groundwater level forecasting using artificial neural networks

Groundwater level forecasting using artificial neural networks

Ioannis N. Daliakopoulosa, Paulin Coulibalya, Ioannis K. Tsanisb,*

aDepartment of Civil Engineering, McMaster University, Hamilton, Ont., CanadabDepartment of Environmental Engineering, Technical University of Crete, Polytechnioupolis, Chania 73100, Greece

Received 17 June 2004; revised 1 November 2004; accepted 8 December 2004

Abstract

A proper design of the architecture of Artificial Neural Network (ANN) models can provide a robust tool in water resources

modeling and forecasting. The performance of different neural networks in a groundwater level forecasting is examined in order

to identify an optimal ANN architecture that can simulate the decreasing trend of the groundwater level and provide acceptable

predictions up to 18 months ahead. Messara Valley in Crete (Greece) was chosen as the study area as its groundwater resources

have being overexploited during the last fifteen years and the groundwater level has been decreasing steadily. Seven different

types of network architectures and training algorithms are investigated and compared in terms of model prediction efficiency

and accuracy. The different experiment results show that accurate predictions can be achieved with a standard feedforward

neural network trained with the Levenberg–Marquardt algorithm providing the best results for up to 18 months forecasts.

q 2004 Published by Elsevier B.V.

Keywords: Artificial neural networks; Groundwater level forecasting; Non-linear modeling; Messara valley; Aquifer overexploitation

1. Introduction

Although conceptual and physically-based models

are the main tool for depicting hydrological variables

and understanding the physical processes taking place

in a system, they do have practical limitations. When

data is not sufficient and getting accurate predictions

is more important than conceiving the actual physics,

empirical models remain a good alternative method,

and can provide useful results without a costly

calibration time. ANN models are such ‘black box’

models with particular properties which are greatly

0022-1694/$ - see front matter q 2004 Published by Elsevier B.V.

doi:10.1016/j.jhydrol.2004.12.001

* Corresponding author.

E-mail address: [email protected] (I.K. Tsanis).

suited to dynamic nonlinear system modeling. The

advantages of ANN models over conventional

simulation methods have been discussed in detail by

French et al. (1992). ANN applications in hydrology

vary, from real-time to event based modeling. They

have been used for rainfall—runoff modeling,

precipitation forecasting and water quality modeling

(Govindaraju and Ramachandra Rao, 2000). One of

the most important features of ANN models is their

ability to adapt to recurrent changes and detect

patterns in a complex natural system. More concepts

and applications of ANN models in hydrology have

been discussed by Govindaraju and Ramachandra Rao

(2000) and by the ASCE Task Committee on

Application of Artificial Neural Networks in

Journal of Hydrology 309 (2005) 229–240

www.elsevier.com/locate/jhydrol

http://www.elsevier.com/locate/jhydrol

I.N. Daliakopoulos et al. / Journal of Hydrology 309 (2005) 229–240230

Hydrology (2000). Neural networks have also been

previously applied with success in groundwater level

prediction (Coulibaly et al., 2001a,b,c). In this paper,

several different neural networks are evaluated in

order to reach conclusions regarding the efficiency of

this forecasting technique in groundwater level

prediction.

Fig. 2. Typical feedforward neural network.

2. Methodology

2.1. Training with different ANN architectures

Neural networks are massive parallel processors

comprised of single artificial neurons. Fig. 1 shows a

typical single neuron with a sigmoid activation

function, three input synapses and one output synapse.

Synapses represent the structure where weight values

are stored. In this paper, three different neural

networks are being used in order to identify the one

which gives the best results in predicting mean

monthly groundwater level values. They are described

below.

2.1.1. Feedforward neural network (FNN)

Feedforward neural networks have been applied

successfully in many different problems since the

advent of the error backpropagation learning algor-

ithm. This network architecture and the corresponding

learning algorithm can be viewed as a generalization

Fig. 1. Typical artificial neuron.

of the popular least-mean-square (LMS) algorithm

(Haykin, 1999).

A multilayer perceptron network consists of an

input layer, one or more hidden layers of computation

nodes, and an output layer. Fig. 2 shows a typical

feedforward network with one hidden layer consisting

of three nodes, four input neurons and one output.

The input signal propagates through the network in a

forward direction, layer by layer. Their main advan-

tage is that they are easy to handle, and can

approximate any input/output map, as established by

Hornik et al. (1989). The key disadvantages are that

they train slowly, and require lots of training data

(typically three times more training samples than

network weights).

2.1.2. Elman or recurrent neural network (RNN)

Fully recurrent networks, introduced by Elman

(1990), feed the outputs of the hidden layer back to

itself. Partially recurrent networks start with a fully

recurrent net and add a feedforward connection that

bypasses the recurrence, effectively treating the

recurrent part as a state memory. Fig. 3 shows

a typical recurrent network consisting of four input

nodes, a hidden layer with 3 nodes and one output. A

context layer is interconnected with the hidden layer

and plays the role of the network memory. These

recurrent networks can have an infinite memory depth

and thus find relationships through time as well as

through the instantaneous input space (Haykin, 1999).

Most real-world data contains information in its time

Fig. 3. Typical recurrent neural network.

I.N. Daliakopoulos et al. / Journal of Hydrology 309 (2005) 229–240 231

structure. Recurrent networks are the state of the art in

nonlinear time series prediction, system identification,

and temporal pattern classification (Zhang et al.,

1998).

2.1.3. Radial basis function network (RBF)

Radial basis function (RBF) networks are non-

linear hybrid networks typically containing a single

hidden layer of computation nodes. This layer uses

Gaussian transfer functions, rather than the standard

sigmoidal functions employed by a FNN. Fig. 4 shows

Fig. 4. Typical radial basis function.

a typical radial basis function consisting of a hidden

layer of four nodes, four inputs and three outputs. The

centers and widths of the Gaussians are set by

unsupervised learning rules, and supervised learning

is applied to the output layer (Haykin, 1999). Radial

basis function networks tend to learn much faster than

a FNN.

2.2. Training with different algorithms

Three different algorithms are being used in order

to identify the one which trains a given network more

efficiently.

2.2.1. Gradient descent with momentum and adaptive

learning rate backpropagation (GDX)

This method uses backpropagation to calculate

derivatives of performance cost function with

respect to the weight and bias variables of the

network. Each variable is adjusted according to the

gradient descent with momentum. For each step of

the optimization, if performance decreases the

learning rate is increased. This is probably the

simplest and most common way to train a network

(Haykin, 1999).

2.2.2. Levenberg–Marquardt (LM)

The Levenberg–Marquardt method is a modifi-

cation of the classic Newton algorithm for finding an

optimum solution to a minimization problem. It uses

an approximation to the Hessian matrix in the

following Newton-like weight update

xkC1 Z xk K ½JT J CmI�K1JT e (1)

where x the weights of neural network, J the Jacobian

matrix of the performance criteria to be minimized, m

a scalar that controls the learning process and e the

residual error vector.

When the scalar m is zero, Eq. (1) is just the

Newton’s method, using the approximate Hessian

matrix. When m is large, Eq. (1) becomes gradient

descent with a small step size. Newton’s method is

faster and more accurate near an error minimum, so

the aim is to shift towards Newton’s method as

quickly as possible.

Levenberg–Marquardt has great computational

and memory requirements and thus it can only be


used in small networks (Maier and Dandy, 1998).

Nevertheless, many researchers have been success-

fully using it (Anctil et al., 2004; Coulibaly et al.,

2000; Coulibaly et al., 2001a,b,c; Maier and Dandy,

1998; Maier and Dandy, 2000; Toth et al., 2000). The

Levenberg–Marquardt algorithm is often character-

ized as more stable and efficient. Also, both Coulibaly

et al. (2000); Toth et al. (2000) point out that it is

faster and less easily trapped in local minima than

other optimization algorithms.

2.2.3. Bayesian regularization (BR)

The Bayesian regularization is an algorithm that

automatically sets optimum values for the parameters

of the objective function. In the approach used,

the weights and biases of the network are assumed to

be random variables with specified distributions. In

order to estimate regularization parameters, which are

related to the unknown variances, statistical tech-

niques are being used. The advantage of this

algorithm is that whatever the size of the network,

the function won’t be over-fitted. Bayesian regulariz-

ation has been effectively used in literature (Anctil

et al., 2004; Coulibaly et al., 2001a,b,c; Porter et al.,

2000).

2.2.4. Network architecture

Several aspects of the architecture of neural

networks that focus on the prediction of variables

associated with hydrology are covered by Maier

and Dandy (2000). Their suggestions were followed

in the development of the current model. The

structure of the network is determined by trial and

error. The size of the input and hidden layer of the

network has been variable depending on the

prediction horizon, whereas the output layer has a

single node. The number of nodes in the hidden

layer and the stopping criteria were optimized in

terms of obtaining precise and accurate output.

Finally, the activation function of the hidden layer

was set to a hyperbolic tangent sigmoid function as

this proved by trial and error to be the best in

depicting the non-linearity of the modeled natural

system, among a set of other options (linear and

log sigmoid). It is noteworthy that there is no well

established direct method for selecting the number

of hidden nodes for an ANN model for a given

problem. Thus the common trial-and-error approach

remains the most widely used method.

Although special learning parameters (e.g.

momentum factor, learning rate etc.) can help to

avoid local minima, no guarantee of finding the global

minimum can be given. The probability of finding the

global minimum was enhanced by selecting various

random start positions.

2.2.5. Criteria of evaluation

Two different criteria are used in order to evaluate

the effectiveness of each network and its ability to

make precise predictions. The Root Mean Square

Error (RMSE) calculated by

RMSE Z

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNiZ1ðyi K yiÞ

2

N

s(2)

where yi is the observed data, yi the calculated data

and N is the number of observations. RMSE indicates

the discrepancy between the observed and calculated

values. The lowest the RMSE, the more accurate the

prediction is.

Also, the R2 efficiency criterion, given by

R2 ¼ 1 K

Pyi K yi

� �2

Py2

i K

Py2

i

n

(3)

representing the percentage of the initial uncertainty

explained by the model. The best fit between observed

and calculated values, which is unlikely to occur,

would have RMSEZ0 and R2Z1.

3. Study area and data description

The neural networks were tested with data taken

from Messara Valley, a basin of 398 km2 at the

southern part of the island of Crete, in Greece (Fig. 5).

The main geological coverage of the valley is

quarternary alluvial clays, silts, sands and gravels

deposited unevenly thus causing great incongruity of

the hydro-geological features of the area. The

hydrogeological basin has an area approximately

112 km2, approximately 25 km long and about 3 km

wide, as shown in Fig. 5 by the shaded area.

Furthermore, the main land-use coverage of the

Messara Valley is olive and vine cultivation which

Fig. 5. Area of study, Messara Valley, Crete, Greece. Black dots represent the locations of pumping wells in the area.


is typical for that part of the island of Crete (Croke

et al., 2000).

Messara Valley faces a severe problem of

depletion of groundwater resources, mainly used in

agriculture. Many wells in the region are illegitimate

and pumping is not regulated resulting in over-

exploitation of the aquifer and as a consequence the

sinking of the groundwater level over the years. The

long term mean annual precipitation for the area has

noticeably decreased from 588 to 516 mm/yr during

the last few years (1985–1995) (Croke et al., 2000).

With an estimated 65% of total evaporation and a

measured discharge of 21 mm/yr, the annual recharge

of the aquifer can be calculated to 159 mm/yr. About

108 mm/yr are lost from subsurface outflow and if

constant abstractions for irrigation are assumed at

97 mm/yr then the average net loss of water resources

sums up to 46 mm/yr. Taking into account the

porosity and area of Messara Valley the annual

decrease of the groundwater level can be calculated to

no less than 1.5 m/yr which is consistent with the

20 m observed drop over an approximately 10-year

period (Croke et al., 2000).

The data acquired from the area consists of rainfall

and temperature time series measured at Pompia, a

village in Messara Valley, the depth of a well and the

discharge of Geropotamos, the main stream of the

valley at the catchment’s outlet at Phaistos. The

time series used in this project are summarized in

the following figures. Monthly precipitation at

Pompia station shows the typical characteristics of

the Mediterranean climate comprised of high rainfall

during the winter months and no rainfall during the

summer months, as shown in Fig. 6. The average

precipitation at Pompia station is 500 mm/yr, slightly

less than the average annual precipitation in the basin.

From the bold line in Fig. 6 it can be inferred that the

average precipitation at the station has had no

noticeable changes for the past 20 years (1981–

2001). The wet (1985, 1988, 1991, 1994 and 1996)

and dry years (1983, 1986, 1990, 1993, 1997, and

2000) can also be distinguished and appear to be

equally distributed with a period of 2–3 years. Table 1

presents the annual precipitation for the station used in

the case study for the period 1981–2001. The

maximum precipitation of this 20-year period

occurred in 1981–1982, giving a total value of

699 mm. In the same table the effective precipitation

is shown, given by

Peff Z P KET KR (4)

where Peff is the effective precipitation, P is the actual

precipitation measured at the station, ET the amount

of water towards evapotranspiration equal to 65% of P

and R the runoff of the stream of Geropotamos, all

measured in mm/yr. In Table 1, runoff can be seen

both as Mm3/yr and mm3/yr. The conversion is made

by dividing the total volume of annual runoff with

Table 1

Annual precipitation, surface discharge and annual effective

precipitation, for the station of Pompia in Messara Valley

Year Precipi-

tation

(mm/yr)

Surface

discharge

(Mm3/yr)

Surface

discharge

(mm/yr)

Effective

precipi-

tation

(mm/yr)

1980–1981 672.5 46.4 116.6 118.8

1981–1982 699 18.8 47.2 197.4

1982–1983 282.5 29.8 74.9 24.0

1983–1984 607.9 48.8 122.6 90.2

1984–1985 646.4 13.5 33.9 192.3

1985–1986 363 10.8 27.1 99.9

1986–1987 466 20.5 51.5 111.6

1987–1988 553 11.7 29.4 164.2

1988–1989 423.5 4.3 10.8 137.4

1989–1990 255 5.2 13.1 76.2

1990–1991 456 2.6 6.5 153.1

1991–1992 330.5 0.0 0.0 115.7

1992–1993 344.5 7.1 17.8 102.7

1993–1994 505.9 4.9 12.3 164.8

1994–1995 488.7 12.0 30.2 140.9

1995–1996 679.9 2.4 6.0 231.9

1996–1997 483.5 0.9 2.3 167.0

1997–1998 472.2 1.3 3.3 162.0

1998–1999 528.6 0.0 0.0 185.0

1999–2000 328.9 0.7 1.8 113.4

2000–2001 512.5 0.0 0.0 179.4

Precipitation and effective precipitation are given in mm/yr and

surface discharge both in mm/yr and Mm3/yr.

Fig. 6. Monthly precipitation in mm versus time in months for the past 15 years in Messara.


the area of the watershed (398 km2). The measured

discharge at the catchment’s outlet at Phaistos for the

period 1985–1995 was averaged at 21 mm/y (Croke

et al., 2000).

Temperature also plays an important role in the

water budget as it affects evapotranspiration. Fig. 7

shows monthly temperature measurements at the

meteorological station of Pompia. Values appear to

vary steadily through the years with a slight increasing

trend as depicted by the bold line in Fig. 7. When

compared with longer datasets this minor trend is

neutralized, showing no significant temperature

variation in a long period of time. Nevertheless, for

the small period of our study, this increase may be of

some importance since during drier years the amount

of groundwater pumped for irrigation is bound to

increase as well.

Fig. 8 represents the monthly discharge of

Geropotamos Stream, the main seasonal stream that

runs through Messara Valley. The water level of

Geropotamos Stream has been steadily decreasing for

the past 20 years as shown by the bold line in Fig. 8

due to the overexploitation of the water resources, part

of which would be otherwise discharged into the sea.

The groundwater level reduction has caused wetlands

in the area to dry up (Croke et al., 2000) and the

stream to have no flow during most of the year.

Fig. 7. Monthly temperature in degrees Celsius versus time in months for the past 15 years in Messara.


This steadily decreasing trend is also depicted in

Fig. 8, where from a maximum of 14 Mm3 in 1983

and 1985 the discharge was diminished to an absolute

zero during the wet period of 2000.

The monthly level of a characteristic well located

in Pompia is represented in Fig. 9. Missing depth

values for this well have been interpolated from

Fig. 8. Monthly discharge of Geropotamos stream in Mm3 v

existing measurements with the help of a cubic spline.

Tests showed that data infilling with the use of a cubic

spline was the best among a series of interpolation

techniques, giving acceptable results even when

monthly data were interpolated from measurements

5 months apart. Fig. 10 shows an example of

interpolated and measured data. In this example,

ersus time in months for the past 15 years in Messara.

Fig. 9. Monthly depth in m versus time in months for the past 15 years for a well in Messara.


a cubic spline has been drawn between peaks and lows

(every 6 months), depicting very well the available

monthly data, giving R2Z0.98 and RMSEZ0.48 m.

For the rest of the timeline the results were equally

good. This fact also indicates that the transition

between different levels of the aquifer through

the year is smooth. The level of this well is

Fig. 10. Example of spline interpolatio

representative of the groundwater level of the area

when compared to the other wells in the area. For the

past 20 years precipitation and temperature appear

to have a steady fluctuation, the discharge of

Geropotamos and the groundwater level have been

steadily decreasing due to over pumping. One of the

goals of this paper is to evaluate the ability of artificial

n in a small part of the dataset.

Table 2

R2 and RMSE goodness of fit criterions for each of the 7 network—algorithm combinations used

Criterion Network

FNN-LM FNN-BR FNN-GDX RNN-LM RNN-BR RNN-GDX RBF

R2 0.985 0.592 0.993 0.911 0.609 0.830 0.744

RMSE (m) 2.11 9.84 5.68 3.31 9.32 5.63 5.23


neural networks to simulate this groundwater level

drop successfully.

For each one of the input variables, the time series

was divided in 3 different subsets. One subset for

training the neural network (1988–1998), one for

model calibration (1998–2000) and one for model

testing (2000–2002). These subsets are indicated with

vertical dotted lines in Figs. 6–9. The reason the whole

timeline was not used is that the statistical properties

of the groundwater level depth values appear to

change significantly after 1988. Intensification of

irrigation after 1988 caused a downward trend,

whereas the increase in the amplitude of the oscillation

of the groundwater level can be attributed to the

smaller porosity of the geological formations in larger

depths. Since our goal is to predict future groundwater

depths, any information concerning aquifer fluctuation

before irrigation was considered redundant as it would

inhibit the efficiency of our data driven model.

4. Results

All tests and results derived through programming

in Matlab 6. By means of trial and error, an optimum

network and parameter configuration for all three

networks was derived. During calibration, the values

that correlated better with all networks where those of

a 5-month moving window through the data series.

Table 3

Seasonal residuals (in meters) for each of the seven ANN-algorithm comb

Time Network

FNN-LM FNN-BR FNN-GDX R

Oct-00 K0.20 1.64 4.51

Apr-01 1.43 15.45 12.90

Oct-01 K3.84 6.26 0.47 K

Apr-02 1.00 18.21 10.88

Thus the input layer in all networks consisted of 20

input nodes; a 5-monthly time-lag was included (time-

lags t, tK1, tK2, tK3 and tK4 considering xt is the

value of a given variable at the present time step) for

precipitation, temperature, stream flow and ground-

water level. The output of the network is a prediction

of the well level at time step tC1. The number of

hidden neurons for both the RNN and FNN was

determined to 3 as suggested in literature (Coulibaly

et al., 2001a,b,c) and through trial and error. This

number of neurons seems to be both time efficient and

adequate to handle the rather small amount of data

of our problem. The number of hidden nodes of the

RBF network was determined automatically to 25.

Other parameters that were adjusted in order to

achieve more accurate results were the goal value of

the error function of the network during calibration,

calculated by the Mean Square Error (MSE), the

learning rate of the training algorithms, the number of

epochs or feeds of each network and the spread of the

RBF network. The need of adjustment of these

parameters lies in the danger of overtraining a

network, an effect that is analogous to over-fitting a

polynomial function.

Tables 2 and 3, summarize the results of the

testing for every network configuration. As expected,

the efficiency of all method decays as the prediction

period increases. The most efficient method is the

one whose efficiency decays with a slower rate

inations

NN-LM RNN-BR RNN-GDX RBF

0.44 1.70 K0.38 0.49

8.91 15.68 12.03 13.64

3.05 6.58 K0.76 2.66

9.98 16.31 13.19 7.88

Fig. 11. (a) Comparison of validation results to observed values. (b) Comparison of validation results to observed values.


and at the same time explains the unknown function

better. The best overall performance for the given

problem was achieved by the feedforward network

trained with the Levenberg–Marquardt algorithm

and the second best by the recurrent neural network

trained with the same algorithm. As we can see from

Table 2, even though the feedforward network

trained with the GDX algorithm seems to explain

better the groundwater level change (R2Z0.993), its

results are shifted rendering the method unsuitable

for the problem. The most unsuitable network was

a recurrent neural network trained with the Bayesian

regularization algorithm. This may indicate that

RNN requires more complex training algorithms

Fig. 12. Comparison of observed groundwater levels with simulated results for 1, 6, 12 and 18 months ahead using a feedforward network

trained with the Levenberg–Marquardt algorithm.


(Coulibaly et al., 2001a,b,c). The rest of the

networks performed relatively well but tended to

overestimate the observed dataset. Also all the

networks performed very well for 1 month ahead

predictions. Since the given problem is aiming at

predicting the level of an aquifer facing depletion,

overestimating models are not of particular interest.

Thus, the most promising techniques seem to be

those using the feedforward neural network trained

with the Levenberg–Marquardt algorithm that under-

estimates part of the groundwater level during the

dry season. The physical meaning of this result is

that the structure of this model allows its weights to

adjust to values that depict the trends of the natural

system we are simulating.

For validating purposes, an 18-months-ahead

prediction is made and compared with observed

values. Fig. 11a and b show how the best 6 out of a

total of 7 combinations predicted the groundwater

level for this 18 month period. Furthermore, Fig. 12

shows a comparison of observed and calculated

groundwater levels for predictions from 1 to 18

months ahead by the best performing network. The

different model results show relative good prediction

of the trend of the groundwater level, however

the model prediction accuracy decreases slightly

with increasing horizon of prediction.

5. Conclusions

Neural networks have proven to be an extremely

useful method of empirical forecasting of hydro-

logical variables. In this paper we made an attempt

to identify the most stable and efficient neural

network configuration for predicting groundwater

level in the Messara Valley. The groundwater in the

area has been steadily decreasing since the late

1980s due to overexploitation due to intensive

irrigation. A total of seven different ANN configur-

ations were tested in terms of optimum results for a

prediction horizon of 18 months. The most suitable

configuration for this task proved to be a 20-3-1

feedforward network trained with the Levenberg–

Marquardt method as it showed the most accurate

predictions of the decreasing groundwater levels.

From the results of the study it can also be inferred

that the Levenberg–Marquardt algorithm is more

appropriate for this problem since the RNN also

performs well when trained with this method.

Moreover, combining two or more methods of

prediction should also be considered as in our case

the FNN-LM method tended to underestimate events

when the rest of the methods overestimated them. In

general, the results of the case study are satisfactory

and demonstrate that neural networks can be


a useful prediction tool in the area of groundwater

hydrology. Most importantly, this paper presents

indications that neural networks can also be applied

in cases where the datasets manifest trends and

shifts and the desired output has lies outside of the

range of previously introduced input, as shown by

the results.

Acknowledgements

The authors gratefully acknowledge the Ministry

of Agriculture for providing the field data. Special

thanks to the reviewer’s for their useful comments that

help improved the paper. The present work was

financially supported by the National Science and

Engineering Research Council (NSERC) Grants

RGP157914-02 and RGP249582-02.

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