scholarly journals Methods of investigating forecast error sensitivity to ensemble size in a limited-area convection-permitting ensemble

2017 ◽  
Author(s):  
Ross Noel Bannister ◽  
Stefano Migliorini ◽  
Alison Clare Rudd ◽  
Laura Hart Baker
Keyword(s):  
Data Assimilation ◽  
Weather Forecasting ◽  
Sampling Error ◽  
Forecast Error ◽  
Significant Degree ◽  
Limited Area ◽  
Ensemble Size ◽  
Sampling Errors ◽  
Convective Scale

Abstract. Ensemble-based predictions are increasingly used as an aid to weather forecasting and to data assimilation, where the aim is to capture the range of possible outcomes consistent with the underlying uncertainties. Constraints on computing resources mean that ensembles have a relatively small size, which can lead to an incomplete range of possible outcomes, and to inherent sampling errors. This paper discusses how an existing ensemble can be relatively easily increased in size, it develops a range of standard and extended diagnostics to help determine whether a given ensemble is large enough to be useful for forecasting and data assimilation purposes, and it applies the diagnostics to a convective-scale case study for illustration. Diagnostics include the effect of ensemble size on various aspects of rainfall forecasts, kinetic energy spectra, and (co)-variance statistics in the spatial and spectral domains. The work here extends the Met Office's 24 ensemble members to 93. It is found that the extra members do develop a significant degree of linear independence, they increase the ensemble spread (although with caveats to do with non-Gaussianity), they reduce sampling error in many statistical quantities (namely variances, correlations, and length-scales), and improve the effective spatial resolution of the ensemble. The extra members though do not improve the probabilistic rain rate forecasts. It is assumed that the 93-member ensemble approximates the error-free statistics, which is a practical assumption, but the data suggests that this number of members is ultimately not enough to justify this assumption, and therefore more ensembles are likely required for such convective-scale systems to further reduce sampling errors, especially for ensemble data assimilation purposes.

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.

Sampling Error Correction Evaluated Using a Convective-Scale 1000-Member Ensemble

2019 ◽  
Vol 148 (3) ◽  
pp. 1229-1249 ◽  
Author(s):  
Tobias Necker ◽  
Martin Weissmann ◽  
Yvonne Ruckstuhl ◽  
Jeffrey Anderson ◽  
Takemasa Miyoshi
Keyword(s):  
Sensitivity Analysis ◽  
Data Assimilation ◽  
Error Correction ◽  
Degrees Of Freedom ◽  
Sampling Error ◽  
Lookup Table ◽  
Ensemble Prediction ◽  
Sampling Errors ◽  
Convective Scale ◽  
The Impact

Abstract State-of-the-art ensemble prediction systems usually provide ensembles with only 20–250 members for estimating the uncertainty of the forecast and its spatial and spatiotemporal covariance. Given that the degrees of freedom of atmospheric models are several magnitudes higher, the estimates are therefore substantially affected by sampling errors. For error covariances, spurious correlations lead to random sampling errors, but also a systematic overestimation of the correlation. A common approach to mitigate the impact of sampling errors for data assimilation is to localize correlations. However, this is a challenging task given that physical correlations in the atmosphere can extend over long distances. Besides data assimilation, sampling errors pose an issue for the investigation of spatiotemporal correlations using ensemble sensitivity analysis. Our study evaluates a statistical approach for correcting sampling errors. The applied sampling error correction is a lookup table–based approach and therefore computationally very efficient. We show that this approach substantially improves both the estimates of spatial correlations for data assimilation as well as spatiotemporal correlations for ensemble sensitivity analysis. The evaluation is performed using the first convective-scale 1000-member ensemble simulation for central Europe. Correlations of the 1000-member ensemble forecast serve as truth to assess the performance of the sampling error correction for smaller subsets of the full ensemble. The sampling error correction strongly reduced both random and systematic errors for all evaluated variables, ensemble sizes, and lead times.

scholarly journals Convective-Scale Sampling Error and Its Impact on the Ensemble Radar Data Assimilation System: A Case Study of a Heavy Rainfall Event on 16 June 2008 in Taiwan

2020 ◽  
Vol 148 (9) ◽  
pp. 3631-3652
Author(s):  
Pin-Ying Wu ◽  
Shu-Chih Yang ◽  
Chih-Chien Tsai ◽  
Hsiang-Wen Cheng
Keyword(s):  
Data Assimilation ◽  
Heavy Rainfall ◽  
Sampling Error ◽  
Rainfall Event ◽  
Heavy Rainfall Event ◽  
Observation Error ◽  
Sampling Errors ◽  
Precipitation Prediction ◽  
Convective Scale ◽  
Assimilation System

ABSTRACT Sampling error stems from the use of ensemble-based data assimilation (EDA) with a limited ensemble size and can result in spurious background error covariances, leading to false analysis corrections. The WRF-LETKF radar assimilation system (WLRAS) is performed separately with 256 and 40 members to investigate the characteristics of convective-scale sampling errors in the EDA and its impact on precipitation prediction based on a heavy rainfall event on 16 June 2008. The results suggest that the sampling errors for this event are sensitive to the relationships between the simulated observations and model variables, the intensity of reflectivity, and how the prevailing wind projects to the radial wind in the areas that the radar cannot resolve U or V wind. The sampling errors lead to an underprediction of heavy rainfall when the horizontal localization radius is inadequately large, but this can be mitigated when a more accurate moisture condition is provided. In addition, being able to use a larger vertical localization plays an important role in providing necessary adjustments for representing the vertical thermodynamical structure of convection, which further improves precipitation prediction. A strategy mitigating the impact of sampling errors associated with the limitation of radial wind measurement by inflating the observation error over sensitive areas can bring benefits to precipitation prediction.

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.

Intercomparison of an Ensemble Kalman Filter with Three- and Four-Dimensional Variational Data Assimilation Methods in a Limited-Area Model over the Month of June 2003

2011 ◽  
Vol 139 (2) ◽  
pp. 566-572 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang ◽  
Xiang-Yu Huang ◽  
Xin Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Wrf Model ◽  
Warm Season ◽  
Variational Data Assimilation ◽  
Lead Times ◽  
Limited Area ◽  
Forecast Errors

Abstract This study compares the performance of an ensemble Kalman filter (EnKF) with both the three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) methods of the Weather Research and Forecasting (WRF) model over the contiguous United States in a warm-season month (June) of 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as data from wind profilers, ships and aircraft, and the cloud-tracked winds from satellites. The performances of these methods are evaluated through verifying the 12- to 72-h forecasts initialized twice daily from the analysis of each method against the standard sounding observations. It is found that 4DVar has consistently smaller error than that of 3DVar for winds and temperature at all forecast lead times except at 60 and 72 h when their forecast errors become comparable in amplitude, while the two schemes have similar performance in moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12–36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the fact that 3DVar fits the sounding observations much more closely at the analysis time. The advantage of the EnKF becomes even more evident at 48–72-h lead times; the 72-h forecast error of the EnKF is comparable in magnitude to the 48-h error of 3DVar/4DVar.

scholarly journals A Comparison of Multiscale GSI-Based EnKF and 3DVar Data Assimilation Using Radar and Conventional Observations for Midlatitude Convective-Scale Precipitation Forecasts

2015 ◽  
Vol 143 (8) ◽  
pp. 3087-3108 ◽  
Author(s):  
Aaron Johnson ◽  
Xuguang Wang ◽  
Jacob R. Carley ◽  
Louis J. Wicker ◽  
Christopher Karstens
Keyword(s):  
Data Assimilation ◽  
Multiscale Analysis ◽  
Multiple Scales ◽  
Three Dimensional ◽  
Forecast Period ◽  
Background Error ◽  
Cold Pools ◽  
Error Covariance ◽  
Convective Scale

Abstract A GSI-based data assimilation (DA) system, including three-dimensional variational assimilation (3DVar) and ensemble Kalman filter (EnKF), is extended to the multiscale assimilation of both meso- and synoptic-scale observation networks and convective-scale radar reflectivity and velocity observations. EnKF and 3DVar are systematically compared in this multiscale context to better understand the impacts of differences between the DA techniques on the analyses at multiple scales and the subsequent convective-scale precipitation forecasts. Averaged over 10 diverse cases, 8-h precipitation forecasts initialized using GSI-based EnKF are more skillful than those using GSI-based 3DVar, both with and without storm-scale radar DA. The advantage from radar DA persists for ~5 h using EnKF, but only ~1 h using 3DVar. A case study of an upscale growing MCS is also examined. The better EnKF-initialized forecast is attributed to more accurate analyses of both the mesoscale environment and the storm-scale features. The mesoscale location and structure of a warm front is more accurately analyzed using EnKF than 3DVar. Furthermore, storms in the EnKF multiscale analysis are maintained during the subsequent forecast period. However, storms in the 3DVar multiscale analysis are not maintained and generate excessive cold pools. Therefore, while the EnKF forecast with radar DA remains better than the forecast without radar DA throughout the forecast period, the 3DVar forecast quality is degraded by radar DA after the first hour. Diagnostics revealed that the inferior analysis at mesoscales and storm scales for the 3DVar is primarily attributed to the lack of flow dependence and cross-variable correlation, respectively, in the 3DVar static background error covariance.

scholarly journals Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part I: Optimality Criteria and Application to Variance Filtering and Covariance Localization

2015 ◽  
Vol 143 (5) ◽  
pp. 1622-1643 ◽  
Author(s):  
Benjamin Ménétrier ◽  
Thibaut Montmerle ◽  
Yann Michel ◽  
Loïk Berre
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Weather Prediction ◽  
Computational Cost ◽  
Analytical Framework ◽  
Companion Paper ◽  
Optimality Criteria ◽  
Linear Filtering ◽  
Sampling Errors ◽  
Output Only

Abstract In data assimilation (DA) schemes for numerical weather prediction (NWP) systems, the estimation of forecast error covariances is a key point to get some flow dependency. As shown in previous studies, ensemble data assimilation methods are the most accurate for this task. However, their huge computational cost raises a strong limitation to the ensemble size. Consequently, covariances estimated with small ensembles are affected by random sampling errors. The aim of this study is to develop a theory of covariance filtering in order to remove most of the sampling noise while keeping the signal of interest and then to use it in the DA scheme of a real NWP system. This first part of a two-part study presents the theoretical aspects of such criteria for optimal filtering based on the merging of the theories of optimal linear filtering and of sample centered moments estimation. Its strength relies on the use of sample estimated quantities and filter output only. These criteria pave the way for new algorithms and interesting applications for NWP. Two of them are detailed here: spatial filtering of variances and covariance localization. Results obtained in an idealized 1D analytical framework are shown for illustration. Applications on real forecast error covariances deduced from ensembles at convective scale are discussed in a companion paper.

Variational Data Assimilation for Renewable Wind Energy Predictions: China Inner Mongolia Case Study

2011 ◽  
Vol 383-390 ◽  
pp. 3685-3689 ◽  
Author(s):  
Hai Feng Wang ◽  
Wen Jun Yin ◽  
Meng Zhang ◽  
Jin Dong
Keyword(s):  
Data Assimilation ◽  
Inner Mongolia ◽  
Forecast Error ◽  
Scale Model ◽  
Initial Condition ◽  
Short Term ◽  
In Situ Observations ◽  
Meso Scale

Advanced data assimilation method is used for the short-term wind power forecasting based on a meso-scale model. Considerable forecast error reduction is concluded from a case study in China, where a better resolved high-resolution initial condition is introduced via assimilating various in-situ observations.

scholarly journals The ALADIN System and its canonical model configurations AROME CY41T1 and ALARO CY40T1

2018 ◽  
Vol 11 (1) ◽  
pp. 257-281 ◽  
Author(s):  
Piet Termonia ◽  
Claude Fischer ◽  
Eric Bazile ◽  
François Bouyssel ◽  
Radmila Brožková ◽  
...  
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Numerical Weather Prediction ◽  
Weather Forecasting ◽  
Weather Prediction ◽  
Forecast Model ◽  
Canonical Model ◽  
Limited Area ◽  
Climate Simulations ◽  
Process Studies

Abstract. The ALADIN System is a numerical weather prediction (NWP) system developed by the international ALADIN consortium for operational weather forecasting and research purposes. It is based on a code that is shared with the global model IFS of the ECMWF and the ARPEGE model of Météo-France. Today, this system can be used to provide a multitude of high-resolution limited-area model (LAM) configurations. A few configurations are thoroughly validated and prepared to be used for the operational weather forecasting in the 16 partner institutes of this consortium. These configurations are called the ALADIN canonical model configurations (CMCs). There are currently three CMCs: the ALADIN baseline CMC, the AROME CMC and the ALARO CMC. Other configurations are possible for research, such as process studies and climate simulations. The purpose of this paper is (i) to define the ALADIN System in relation to the global counterparts IFS and ARPEGE, (ii) to explain the notion of the CMCs, (iii) to document their most recent versions, and (iv) to illustrate the process of the validation and the porting of these configurations to the operational forecast suites of the partner institutes of the ALADIN consortium. This paper is restricted to the forecast model only; data assimilation techniques and postprocessing techniques are part of the ALADIN System but they are not discussed here.

scholarly journals Operational Implementation of the 1D+3D-Var Assimilation Method of Radar Reflectivity Data in the AROME Model

2014 ◽  
Vol 142 (5) ◽  
pp. 1852-1873 ◽  
Author(s):  
Eric Wattrelot ◽  
Olivier Caumont ◽  
Jean-François Mahfouf
Keyword(s):  
Relative Humidity ◽  
Data Assimilation ◽  
Three Dimensional ◽  
Radar Reflectivity ◽  
Precipitation Forecast ◽  
Limited Area ◽  
Short Term ◽  
Background Error ◽  
Reflectivity Data

AbstractThis paper presents results from radar reflectivity data assimilation experiments with the nonhydrostatic limited-area model Application of Research to Operations at Mesoscale (AROME) in an operational context. A one-dimensional (1D) Bayesian retrieval of relative humidity profiles followed by a three-dimensional variational data assimilation (3D-Var) technique is adopted. Several preprocessing procedures of raw reflectivity data are presented and the use of the nonrainy signal in the assimilation is widely discussed and illustrated. This two-step methodology allows the authors to build up a screening procedure that takes into account the evaluation of the results from the 1D Bayesian retrieval. In particular, the 1D retrieval is checked by comparing a pseudoanalyzed reflectivity to the observed reflectivity. Additionally, a physical consistency between the reflectivity innovations and the 1D relative humidity increments is imposed before assimilating relative humidity pseudo-observations with other observations. This allows the authors to counteract the difficulty of the current 3D-Var system to correct strong differences between model and observed clouds from the crude specification of background-error covariances. Assimilation experiments of radar reflectivity data in a preoperational configuration are first performed over a 1-month period. Positive impacts on short-term precipitation forecast scores are systematically found. The evaluation shows improvements on the analysis and also on objective conventional forecast scores, in particular for the model wind field up to 12 h. A case study for a specific precipitating system demonstrates the capacity of the method for improving significantly short-term forecasts of organized convection.

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