Nonlinear multivariate rainfall–stage model for large wetland systems

Wetland restoration is often measured by how close the spatial and temporal water level (stage) patterns are to the pre-drainage conditions. Driven by rainfall, such multivariate conditions are governed by nonstationary, nonlinear, and nonGaussian processes and are often simulated by physically based distributed models which are difficult to run in real time due to extensive data requirements. The objective of this study is to provide the wetland restorationists with a real time rainfall–stage modeling tool of simpler input structure and capability to recognize the wetland system complexity. A dynamic multivariate Nonlinear AutoRegressive network with eXogenous inputs (NARX) combined with Principal Component Analysis (PCA) was developed. An implementation procedure was proposed and an application to Florida Everglade’s wetland systems was presented. Inputs to the model are time lagged rainfall, evapotranspiration and previously simulated stages. Data locations, preliminary time lag selection, spatial and temporal nonstationarity are identified through exploratory data analysis. PCA was used to eliminate input variable interdependence and to reduce the problem dimensions by more than 90% while retaining more than 80% of the process variance. A structured approach to select optimal time lags and network parameters was provided. NARX model results were compared to those of the linear Multivariate AutoRegressive model with eXogenous inputs. While one step ahead prediction shows comparable results, recursive prediction by NARX is far more superior to that of the linear model. Also, NARX testing under drastically different climatic conditions from those used in the development demonstrates a very good and robust performance. Driven by net rainfall, NARX exhibited robust stage prediction with an overall Efficiency Coefficient of 88%, Mean Square Error less than 0.004 m2, a standard error less than 0.06 m, a bias close to zero and normal probability plots show that the errors are close to normal distributions.