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Phase-space reconstruction and self-exciting threshold modeling approach to forecast lake water levels

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Abstract

Lake water level forecasting is very important for an accurate and reliable management of local and regional water resources. In the present study two nonlinear approaches, namely phase-space reconstruction and self-exciting threshold autoregressive model (SETAR) were compared for lake water level forecasting. The modeling approaches were applied to high-quality lake water level time series of the three largest lakes in Sweden; Vänern, Vättern, and Mälaren. Phase-space reconstruction was applied by the k-nearest neighbor (k-NN) model. The k-NN model parameters were determined using autocorrelation, mutual information functions, and correlation integral. Jointly, these methods indicated chaotic behavior for all lake water levels. The correlation dimension found for the three lakes was 3.37, 3.97, and 4.44 for Vänern, Vättern, and Mälaren, respectively. As a comparison, the best SETAR models were selected using the Akaike Information Criterion. The best SETAR models in this respect were (10,4), (5,8), and (7,9) for Vänern, Vättern, and Mälaren, respectively. Both model approaches were evaluated with various performance criteria. Results showed that both modeling approaches are efficient in predicting lake water levels but the phase-space reconstruction (k-NN) is superior to the SETAR model.

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Acknowledgments

R. Berndtsson acknowledges helpful funding from the MECW project at the Center for Middle Eastern Studies, Lund University.

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  1. Department of Civil Engineering, Engineering Faculty, Süleyman Demirel University, 32260, Isparta, Turkey

    Hakan Tongal

  2. Department of Water Resources Engineering, Center for Middle Eastern Studies, Lund University, 221 00, Lund, Sweden

    Ronny Berndtsson

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  1. Hakan Tongal
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Correspondence to Hakan Tongal.

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Tongal, H., Berndtsson, R. Phase-space reconstruction and self-exciting threshold modeling approach to forecast lake water levels. Stoch Environ Res Risk Assess 28, 955–971 (2014). https://doi.org/10.1007/s00477-013-0795-x

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