Simulation of Karst Springs Discharge Using Artificial Neural Network (Case Study: Central Alborz Highlands)

Introduction
Springs are one of the most important water resources that provide a part of human required water. Springs discharge study and their simulation is very important for water resources protection and planning. Karstification is highly influenced by precipitation and terrain, which can cause large differences in karst spring flow between different regions. Present research has been done to investigate the effective factors on karst springs discharge and to simulate springs discharge in the central Alborz highlands (Mazandaran Province, northern Iran).

Methodology
Mazandaran province located in northern Iran that includes Caspian southern coasts and central Alborz highlands. The present research has been done on the surface of central Alborz highlands (karst areas). Extensive data were collected from TAMAB, Surveying and Climatology Organizations. In this study, the efficiency of Artificial Neural Network (ANN) was considered for simulating Karst springs discharge in the central Alborz highlands. So, 80 Karst springs were studied. The quantitative values of the spring's discharge factors were estimated such as: porosity (%) of aquifer formation, site elevation, slope, annual mean precipitation and distance from water resources.
The purpose of network education is to have a network that can improve the relationship between input and output of the model. Due to the lack of any special value for planning Artificial Neural Network, various structures were investigated. 80% of the data were used in education stage and 20% in testing or validating step. For educating and testing a neural network, the number and type of input parameter in model are very important. 8 input models planned for springs discharge simulation are the following:

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In the above formulas:
the Qspring is spring discharge (Lit/s). P: Porosity (%) of aquifer formation.
L: distance from water resources (m). R: annual mean precipitation (mm).
H: site elevation (m). S: Land slope (?).

The efficiency of Artificial Neural Network (ANN) has been considered through two parameters: Median Root of Square of the Error (RMSE) and co- efficiency between the actual and desirable outputs (R).
Obs refers to observed values, calc to values calculated by network and model, and n to the number of data in each step. The Nearer is RMSE to zero, the nearer are the observed and calculated values to each other and the more accurate is the simulation in each step.
9) RMSE=
10) Rsqr =

Results and Discussion
The results showed that ANN is capable in simulating springs discharge and also, the porosity(%) of aquifer formation, elevation and distance from water resources are the main factors on Karst springs discharge in the central Alborz highlands. The efficiency of Artificial Neural Network with multi-layered perceptron format with LM learning technique has been the finding of this study. Considering the results of efficiency of network for the different models, and comparing the obtained results with real data, it can be said that the second model among the 8 suggested models is the best one. In this study, educating the network through 3 learning equations was investigated and the results indicated that in comparison to CG, GDX learning equations, LM learning equation shows higher learning speed and higher error decrease in all models. Comparison of the results in Tables 1 can be concluded that it is easy to tell the LM algorithm is superior to the GDX and CG algorithm between the used models and phases.

Conclusion
Results showed clearly that the artificial neural networks are capable for modeling rainfall process. Thus, confirming the general enhancement achieved by using neural networks in many other hydrological fields. Using ANN for Hydrologic parameters prediction has been with good results in the past and in most cases there have been high correlation between simulated and observed hydrographs (Olsson et al., 2004). The results of this study showed that aquifer formation porosity(%), site elevation and distance from water resources have the most correlation with karst springs discharge.
The results showed clearly that the artificial neural networks are capable for modeling spring discharge. Thus, confirming the general enhancement achieved by using neural networks in many other hydrological fields. Using ANN for Hydrologic parameters prediction has been with good results in the past and in most cases there have been high correlation between simulated and observed hydrographs (Olsson et al., 2004). ANN can be applied to simulate springs discharge (the sites have not been studied).

Model Algorithms The best structure
Train stage Test stage
R RMSE R RMSE
1 LM 3-12-1 0.84 0.78 0.79 1
CG 3-8-1 0.65 1.2 0.55 2.5
GDX 3-14-1 0.6 1.5 0.51 2.8

2 LM 3-18-1 0.89 0.68 0.85 0.72
CG 3-12-1 0.78 1.02 0.64 1.4
GDX 3-18-1 0.80 0.78 0.75 0.95

3 LM 2-8-1 0.77 0.85 0.74 0.90
CG 2-12-1 0.65 1.2 0.61 1.4
GDX 2-14-1 0.71 0.89 0.67 1.1

4 LM 5-4-1 0.7 1.5 0.65 1.7
CG 5-12-1 0.61 1.7 0.52 2.2
GDX 5-8-1 0.60 1.7 0.54 2.0

5 LM 3-8-1 0.56 1.9 0.50 2.7
CG 3-10-1 0.51 2.8 0.4 3.1
GDX 3-6-1 0.51 2.7 0.45 2.9

6 LM 2-14-1 0.78 0.9 0.71 1.1
CG 2-10-1 0.62 1.7 0.52 2.1
GDX 2-14-1 0.65 1.4 0.55 1.9

7 LM 2-10-1 0.52 1.9 0.41 2.7
CG 2-12-1 0.44 2.9 0.37 3.5
GDX 2-4-1 0.48 2.5 0.41 3.6

8 LM 3-20-1 0.71 1.8 0.65 1.2
CG 3-12-1 0.52 2.2 0.48 2.7
GDX 3-16-1 0.58 1.4 0.51 1.7