scholarly journals Pseudo-Orbit Data Assimilation. Part II: Assimilation with Imperfect Models

2014 ◽  
Vol 71 (2) ◽  
pp. 483-495 ◽  
Author(s):  
Hailiang Du ◽  
Leonard A. Smith
Keyword(s):  
Data Assimilation ◽  
State Estimation ◽  
Structural Model ◽  
Weather Forecasting ◽  
Nonlinear Models ◽  
Model Error ◽  
Promising Alternative ◽  
Model State ◽  
State Dependent ◽  
Orbit Data

Abstract Data assimilation and state estimation for nonlinear models is a challenging task mathematically. Performing this task in real time, as in operational weather forecasting, is even more challenging as the models are imperfect: the mathematical system that generated the observations (if such a thing exists) is not a member of the available model class (i.e., the set of mathematical structures admitted as potential models). To the extent that traditional approaches address structural model error at all, most fail to produce consistent treatments. This results in questionable estimates both of the model state and of its uncertainty. A promising alternative approach is proposed to produce more consistent estimates of the model state and to estimate the (state dependent) model error simultaneously. This alternative consists of pseudo-orbit data assimilation with a stopping criterion. It is argued to be more efficient and more coherent than one alternative variational approach [a version of weak-constraint four-dimensional variational data assimilation (4DVAR)]. Results that demonstrate the pseudo-orbit data assimilation approach can also outperform an ensemble Kalman filter approach are presented. Both comparisons are made in the context of the 18-dimensional Lorenz96 flow and the two-dimensional Ikeda map. Many challenges remain outside the perfect model scenario, both in defining the goals of data assimilation and in achieving high-quality state estimation. The pseudo-orbit data assimilation approach provides a new tool for approaching this open problem.

scholarly journals Pseudo-Orbit Data Assimilation. Part I: The Perfect Model Scenario

2014 ◽  
Vol 71 (2) ◽  
pp. 469-482 ◽  
Author(s):  
Hailiang Du ◽  
Leonard A. Smith
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
State Estimation ◽  
Ensemble Kalman Filter ◽  
Weather Forecasting ◽  
Weather Prediction ◽  
Attractive Alternative ◽  
Perfect Model ◽  
Improved Performance ◽  
Orbit Data

Abstract State estimation lies at the heart of many meteorological tasks. Pseudo-orbit-based data assimilation provides an attractive alternative approach to data assimilation in nonlinear systems such as weather forecasting models. In the perfect model scenario, noisy observations prevent a precise estimate of the current state. In this setting, ensemble Kalman filter approaches are hampered by their foundational assumptions of dynamical linearity, while variational approaches may fail in practice owing to local minima in their cost function. The pseudo-orbit data assimilation approach improves state estimation by enhancing the balance between the information derived from the dynamic equations and that derived from the observations. The potential use of this approach for numerical weather prediction is explored in the perfect model scenario within two deterministic chaotic systems: the two-dimensional Ikeda map and 18-dimensional Lorenz96 flow. Empirical results demonstrate improved performance over that of the two most common traditional approaches of data assimilation (ensemble Kalman filter and four-dimensional variational assimilation).

scholarly journals Model error in weather forecasting

2001 ◽  
Vol 8 (6) ◽  
pp. 357-371 ◽  
Author(s):  
D. Orrell ◽  
L. Smith ◽  
J. Barkmeijer ◽  
T. N. Palmer
Keyword(s):  
Prediction Models ◽  
Weather Forecasting ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Model Error ◽  
Local Model ◽  
State Dependent ◽  
Rapid Divergence ◽  
Dependent Model

Abstract. Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.

scholarly journals Climate Model State Estimation Using Variants of EnKF Coupled Data Assimilation

2020 ◽  
Vol 148 (6) ◽  
pp. 2411-2431
Author(s):  
Paul A. Sandery ◽  
Terence J. O’Kane ◽  
Vassili Kitsios ◽  
Pavel Sakov
Keyword(s):  
Data Assimilation ◽  
State Estimation ◽  
Climate Model ◽  
Present System ◽  
Geophysical Fluid Dynamics Laboratory ◽  
Error Growth ◽  
Near Surface ◽  
Model State ◽  
Ocean Atmosphere ◽  
The Cross

Abstract Data assimilation (DA) experiments are performed to assess impacts of observations in climate model state estimation through the cross-domain ocean–atmosphere forecast error covariances (cross covariances). Specifically, we explore strongly and weakly coupled DA variants using the Climate Analysis Forecast Ensemble (CAFE) system. This comprises 96 ensemble members of the Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 climate model assimilating observational data from the ocean, atmosphere, and sea ice realms with the ensemble Kalman filter (EnKF). Sequences of atmospheric synoptic time-scale coupled forecasts (7 days) are carried out with model consistent initialization. Unassimilated forward-independent observations are used to quantify forecast innovation error-growth rates. The results show benefit for the slow components of the atmosphere and ocean subsurface when strongly coupling ocean observations to the atmosphere. In the present system, projecting fast atmospheric observations onto the ocean subsurface through the cross covariances benefits the oceanic and atmospheric near-surface layers; however, this leads to deterioration in the ocean subsurface. Particular variants of coupled DA are able to constrain the ocean and atmosphere. The forecasts initialized with these variants have predictability at intraseasonal time scales. Errors associated with the dominant intraseasonal mode of variability, the Madden–Julian oscillation (MJO), are decomposed into normal mode functions. Consistent with recent studies showing large MJO events are concurrent with rapid error growth associated with nonlinear interactions, we find a clear relationship between the strength of a given MJO event and the related forecast innovations. Our results demonstrate consistent system behavior in relation to capturing real-world disturbances that affect climate predictability.

scholarly journals Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

2015 ◽  
Vol 143 (5) ◽  
pp. 1568-1582 ◽  
Author(s):  
Juan Ruiz ◽  
Manuel Pulido
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Model Error ◽  
Forecast Skill ◽  
Moist Convection ◽  
Treatment Techniques ◽  
Correction Technique ◽  
Error Treatment ◽  
Data Assimilation System ◽  
Assimilation System

Abstract This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

TOMOREF operator as a tool to improve weather forecasts

2021 ◽  
Author(s):  
Natalia Hanna ◽  
Estera Trzcina ◽  
Maciej Kryza ◽  
Witold Rohm
Keyword(s):  
Data Assimilation ◽  
Weather Forecasting ◽  
Positive Impact ◽  
Precipitation Event ◽  
Initial State ◽  
Total Delay ◽  
Numerical Weather ◽  
Numerical Weather Model ◽  
Weather Model ◽  
Tomography Data

<p>The numerical weather model starts from the initial state of the Earth's atmosphere in a given place and time. The initial state is created by blending the previous forecast runs (first-guess), together with observations from different platforms. The better the initial state, the better the forecast; hence, it is worthy to combine new observation types. The GNSS tomography technique, developed in recent years, provides a 3-D field of humidity in the troposphere. This technique shows positive results in the monitoring of severe weather events. However, to assimilate the tomographic outputs to the numerical weather model, the proper observation operator needs to be built.</p><p>This study demonstrates the TOMOREF operator dedicated to the assimilation of the GNSS tomography‐derived 3‐D fields of wet refractivity in a Weather Research and Forecasting (WRF) Data Assimilation (DA) system. The new tool has been tested based on wet refractivity fields derived during a very intense precipitation event. The results were validated using radiosonde observations, synoptic data, ERA5 reanalysis, and radar data. In the presented experiment, a positive impact of the GNSS tomography data assimilation on the forecast of relative humidity (RH) was noticed (an improvement of root‐mean‐square error up to 0.5%). Moreover, within 1 hour after assimilation, the GNSS data reduced the bias of precipitation up to 0.1 mm. Additionally, the assimilation of GNSS tomography data had more influence on the WRF model than the Zenith Total Delay (ZTD) observations, which confirms the potential of the GNSS tomography data for weather forecasting.</p>

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

scholarly journals A Scale-Selective Data Assimilation Approach to Improving Tropical Cyclone Track and Intensity Forecasts in a Limited-Area Model: A Case Study of Hurricane Felix (2007)

2012 ◽  
Vol 27 (1) ◽  
pp. 124-140 ◽  
Author(s):  
Bin Liu ◽  
Lian Xie
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Dynamical Downscaling ◽  
Weather Forecasting ◽  
Forecast Error ◽  
Regional Model ◽  
Small Scale ◽  
Limited Area ◽  
Track Forecast ◽  
Global Models

Abstract Accurately forecasting a tropical cyclone’s (TC) track and intensity remains one of the top priorities in weather forecasting. A dynamical downscaling approach based on the scale-selective data assimilation (SSDA) method is applied to demonstrate its effectiveness in TC track and intensity forecasting. The SSDA approach retains the merits of global models in representing large-scale environmental flows and regional models in describing small-scale characteristics. The regional model is driven from the model domain interior by assimilating large-scale flows from global models, as well as from the model lateral boundaries by the conventional sponge zone relaxation. By using Hurricane Felix (2007) as a demonstration case, it is shown that, by assimilating large-scale flows from the Global Forecast System (GFS) forecasts into the regional model, the SSDA experiments perform better than both the original GFS forecasts and the control experiments, in which the regional model is only driven by lateral boundary conditions. The overall mean track forecast error for the SSDA experiments is reduced by over 40% relative to the control experiments, and by about 30% relative to the GFS forecasts, respectively. In terms of TC intensity, benefiting from higher grid resolution that better represents regional and small-scale processes, both the control and SSDA runs outperform the GFS forecasts. The SSDA runs show approximately 14% less overall mean intensity forecast error than do the control runs. It should be noted that, for the Felix case, the advantage of SSDA becomes more evident for forecasts with a lead time longer than 48 h.

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