Comparing diagnosed observation uncertainties with independent estimates: A case study using aircraft-based observations and a convection-permitting data assimilation system

Aircraft can report in situ observations of the ambient temperature by using aircraft meteorological data relay (AMDAR) or these can be derived using mode-select enhanced tracking data (Mode-S EHS). These observations may be assimilated into numerical weather prediction models to improve the initial conditions for forecasts. The assimilation process weights the observation according to the expected uncertainty in its measurement and representation. The goal of this paper is to compare observation uncertainties diagnosed from data assimilation statistics with independent estimates. To quantify these independent estimates, we use metrological comparisons, made with in-situ research-grade instruments, as well as previous studies using collocation methods between aircraft (mostly AMDAR reports) and other observing systems such as radiosondes. In this study we diagnose a new estimate of the vertical structure of the uncertainty variances using observation-minus-background and observation-minus-analysis statistics from a Met Office limited area three-dimensional variational data assimilation system (3 km horizontal grid-length, 3-hourly cycle). This approach for uncertainty estimation is simple to compute but has several limitations. Nevertheless, the resulting diagnosed variances have a vertical structure that is like that provided by the independent estimates of uncertainty. This provides confidence in the uncertainty estimation method, and in the diagnosed uncertainty estimates themselves. In the future our methodology, along with other results, could provide ways to estimate the uncertainty for the assimilation of aircraft-based temperature observations.