PH modelling by neural networks. Application of control and validation data series in the Middle Loire river

Abstract

Artificial neural networks (ANNs) are applied as a new type of model to estimate the daily pH of the Middle Loire river. The model is used for pH measurement screening, error detection (abnormal values, discontinuities and recording drifts) and validating the collected data. The measured values of pH are compared with the values estimated by the ANN model using statistical tests to verify homogeneity and stationarity. River water pH is affected by numerous processes: biological, physical and geochemical. Examples are: CO 2 pressure equilibrium with the atmosphere, photosynthesis, respiration of plants, organic matter degradation, geological and mineral background, pollution etc. Inter-relationships between these processes and pH values are complex, non-linear and not well understood. As a neural network provides a non-linear function mapping of a set of input variables into the corresponding network output, without the requirement of having to specify the actual mathematical form of the relation between the input and output variables, it has the versatility for modelling a wide range of complex non-linear phenomena. For this reason the neural network approach has been selected and tested for pH modelling. We used the classical multilayer perceptron model (MLP). River discharge and solar radiation variables are used as inputs to the MLP model. The choice of these variables is dictated by what are perceived to be the predominant processes that control pH in the Middle Loire river, which is typically eutrophic during the low-flow summer period. The influence of the previous day’s flows and radiation has been evaluated in the calibration and verification test. The best network found to simulate pH was one with two input nodes and three hidden nodes. The inputs are: daily discharge and a variable called ‘Index of anterior radiation’, i.e. calculated as an exponential smoothing of the daily radiation variable. When calibrated over 4 years of data and tested (i.e. verified) for a one-year independent set of data, the model proved satisfactory on pH simulations, with accuracies in the order of 86%. After elaborating the pH model, the Student test and the cumulative Page–Hinkley test were applied for automatic detection of changes in the mean of the residuals from the ANN pH model. This analysis has shown that such tests are capable of detecting a measurement error occurring over a short period of time (1–4 days).