Applying principles of metrology to historical Earth observations from satellites

Approaches from metrology can assist earth observation (EO) practitioners to develop quantitative characterisation of uncertainty in EO data. This is necessary for the credibility of statements based on Earth observations in relation to topics of public concern, particularly climate and environmental change. This paper presents the application of metrological uncertainty analysis to historical Earth observations from satellites, and is intended to aid mutual understanding of metrology and EO. The nature of satellite observations is summarised for different EO data processing levels, and key metrological nomenclature and principles for uncertainty characterisation are reviewed. We then address metrological approaches to developing estimates of uncertainty that are traceable from the satellite sensor, through levels of data processing, to products describing the evolution of the geophysical state of the Earth. EO radiances have errors with complex error correlation structures that are significant when performing common higher-level transformations of EO imagery. Principles of measurement-function-centred uncertainty analysis are described that apply sequentially to each EO data processing level. Practical tools for organising and traceably documenting uncertainty analysis are presented. We illustrate these principles and tools with examples including some specific sources of error seen in EO satellite data as well as with an example of the estimation of sea surface temperature from satellite infra-red imagery. This includes a simulation-based estimate for the error distribution of clear-sky infra-red brightness temperature in which calibration uncertainty and digitisation are found to dominate. The propagation of these errors to sea surface temperature is then presented, illustrating the relevance of the approach to derivation of EO-based climate datasets. We conclude with a discussion arguing that there is broad scope and need for improvement in EO practice as a measurement science. EO practitioners and metrologists willing to extend and adapt their disciplinary knowledge to meet this need can make valuable contributions to EO.