Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction(NWP).To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations,hydrometeor control variables are necessary.Common data assimilation systems theoretically require that the probability density functions(PDFs)of analysis,background,and observation errors should satisfy the Gaussian unbiased assumptions.In this study,a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables,which is modified from the Softmax function and renamed as Quasi-Softmax transform.The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform.The spatial distribution,the non-Gaussian nature of the background errors,and the characteristics of the background errors of hydrometeors in each method are studied.Compared to the logarithmic and Softmax transform,the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent.The results of the D′Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods.The Gaussian transform has been added to the control variable transform to estimate the background error covariances.Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method.The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system,and are promising control variables for data assimilation systems.

Improvement in Background Error Covariances Using Ensemble Forecasts for Assimilation of High-Resolution Satellite Data

Satellite data obtained over synoptic data-sparse regions such as an ocean contribute toward improving the quality of the initial state of limited-area models. Background error covariances are crucial to the proper distribution of satellite-observed information in variational data assimilation. In the NMC （National Meteorological Center） method, background error covariances are underestimated over data-sparse regions such as an ocean because of small differences between different forecast times. Thus, it is necessary to reconstruct and tune the background error covariances so as to maximize the usefulness of the satellite data for the initial state of limited-area models, especially over an ocean where there is a lack of conventional data. In this study, we attempted to estimate background error covariances so as to provide adequate error statistics for data-sparse regions by using ensemble forecasts of optimal perturbations using bred vectors. The background error covariances estimated by the ensemble method reduced the overestimation of error amplitude obtained by the NMC method. By employing an appropriate horizontal length scale to exclude spurious correlations, the ensemble method produced better results than the NMC method in the assimilation of retrieved satellite data. Because the ensemble method distributes observed information over a limited local area, it would be more useful in the analysis of high-resolution satellite data. Accordingly, the performance of forecast models can be improved over the area where the satellite data are assimilated.

The importance of data assimilation components for initial conditions and subsequent error growth

Despite a specific data assimilation method,data assimilation(DA)in general can be decomposed into components of the prior information,observation forward operator that is given by the observation type,observation error covariances,and background error covariances.In a classic Lorenz model,the influences of the DA components on the initial conditions(ICs)and subsequent forecasts are systematically investigated,which could provide a theoretical basis for the design of DA for different scales of interests.The forecast errors undergo three typical stages:a slow growth stage from 0 h to 5 d,a fast growth stage from 5 d to around 15 d with significantly different error growth rates for ensemble and deterministic forecasts,and a saturation stage after 15 d.Assimilation strategies that provide more accurate ICs can improve the predictability.Cycling assimilation is superior to offline assimilation,and a flow-dependent background error covariance matrix(Pf)provides better analyses than a static background error covariance matrix(B)for instantaneous observations and frequent time-averaged observations;but the opposite is true for infrequent time-averaged observations,since cycling simulation cannot construct informative priors when the model lacks predictive skills and the flow-dependent Pf cannot effectively extract information from low-informative observations as the static B.Instantaneous observations contain more information than time-averaged observations,thus the former is preferred,especially for infrequent observing systems.Moreover,ensemble forecasts have advantages over deterministic forecasts,and the advantages are enlarged with less informative observations and lower predictive-skill model priors.

An effective method for improving the accuracy of Argo objective analysis

Based on the optimal interpolation objective analysis of the Argo data, improvements are made to the em- pirical formula of a background error covariance matrix widely used in data assimilation and objective anal- ysis systems. Specifically, an estimation of correlation scales that can improve effectively the accuracy of Ar- go objective analysis has been developed. This method can automatically adapt to the gradient change of a variable and is referred to as ＂gradient-dependent correlation scale method＂. Its effect on the Argo objective analysis is verified theoretically with Gaussian pulse and spectrum analysis. The results of one-dimensional simulation experiment show that the gradient-dependent correlation scales can improve the adaptability of the objective analysis system, making it possible for the analysis scheme to fully absorb the shortwave information of observation in areas with larger oceanographic gradients. The new scheme is applied to the Argo data obiective analysis system in the Pacific Ocean. The results are obviously improved.

An Ocean Data Assimilation System in the Indian Ocean and West Pacific Ocean

The development and application of a regional ocean data assimilation system are among the aims of the Global Ocean Data Assimilation Experiment. The ocean data assimilation system in the regions including the Indian and West Pacific oceans is an endeavor motivated by this goal. In this study, we describe the system in detail. Moreover, the reanalysis in the joint area of Asia, the Indian Ocean, and the western Pacific Ocean （hereafter AIPOcean） constructed using multi-year model integration with data assimilation is used to test the performance of this system. The ocean model is an eddy-resolving, hybrid coordinate ocean model. Various types of observations including in-situ temperature and salinity profiles （mechanical bathythermograph, expendable bathythermograph, Array for Real-time Geostrophic Oceanography, Tropical Atmosphere Ocean Array, conductivity-temperature-depth, station data）, remotely-sensed sea surface temperature, and altimetry sea level anomalies, are assimilated into the reanalysis via the ensemble optimal interpolation method. An ensemble of model states sampled from a long-term integration is allowed to change with season, rather than remaining stationary. The estimated background error covariance matrix may reasonably reflect the seasonality and anisotropy. We evaluate the performance of AIPOcean during the period 1993-2006 by comparisons with independent observations, and some reanalysis products. We show that AIPOcean reduces the errors of subsurface temperature and salinity, and reproduces mesoscale eddies. In contrast to ECCO and SODA products, AIPOcean captures the interannual variability and linear trend of sea level anomalies very well. AIPOcean also shows a good consistency with tide gauges.

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System （OVALS）, which has been widely used in various applications, an improved OVALS （OVALS2） is developed based on the recursive filter （RF） algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control variable. For comparing the effectiveness between OVALS2 and OVALS, a set of experiments was implemented by assimilating expendable bathythermograph （XBT） and ARGO data into the Tropical Pacific circulation model. The results show that the efficiency of OVALS2 is much higher than that of OVALS. The computational time and the computer storage in the assimilation process were reduced by 83% and 77%, respectively. Additionally, the corresponding results produced by the RF are almost as good as those obtained by OVALS. These results prove that OVALS2 is suitable for operational numerical oceanic forecasting.

Assimilation of temperature and salinity using isotropic and anisotropic recursive filters in Tropic Pacific

A data assimilation scheme used in the updated Ocean three-dimensional Variational Assimila- tion System （OVALS）, OVALS2, is described. Based on a recursive filter （RF） to estimate the background error covariance （BEC） over a predetermined scale, this new analysis system can be implemented with anisotropic and isotropic BECs. Similarities and differences of these two BEC schemes are briefly discussed and their impacts on the model simulation are also investigated. An idealized experiment demonstrates the ability of the updated analysis system to construct different BECs. Furthermore, a set of three years experiments is implemented by assimilating expendable bathythermograph （XBT） and ARGO data into a Tropical Pacific circulation model. The TAO and WOA01 data are used to validate the assimilation results. The results show that the model simu- lations are substantially improved by OVALS2. The inter-comparison of isotropic and anisotropic BEC shows that the corresponding temperature and salinity produced by the anisotropic BEC are almost as good as those obtained by the isotropic one. Moreover, the result of anisotropic RF is slightly closer to WOA01 and TAO than that of isotropic RF in some special area （e.g. the cold tongue area in the Tropic Pacific）.