Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors

Abstract

SUMMARYThis paper seeks to represent the tropical short-range forecast error covariances of the European Centre for Medium-Range Weather Forecasts (ECMWF) model in terms of equatorial waves. The motivation for undertaking this investigation is increasing observational evidence indicating that a substantial fraction of the tropical largescale variability can be explained by equatorially trapped wave solutions known from shallow-water theory. Shortrange forecast differences from a data-assimilation ensemble were taken to serve as a proxy for background errors.It was found that the equatorial waves coupled to convection can explain on average 60-70% of the error variance in the tropical free atmosphere. The largest part of this explained variance is represented by the equatorial Rossby (ER) modes, and a significant percentage pertains to the equatorial inertio-gravity (EIG) modes. Eastwardpropagating EIG modes have maximum variance in the stratosphere, where the short-wave variance in westwardmoving waves is particularly small. This feature is most likely related to the phase of the quasi-biennial oscillation during the study period, suggesting that significant temporal variations could be present in longer-term time series of such statistics.The vertical correlations for ER modes display characteristics similar to those of their extratropical counterparts: correlations narrow towards shorter scales and in the stratosphere. However, the present statistics do not display the significant increase with altitude of the horizontal correlation scale for the height field which is typical for global, quasi-geostrophic statistics commonly used in current data-assimilation schemes. Furthermore, tropospheric ER correlations are vertically asymmetric and deeper for the n = 1 mode than for higher modes. Most likely, deep convection, acting as a generator of equatorial wave motion, is the dominant mechanism underlying these results.In spite of its relatively small contribution to the tropospheric variance, the Kelvin-wave coupling plays a decisive role for determining the characteristics of the horizontal correlation near the equator. EIG modes also play an important role for the tropical mass-wind coupling; these waves have a major impact by reducing the meridional correlation scales and the magnitudes of the balanced height-field increments.

Objective filtering of ensemble‐based background‐error variances

“…In particular, low values are found in the Tropics and in data-rich areas (North America, Europe, Asia), whereas much higher values are observed in data-poor areas (such as over sea) and in the storm-track regions (Northern/Southern Atlantic, Northern/Southern Pacific). Another interesting point is the frequent occurrence of relatively large errors along the intertropical convergence zone (ITCZ), which is in accordance with the results of Zagar et al (2005) for the error in the zonal wind field.…”

Feasibility of a 100-Year Reanalysis Using Only Surface Pressure Data

“…The wind field is poorly recovered, with correlations below 0.2 in many areas. Previous studies (e.g., Parrish and Derber 1992; Zagar et al 2005) have shown that a tropical pressure observation makes little change to the tropical wind first guess and, therefore, has little impact on the tropical wind analysis. In contrast, we find that the ensemble filter can produce a substantial covariance between the first-guess surface pressure and tropical wind fields, resulting in modifications to the first-guess tropical wind field that are on the same order (0.5-1 m s _1 ) as in the midlatitudes.…”

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

“…Again, the averaging may be carried out instantaneously over the N − 1 pairs or additionally over many assimilation cycles. Recently, the ECMWF have started to use (27) (averaging additionally over one month) to determine their B-matrix (replacing the NMC method) in the way described in Fisher and Andersson (2001), Fisher (2003) andŽagar, Andersson and Fisher (2005), and Météo-France ) use a similar ensemble-based method. Isaksen, Fisher and Berner (2007) have used the method to investigate flowdependent variances in the ECMWF system.…”