Improvement of Accuracy of Global Numerical Weather Prediction Using Refined Error Covariance Matrices

Abstract

In data assimilation for NWP, accurate estimation of error covariance matrices (ECMs) and their use are essential to improve NWP accuracy. The objective of this study is to estimate ECMs of all observations and background variables using sampling statistics, and improve global NWP accuracy by using them. This study presents the first results of such all ECM refinement. ECM diagnostics combining multiple methods, and analysis and forecast cycle experiments were performed on the JMA global NWP system, where diagonal components of all ECMs and off-diagonal components of radiance observations are refined. The ECM diagnostic results are as follows: 1) the diagnosed error standard deviations (SDs) are generally much smaller than those of the JMA operational system (CNTL); 2) interchannel correlations in humidity-sensitive radiance errors are much larger than 0.2; and 3) horizontal correlation distances of AMSU-A are ;50 km, excluding channel 4. The experimental results include the following: 1) the diagnosed ECMs generally improve forecast accuracy over CNTL even without additional tunings; 2) the supplemental tuning parameter, which is the deflation factor (0.6 in SD) applied for the estimated ECMs of nonsatellite conventional data and GPS radio occultation data, statistically significantly improves forecast accuracy; 3) this value 0.6 is set as the same value as the ratio of the estimated background error SD to that in CNTL; 4) high-density assimilation (10 times) of AMSU-A is better than CNTL, not better than that with 5 times; and 5) ECMs estimated using boreal summer data can improve forecast accuracy in winter, which indicates their robustness.

All‐sky infrared radiance assimilation of a geostationary satellite in the Japan Meteorological Agency's global system

“…On the on‐line basis, one of them was then selected according to C A of the lowest peaking band (band 10 in AHI) at each observation in 4D‐Var. This approach follows Ishibashi (2020). All elements of the error covariance matrix were then inflated so that value of its diagonal element was equal to the square of the observation error SD estimated from the model described in the previous paragraph while keeping the structure of the observation error correlation, as in Equation (): $$$$ {R}_{ijk}={\sigma}_i{\sigma}_j{C}_{ijk}, $$$$ where R ijk is observation error covariance of band i and j for C A group k ( k = 1–3), $$$ {\sigma}_i $$$ is the observation error SD at band i estimated from the error SD model, and C ijk is the precalculated observation error correlation between band i and j for C A group k .…”

“…On the on-line basis, one of them was then selected according to C A of the lowest peaking band (band 10 in AHI) at each observation in 4D-Var. This approach follows Ishibashi (2020). All elements of the error covariance matrix were then inflated so that value of its diagonal element was equal to the square of the observation error SD estimated from the model described in the previous…”

Background Error in WRF Model

“…winds, pressure, temperature, humidity, etc.) to analyse, at every grid point of the 3-dimensional (3-D) model computational grid [6]. δx is difference between the analysis xa and reference state or the 'first guess' xg, i.e.…”

“…The variational approach involves finding the analysis that minimises a cost function J (see eq.1). Let J write as the sum of two members -the penalty contribution by the model ( b) and observations ( o) ( ) = b ( , , ) + o ( , , ) (6) Assuming that the prior and likelihood follow a Gaussian probability distribution, we apply Bayes' theorem to determine the posterior. b is larger if deviates more from with smaller background errors.…”

“…To consider the flow dependence of forecast errors in the DA process, various forms of ensemble Kalman filters and variational techniques have been tested. More recently, hybrids between variational and ensemble DA methods have been proposed and are mainstreamed into Global centers [5,6]. The background error statistics are measured, described and used by each of the centers in different ways [7,8].…”