On the interaction of observation and prior error correlations in data assimilation

Abstract

The importance of prior error correlations in data assimilation has long been known; however, observation-error correlations have typically been neglected. Recent progress has been made in estimating and accounting for observation-error correlations, allowing for the optimal use of denser observations. Given this progress, it is now timely to ask how prior and observation-error correlations interact and how this affects the value of the observations in the analysis. Addressing this question is essential to understanding the optimal design of future observation networks for high-resolution numerical weather prediction. This article presents new results, which unify and advance upon previous studies on this topic.The interaction of the prior and observation-error correlations is illustrated with a series of two-variable experiments in which the mapping between the state and observed variables (the observation operator) is allowed to vary. In an optimal system, the reduction in the analysis-error variance and spread of information is shown to be greatest when the observation and prior errors have complementary statistics: for example, in the case of direct observations, when the correlations between the observation and prior errors have opposite signs. This can be explained in terms of the relative uncertainty of the observations and prior on different spatial scales. The results from these simple two-variable experiments are used to inform the optimal observation density for observations of a circular domain (with 32 grid points). It is found that dense observations are most beneficial when they provide a more accurate estimate of the state at smaller scales than the prior estimate. In the case of second-order auto-regressive correlation functions, this is achieved when the length-scales of the observation-error correlations are greater than those of the prior estimate and the observations are direct measurements of the state variables.

Technical note: Assessment of observation quality for data assimilation in flood models

“…In this study we use the "nearest wet pixel" approach described in García-Pintado et al (2013). The mapping in the nearest wet pixel approach is dependent on the inundation status at the model location.…”

“…There have been recent advances in real-time 2-D hydrodynamic modelling and the acquisition and processing of relevant remote sensing observations (earth observations, EOs) (Raclot, 2006;Andreadis et al, 2007;Schumann et al, 2007Schumann et al, , 2011Mason et al, 2010aMason et al, , 2012aMason et al, , 2014. Consequently, several studies have shown the benefit of applying DA to operational flood forecasting (Durand et al, 2008(Durand et al, , 2014Montanari et al, 2009;Roux and Dartus, 2008;Neal et al, 2009;Matgen et al, 2010;Mason et al, 2010b;Giustarini et al, 2011;García-Pintado et al, 2013, 2015. Grimaldi et al (2016) review the potential of EOs for inundation mapping and water level estimation and their use for calibration, validation and constraint of real-time hydraulic flood forecasting models.…”

“…To make the assumption of uncorrelated errors valid the current approach is to thin the data. Hence, in hydrology, one scenario that would benefit from improved understanding of the observation uncertainties is the assimilation of the satellite-derived water level observations (WLOs) for either operational flood forecast or hindcast analyses (Mason et al, 2010a;García-Pintado et al, 2013). A more detailed understanding of the observation uncertainties would be highly useful as understanding the error statistics may permit more observations to be included in the assimilation, which should allow the information from dense observation sets to be fully exploited.…”

“…A more detailed understanding of the observation uncertainties would be highly useful as understanding the error statistics may permit more observations to be included in the assimilation, which should allow the information from dense observation sets to be fully exploited. Additionally, accurate estimates of observation uncertainties can inform the thinning strategy and suggest which observations may benefit the assimilation most (Fowler et al, 2018). There is a clear potential to improve the flood forecast if all the SAR WLOs could be assimilated in an appropriate way.…”

A practical assimilation approach to extract smaller‐scale information from observations with spatially correlated errors: An idealized study

“…As in Fowler et al . () and Simonin et al . (), the analysis error STD is reduced when increasing the density of assimilated observations by retrieving some of the small‐scale information that is lost when thinning the observations.…”