Estimation of ground‐based GNSS Zenith Total Delay temporal observation error correlations using data from the NOAA and E‐GVAP networks

Abstract

In preparation for possible higher frequency assimilation of ground-based Global Navigation Satellite System (GB-GNSS) Zenith Total Delay (ZTD) observations at Environment and Climate Change Canada (ECCC), two popular diagnostic methods are applied to observation-minus-background and observation-minus-analysis departures from the ECCC Global Deterministic Prediction System (GDPS) to estimate temporal ZTD observation error correlations within the 6 h assimilation window. The GDPS uses a four-dimensional ensemble-variational (4D-EnVar) data assimilation system with a background error covariance matrix (B-matrix) obtained from an equal blend of 3D static and 4D flow-dependent (ensemble-based) background error covariances. The two diagnostic methods, the Desroziers method and the Hollingsworth-Lönnberg method, are applied using ZTD observations from the North American NOAA network and the European EIG EUMETNET GNSS Water Vapour Programme (E-GVAP) network with similar results obtained for both networks. Correlations estimated with the Desroziers method drop off rapidly with time difference becoming significantly negative for observations separated by more than 2-3 h. The results are unexpected as there is no obvious physical basis for negative correlations. It is shown how suboptimal specification of the background error covariances in the 4D-EnVar assimilation system B-matrix could explain the unexpected aspects of the results obtained with this method. In contrast, diagnosed observation error covariances without negative temporal correlations are obtained with the Hollingsworth-Lönnberg method, where a decorrelation time-scale on the order of 4 h is found. Both methods capture some expected features of the error correlations, such as highly correlated errors between observations within the same 1 h data processing blocks. While considerable uncertainty is associated with the results due to the inherent assumptions and limitations of both methods, the results do suggest that ZTD observation error decorrelation time-scales are on the order of a few hours rather than days as suggested by early pioneering work with different error correlation estimation methods.

Assimilation of GNSS Zenith Total Delay in NAVGEM

“…The source codes developed as part of this study have been delivered to FNMOC and the operational NAVGEM data assimilation system is scheduled to begin in August 2022. Additional focus on optimizing the data usage, such as spatial thinning (Poli et al., 2007) and better uncertainty estimation (S. Macpherson & Laroche, 2019), is additional future directions to pursue. The static bias calculation scheme in the current study can also be further modified in a real‐time operational cycled system, where the biases can be estimated with a moving average of observation‐minus‐background differences using a time period prior to the analysis time.…”

Framework for the comparison of a priori and a posteriori error variance estimation and tuning schemes

“…In this method, assuming that the observation errors are spatially uncorrelated (or have a small length-scale in comparison to the spatial correlations of the background errors) allows one to distinguish and estimate the statistics of the observation and background errors. The HL method has been successfully extended to estimate multichannel observation-error covariances (Garand et al, 2007;, temporal correlations of observation errors (Macpherson and Laroche, 2019), and to incorporate spatial observation-error correlations (Eresmaa and Järvinen, 2005). In the context of atmospheric chemistry, chemical error statistics have been obtained by using the HL method with a single polar-orbiting satellite by using the distance between consecutive measurements along the satellite track (Ménard et al, 2019).…”

“…As the D05 method is often easier to apply for high-dimensional problems, this method gained popularity in numerical weather prediction, especially for the estimation of satellite observation-error covariances Stewart et al, 2014;Weston et al, 2014;Todling, 2015;Gauthier et al, 2018). The D05 method has also been used to estimate model-error variances in ensemble Kalman filtering (Li et al, 2009), Doppler radar radial wind error correlations (Waller et al, 2016b), spatial and temporal observation-error correlations for ground-based Global Navigation Satellite System (GNSS) Zenith Total Delay observations (Bennitt et al, 2017;Macpherson and Laroche, 2019), and observation errors in multi-species atmospheric chemical constituent assimilations (Skachko et al, 2016). Although devised as an iterative algorithm, most operational applications of the D05 algorithm only apply one iteration due to the added computational cost of computing multiple analyses.…”

“…While a number of the studies referenced above have examined the behaviour of the D05 algorithm, there have been relatively few comparisons between the D05, DI01, and HL methods. In one of the few studies that compare the D05 and HL methods, Macpherson and Laroche (2019) found that the two methods produced significantly different results for the temporal correlations for GNSS Zenith Total Delay observation errors. The lack of a mathematical formalism for these comparisons contributes to the difficulty of comparing these methods.…”

Assessing the Impact of GNSS ZTD Data Assimilation into the WRF Modeling System during High-Impact Rainfall Events over Greece

“…Boniface et al [24] identified that the impact of ZTD assimilation in AROME model depends on the rainfall synoptic conditions, while Arriola et al [16] highlighted the importance of ZTD observations processing before the assimilation application. More recent studies focused on investigating different observational bias correction methods and on estimating spatiotemporal correlations of observations errors for application on ZTD data used for data assimilation [25][26][27].The literature review shows that improvements in the precipitation forecast skill may be gained by assimilating ZTD observations into NWP models. However, regional studies using the WRF modeling system are relatively rare (e.g., Rohm et al [28]), while no research focusing on Greece has ever been conducted.…”