Keywords: neural networks, stream flow, degree-day, modelling, hystereses, inverse distance weighted interpolation, spectral analysis.

Owing to the complex nature of hydrological processes and motivated by the ability of artificial neural networks (ANNs) to model complicated non-linear relationships, a wide spread application of ANNs in stream flow modelling has been supported by the literature. Previous efforts have demonstrated that ANN models performed at least comparative to, if not better than, other deterministic and statistical modelling approaches. However, most of these models, albeit successful in simulating stream flow and forecasting flow at different lead times, failed to address the topic of modelling stream flow of ungauged watersheds. In this class of models, past values of flow are used to predict future ones. Thus, although important to real time forecasting of gauged watersheds, they cannot provide flow predictions in ungauged watersheds due to the lack of pertinent model inputs in such cases.

In Canada and elsewhere, prediction of daily stream flow is important to evaluate downstream hydrologic impacts, to simulate the impact of extreme floods and droughts, and thus to safeguard against any expected adverse consequences. Providing the resources to gauge all watersheds of interest is practically impossible, thus a class of models that could simulate the response of ungauged watersheds at a reasonable accuracy is important to guide watershed management activities and water resources planning. Hence, the objectives of this study were: (1) to develop a neural network modelling algorithm capable of modelling ungauged watersheds, (2) to apply the developed model on four watersheds on the Canadian Boreal forest, (3) and to give an example on the applicability of the approach based on an ungauged watershed case study.

A stream flow modelling algorithm that utilizes a feed-forward multi-layer percepteron (FF-MLP) neural network is proposed in this study. The algorithm devised relies only on low-cost readily available meteorological data and careful time series manipulation prior to model building. The inverse distance weighted interpolation technique was used for better rainfall representation. The temperature index snow melt approach was used to account for snow melt. Cross correlation analysis was used to identify time-lagged inputs and spectral analysis was utilized to feed the ANN model with information regarding flow / rainfall hystereses loops and the flow seasonal cyclic behaviour.

The algorithm was applied to four watersheds (basin area of, 5 to 130 km²) in the Canadian Boreal Plain. All models managed to simulate stream flow fairly well at all data ranges. The coefficient of multiple determination (R²) exceeded 0.9 for training data sets and was close to 0.8 for testing and cross-validation data sets. In all cases the best network architecture was a FF-MLP ANN with a single hidden layer. The hidden layer neurons were operating with three different activation functions. Interestingly, this division was analogous to the three main driving forces of stream flow (base flow, snow melt, and rainfall events).

To demonstrate the applicability of the proposed approach in modelling ungauged watersheds, the model initially developed for 1A watershed (5 km²) was used in a predictive mode to simulate three years of stream flow for Cassidy watershed (6 km²). Initial results based on this application are very promising. The prediction accuracy was fair in all years except in predicting the early snow melt in 2003. Unlike Cassidy watershed, watershed 1A has a distinct wetland dominated soil and is thus thought to be controlled by different hydrologic processes. Yet, the results are very encouraging even with the highlighted dissimilarities; fair prediction of three years of stream flow was achieved for an ungauged watershed (i.e. without being trained with the specific watershed information even with a single data point). Further empirical studies to apply the proposed algorithm to other watersheds at different scales and dominated by different hydrologic regimes is required to reinforce these conclusions.

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