scholarly journals The Characteristics of Key Analysis Errors. Part I: Dynamical Balance and Comparison with Observations

2007 ◽  
Vol 135 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche ◽  
Peter Zwack
Keyword(s):  
Forecast Error ◽  
Forecast Errors ◽  
Control Analysis ◽  
Initial Condition ◽  
Initial State ◽  
Mass Correction ◽  
Current Algorithm ◽  
Dynamical Balance ◽  
Analysis Error ◽  
Analysis Errors

Abstract The characteristics of the initial corrections obtained from the Canadian Meteorological Centre (CMC) energy-norm-based key analysis error algorithm that minimizes short-range (24 h) forecast errors were investigated for four specific CMC operational analyses. The results show that both the rotational and the divergent components of the initial corrections are strongly out of balance. Some dispersive modes are also present in the mass component of the initial corrections. The results from one experiment where the initial state errors were known suggest that the current algorithm always selects a set of unbalanced initial corrections with more mass correction than wind correction, regardless of the characteristics of the real initial condition errors. Comparison with observational data showed that the corrected analysis is systematically farther away from the observations than the control analysis even in large forecast error events where most of the forecast errors are believed to have originated from errors in the initial state.

Initial Condition Sensitivity of Western Pacific Extratropical Transitions Determined Using Ensemble-Based Sensitivity Analysis

2009 ◽  
Vol 137 (10) ◽  
pp. 3388-3406 ◽  
Author(s):  
Ryan D. Torn ◽  
Gregory J. Hakim
Keyword(s):  
Sensitivity Analysis ◽  
Tropical Cyclone ◽  
Initial Conditions ◽  
Forecast Error ◽  
Wrf Model ◽  
Weather Research And Forecasting ◽  
Forecast Errors ◽  
Initial Condition ◽  
Ensemble Forecasts ◽  
The Relationship

Abstract An ensemble Kalman filter based on the Weather Research and Forecasting (WRF) model is used to generate ensemble analyses and forecasts for the extratropical transition (ET) events associated with Typhoons Tokage (2004) and Nabi (2005). Ensemble sensitivity analysis is then used to evaluate the relationship between forecast errors and initial condition errors at the onset of transition, and to objectively determine the observations having the largest impact on forecasts of these storms. Observations from rawinsondes, surface stations, aircraft, cloud winds, and cyclone best-track position are assimilated every 6 h for a period before, during, and after transition. Ensemble forecasts initialized at the onset of transition exhibit skill similar to the operational Global Forecast System (GFS) forecast and to a WRF forecast initialized from the GFS analysis. WRF ensemble forecasts of Tokage (Nabi) are characterized by relatively large (small) ensemble variance and greater (smaller) sensitivity to the initial conditions. In both cases, the 48-h forecast of cyclone minimum SLP and the RMS forecast error in SLP are most sensitive to the tropical cyclone position and to midlatitude troughs that interact with the tropical cyclone during ET. Diagnostic perturbations added to the initial conditions based on ensemble sensitivity reduce the error in the storm minimum SLP forecast by 50%. Observation impact calculations indicate that assimilating approximately 40 observations in regions of greatest initial condition sensitivity produces a large, statistically significant impact on the 48-h cyclone minimum SLP forecast. For the Tokage forecast, assimilating the single highest impact observation, an upper-tropospheric zonal wind observation from a Mongolian rawinsonde, yields 48-h forecast perturbations in excess of 10 hPa and 60 m in SLP and 500-hPa height, respectively.

scholarly journals The Characteristics of Key Analysis Errors. Part II: The Importance of the PV Corrections and the Impact of Balance

2007 ◽  
Vol 135 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche ◽  
Peter Zwack
Keyword(s):  
Short Range ◽  
Vertical Motion ◽  
Forecast Errors ◽  
Divergent Part ◽  
Essential Information ◽  
Original Analysis ◽  
Analysis Error ◽  
Motion Corrections ◽  
The Impact ◽  
Analysis Errors

Abstract This study examines a few approaches to isolate the balanced component of the initial corrections from the Canadian Meteorological Centre energy-norm-based key analysis error algorithm, in an attempt to capture the part of the key analysis errors responsible for short-range forecast errors. The best results were obtained with the nonlinear balance potential vorticity (PV) inversion technique. It was shown that the PV component of the initial corrections contains the essential information for reducing short-range forecast errors. The remaining imbalance part of the initial corrections does not grow in time and does not contribute to the improvement of the forecast. The removal of the imbalance part of the initial corrections makes the corrected analysis slightly closer to the observations, but remains systematically farther away as compared with the original analysis. Thus the balanced part of the key analysis errors cannot justifiably be associated to analysis errors. A methodology to balance the divergent part of the initial corrections, which reduces significantly the spinup in the vertical motion corrections, is also presented. Finally, in light of the results presented in this paper, some recommendations to improve the key analysis error algorithm are proposed.

scholarly journals The Characteristics of Key Analysis Errors. Part III: A Diagnosis of Their Evolution

2007 ◽  
Vol 135 (7) ◽  
pp. 2754-2777 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche
Keyword(s):  
Level Structure ◽  
Potential Temperature ◽  
Initial Time ◽  
Forecast Errors ◽  
Diagnostic Study ◽  
Low Level ◽  
Diabatic Processes ◽  
Upper Level ◽  
Analysis Error ◽  
Analysis Errors

Abstract This paper presents a diagnostic study of the evolution of initial corrections obtained from the key analysis error algorithm that minimizes the short-range (24 h) forecast errors for four specific events poorly forecasted over the eastern part of North America. A potential vorticity (PV) perspective is employed. It is shown that the modification to the low-level structure at the initial time is mainly attributed to the modification of the low-level PV distribution, while changes in the upper-level structure are attributed to the modification of the upper-level PV distribution. The low-level corrections grow mainly through background surface potential temperature advection by the wind corrections attributable to the interior PV corrections. Changes in the diabatic processes and the vertical alignment of low-level PV corrections by differential PV advection also increase the magnitude of the low-level corrections with time. The upper-level corrections grow by advection of background PV from wind corrections. However, the cause of these latter wind corrections responsible for upper-level background PV advection varies from case to case. An investigation of the relative importance of the low-level and of the upper-level initial corrections to produce the final-time corrections also reveals strong variability between cases. Finally, comparison of two cases in which the key analysis errors propagate vertically with two others without significant vertical propagation shows how the relative position of the key analysis errors with respect to the structure of the background flow can influence the evolution of the initial corrections.

Cyclogenetic Perturbations and Analysis Errors Decomposed into Singular Vectors

2005 ◽  
Vol 62 (7) ◽  
pp. 2234-2247 ◽  
Author(s):  
Chris Snyder ◽  
Gregory J. Hakim
Keyword(s):  
Potential Vorticity ◽  
Vertical Structure ◽  
Energy Norm ◽  
Vertical Shear ◽  
Initial Time ◽  
Forecast Errors ◽  
Ensemble Forecasts ◽  
Singular Vectors ◽  
Analysis Error ◽  
Analysis Errors

Abstract Singular vectors (SVs) have been applied to cyclogenesis, to initializing ensemble forecasts, and in predictability studies. Ideally, the calculation of the SVs would employ the analysis error covariance norm at the initial time or, in the case of cyclogenesis, a norm based on the statistics of initial perturbations, but the energy norm is often used as a more practical substitute. To illustrate the roles of the choice of norm and the vertical structure of initial perturbations, an upper-level wave with no potential vorticity perturbation in the troposphere is considered as a typical cyclogenetic perturbation or analysis error, and this perturbation is then decomposed by its projection onto each energy SV. All calculations are made, for simplicity, in the context of the quasigeostrophic Eady model (i.e., for a background flow with constant vertical shear and horizontal temperature gradient). Viewed in terms of the energy SVs, the smooth vertical structure of the typical perturbation, as well as its evolution, results from strong cancellation between the growing and decaying SVs, most of which are highly structured and tilted in the vertical. A simpler picture, involving less cancellation, follows from decomposition of the typical perturbation into SVs using an alternative initial norm, which is based on the relation between initial norms and the statistics of initial perturbations together with the empirical assumption that the initial perturbations are not dominated by interior potential vorticity. Differences between the energy SVs and those based on the alternative initial norm can be understood by noting that the energy norm implicitly assumes initial perturbations with second-order statistics given by the covariance matrix whose inverse defines the energy norm. Unlike the “typical” perturbation, perturbations with those statistics have large variance of potential vorticity in the troposphere and fine vertical structure. Finally, a brief assessment is presented of the extent to which the upper wave, and more generally the alternative initial norm, is representative of cyclogenetic perturbations and analysis errors. There is substantial evidence supporting deep perturbations with little vertical structure as frequent precursors to cyclogenesis, but surrogates for analysis errors are less conclusive: operational midlatitude analysis differences have vertical structure similar to that of the perturbations implied by the energy norm, while short-range forecast errors and analysis errors from assimilation experiments with simulated observations are more consistent with the alternative norm.

scholarly journals Local modal participation analysis of nonlinear systems using Poincaré linearization

2019 ◽  
Vol 99 (1) ◽  
pp. 803-811 ◽  
Author(s):  
Boumediene Hamzi ◽  
Eyad H. Abed
Keyword(s):  
Nonlinear Systems ◽  
Autonomous Systems ◽  
Analytical Formula ◽  
Linear Case ◽  
Local Mode ◽  
Initial Condition ◽  
Initial State ◽  
State Participation ◽  
Symmetry Assumption ◽  
Definition Of

AbstractThe paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear case. The work follows Hashlamoun et al. (IEEE Trans Autom Control 54(7):1439–1449 2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure over an uncertain set of system initial state. Poincaré linearization is used to replace the nonlinear system with a locally equivalent linear system. It is found that under a symmetry assumption on the distribution of the initial state, the tractable calculation and analytical formula for mode-in-state participation factors found for the linear case persists to the nonlinear setting. This paper is dedicated to the memory of Professor Ali H. Nayfeh.

scholarly journals Application of Adjoint-Derived Forecast Sensitivities to the 24–25 January 2000 U.S. East Coast Snowstorm

2005 ◽  
Vol 133 (11) ◽  
pp. 3148-3175 ◽  
Author(s):  
Daryl T. Kleist ◽  
Michael C. Morgan
Keyword(s):  
Response Function ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Lower Troposphere ◽  
Vertical Motion ◽  
Initial Condition ◽  
Response Functions ◽  
Eastern United States ◽  
Surface Cyclone

Abstract The 24–25 January 2000 eastern United States snowstorm was noteworthy as operational numerical weather prediction (NWP) guidance was poor for lead times as short as 36 h. Despite improvements in the forecast of the surface cyclone position and intensity at 1200 UTC 25 January 2000 with decreasing lead time, NWP guidance placed the westward extent of the midtropospheric, frontogenetically forced precipitation shield too far to the east. To assess the influence of initial condition uncertainties on the forecast of this event, an adjoint model is used to evaluate forecast sensitivities for 36- and 48-h forecasts valid at 1200 UTC 25 January 2000 using as response functions the energy-weighted forecast error, lower-tropospheric circulation about a box surrounding the surface cyclone, 750-hPa frontogenesis, and vertical motion. The sensitivities with respect to the initial conditions for these response functions are in general very similar: geographically isolated, maximized in the middle and lower troposphere, and possessing an upshear vertical tilt. The sensitivities are maximized in a region of enhanced low-level baroclinicity in the vicinity of the surface cyclone’s precursor upper trough. However, differences in the phase and structure of the gradients for the four response functions are evident, which suggests that perturbations could be constructed to alter one response function but not necessarily the others. Gradients of the forecast error response function with respect to the initial conditions are used in an iterative procedure to construct initial condition perturbations that reduce the forecast error. These initial condition perturbations were small in terms of both spatial scale and magnitude. Those initial condition perturbations that were confined primarily to the midtroposphere grew rapidly into much larger amplitude upper-and-lower tropospheric perturbations. The perturbed forecasts were not only characterized by reduced final time forecast error, but also had a synoptic evolution that more closely followed analyses and observations.

scholarly journals Southern High-Latitude Ensemble Data Assimilation in the Antarctic Mesoscale Prediction System

2005 ◽  
Vol 133 (12) ◽  
pp. 3431-3449 ◽  
Author(s):  
D. M. Barker
Keyword(s):  
Data Assimilation ◽  
Sampling Error ◽  
Forecast Error ◽  
Weather Prediction ◽  
Forecast Errors ◽  
Prediction System ◽  
Spatial Covariance ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
The Antarctic

Abstract Ensemble data assimilation systems incorporate observations into numerical models via solution of the Kalman filter update equations, and estimates of forecast error covariances derived from ensembles of model integrations. In this paper, a particular algorithm, the ensemble square root filter (EnSRF), is tested in a limited-area, polar numerical weather prediction (NWP) model: the Antarctic Mesoscale Prediction System (AMPS). For application in the real-time AMPS, the number of model integrations that can be run to provide forecast error covariances is limited, resulting in an ensemble sampling error that degrades the analysis fit to observations. In this work, multivariate, climatologically plausible forecast error covariances are specified via averaged forecast difference statistics. Ensemble representations of the “true” forecast errors, created using randomized control variables of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) three-dimensional variational (3DVAR) data assimilation system, are then used to assess the dependence of sampling error on ensemble size, data density, and localization of covariances using simulated observation networks. Results highlight the detrimental impact of ensemble sampling error on the analysis increment structure of correlated, but unobserved fields—an issue not addressed by the spatial covariance localization techniques used to date. A 12-hourly cycling EnSRF/AMPS assimilation/forecast system is tested for a two-week period in December 2002 using real, conventional (surface, rawinsonde, satellite retrieval) observations. The dependence of forecast scores on methods used to maintain ensemble spread and the inclusion of perturbations to lateral boundary conditions are studied.

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

Effect of Assimilating Himawari-8 Atmospheric Motion Vectors on Forecast Errors over East Asia

2018 ◽  
Vol 35 (9) ◽  
pp. 1737-1752 ◽  
Author(s):  
Dae-Hui Kim ◽  
Hyun Mee Kim
Keyword(s):  
East Asia ◽  
Geopotential Height ◽  
Forecast Error ◽  
Experimental Period ◽  
Energy Norm ◽  
Observation System ◽  
Forecast Errors ◽  
Motion Vectors ◽  
Atmospheric Motion ◽  
Atmospheric Motion Vectors

AbstractIn this study, the effect of assimilating Himawari-8 (HIMA-8) atmospheric motion vectors (AMVs) on forecast errors in East Asia is evaluated using observation system experiments based on the Weather Research and Forecasting Model and three-dimensional variational data assimilation system. The experimental period is from 1 August to 30 September 2015, during which both HIMA-8 and Multifunctional Transport Satellite-2 (MTSAT-2) AMVs exist. The energy-norm forecast error based on the analysis of each experiment as reference was reduced more by replacing MTSAT-2 AMVs with HIMA-8 AMVs than by adding HIMA-8 AMVs to the MTSAT-2 AMVs. When the HIMA-8 AMVs replaced or were added to MTSAT-2 AMVs, the observation impact was reduced, which implies the analysis–forecast system was improved by assimilating HIMA-8 AMVs. The root-mean-square error (RMSE) of the 500-hPa geopotential height forecasts based on the analysis of each experiment decreases more effectively when the region lacking in upper-air wind observations is reduced by assimilating both MTSAT-2 and HIMA-8 AMVs. When the upper-air radiosonde (SOUND) observations are used as reference, assimilating more HIMA-8 AMVs decreases the forecast error. Based on various measures, the assimilation of HIMA-8 AMVs has a positive effect on the reduction of forecast errors. The effects on the energy-norm forecast error and the RMSE based on SOUND observations are greater when HIMA-8 AMVs replaced MTSAT-2 AMVs. However, the effects on the RMSE of the 500-hPa geopotential height forecasts are greater when both HIMA-8 and MTSAT-2 AMVs were assimilated, which implies potential benefits of assimilating AMVs from several satellites for forecasts over East Asia depending on the choice of measurement.

scholarly journals Verification of surface minimum, mean, and maximum temperature forecasts in Calabria for summer 2008

2011 ◽  
Vol 11 (2) ◽  
pp. 487-500 ◽  
Author(s):  
S. Federico
Keyword(s):  
Forecast Error ◽  
Background Field ◽  
Horizontal Resolution ◽  
Atmospheric Modeling ◽  
Forecast Skill ◽  
Maximum Temperature ◽  
Model Forecast ◽  
Maximum Temperatures ◽  
Analysis Error ◽  
The Impact

Abstract. Since 2005, one-hour temperature forecasts for the Calabria region (southern Italy), modelled by the Regional Atmospheric Modeling System (RAMS), have been issued by CRATI/ISAC-CNR (Consortium for Research and Application of Innovative Technologies/Institute for Atmospheric and Climate Sciences of the National Research Council) and are available online at http://meteo.crati.it/previsioni.html (every six hours). Beginning in June 2008, the horizontal resolution was enhanced to 2.5 km. In the present paper, forecast skill and accuracy are evaluated out to four days for the 2008 summer season (from 6 June to 30 September, 112 runs). For this purpose, gridded high horizontal resolution forecasts of minimum, mean, and maximum temperatures are evaluated against gridded analyses at the same horizontal resolution (2.5 km). Gridded analysis is based on Optimal Interpolation (OI) and uses the RAMS first-day temperature forecast as the background field. Observations from 87 thermometers are used in the analysis system. The analysis error is introduced to quantify the effect of using the RAMS first-day forecast as the background field in the OI analyses and to define the forecast error unambiguously, while spatial interpolation (SI) analysis is considered to quantify the statistics' sensitivity to the verifying analysis and to show the quality of the OI analyses for different background fields. Two case studies, the first one with a low (less than the 10th percentile) root mean square error (RMSE) in the OI analysis, the second with the largest RMSE of the whole period in the OI analysis, are discussed to show the forecast performance under two different conditions. Cumulative statistics are used to quantify forecast errors out to four days. Results show that maximum temperature has the largest RMSE, while minimum and mean temperature errors are similar. For the period considered, the OI analysis RMSEs for minimum, mean, and maximum temperatures vary from 1.8, 1.6, and 2.0 °C, respectively, for the first-day forecast, to 2.0, 1.9, and 2.6 °C, respectively, for the fourth-day forecast. Cumulative statistics are computed using both SI and OI analysis as reference. Although SI statistics likely overestimate the forecast error because they ignore the observational error, the study shows that the difference between OI and SI statistics is less than the analysis error. The forecast skill is compared with that of the persistence forecast. The Anomaly Correlation Coefficient (ACC) shows that the model forecast is useful for all days and parameters considered here, and it is able to capture day-to-day weather variability. The model forecast issued for the fourth day is still better than the first-day forecast of a 24-h persistence forecast, at least for mean and maximum temperature. The impact of using the RAMS first-day forecast as the background field in the OI analysis is quantified by comparing statistics computed with OI and SI analyses. Minimum temperature is more sensitive to the change in the analysis dataset as a consequence of its larger representative error.

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