Application of Multi-Layer Artificial Neural Networks for Forecasting Groundwater Level (Case study: Yolo County, California)

Introduction
Groundwater is one of the most critical sources of potable, agricultural and industrial water [1-3]. Improper exploitation of groundwater resources in recent years disturbs its natural balance and groundwater level has been negative in aquifers in parts of the world. To be aware of the status of these resources and their optimal management, it is necessary accurate prediction of groundwater level fluctuations. Evaluation and forecasting of groundwater levels through models with proof capabilities of intelligent models in time series, in particular, helps to predict groundwater resources modeling. In recent years, the application of these models in modeling groundwater has intensified [4]. Two critical characteristics of groundwater are the quality parameters and groundwater level (GWL). Therefore, scientists are challenged to search for approaches to investigate both quality and quantity of GW [4-8].
In evaluating the groundwater system, using short-term and long-term groundwater data and the primary source of information on the potential of hydrological stress is important [9-11]. Most hydrological time series, such as groundwater level changes, always involve unfamiliar and complex processes that cannot be well described and modeled using conventional and classical linear models. Therefore, to model these hydrological phenomena, it is necessary to use nonlinear models [12]. In any simulation process, especially groundwater resource management strategy, a complex model can study the actions and reactions, and in many different aspects, choosing a good model is very important. The most common subject that all researchers are to investigate is to predicting and forecast the depth and quality of groundwater. Gao et al., 2020, researched the impact of shallow groundwater on crops [13]. The effect of groundwater discharge from adjacent aquifers is investigated by Mo et al., 2021 and Burnett et al., 2006 [6,14]. According to the presented experimental results, the observed GWL data show cycle patterns, including annual rotation [15]. Many factors such as global climate events, temperature, evaporations, precipitation, soil texture and permeability can affect GWL changes [16]. Furthermore, pumping rates, tidal fluctuations and GWL itself can affect its evaluations [17]. Yan et al., 2018 demonstrate that the influencing factors on the groundwater level can be in the order of 1- precipitation, 2- river stage and 3- evaporation [18].
There are many studies try to find the relation between groundwater (level and quality) and effective parameters. In some studies, researchers propose model(s) or present equation(s) to show the relation(s) between parameters. Table 1 shows a summary of research that has investigated methods to find an optimal algorithm to forecast and simulate GWL. In some research articles author(s) have tried to predict and simulate the GW quality (Table 1).

Table 1 Groundwater studies performed worldwide
Ref
Author(s)
Study Area Parameter(s) that are used as input data Target of the study Result(s)
[19] Kamińska et al. Sosnowica, West Polesie GWL data points as surface generation 2011 GWL(mm) Compares Radial Basis Functions (RBF) and Inverse Distance Weighting (IDW) for forecasting the GWL and shows that RBF method is more accurate
[20] Ahn Collier County, Florida daily GWL (m) 1985-1990 GWL(m) Showed that the second-order difference model in some cases produces lower interpolation error than that of the first-order difference model
[21] Nurul Islam et al. Godagari Upazill Bangladesh annual rainfall (in) 1986-2014 annual GW recharges (in) Using non-linear regression technique to estimate GW recharges
[22] Sun three states of US GRACE (3) satellite and withdrawal (in 106 g/d) data 2005 GWL changes Used input data to train a Multilayer Perceptron (MLP) neural network for estimating GWL changes
[23] Chang et al. As-contaminated area in Taiwan Alk, Ca2+, pH 1992-2005 As(mg/lit) Developed a systematical dynamic-neural model (SDM) to estimate the As concentration
[24] Abbasi Maedeh et al. Tehran,
Iran SO₄, Na, Cl, Th, Mg, Ca, K, SAR, HCo₃2002-2011 TDS (mg/lit) Training 5 ANN models, for each model assuming some of the input data as model input for estimate TDS and find best model between them
[25] Taormina et al. Venice,
Italy rainfall, evapotranspiration (mm) 2005-2008 hourly GWL(mm) Made an ANN model to forecast GWL due to rainfall and evaporation from GW
[26] Jalalkamali et al. Kerman,
Iran monthly air temperature, rainfall, GWL in neighboring wells 1988-2009 GWL(mm) Comparing between results of ANN model and neuro fuzzy model and find the NF method to has better performance
[27] Adamowski et al. two sites in Quebec, Canada monthly total precipitation (mm), average temperature (°C) 2002-2009 average monthly GWL (mm) Representing 3 models: ANN, ARIMA,WA-ANN, and comparing between the results showed that WA-ANN is the best model
[28] Shiri et al. Canada Temperature (C), precipitation (mm), GWL (mm) 1974-2005 Wavelet coherence charts between GWL and T, P, and large-scale
climatic patterns Analyzed the impacts of 4 large-scale climatic patterns such as El Niño on the T,P,GWL by applying the wavelet transform on data
[29] Seyam, and Mogheir Gaza, Palestine Initial chloride (mg/l), recharge rate (mm/m2/month), abstraction (m3/hour), life time (y) and aquifer thickness (m) 1997-2004 GW salinity (mg/l) Made a Multilayer Perceptron NN (MLP) with four layers for predicting the GW salinity
[30] Sethi et al. Orissa,
India monthly rainfall, potential evapotranspiration (PET), water table depth, influencing wells data 2005-2008 one month ahead water table depth (m) Tested 10 ANN models all with 3 hidden layer but different numbers of neurons in layers then compare their precisions
[31] Joorabchi et al. 5 coastal areas of Australia GWL, tide elevation, beach slope and hydraulic conductivity GW elevation(m) Trained a feed forward NN with two hidden layers and back propagation algorithm to predict GW elevation then illustrated by sensitivity analysis that variation in tide evaluations is the most important effective parameter.
[32] Yang et al. Jilin, China six antecedent values of GWL (mm) 1986-2000 GWL (mm) Produced two models, Integrated Time Series (ITS) and ANN and showed that ANN model works slightly better
[33] Affandi et al. Jakarta, Indonesia GWL fluctuation GWL fluctuation Used multi-layer back-propagation to predict GWL fluctuation
[34] Gundogdu et al. Marmara region,
Turkey monthly GWL (mm) 2002 monthly GWL (mm) Determined which of 10 empirical semi-variogram models (e.g. Gaussian, exponential, rational quadratic) will be best matched with GWL and resulted that the last one is the best.
[35] Giustol et al. Salento Peninsula in Apulia, Italy monthly rainfall (cm) and GWL (m) 1953-1996 GWL (m) Presented an initial multi-objective strategy for the optimal design of ANNs and found the selection of the best network structure

There are various methods such as probability properties, time series methods, multiple regression, artificial data generation and artificial intelligence networks with different algorithms for analyzing groundwater level fluctuations [15]. GWL depends on several parameters; therefore, it is hard to estimate [36]. An artificial neural network (ANN) for developing a model to forecast GWL can solve this complexity. ANN algorithms can predict accurate results and are appropriate tools for monitoring and managing GWL fluctuations. This method can also perform as a means to solve engineering and environmental problems [37].
In this study, it is assumed the oscillation factors that discussed above exist as a feature of GWL. Moreover, the probable presence of variables such as global climate events, temperature, precipitation, evaporations, soil texture and permeability, pumping and tidal fluctuations may affect GWL. However, as an assumption, it can’t be affected by an unpredicted event such as big earthquakes. To account for effects of pumping, we assume that the pumping from the aquifer can change GWL. In order to increase efficiency in verification and simulation results, ANN models can be adapted to drastic changes of variables through learning algorithm process. The current study shows that a reliable forecasting model can be developed without the need for any detailed analysis of each influential variable on GWL. The presented models use only one influential parameter such as seasonal variations in GWL fluctuations and simulation analyses.

2. Method and materials

Local GWL models are valuable tools for monitoring and assessment. The effective parameters such as geographical site location, spatial distribution of soil characteristics, and impact of probabilistic hydrogeological parameters have a natural of uncertainty. To develop GWL simulation models, there is an essential necessity to have GWL time series data. In this study two wells in Yolo County have been chosen to show how effectively and accurately local ANN models can simulate and predict the GWL. Information on the location of observation wells used in the groundwater model is shown in Table 2.

Table 2 Information on the location of observation wells of the study sites in Yolo County

Depth(ft) Station ID Latitude Longitude
well #1 80-90 09N03E08C001M 38-38-46.405 N 121-40-3.009 W
well #2 140-150 09N03E08C002M 38-38-46.405 N 121-40-3.009 W


Figure 1 shows the data sets which are used for the modeling. They have been recorded since 4/1/1992, by Department of Water Resources of California that are published and exhibited on their site at www.water.ca.gov/waterdatalibrary/docs/Hydstra/index.cfm. These data are the daily mean of GWL (Figure 1). In first step, daily data transformed to monthly data sets (Figure 2). For well #1 and #2 we have a negligible number of missed data (27 and 28 days respectively).