Predicting seasonal and hydro-meteorological impact in environmental variables modelling via Kalman filtering

Abstract

This study focuses on the potential improvement of environmental variables modelling by using linear state-space models, as an improvement of the linear regression model, and by incorporating a constructed hydrometeorological covariate. The Kalman filter predictors allow to obtain accurate predictions of calibration factors for both seasonal and hydro-meteorological components. This methodology can be used to analyze the water quality behaviour by minimizing the effect of the hydrological conditions. This idea is illustrated based on a rather extended data set relative to the River Ave basin (Portugal) that consists mainly of monthly measurements of dissolved oxygen concentration (DO) in a network of water quality monitoring sites. The hydrometeorological factor is constructed for each monitoring site based on monthly precipitation estimates obtained by means of a rain gauge network associated with stochastic interpolation (Kriging). A linear state-space model is fitted for each homogeneous group (obtained by clustering techniques) of water monitoring sites. The adjustment of linear state-space models is performed by using distribution-free estimators developed in a separate section.

Trends in the average temperature in Finland, 1847–2013

“…It has been shown (e.g., Bloomfield 1992; Gao and Hawthorne 2006;Wu and Zhao 2007;Keller 2009) that this increase is statistically significant and that it can, for the most part, be attributed to human-induced climate change (IPCC 2013;Foster and Rahmstorf 2011). A temperature increase is obvious also in regional and local temperatures in many parts of the world.…”

Statistical Modelling of Water Quality Time Series – The River Vouga Basin Case Study

“…As expected, from the DO perspective, the water quality was better in the winter months and worse during the summer months. The DO concentration is associated with weather conditions, particularly with precipitation amounts [23].…”

“…For example, distribution-free estimators can be adopted, which do not assume any distribution for the disturbances (see [27,23]). …”

A mixed-effect state space model to environmental data

“…A temporal correlation structure on environmental data are very common. For instance, [6] applies state space models in order to accommodate the time dependence of monthly water quality variables, [1] presents inference propers of regression models which residuals follow any autoregressive stationary process. One of the most common properties is the non-stationarity of a time series.…”

“…Data were collected from the SNIRH (Sistema Nacional de Recursos Hídricos), the national information system for water resources of Portugal, at http://snirh.apambiente.pt/. The modeling of water quality variables will be performed using both linear regression ( [5,11]) and state space models ( [3,6]). Linear models are usually applied for their simplicity and well known statistical properties.…”