Isaac Newton Institute for Mathematical Sciences

Nonlinear and Nonstationary Signal Processing

July to December 1998

Organisers: W J Fitzgerald (Cambridge), R L Smith (University of North Carolina), A Walden (Imperial College, London) and P C Young (Lancaster University)

A Newton Institute Workshop

Environmental Modelling and Signal Processing

17 - 22 August 1998

Programme now available

Signal processing in the environmental sciences tends to take three basic forms: a purely data-based, 'black box' approach which is often based on classical signal processing concepts and procedures but tends to have its own special identity; a 'mechanistic' approach which normally involves the construction of (often deterministic) models which attempt to simulate the environment in physically meaningful terms; and a 'data-based mechanistic' or 'grey box' approach which, in various ways, attempts to blend the concepts and procedures of the other two approaches to yield statistically identified and estimated models that are efficiently parameterised and yet retain a distinct physical meaning that satisfies the predilections of the environmental scientist.

This workshop (which takes place as part of the six-month programme Nonlinear and Nonstationary Signal Processing) will concentrate on the importance of nonlinear and nonstationary signal processing as it relates to all three of these approaches, although the emphasis in the mechanistic case will be on stochastic, rather than deterministic, models. While this will involve wide ranging discussions, particular attention will be focused on the following important themes:

1. Spatio-Temporal Signal Processing: Extensions of classical geostatistical methods to include nonstationary and non Gaussian spatial processes, including models defined by families of conditional probabilities, and hierarchical models. Spatio-temporal processes: separable processes; processes defined by EOFs and related techniques; and other constructions. Applications will include: spatial monitoring of air pollutants; meteorological data including the special models developed for rainfall processes; and spatial models in agricultural and epidemiological applications.

2. Recursive Estimation and Data Assimilation: Extrapolation, interpolation and smoothing of nonstationary and nonlinear time series; signal decomposition (extraction) and seasonal adjustment; trend estimation; nonlinear system identification, estimation and adaptive forecasting; data assimilation for nonlinear stochastic systems (including the debate about simple vs complex models in this regard). Applications to include: on-line and off-line processing of hydrological, water quality, meteorological and climate data, including data assimilation procedures; rainfall-flow modelling and adaptive flow forecasting, including the processing of weather radar data; climate modelling and the prediction of climate change.

3. Nonlinear Modelling and Stochastic Processing: Identification, estimation and validation (calibration) of nonlinear models, including non-parametric, time variable and state-dependent parameter models; Maximum Likelihood and Bayesian estimation methods; Monte-Carlo (MC) simulation-based analysis of nonlinear, stochastic, dynamic systems; the analysis of predictive uncertainty in nonstationary and nonlinear stochastic systems; sensitivity analysis using MC and other methods; MCMC methods; issues of scale and complexity in environmental models. Applications to include: hydrological, water quality , air quality, geophysical and climate modelling; the use of stochastic models in environmental management and planning.

4. Monitoring and Standards: Statistical information can or should translate itself into standards, which will, of necessity, include a "signal processing" element, in the sense that the problem is basically one of inferring the true state of nature from noisy data. This topic will include extreme value techniques and could deal with various aspects of environmental planning and operational control.

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