scholarly journals Strong Solvability of a Variational Data Assimilation Problem for the Primitive Equations of Large-Scale Atmosphere and Ocean Dynamics

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Initial Conditions ◽  
Strong Solutions ◽  
Variational Data Assimilation ◽  
Ocean Dynamics ◽  
Primitive Equations ◽  
Cost Functional ◽  
Strong Solvability ◽  
Gradient Based

AbstractFor the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose novel elements is to use norms in the variational cost functional that reflects the $$H^1$$ H 1 -regularity of strong solutions of the primitive equations. For such a cost functional, we prove the existence of minima and a first-order adjoint condition for strong solutions that provides the basis for computing these minima. We prove the local convergence of a gradient-based descent algorithm to optimal initial conditions using the second-order adjoint primitive equations. The algorithmic modifications due to the $$H^1$$ H 1 -norms are straightforwardly to implement into a variational algorithm that employs the standard $$L^2$$ L 2 -metrics.

scholarly journals Using adjoint sensitivity as a local structure function in variational data assimilation

2001 ◽  
Vol 8 (6) ◽  
pp. 347-355 ◽  
Author(s):  
G. Hello ◽  
F. Bouttier
Keyword(s):  
Data Assimilation ◽  
Structure Function ◽  
Local Structure ◽  
Initial Conditions ◽  
Storm Track ◽  
Variational Data Assimilation ◽  
Sensitive Area ◽  
Adjoint Sensitivity ◽  
Weather Events ◽  
Gradient Fields

Abstract. One approach recently proposed in order to improve the forecast of weather events, such as cyclogenesis, is to increase the number of observations in areas depending on the flow configuration. These areas are obtained using, for example, the sensitivity to initial conditions of a selected predicted cyclone. An alternative or complementary way is proposed here. The idea is to employ such an adjoint sensitivity field as a local structure function within variational data assimilation, 3D-Var in this instance. Away from the sensitive area, observation increments project on the initial fields with the usual climatological (or weakly flow-dependent, in the case of 4D-Var) structure functions. Within the sensitive area, the gradient fields are projected using all the available data in the zone, conventional or extra, if any. The formulation of the technique is given and the approach is further explained by using a simple 1D scheme. The technique is implemented in the ARPEGE/IFS code and applied to 11 FASTEX (Fronts and Atlantic Storm-Track Experiment) cyclone cases, together with the targeted observations performed at the time of the campaign. The new approach is shown to allow for the desired stronger impact of the available observations and to systematically improve the forecasts of the FASTEX cyclones, unlike the standard 3D-Var.

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 Variational data assimilation with superparameterization

2015 ◽  
Vol 2 (2) ◽  
pp. 513-536 ◽  
Author(s):  
I. Grooms ◽  
Y. Lee
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Climate Models ◽  
Low Cost ◽  
Ocean Model ◽  
Variational Data Assimilation ◽  
Scale Model ◽  
Small Scale ◽  
New Applications ◽  
Lorenz 96

Abstract. Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted {Yi}, with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.

scholarly journals Simulation of Monsoon Depressions Using WRF-VAR: Impact of Different Background Error Statistics and Lateral Boundary Conditions

2014 ◽  
Vol 142 (10) ◽  
pp. 3586-3613 ◽  
Author(s):  
A. Routray ◽  
S. C. Kar ◽  
P. Mali ◽  
K. Sowjanya
Keyword(s):  
Data Assimilation ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Variational Data Assimilation ◽  
Error Statistics ◽  
Background Error ◽  
Single Observation ◽  
Monsoon Depressions ◽  
Data Assimilation System ◽  
Assimilation System

Abstract In a variational data assimilation system, background error statistics (BES) spread the influence of the observations in space and filter analysis increments through dynamic balance or statistical relationships. In a data-sparse region such as the Bay of Bengal, BES play an important role in defining the location and structure of monsoon depressions (MDs). In this study, the Indian-region-specific BES have been computed for the Weather Research and Forecasting (WRF) three-dimensional variational data assimilation system. A comparative study using single observation tests is carried out using the computed BES and global BES within the WRF system. Both sets of BES are used in the assimilation cycles and forecast runs for simulating the meteorological features associated with the MDs. Numerical experiments have been conducted to assess the relative impact of various BES in the analysis and simulations of the MDs. The results show that use of regional BES in the assimilation cycle has a positive impact on the prediction of the location, propagation, and development of rainbands associated with the MDs. The track errors of MDs are smaller when domain-specific BES are used in the assimilation cycle. Additional experiments have been conducted using data from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) as initial and boundary conditions (IBCs) in the assimilation cycle. The results indicate that the use of domain-dependent BES and high-resolution ERA-I data as IBCs further improved the initial conditions for the model leading to better forecasts of the MDs.

scholarly journals CIRA/CSU Four-Dimensional Variational Data Assimilation System

2005 ◽  
Vol 133 (4) ◽  
pp. 829-843 ◽  
Author(s):  
Milija Zupanski ◽  
Dusanka Zupanski ◽  
Tomislava Vukicevic ◽  
Kenneth Eis ◽  
Thomas Vonder Haar
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Control Variable ◽  
Three Dimensional ◽  
Atmospheric Modeling ◽  
Variational Data Assimilation ◽  
Regional Atmospheric Modeling ◽  
The Impact ◽  
Data Assimilation System ◽  
Assimilation System

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

scholarly journals Sensitivity of 0–12-h Warm-Season Precipitation Forecasts over the Central United States to Model Initialization

2012 ◽  
Vol 27 (4) ◽  
pp. 832-855 ◽  
Author(s):  
Juanzhen Sun ◽  
Stanley B. Trier ◽  
Qingnong Xiao ◽  
Morris L. Weisman ◽  
Hongli Wang ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Case Studies ◽  
Large Scale ◽  
Initial Conditions ◽  
Warm Season ◽  
Radar Data ◽  
Short Wave ◽  
Forecast Skill ◽  
Precipitation Forecast ◽  
Scale Model

Abstract Sensitivity of 0–12-h warm-season precipitation forecasts to atmospheric initial conditions, including those from different large-scale model analyses and from rapid cycled (RC) three-dimensional variational data assimilations (3DVAR) with and without radar data, is investigated for a 6-day period during the International H2O Project. Neighborhood-based precipitation verification is used to compare forecasts made with the Advanced Research core of the Weather Research and Forecasting Model (ARW-WRF). Three significant convective episodes are examined by comparing the precipitation patterns and locations from different forecast experiments. From two of these three case studies, causes for the success and failure of the RC data assimilation in improving forecast skill are shown. Results indicate that the use of higher-resolution analysis in the initialization, rapid update cycling via WRF 3DVAR data assimilation, and the additional assimilation of radar observations each play a role in shortening the period of the initial precipitation spinup as well as in placing storms closer to observations, thus improving precipitation forecast skill by up to 8–9 h. Impacts of data assimilation differ for forecasts initialized at 0000 and 1200 UTC. The case studies show that the pattern and location of the forecasted precipitation were noticeably improved with radar data assimilation for the two late afternoon cases that featured lines of convection driven by surface-based cold pools. In contrast, the RC 3DVAR, both with and without radar data, had negative impacts on convective forecasts for a case of morning elevated convection associated with a midlatitude short-wave trough.

scholarly journals Hybridizing Bayesian and variational data assimilation for robust high-resolution hydrologic forecasting

2017 ◽  
Author(s):  
Felipe Hernández ◽  
Xu Liang
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Predictive Accuracy ◽  
Initial Conditions ◽  
Time Estimation ◽  
Variational Data Assimilation ◽  
Streamflow Forecasting ◽  
Infiltration Capacity ◽  
Computational Overhead ◽  
Capacity Model

Abstract. The success of real-time estimation and forecasting applications based on geophysical models has been possible thanks to the two main frameworks for the determination of the models’ initial conditions: Bayesian data assimilation and variational data assimilation. However, while there have been efforts to unify these two paradigms, existing attempts struggle to fully leverage the advantages of both in order to face the challenges posed by modern high-resolution models – mainly related to model indeterminacy and steep computational requirements. In this article we introduce a hybrid algorithm called OPTIMISTS (Optimized PareTo Inverse Modeling through Integrated STochastic Search) which is targeted at non-linear high-resolution problems and that brings together ideas from particle filters, 4-dimensional variational methods, evolutionary Pareto optimization, and kernel density estimation in a unique way. Streamflow forecasting experiments were conducted to test which specific parameterizations of OPTIMISTS led to higher predictive accuracy. The experiments analysed two watersheds, one with a low resolution using the VIC (Variable Infiltration Capacity) model and one with a high-resolution using the DHSVM (Distributed Hydrology Soil Vegetation Model). By selecting kernel-based non-parametric sampling, non-sequential evaluation of candidate particles, and through the multi-objective minimization of departures from the streamflow observations and from the background states, OPTIMISTS was shown to outperform a particle filter and a 4D variational method. Moreover, the experiments demonstrated that OPTIMISTS scales well in high-resolution cases without imposing a significant computational overhead and that it was successful in mitigating the harmful effects of overfitting. With these combined advantages, the algorithm shows the potential to increase the accuracy and efficiency of operational prediction systems for the improved management of natural resources.

scholarly journals Hybrid Neural Network – Variational Data Assimilation algorithm to infer river discharges from SWOT-like data

2020 ◽  
Author(s):  
Kevin Larnier ◽  
Jerome Monnier
Keyword(s):  
Neural Network ◽  
Data Assimilation ◽  
Large Scale ◽  
Mean Value ◽  
Variational Data Assimilation ◽  
Consistent Estimation ◽  
Hybrid Neural Network ◽  
Global Estimation ◽  
Surface Measurements ◽  
Time Variations

Abstract. A new algorithm to estimate river discharges from altimetry measurements only is designed. A first estimation is obtained by an artificial neural network trained from the altimetry large scale water surface measurements plus drainage area information. The combination of this purely data-based estimation and a dedicated algebraic flow model provides a first physically-consistent estimation. The latter is next employed as the first guess of an advanced variational data assimilation formulation. The final estimation is highly accurate for rivers presenting features within the learning partition; for rivers far outside the learning partition, the space-time variations of discharge remain accurately approximated however the global estimation presents a potential bias. Indeed, it is shown that if the estimation is based on the hydrodynamics models only, the inverse problem may be well-defined but up to a bias only (the bias scales the global estimation). This bias is removed thanks to the ANN but for rivers in the learning partition only. For rivers outside the learning partition, any mean value (eg. annual, seasonal) enables to remove the bias. Finally, the present hybrid and hierarchical inversion strategy seems to provide much more accurate estimations compared to the state-of-the-art for the considered 29 heterogeneous river portions.

scholarly journals Inclusion of Linearized Moist Physics in NASA’s Goddard Earth Observing System Data Assimilation Tools

2014 ◽  
Vol 142 (1) ◽  
pp. 414-433 ◽  
Author(s):  
Daniel Holdaway ◽  
Ronald Errico ◽  
Ronald Gelaro ◽  
Jong G. Kim
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Weather Forecast ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Adjoint Sensitivity ◽  
Earth Observing System ◽  
Sensitivity Studies ◽  
System Data ◽  
Simple Conversion

Abstract Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa–Schubert (RAS) convection scheme has been developed and tested in NASA’s Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

Sign in / Sign up

Export Citation Format

Share Document