Spatial regression of multi-fidelity meteorological observations using a proxy-based measurement error model

Abstract

<p><strong>Challenge.</strong> Meteorological observations are fundamental to sustain a wide range of applications at national meteorological and hydrological services (NMHSs), including gridded climate datasets. Typically, NMHSs use high-quality observations from the networks they operate. However, in recent years, alternative weather data sources are becoming available. Government agencies, organizations, or citizens are joining the effort of monitoring the weather by placing sensors in public or private spaces. The promise of such alternative networks is that they are available at higher spatial resolution that the official ones, which implies the weather observations could contribute to add more spatial detail to the Climate Services. Although the alternative measurements are indeed provided at a higher spatial resolution, they also contain substantial bias and noise, which needs to be addressed.</p><p><strong>Approach.</strong> The quantification of bias and noise, or measurement errors, is becoming a central theme in science. Measurement error can have a large effect on reliable spatial regression of multifidelity data, therefore it is important to provide a quantified bias and noise level to the regression algorithm. This proper treatment of bias and noise in multi-fidelity data is required, for example, when delivering gridded datasets. Such error treatment does not only improve the reliability of the predicted mean grid (ensemble mean), but also has a notable effect on the predicted uncertainty in the grid (ensemble spread). Since in most cases no quantified bias or noise level is available from the datasets, we propose to use a proxy-based model to learn the bias and noise from the data. Proxies for bias and noise of multi-fidelity meteorological data can be ‘covariates’ like population density, forest cover, radiation intensity, or similar.</p><p><strong>Results.</strong> In the present work, we use multi-fidelity kriging to combine three datasets in the Netherlands: the network of the National Meteorological Service KNMI, data measured along the national road network by Rijkswaterstaat (Directorate-General for Public Works and Water Management), and crowd-sourced data from the WOW-NL network (http://wow.knmi.nl). In our study, we test our methods on synthetic data and then apply those methods to observed data. We investigate and quantify the improvements in gridded temperature (mean and uncertainty of grid) which we observe when applying a proxy-based error model.</p>