scholarly journals Some Aspects of Sensitivity Analysis in Variational Data Assimilation for Coupled Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Sergei Soldatenko ◽  
Peter Steinle ◽  
Chris Tingwell ◽  
Denis Chichkine
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Weather Prediction ◽  
Computational Cost ◽  
Variational Data Assimilation ◽  
Practical Implementation ◽  
Parameter Uncertainties ◽  
Sensitivity Functions ◽  
Sensitivity Analysis Method

Variational data assimilation (VDA) remains one of the key issues arising in many fields of geosciences including the numerical weather prediction. While the theory of VDA is well established, there are a number of issues with practical implementation that require additional consideration and study. However, the exploration of VDA requires considerable computational resources. For simple enough low-order models, the computational cost is minor and therefore models of this class are used as simple test instruments to emulate more complex systems. In this paper, the sensitivity with respect to variations in the parameters of one of the main components of VDA, the nonlinear forecasting model, is considered. For chaotic atmospheric dynamics, conventional methods of sensitivity analysis provide uninformative results since the envelopes of sensitivity functions grow with time and sensitivity functions themselves demonstrate the oscillating behaviour. The use of sensitivity analysis method, developed on the basis of the theory of shadowing pseudoorbits in dynamical systems, allows us to calculate sensitivity functions correctly. Sensitivity estimates for a simple coupled dynamical system are calculated and presented in the paper. To estimate the influence of model parameter uncertainties on the forecast, the relative error in the energy norm is applied.

scholarly journals Cloud and Precipitation Parameterizations in Modeling and Variational Data Assimilation: A Review

2007 ◽  
Vol 64 (11) ◽  
pp. 3766-3784 ◽  
Author(s):  
Philippe Lopez
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Large Scale ◽  
Weather Prediction ◽  
General Circulation Models ◽  
Variational Data Assimilation ◽  
Current Status ◽  
General Question ◽  
Observation Error ◽  
Moist Processes

Abstract This paper first reviews the current status, issues, and limitations of the parameterizations of atmospheric large-scale and convective moist processes that are used in numerical weather prediction and climate general circulation models. Both large-scale (resolved) and convective (subgrid scale) moist processes are dealt with. Then, the general question of the inclusion of diabatic processes in variational data assimilation systems is addressed. The focus is put on linearity and resolution issues, the specification of model and observation error statistics, the formulation of the control vector, and the problems specific to the assimilation of observations directly affected by clouds and precipitation.

scholarly journals Multiplicative and Additive Incremental Variational Data Assimilation for Mixed Lognormal–Gaussian Errors

2014 ◽  
Vol 142 (7) ◽  
pp. 2521-2544 ◽  
Author(s):  
Steven J. Fletcher ◽  
Andrew S. Jones
Keyword(s):  
Data Assimilation ◽  
Lognormal Distribution ◽  
Weather Prediction ◽  
Variational Data Assimilation ◽  
Incremental Formulation ◽  
Incremental Scheme ◽  
Observational Errors ◽  
Mixed Approach ◽  
The Cost ◽  
Gaussian Space

Abstract An advance that made Gaussian-based three- and four-dimensional variational data assimilation (3D- and 4DVAR, respectively) operationally viable for numerical weather prediction was the introduction of the incremental formulation. This reduces the computational costs of the variational methods by searching for a small increment to a background state whose evolution is approximately linear. In this paper, incremental formulations for 3D- and 4DVAR with lognormal and mixed lognormal–Gaussian-distributed background and observation errors are presented. As the lognormal distribution has geometric properties, a geometric version for the tangent linear model (TLM) is proven that enables the linearization of the observational component of the cost functions with respect to a geometric increment. This is combined with the additive TLM for the mixed distribution–based cost function. Results using the mixed incremental scheme with the Lorenz’63 model are presented for different observational error variances, observation set sizes, and assimilation window lengths. It is shown that for sparse accurate observations the scheme has a relative error of ±0.5% for an assimilation window of 100 time steps. This improves to ±0.3% with more frequent observations. The distributions of the analysis errors are presented that appear to approximate a lognormal distribution with a mode at 1, which, given that the background and observational errors are unbiased in Gaussian space, shows that the scheme is approximating a mode and not a median. The mixed approach is also compared against a Gaussian-only incremental scheme where it is shown that as the z-component observational errors become more lognormal, the mixed approach appears to be more accurate than the Gaussian approach.

scholarly journals Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part I: Optimality Criteria and Application to Variance Filtering and Covariance Localization

2015 ◽  
Vol 143 (5) ◽  
pp. 1622-1643 ◽  
Author(s):  
Benjamin Ménétrier ◽  
Thibaut Montmerle ◽  
Yann Michel ◽  
Loïk Berre
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Weather Prediction ◽  
Computational Cost ◽  
Analytical Framework ◽  
Companion Paper ◽  
Optimality Criteria ◽  
Linear Filtering ◽  
Sampling Errors ◽  
Output Only

Abstract In data assimilation (DA) schemes for numerical weather prediction (NWP) systems, the estimation of forecast error covariances is a key point to get some flow dependency. As shown in previous studies, ensemble data assimilation methods are the most accurate for this task. However, their huge computational cost raises a strong limitation to the ensemble size. Consequently, covariances estimated with small ensembles are affected by random sampling errors. The aim of this study is to develop a theory of covariance filtering in order to remove most of the sampling noise while keeping the signal of interest and then to use it in the DA scheme of a real NWP system. This first part of a two-part study presents the theoretical aspects of such criteria for optimal filtering based on the merging of the theories of optimal linear filtering and of sample centered moments estimation. Its strength relies on the use of sample estimated quantities and filter output only. These criteria pave the way for new algorithms and interesting applications for NWP. Two of them are detailed here: spatial filtering of variances and covariance localization. Results obtained in an idealized 1D analytical framework are shown for illustration. Applications on real forecast error covariances deduced from ensembles at convective scale are discussed in a companion paper.

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