Propagating uncertainty through temporal and spatial re-meshing
by Dr. Maurice Cox, Dr. Xavier Loizeau, Dr. Bernardo Mota, Dr. Emma Woolliams

Abstract

Structured data, such as time-series data or image data, can be considered as a noisy and discretised version of a continuous quantity. Due to data discreteness, interpolation (or smoothing) and re-meshing are crucial aspects of estimating the value of the underlying object at a specific date or location and harmonizing two source data sets covering similar periods of time or areas but for which sampling does not coincide. Re-meshing onto a target grid is required in subsequent calculations to provide derived quantities such as essential climate variables. Propagation of uncertainty from source data sets to the target must be undertaken carefully so target uncertainties are reported properly. A key, often overlooked, aspect is accounting for the covariance of the interpolated data, which arises even for a set of independent source data points. Failing to report the covariance of the interpolated data can result in misguided decisions based on models trained on this data and loss of credibility. Another key aspect is the emergence of systematic error in interpolated data. While it may seem reasonable to interpolate using large windows when considering the covariance matrix of the resulting data set, any potential reduction of uncertainty comes at the cost of loss in spatial information (resolution), which can be interpreted as a systematic error. We consider (i) the temporal interpolation of Global Mean Sea Level (GMSL) data and (ii) the spatial re-meshing of satellite imaging data. For (i), we consider satellite altimetry data along with its covariance matrix and illustrate how different interpolation methods affect the target covariance matrix and their impact on model fitting. For (ii), we re-mesh to a common target grid two near-simultaneous satellite-based Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) products derived from Sentinel-3 (A and B) covering an area of 900 km2 over the Sahel region characterized by high landscape heterogeneity. Considerable work will be required to develop appropriate re-meshing techniques accounting for the data structures. Tools will be needed for sound re-meshing for each main structure, and to propagate uncertainties with results reported in a format to suit users. Different structures need to be covered: temporal (time series), spatial (images), spatio-temporal (videos) and hyperspectral. Meaningful visualization of propagated uncertainties that account for any bias induced by the interpolation method is also paramount for communication of these results.