Joanna Horabik-Pyzel

The main goal of this PhD project was to develop an approach for spatial disaggregation of data from a coarse to a fine grid, conditional on the observable covariate information and accounting for spatial correlation of the phenomenon. The task was motivated with real-life situations encountered in the area of atmospheric sciences, where it is often required to develop air quality data in a resolution higher than the one readily available e.g. from dispersion models.

The proposed approach applies the methods of spatial scaling, and spatial dependence is modelled with the conditional autoregressive structure.  The mathematical formulae were developed for parameter estimators (expected value and covariance matrix) of probability distribution of random variables associated with missing values in a fine grid. The optimal predictors have been developed to assess missing values in a fine grid, along with the assessment of prediction error. Also,  the formulae have been evaluated for the standard errors of estimated parameters, based on the expected and observed Fisher information matrices; model parameters are estimated with the maximum likelihood approach.

Performance of the proposed technique was tested for three disaggregation case studies: (i) inventory of ammonia emissions in Pomeranian Voivodeship; (ii) agricultural activity data within the national GHG inventory in Poland; and (iii) atmospheric concentrations of PM10 and NOx as an output from the dispersion model, run for Warsaw agglomeration. The method provided far better results than a widely used naive approach (where equal values are assumed for each fine grid cell within a respective coarse grid area) or linear models with no account of spatial correlation. For livestock inventory data, an improvement of 9% in terms of the mean squared error was reported. In certain situations, predictive power of the proposed procedure outperformed the geostatistical approach. Particularly, for high range of NOx and PM10 concentrations, the proposed model based on the CAR scheme, provided more accurate predictions, while the geostatistical one revealed a tendency to underestimate these values.

The basic version of the model has been also extended to account for possibly diversified regression models among regions (e.g. voivodeships in the case of national GHG inventory). 

The obtained results have been presented in several publications, among others in the Springer’s journal Climatic Change. Information on further publications may be find here.

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