The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field

Abstract

This paper analyses the statistical structure of the errors of the short‐range wind forecasts used in the global data assimilation system at ECMWF, by verifying the forecasts against radiosonde data over North America. The kinematics of two‐dimensional homogeneous turbulence is used to partition the perceived forecast errors into prediction errors which are horizontally correlated, and observational errors which are assumed to be horizontally uncorrelated. The theory further partitions the wind prediction errors into three components, viz. large‐scale, rotational and divergent components, and provides a spectral description of the covariance and cross‐covariance functions for stream function and velocity potential. The calculations also provide an estimate of the vertical error covariance matrices for prediction error and for radiosonde observational error, by which we mean the combined effects of instrumental error and errors of representativeness. The basic assumptions are that the forecast errors are horizontally homogeneous and that the observational errors are horizontally uncorrelated. Several important results are found. The wind prediction errors are comparable in magnitude with the wind observation errors. The prediction errors are dominated by the synoptic scales, but there is a substantial large scale wind error which reverses phase between the stratosphere and troposphere. The synoptic scale errors are largely non‐divergent in the troposphere. There are good grounds for increasing the resolution of the analysis system, both in the horizontal and the vertical, over North America and other data‐rich regions.

Assimilation of GPS Refractivity from FORMOSAT-3/COSMIC Using a Nonlocal Operator with WRF 3DVAR and Its Impact on the Prediction of a Typhoon Event

“…First, the ap par ent er ror can be es ti mated by calculating the dif fer ences be tween the fore cast re sults and the ob ser va tions. Then, we es ti mate the fore cast er rors follow ing the method used by Hollingsworth and Lönnberg (1986). It is as sumed that the ob ser va tion er rors are uncorrelated with each other, and they are also uncorrelated with the fore cast er rors.…”

Background error statistics for aerosols

“…observations minus model differences at observation locations, or on model fields generated on the model grid and whose statistics are assumed to be similar to those of the background error. An example of the first category of approaches is the Hollingsworth and Lönnberg (1986) method which consists of assuming that the observations are uncorrelated and plotting the innovation statistics as a function of the distance between pairs of observations. While this allows the relative contribution of background and observation errors to the variance of the innovations to be estimated, it requires a highdensity, good quality observing network, which might not be available globally.…”

A perspective on the fundamental quality of GPS radio occultation data

“…Thus, the high positive correlation among the collocated pairs reflects the systematic NWP error common to the pairs. Indeed, this is a well-accepted way of characterizing spatial error correlation in NWP data (Hollingsworth and Lönnberg, 1986;Kuo et al, 2004;Desroziers et al, 2005). Figure 4a and b compare OP and RA in the systematic difference and standard deviation from measured phase paths.…”