Distributed Forcing of Forecast and Assimilation Error Systems

2005 ◽  
Vol 62 (2) ◽  
pp. 460-475 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Forecast Error ◽  
Model Error ◽  
Time Interval ◽  
Error Growth ◽  
Error Sources ◽  
Linear Observer ◽  
Error System ◽  
Optimal Set ◽  
Observer System ◽  
Intrinsic Error

Abstract Temporally distributed deterministic and stochastic excitation of the tangent linear forecast system governing forecast error growth and the tangent linear observer system governing assimilation error growth is examined. The method used is to determine the optimal set of distributed deterministic and stochastic forcings of the forecast and observer systems over a chosen time interval. Distributed forcing of an unstable system addresses the effect of model error on forecast error in the presumably unstable forecast error system. Distributed forcing of a stable system addresses the effect on the assimilation of model error in the presumably stable data assimilation system viewed as a stable observer. In this study, model error refers both to extrinsic physical error forcing, such as that which arises from unresolved cumulus activity, and to intrinsic error sources arising from imperfections in the numerical model and in the physical parameterizations.

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 Optimization of Gravity Wave Source Parameters for Improved Seasonal Prediction of the Quasi-Biennial Oscillation

2019 ◽  
Vol 76 (9) ◽  
pp. 2941-2962
Author(s):  
Cory A. Barton ◽  
John P. McCormack ◽  
Stephen D. Eckermann ◽  
Karl W. Hoppel
Keyword(s):  
Gravity Wave ◽  
Optimal Parameter ◽  
Forecast Error ◽  
Source Parameters ◽  
Phase Speed ◽  
Time Interval ◽  
Quasi Biennial Oscillation ◽  
Wave Source ◽  
Forecast Lead Time ◽  
Biennial Oscillation

Abstract A methodology is presented for objectively optimizing nonorographic gravity wave source parameters to minimize forecast error for target regions and forecast lead times. In this study, we employ a high-altitude version of the Navy Global Environmental Model (NAVGEM-HA) to ascertain the forcing needed to minimize hindcast errors in the equatorial lower stratospheric zonal-mean zonal winds in order to improve forecasts of the quasi-biennial oscillation (QBO) over seasonal time scales. Because subgrid-scale wave effects play a large role in driving the QBO, this method leverages the nonorographic gravity wave drag (GWD) parameterization scheme to provide the necessary forcing. To better constrain the GWD source parameters, we utilize ensembles of NAVGEM-HA hindcasts over the 2014–16 period with perturbed source parameters and develop a cost function to minimize errors in the equatorial lower stratosphere compared to analysis. Thus, we may determine the set of GWD source parameters that yields a forecast state that most closely agrees with observed QBO winds over each optimization time interval. Results show that the source momentum flux and phase speed spectrum width are the most important parameters. The seasonal evolution of optimal parameter value, specifically a robust semiannual periodicity in the source strength, is also revealed. Changes in optimal source parameters with increasing forecast lead time are seen, as the GWD parameterization takes on a more active role as QBO driver at longer forecast lengths. Implementation of a semiannually varying source function at the equator provides RMS error improvement in QBO winds over the default constant value.

scholarly journals Application of an Estimation Method in the Lure System

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhaoxia Huang
Keyword(s):  
Nonlinear Term ◽  
Estimation Method ◽  
Observer Design ◽  
Set Valued Mapping ◽  
System Trajectory ◽  
System Output ◽  
Error System ◽  
Interval Observer ◽  
The Stability ◽  
Observer System

The presence of set-valued mapping affects the stability of the output of the lure system, adding to the difficulty in observer design. To overcome the difficulty, the author mapped the system output error to the nonlinear term of the framer, creating a framer of the extended Luenberger structure, and analyzed the coordination of the error system by the monotonic system theory. On this basis, the interval observer was designed for the lure system. Then, the lure system and its observer systems were proved as asymptotically stable. Finally, it is proved that the observer system trajectory always followed the original state trajectory through the simulation under the different selections of set-valued mapping.

scholarly journals Correcting for Surface Pressure Background Bias in Ensemble-Based Analyses

2009 ◽  
Vol 137 (7) ◽  
pp. 2349-2364 ◽  
Author(s):  
Seung-Jong Baek ◽  
Istvan Szunyogh ◽  
Brian R. Hunt ◽  
Edward Ott
Keyword(s):  
Surface Pressure ◽  
Bias Correction ◽  
Correction Term ◽  
Forecast Error ◽  
Model Error ◽  
Model Bias ◽  
Analysis Scheme ◽  
Environmental Prediction ◽  
Hydrostatic Balance ◽  
Bias Correction Term

Model error is the component of the forecast error that is due to the difference between the dynamics of the atmosphere and the dynamics of the numerical prediction model. The systematic, slowly varying part of the model error is called model bias. This paper evaluates three different ensemble-based strategies to account for the surface pressure model bias in the analysis scheme. These strategies are based on modifying the observation operator for the surface pressure observations by the addition of a bias-correction term. One estimates the correction term adaptively, while another uses the hydrostatic balance equation to obtain the correction term. The third strategy combines an adaptively estimated correction term and the hydrostatic-balance-based correction term. Numerical experiments are carried out in an idealized setting, where the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model is integrated at resolution T62L28 to simulate the evolution of the atmosphere and the T30L7 resolution Simplified Parameterization Primitive Equation Dynamics (SPEEDY) model is used for data assimilation. The results suggest that the adaptive bias-correction term is effective in correcting the bias in the data-rich regions, while the hydrostatic-balance-based approach is effective in data-sparse regions. The adaptive bias-correction approach also has the benefit that it leads to a significant improvement of the temperature and wind analysis at the higher model levels. The best results are obtained when the two bias-correction approaches are combined.

PRACTICAL STABILITY OF IMPULSIVE SYNCHRONIZATION BETWEEN TWO NONAUTONOMOUS CHAOTIC SYSTEMS

2000 ◽  
Vol 10 (04) ◽  
pp. 859-867 ◽  
Author(s):  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Differential Equation ◽  
Impulsive Differential Equation ◽  
Chaotic Systems ◽  
Practical Stability ◽  
Time Interval ◽  
Theoretical Methods ◽  
Synchronization Errors ◽  
Impulsive Synchronization ◽  
Error System ◽  
Theoretical Results

The practical stability of impulsive synchronization between two nonautonomous chaotic systems is studied in this paper, and this is equivalent to that of the origin of the synchronization error system, which is modeled by an impulsive differential equation. We develop theoretical methods of choosing the time interval between two successive synchronization impulses and strengths of synchronization impulses for restricting synchronization errors within prescribed regions around the origin. Numerical experimental results are given to demonstrate theoretical results.

scholarly journals Real-time flood stage forecasting by Variable Parameter Muskingum Stage hydrograph routing method

2011 ◽  
Vol 42 (2-3) ◽  
pp. 150-161 ◽  
Author(s):  
Muthiah Perumal ◽  
Tommaso Moramarco ◽  
Silvia Barbetta ◽  
Florisa Melone ◽  
Bhabagrahi Sahoo
Keyword(s):  
Real Time ◽  
Forecast Error ◽  
Central Italy ◽  
Variable Parameter ◽  
Warning System ◽  
Forecast Model ◽  
Flood Forecasting ◽  
Time Interval ◽  
Tiber River ◽  
Routing Method

The application of a Variable Parameter Muskingum Stage (VPMS) hydrograph routing method for real-time flood forecasting at a river gauging site is demonstrated in this study. The forecast error is estimated using a two-parameter linear autoregressive model with its parameters updated at every routing time interval of 30 minutes at which the stage observations are made. This hydrometric data-based forecast model is applied for forecasting floods at the downstream end of a 15 km reach of the Tiber River in Central Italy. The study reveals that the proposed approach is able to provide reliable forecast of flood estimate for different lead times subject to a maximum lead time nearly equal to the travel time of the flood wave within the selected routing reach. Moreover, a comparative study of the VPMS method for real-time forecasting and the simple stage forecasting model (STAFOM), currently in operation as the Flood Forecasting and Warning System in the Upper-Middle Tiber River basin of Italy, demonstrates the capability of the VPMS model for its field use.

The Strategy and Advantage in Use of an Electronic Probe for Attachment Measurement

1993 ◽  
Vol 7 (2) ◽  
pp. 152-157 ◽  
Author(s):  
W.B. Clark ◽  
I. Magnusson ◽  
Y.Y. Namgung ◽  
M.C.K. Yang
Keyword(s):  
Clinical Setting ◽  
Gold Standard ◽  
Large Error ◽  
Gingival Tissue ◽  
Time Interval ◽  
Error Sources ◽  
Designed Experiments ◽  
Electronic Probe ◽  
Periodontal Probing ◽  
Attachment Level

Attachment level has been used as the "gold standard" for assessment of the progression of periodontal disease. However, the measurement of attachment level by periodontal probing can be subject to a large number of error sources. Recently, we have designed experiments by using an electronic probe to identify the magnitude of error components due to the instrument, gingival tissue condition, position or probing angle, and time interval between replicate probings. Even with a very careful clinical setting, a few percent of uncontrollable large errors or outliers could not be avoided. A previously used 'option-3' probing scheme to reduce the unexpected large error is justified from the mathematical viewpoint.

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