hàm Luông) is a branch of the Mekong River in the Mekong Delta region that flows entirely within Ben Tre Province (BTP). HLR has played a crucial role in supporting the livelihoods of local residents, giving a productive environment for agriculture, aquaculture, capture fisheries, non-fish aquatic goods, and tourism revenue1. However, saline intrusion (SI) has been ex- panding in Mekong Delta, especially in BTP in recent years, which seriously affect the productive agricul- ture, aquaculture, and also causes tremendous diffi- culties for local people’s lives2. In the dry season, the saline water from the East Sea has intruded into HLR, and after that continued intrusion into complicated canal networks in BTP. SI is a complex phenomenon depending on a variety of variables include freshwater discharge from upstream, capacity, and morphology of the rivers/canals, a configuration of the drainage network, tidal conditions, and presence of control ar- tificial structures such as dams, sluice gates3,4. More- over, the impacts of climate change and sea-level rise also exacerbate the damage of SI5. However, SI might be predicted by using statistical models. Therefore, it is crucial to have research for forecast SI in HLR in or- der to give useful information that can be used in wa- ter resourcemanagement and saltwatermonitoring as well. Nowadays, capabilities to predict SI was a principle of interest in many studies. Various models have been developed to predict SI in main rivers. An artificial intelligence model, like an Artificial Neural Network (ANN) model6, simulate SI using a trained neural network. Remote sensing techniques, like resolution applications of available satellite images for detecting SI5. However, these methods mostly rely on complex statistics, artificial intelligence techniques, and large amounts of meteorological and topographic data 7. This leads to needing a model that is reliability, ac- curate, suitability whereas small amounts of hydrody- namic. The Auto regressive integrated moving aver- age (ARIMA)model is regarded as a smooth method, and it is applicable when the data is reasonably long and the correlation between past observations is sta- ble8. ARIMAmodel9, also known as the Box-Jenkins model or methodology, is commonly used in fore- casting and analysis. Some significant advantages of ARIMA forecasting are: first, it only needs endoge- nous variables and does not need to use other exoge- nous variables. Second, the ARIMA technique only Cite this article : Thanh Tran T, Duc Thien L, Xuan Quang N, Van Tan L. Forecasting of saline intrusion in Ham Luong river, Ben Tre province (Southern Vietnam) using Box-Jenkins ARIMAmodels. Sci. Tech. Dev. J.; 23(1):446-453. 446 Copyright © VNU-HCM Press. This is an open- access article distributed under the terms of the Creative Commons Attribution 4.0 International license. Science & Technology Development Journal, 23(1):446-453 requires the prior data of a time series to generalize the forecast. Hence, it can increase the forecast ac- curacy while keeping the number of parameters to a minimum10. This lead to the ARIMAmodel has been applied to analyze hydrological time series, especially at the monthly scale 11. Several studies in the literature have used the ARMA model for saline intrusion prediction. Sun and Koch (2001) used ARIMA to analyze and forecast of salin- ity in Apalachicola Bay, Florida. The results show that ARMIAhas been possible to statistically define the in- teraction of different parameters that affect the salin- ity change in Apalachicola Bay provided help one un- derstand the hydrodynamic circulation of the water body through the approach of data analysis12. Felisa et al. (2015) applied the ARIMA model to forecast the groundwater salinization in Ravenna (Italy). The resulting predictive models were validated by com- parison with data and demonstrated that data-driven approaches may provide useful information in situa- tions where physics-based models have only limited success in characterizing the phenomenon of inter- est13. As well as this, the ARIMA model is a ma- jor technique in hydrology and has been used exten- sively, mainly for the prediction of natural phenom- ena such as precipitation, streamflow events, solar ra- diation11,14,15. Here, our primary objective was to develop the ARIMA model to forecast the weekly SI of HLR, BTP in consideration of the accuracy, suitability, ad- equacy, and timeliness of a collected data, which have been obtained from Ben Tre Province’s Hydro- Meteorological Forecasting Center (BTHMFC) over eight years (from 2012 to 2019). The reliability, ac- curacy, suitability, and performance of the model are investigated in comparison with those of established tests, such as standardized residuals. MATERIALS ANDMETHODS Study area and dataset collection HLR is separated from Tien River in Tan Phu Com- mune, Chau Thanh District, BTP, creating a natural border between Bao andMinh islet. It has 72 km long, from 12 to 15 m in-depth, and from 1,200 to 1,500 m (over 3,000 m at estuary) in width. During the rainy season, average river flows are approximately 3,300– 3,400 m3/s, while around 800–850 m3/s in the dry season16. There are six saltwater monitoring stations (from es- tuary to upstream) situated in An Thuan-AT (Tiem Tom harbor, Ba Tri District), Son Doc-SD (Hung Le Commune, Giong Trom District), Phu Khanh- PK (Phu Khanh Commune, Thanh Phu District), My Hoa-MH(BenTre city), AnHiep-AH (AnHiepCom- mune, ChauThanhDistrict), andVamMon-VM(Phu Son Commune, Cho Lach District) (Figure 1). In each station, the saltwater monitoring data were col- lected one time per week for a period of 23 weeks (from January to June that is the dry season inMekong Delta). The river saltwater monitoring data from 2012 to 2019 were provided by BTHMFC (available at /TongQuat.aspx). The present study forecast the SI in HLR from Jan 1st -Jan 8th (week 1) to Jun 4th-Jun 11st (week 23) of 2020 based on saltwater monitoring data from 2012 to 2019 (Appendix 1). Figure 1: MapofHamLuongRiver and its saltwa- ter monitoring stations. ARIMA models description and application ARIMAwas first formed by Box and Jenkin in 1976 9. The general equation of successive differences at the dth difference of Xt is briefly expressed as follows: DdXt = (1B)dXt, where d is the different order, and B is the backshift operator The successive difference at one-time lag equals to: D1Xt = (1B)Xt = XtXt1 In this situation, the general non-seasonal ARIMA (p, d, q) is as follows: Fp(B)Wt = qq(B)et, where Fp(B) is an auto- regressive operator of order p, qq(B) is a moving av- erage operator of order q, andWt = DdXt A general nonseasonal/seasonal ARIMA (p, d, q)x(P, D, Q)s model with nonseasonal parameters p, d, q, seasonal parameters P, D, Q, and seasonality s that consists of several terms: A nonseasonal autoregres- sive term of order p, a onseasonal differencing of or- der d, a nonseasonal moving average term of order 447 Science & Technology Development Journal, 23(1):446-453 q, a seasonal autoregressive term of order P, a sea- sonal differencing of orderD, a seasonal moving aver- age term of orderQ. ARIMA(0,1,1)x(0,1,1)s–seasonal and nonseasonal MA terms of order 1 which was a common nonseasonal/seasonal ARIMA model. For a more detailed description of the terminology, see Box and Jenkins (1976)9, Bowerman and O’Connell (1987)17, and Pankraz (1991) 18. ARIMA modeling was developed using Statgraphics Centurion ver. 18 software. Model performance was evaluated using the root mean squared error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), the mean error (ME), the mean percentage error (MPE)19. Map visualizations An Inverse DistanceWeighting (IDW)method in Ar- cGIS 10.3 was used to interpolate forecast point data to create continuous surface maps20: l i= åGj=1 l j=Di j p åGj=1 1=Di j where l i was the property at location i; l j was the property at location jDij was the distance from i to j G was the number of sampled locations, and was the inverse-distance weighting power. RESULTS Long-term saline intrusion data in Ham Lu- ong River from 2012 to 2019 The saline concentration data in HLR for eight years that is obtained from the BTHMFC and Figure 2 pre- sented the basic trends of the collected data. Overall, the saltwater concentration in HLR increased from February to April. The maximum saltwater occurred at the end ofMarch or the beginning of April in which was the driest months in the year. Subsequently, the saltwater concentration decreased slightly in late May and fell rapidly in early June because of the seasonal change with rainfall in May. In early June, it is the be- ginning of the rainy season with much rainfall than those in May; therefore, the saline concentration de- creased rapidly in the whole river. Notably, the high- est saltwater concentration in HLR was observed in 2016 because of a severe El Niño, BTP experienced serious SI. The maximum saltwater concentration was 31.50 ‰ (05/02/2016), 26.01‰ (03/12/2016), 14.50‰ (03/12/2016), 12.40 (03/05/2016), 9.90‰ (03/12/2016), and 6.7% (03/12/2016) observed in AT, SD, PK, MH, AH, and VM, respectively. Saltwater (approximately 10‰) expanded through HLR by up to 50-60 km, considered to be themost extensive SI in the last 90 years. The ARIMA model for the forecast of saline intrusion in Ham Luong River In AT station, the highest saline concentration of 25.34 ‰ is observed in week 6, followed by 21.25‰ (week 10) and 21.16‰ (week 9). Furthermore, week 12 was expressed as the highest saltwater concentra- tion (13.24‰), week 5 (8.95‰), week 12 (4.67‰), week 4 (1.68‰), week 11 (0.72‰). By contrast, the lowest saltwater concentration of 12.46‰ is observed in week 23. The saltwater concentration measured from 5.09 (week 22) to 13.24 (week 12), 4.31 (week 22)-9.40 (week 12), 1.61 (week 22) to 4.67 (week 12), 0.00 (week 22)-1.49 (week 12), and 0.00 (week 22)- 0.72 (week 11) in SD, PL, MY, AH, and VM, respec- tively. Clearly, at the beginning of the rainy season (from May 28th to Jun 11st ) observed with the low- est saltwater concentration. In turn, saline intrusion began in mid-March, saltwater entered deep to in- land (Appendix 2). Table 1 showed an overview of the monthly average of the forecasted saltwater con- centration for all stations in HLR from January to June 2020. Generally, the saltwater concentration in- creased from January to March and then decreased from April to June. Themaximum saltwater occurred in February andMarch while the lowest saltwater was observed in early June. Figure 3 showed the historical data, the forecasts, and the forecast limits (95% P.I.) Testing forecast models A normal probability plot of the residuals can be dis- played in Figure 4. If the residuals come from a nor- mal distribution, they should fall close to the line. In fact, the residual plot in AT, SD, PK, AH showed some curvature away from the line while MH and VM did not. There are five tests have been run to determine whether or not the residuals form a random sequence of numbers. If a p-value for each test is greater than or equal to 0.05, we can not reject the hypothesis that the series is random at the 95.0% or higher confidence level. ARIMA forecasting model in AT, SD, PK, AH passed five tests while MH and VM did not (Table 2). DISCUSSION Theperspective viewof the saline intrusion in Ham Luong River in 2020 is predicted by the ARIMAmodel At the beginning of the dry season (January), the saltwater levels of 10‰ will have occurred in a lo- cation where between Mo Cay Nam and Thanh Phu District, over 50 km away from Ham Luong estuary. 448 Science & Technology Development Journal, 23(1):446-453 Figure 2: The trend of saline intrusion in Ham Luong River from 2012 to 2019. Table 1: Monthly average saltwater concentration (‰) in Ham Luong River from January to June of 2020. For: Forecast, 95% (L/H): the 95% prediction interval (low/high) Month AT SD PK For 95% (L/H) For 95% (L/H) For 95% (L/H) January 19.54 10.90/28.18 10.96 1.38/20.54 8.38 1.99/14.77 February 20.98 10.14/31.83 12.29 0.07/26.24 8.61 0.14/17.47 March 20.50 8.03/32.97 12.99 0.00/29.85 8.96 0.00/19.52 April 17.71 3.64/31.78 10.79 0.00/30.41 7.67 0.00/19.87 May 13.51 0.00/29.02 6.45 0.00/28.49 5.49 0.00/19.12 June 12.46 0.00/28.72 5.17 0.00/28.45 5.50 0.00/19.88 Month MH AH VM For 95% (L/H) For 95% (L/H) For 95% (L/H) January 3.92 0.00/8.10 0.85 0.00/3.84 0.29 0.00/2.28 February 3.97 0.00/10.30 1.05 0.00/5.61 0.54 0.00/3.53 March 4.53 0.00/12.26 1.40 0.00/6.97 0.60 0.00/4.24 April 3.62 0.00/12.66 0.67 0.00/7.20 0.17 0.00/4.43 May 1.94 0.00/12.14 0.09 0.00/7.45 0.08 0.00/4.88 June 2.40 0.00/13.18 0.00 0.00/7.78 0.08 0.00/5.15 Also, the saltwater levels from 5-10‰ will cover al- most all of Giong Trom and half of Mo Cay Nam District. These districts in upstream such as Chau Thanh andCho LachDistrict will be covered by under 2‰ (Figure 5A). Subsequently, at the driest month (February andMarch), saltwater will be intruded into an area within 60-70 km from the mouth of HLR; therefore all of Giong Trom andMoCayNamDistrict will be affected with the saltwater rate 10‰. Ben Tre City and a small part of Chau Thanh District will be covered by under 5‰ (Figure 5B, C). Finally, at the beginning of the rainy season (early June), saltwater will be pushed away from the inland. The saltwater levels of 10‰ will be observed in Ba Tri District, ap- proximately 10km away from the estuary (Figure 5F). Based on the forecasting results of the ARIMAmodel, saltwater with 5‰ will be entered up to 60-70 km deep inland that means Ben Tre city (areas with the highest population) and Chau Thanh District (areas with large-scale fruit production) seems to be affected by SI. Outcomes of this study are useful for reducing damages caused by the saline intrusion in theMekong 449 Science & Technology Development Journal, 23(1):446-453 Figure 3: Time sequence plot displays for saltwater concentration in Ham Luong River include the forecasts and the forecast limits. Figure 4: Residual normal probability plot. Table 2: Tests for the randomness of residuals. RUNS = Test for excessive runs up and down, RUNM= Test for excessive runs above and belowmedian, AUTO = Ljung-Box test for excessive autocorrelation, MEAN = Test for difference inmean 1st half to 2nd half, VAR = Test for difference in variance 1st half to 2nd half Test types AT SD PK MH AH VM RUNS N.S. N.S. N.S. N.S. N.S. N.S. RUNM N.S. N.S. N.S. N.S. N.S. N.S. AUTO N.S. N.S. N.S. * N.S. * MEAN N.S. N.S. N.S. N.S. N.S. N.S. VAR N.S. N.S. N.S. N.S. N.S. * N.S.= not significant (p >= 0.05), * = marginally significant (0.01 <p 0.05) 450 Science & Technology Development Journal, 23(1):446-453 Figure 5: The interpolation map showed the forecast of saline intrusion in Ham Luong River. (A) January, (B) February, (C) March, (D) April, (E) May, (F) June. Delta, also BTP in saline season 2020. The ARIMA model: advantages and disad- vantages Forecast is an activity to calculate or predict future events or situations, usually as a result of rational study or analysis of suitable data 21. The accurate in- formation for saline forecast will become more and more difficult to predict due to climate change and extreme weather22. In recent years, there are sev- eral quantitative forecast techniques available such as ARIMA models, Random walk models, Trend mod- els, or Exponential Smoothing. Generally, ARIMA models are considered as statistical theory and math- ematically complex techniques while the others are defined as simple prediction techniques. Therefore, the ARIMA model has been regarded as the most ef- ficient prediction technique in hydrology12. In the empirical research, many advantages of the ARIMA model were found and support it as a proper way in especially short-term time series forecasting23. The ARIMAmodel requires fewer the prior data inputs to generalize the forecast., only needs endogenous vari- ables and does not need to use other exogenous vari- ables. Basically, this model is relatively more robust and efficient than other complex structural models in relation to short-run predictions24. However, the main limitation of ARIMA is the lack of a determinis- tic cause 25. In addition, many traditional techniques for time series forecast, such as ARIMA, which as- sume that the series is generated from linear processes 451 Science & Technology Development Journal, 23(1):446-453 and as a result might be inappropriate for most real- world problems that are nonlinear26,27. This problem has now been circumvented through large numbers of past data inputs, stochastic events, and the accuracy of past data inputs that must be enhanced. CONCLUSION This paper presents a new approach to forecasting the SI in HLR of the Mekong River systems based on ARIMA forecasting model. Our result showed that the nonseasonal/seasonal ARIMA (0,1,1)x(0,1,1)23 model has been applied successfully for the forecast- ing of SI in HLR. However, the ARIMA forecasting model in AH and VM could be improved upon by other forecasting methods or still ARIMA with other parameters. ARIMA model with its convenience, ac- curate forecasting, low data input requirement, and simple computational process, it is bound to obtain a good picture of the prediction of SI over the main river. This makes the analytical model a powerful tool to guide future adaptation management on climate change and also SI in the Mekong Delta. LIST OF ABBREVIATIONS AH: An Hiep ANN: Artificial Neural Network ARIMA: Auto regressive integrated moving average AT: AnThuan AUTO: Ljung-Box test for excessive autocorrelation BTHMFC: Ben Tre Province’s Hydro-Meteorological Forecasting Center BTP: Ben Tre Province CI: Confidence interval HLR:Ham Luong River IDW: Inverse Distance Weighting MAE:Mean absolute error MAPE:Mean absolute percentage error ME:Mean error MEAN: Test for difference in mean 1sthalf to 2nd half MH:My Hoa MPE:Mean percentage error PK: Phu Khanh RMSE: Root mean squared error RUNM: Test for excessive runs above and below me- dian RUNS: Test for excessive runs up and down SD: Son Doc SI: Saline intrusion VAR: Test for difference in variance 1st half to 2ndhalf VM: VamMon COMPETING INTERESTS The authors declare that they have no conflicts of in- terest. AUTHORS’ CONTRIBUTIONS Thai Thanh Tran has contributed to collections, analyses, interpretation of data, and writing the manuscript. 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