scholarly journals Nonlinear effects in 4D-Var

2018 ◽  
Vol 25 (3) ◽  
pp. 713-729 ◽  
Author(s):  
Massimo Bonavita ◽  
Peter Lean ◽  
Elias Holm
Keyword(s):  
Data Assimilation ◽  
Prognostic Model ◽  
Nonlinear Effects ◽  
Model Resolution ◽  
Test Models ◽  
Incremental Formulation ◽  
The Cost ◽  
The Relationship ◽  
Data Assimilation System ◽  
Global Data

Abstract. The ability of a data assimilation system to deal effectively with nonlinearities arising from the prognostic model or the relationship between the control variables and the available observations has received a lot of attention in theoretical studies based on very simplified test models. Less work has been done to quantify the importance of nonlinearities in operational, state-of-the-art global data assimilation systems. In this paper we analyse the nonlinear effects present in ECMWF 4D-Var and evaluate the ability of the incremental formulation to solve the nonlinear assimilation problem in a realistic NWP environment. We find that nonlinearities have increased over the years due to a combination of increased model resolution and the ever-growing importance of observations that are nonlinearly related to the state. Incremental 4D-Var is well suited for dealing with these nonlinear effects, but at the cost of increasing the number of outer loop relinearisations. We then discuss strategies for accommodating the increasing number of sequential outer loops in the tight schedules of operational global NWP.

scholarly journals Nonlinear effects in 4D-Var

2018 ◽  
Author(s):  
Massimo Bonavita ◽  
Peter Lean ◽  
Elias Holm
Keyword(s):  
Data Assimilation ◽  
Prognostic Model ◽  
Nonlinear Effects ◽  
Model Resolution ◽  
Test Models ◽  
Incremental Formulation ◽  
The Cost ◽  
The Relationship ◽  
Data Assimilation System ◽  
Global Data

Abstract. The ability of a data assimilation system to deal effectively with nonlinearities arising from the prognostic model or the relationship between the control variables and the available observations has received a lot of attention in theoretical studies based on very simplified test models. Less work has been done to quantify the importance of nonlinearities in operational, state-of-the-art global data assimilation systems. In this paper we analyse the nonlinear effects present in ECMWF 4D-Var and evaluate the ability of the incremental formulation to solve the nonlinear assimilation problem in a realistic NWP environment. We find that nonlinearities have increased over the years due to a combination of increased model resolution and the ever-growing importance of observations that are nonlinearly related to the state. Incremental 4D-Var is well suited for dealing with these nonlinear effects, but at the cost of increasing the number of outer loop relinearisations. We then discuss strategies for accommodating the increasing number of sequential outer loops in the tight schedules of operational global NWP.

Assessment of the Impact of Simulated Satellite Lidar Wind and Retrieved 183 GHz Water Vapor Observations on a Global Data Assimilation System

1990 ◽  
Vol 118 (12) ◽  
pp. 2513-2542 ◽  
Author(s):  
Ross N. Hoffman ◽  
Christopher Grassotti ◽  
Ronald G. Isaacs ◽  
Jean-Francois Louis ◽  
Thomas Nehrkorn ◽  
...  
Keyword(s):  
Water Vapor ◽  
Data Assimilation ◽  
Global Data Assimilation System ◽  
The Impact ◽  
Data Assimilation System ◽  
Global Data ◽  
Assimilation System

Forecast Impact of Assimilating Aircraft WVSS-II Water Vapor Mixing Ratio Observations in the Global Data Assimilation System (GDAS)

2017 ◽  
Vol 32 (4) ◽  
pp. 1603-1611 ◽  
Author(s):  
Brett T. Hoover ◽  
David A. Santek ◽  
Anne-Sophie Daloz ◽  
Yafang Zhong ◽  
Richard Dworak ◽  
...  
Keyword(s):  
Water Vapor ◽  
Data Assimilation ◽  
Positive Impact ◽  
Weather Prediction ◽  
Warm Season ◽  
Precipitation Forecast ◽  
Global Data Assimilation System ◽  
Data Assimilation System ◽  
Global Data ◽  
Assimilation System

Abstract Automated aircraft observations of wind and temperature have demonstrated positive impact on numerical weather prediction since the mid-1980s. With the advent of the Water Vapor Sensing System (WVSS-II) humidity sensor, the expanding fleet of commercial aircraft with onboard automated sensors is also capable of delivering high quality moisture observations, providing vertical profiles of moisture as aircraft ascend out of and descend into airports across the continental United States. Observations from the WVSS-II have to date only been monitored within the Global Data Assimilation System (GDAS) without being assimilated. In this study, aircraft moisture observations from the WVSS-II are assimilated into the GDAS, and their impact is assessed in the Global Forecast System (GFS). A two-season study is performed, demonstrating a statistically significant positive impact on both the moisture forecast and the precipitation forecast at short range (12–36 h) during the warm season. No statistically significant impact is observed during the cold season.

Introduction of the GSI into the NCEP Global Data Assimilation System

2009 ◽  
Vol 24 (6) ◽  
pp. 1691-1705 ◽  
Author(s):  
Daryl T. Kleist ◽  
David F. Parrish ◽  
John C. Derber ◽  
Russ Treadon ◽  
Wan-Shu Wu ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Environmental Modeling ◽  
Analysis Scheme ◽  
Global Data Assimilation System ◽  
Analysis System ◽  
Data Assimilation System ◽  
Global Data ◽  
Statistical Interpolation ◽  
New System ◽  
Assimilation System

Abstract At the National Centers for Environmental Prediction (NCEP), a new three-dimensional variational data assimilation (3DVAR) analysis system was implemented into the operational Global Data Assimilation System (GDAS) on 1 May 2007. The new analysis system, the Gridpoint Statistical Interpolation (GSI), replaced the Spectral Statistical Interpolation (SSI) 3DVAR system, which had been operational since 1991. The GSI was developed at the Environmental Modeling Center at NCEP as part of an effort to create a more unified, robust, and efficient analysis scheme. The key aspect of the GSI is that it formulates the analysis in model grid space, which allows for more flexibility in the application of the background error covariances and makes it straightforward for a single analysis system to be used across a broad range of applications, including both global and regional modeling systems and domains. Due to the constraints of working with an operational system, the final GDAS package included many changes other than just a simple replacing of the SSI with the new GSI. The new GDAS package contained an upgrade to the Global Forecast System model, including a new vertical coordinate, as well as new features in the GSI that were never developed for the SSI. Some of these new features included changes to the observation selection, quality control, minimization algorithm, dynamic balance constraint, and assimilation of new observation types. The evaluation of the new system relative to the SSI-based system was performed for nearly an entire year of analyses and forecasts. The objective and subjective evaluations showed that the new package exhibited superior forecast performance relative to the old SSI-based system. The new system has been shown to improve forecast skill in the tropics and substantially reduce the short-term forecast error in the extratropics. This implementation has laid the groundwork for future scientific advancements in data assimilation at NCEP.

The Canadian Global Data Assimilation System: Description and Evaluation

1993 ◽  
Vol 121 (5) ◽  
pp. 1467-1492 ◽  
Author(s):  
Herschel L. Mitchell ◽  
Cécilien Charette ◽  
Steven J. Lambert ◽  
Jacques Hallé ◽  
Clément Chouinard
Keyword(s):  
Data Assimilation ◽  
System Description ◽  
Global Data Assimilation System ◽  
Data Assimilation System ◽  
Global Data ◽  
Assimilation System

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.

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