scholarly journals Multiple-scale error growth in a convection-resolving model

2015 ◽  
Vol 22 (1) ◽  
pp. 1-13 ◽  
Author(s):  
F. Uboldi ◽  
A. Trevisan
Keyword(s):  
Forecast Error ◽  
Multiple Scale ◽  
Forecast Model ◽  
Dimensional Subspace ◽  
Error Growth ◽  
Breeding Technique ◽  
Initial Errors ◽  
Bred Vectors ◽  
Scale Error ◽  
Analysis Error

Abstract. The properties of the multiple-scale instabilities present in a non-hydrostatic forecast model are investigated. The model simulates intense convection episodes occurring in northern Italy. A breeding technique is used to construct ensembles of perturbations of the model trajectories aimed at representing the instabilities that are responsible for error growth on various timescales and space scales. By means of perfect model twin experiments it is found that, for initial errors of the order of present-day analysis error, a non-negligible fraction of the forecast error can be explained by a bred vector ensemble of reasonable size representing the growth of errors on intermediate scales. In contrast, when the initial error is much smaller, the spectrum of bred vectors representing the fast convective-scale instabilities becomes flat, and the number of ensemble members needed to explain even a small fraction of the forecast error becomes extremely large. The conclusion is that as the analysis error is decreased, it becomes more and more computationally demanding to construct an ensemble that can describe the high-dimensional subspace of convective instabilities and that can thus be potentially useful for controlling the error growth.

scholarly journals Multiple scale error growth in a convection-resolving model

2014 ◽  
Vol 1 (1) ◽  
pp. 447-478
Author(s):  
F. Uboldi ◽  
A. Trevisan
Keyword(s):  
Forecast Error ◽  
Multiple Scale ◽  
Forecast Model ◽  
Dimensional Subspace ◽  
Error Growth ◽  
Breeding Technique ◽  
Initial Errors ◽  
Bred Vectors ◽  
Scale Error ◽  
Analysis Error

Abstract. The properties of the multiple scale instabilities present in a non-hydrostatic forecast model are investigated. The model simulates intense convection episodes occurring in Northern Italy. A breeding technique is used to construct ensembles of perturbations of the model trajectories aimed to represent the instabilities that are responsible for error growth at various time and space scales. It is found that for initial errors of the order of present-day analysis error, error growth is mainly determined by intermediate scale instabilities, and that a non-negligible fraction of the forecast error can be explained by an ensemble of bred vectors of reasonable size. In contrast, when the initial error is much smaller, the spectrum of bred vectors representing the fast convective-scale instabilities becomes flat and the number of ensemble members needed to explain even a small fraction of the forecast error becomes extremely large. The conclusion is that as the analysis error is decreased, it becomes more and more computationally demanding to construct an ensemble that can describe the high-dimensional subspace of convective instabilities and that can thus be potentially useful for controlling the error growth.

Error Growth Dynamics within Convection-Allowing Ensemble Forecasts over Central U.S. Regions for Days of Active Convection

2021 ◽  
Author(s):  
Xiaoran Zhuang ◽  
Ming Xue ◽  
Jinzhong Min ◽  
Zhiming Kang ◽  
Naigeng Wu ◽  
...  
Keyword(s):  
Diurnal Cycle ◽  
Large Scale ◽  
Response Times ◽  
Forecast Error ◽  
Small Scale ◽  
Forecast Errors ◽  
Error Growth ◽  
Ensemble Forecasts ◽  
Scale Error ◽  
Active Convection

AbstractError growth is investigated based on convection-allowing ensemble forecasts starting from 0000 UTC for 14 active convection events over central to eastern U.S. regions from spring 2018. The analysis domain is divided into the NW, NE, SE and SW quadrants (subregions). Total difference energy and its decompositions are used to measure and analyze error growth at and across scales. Special attention is paid to the dominant types of convection with respect to their forcing mechanisms in the four subregions and the associated difference in precipitation diurnal cycles. The discussions on the average behaviors of error growth in each region are supplemented by 4 representative cases. Results show that the meso-γ-scale error growth is directly linked to precipitation diurnal cycle while meso-α-scale error growth has strong link to large scale forcing. Upscale error growth is evident in all regions/cases but up-amplitude growth within own scale plays different roles in different regions/cases.When large-scale flow is important (as in the NE region), precipitation is strongly modulated by the large-scale forcing and becomes more organized with time, and upscale transfer of forecast error is stronger. On the other hand, when local instability plays more dominant roles (as in the SE region), precipitation is overall least organized and has the weakest diurnal variations. Its associated errors at the γ– and β-scale can reach their peaks sooner and meso-α-scale error tends to rely more on growth of error with its own scale. Small-scale forecast errors are directly impacted by convective activities and have short response time to convection while increasingly larger scale errors have longer response times and delayed phase within the diurnal cycle.

scholarly journals Comparison of Nonlinear Local Lyapunov Vectors and Bred Vectors in Estimating the Spatial Distribution of Error Growth

2018 ◽  
Vol 75 (4) ◽  
pp. 1073-1087 ◽  
Author(s):  
Jie Feng ◽  
Jianping Li ◽  
Ruiqiang Ding ◽  
Zoltan Toth
Keyword(s):  
Spatial Distribution ◽  
Weather Forecasting ◽  
Forecast Error ◽  
Critical Role ◽  
Orthogonal Basis ◽  
Nonlinear Perturbations ◽  
Error Growth ◽  
Local Dimension ◽  
Ensemble Spread ◽  
Bred Vectors

Abstract Instabilities play a critical role in understanding atmospheric predictability and improving weather forecasting. The bred vectors (BVs) are dynamically evolved and flow-dependent nonlinear perturbations, indicating the most unstable modes of the underlying flow. Especially over smaller areas, however, BVs with different initial seeds may to some extent be constrained to a small subspace, missing potential forecast error growth along other unstable perturbation directions. In this paper, the authors study the nonlinear local Lyapunov vectors (NLLVs) that are designed to capture an orthogonal basis spanning the most unstable perturbation subspace, thus potentially ameliorating the limitation of BVs. The NLLVs are theoretically related to the linear Lyapunov vectors (LVs), which also form an orthogonal basis. Like BVs, NLLVs are generated by dynamically evolving perturbations with a full nonlinear model. In simulated forecast experiments, a set of mutually orthogonal NLLVs show an advantage in predicting the structure of forecast error growth when compared to using a set of BVs that are not fully independent. NLLVs are also found to have a higher local dimension, enabling them to better capture localized instabilities, leading to increased ensemble spread.

A New Approach for Estimating the Observation Impact in Ensemble–Variational Data Assimilation

2018 ◽  
Vol 146 (2) ◽  
pp. 447-465 ◽  
Author(s):  
Mark Buehner ◽  
Ping Du ◽  
Joël Bédard
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Observation Error ◽  
New Approach ◽  
Regional Prediction ◽  
Observation Impact ◽  
Adjoint Approach ◽  
The Impact

Abstract Two types of approaches are commonly used for estimating the impact of arbitrary subsets of observations on short-range forecast error. The first was developed for variational data assimilation systems and requires the adjoint of the forecast model. Comparable approaches were developed for use with the ensemble Kalman filter and rely on ensembles of forecasts. In this study, a new approach for computing observation impact is proposed for ensemble–variational data assimilation (EnVar). Like standard adjoint approaches, the adjoint of the data assimilation procedure is implemented through the iterative minimization of a modified cost function. However, like ensemble approaches, the adjoint of the forecast step is obtained by using an ensemble of forecasts. Numerical experiments were performed to compare the new approach with the standard adjoint approach in the context of operational deterministic NWP. Generally similar results are obtained with both approaches, especially when the new approach uses covariance localization that is horizontally advected between analysis and forecast times. However, large differences in estimated impacts are obtained for some surface observations. Vertical propagation of the observation impact is noticeably restricted with the new approach because of vertical covariance localization. The new approach is used to evaluate changes in observation impact as a result of the use of interchannel observation error correlations for radiance observations. The estimated observation impact in similarly configured global and regional prediction systems is also compared. Overall, the new approach should provide useful estimates of observation impact for data assimilation systems based on EnVar when an adjoint model is not available.

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.

Atmospheric Predictability: Why Butterflies Are Not of Practical Importance

2014 ◽  
Vol 71 (7) ◽  
pp. 2476-2488 ◽  
Author(s):  
Dale R. Durran ◽  
Mark Gingrich
Keyword(s):  
Kinetic Energy ◽  
Turbulence Model ◽  
Large Scale ◽  
Mesoscale Model ◽  
Practical Importance ◽  
Absolute Magnitude ◽  
Error Growth ◽  
Initial Error ◽  
Initial Errors ◽  
Relative Errors

Abstract The spectral turbulence model of Lorenz, as modified for surface quasigeostrophic dynamics by Rotunno and Snyder, is further modified to more smoothly approach nonlinear saturation. This model is used to investigate error growth starting from different distributions of the initial error. Consistent with an often overlooked finding by Lorenz, the loss of predictability generated by initial errors of small but fixed absolute magnitude is essentially independent of their spatial scale when the background saturation kinetic energy spectrum is proportional to the −5/3 power of the wavenumber. Thus, because the background kinetic energy increases with scale, very small relative errors at long wavelengths have similar impacts on perturbation error growth as large relative errors at short wavelengths. To the extent that this model applies to practical meteorological forecasts, the influence of initial perturbations generated by butterflies would be swamped by unavoidable tiny relative errors in the large scales. The rough applicability of the authors’ modified spectral turbulence model to the atmosphere over scales ranging between 10 and 1000 km is supported by the good estimate that it provides for the ensemble error growth in state-of-the-art ensemble mesoscale model simulations of two winter storms. The initial-error spectrum for the ensemble perturbations in these cases has maximum power at the longest wavelengths. The dominance of large-scale errors in the ensemble suggests that mesoscale weather forecasts may often be limited by errors arising from the large scales instead of being produced solely through an upscale cascade from the smallest scales.

scholarly journals Error budget in systems with time-dependent forcings

1998 ◽  
Vol 5 (4) ◽  
pp. 255-259 ◽  
Author(s):  
P. Sancho
Keyword(s):  
Time Dependent ◽  
Saturation Level ◽  
Initial Time ◽  
Error Growth ◽  
Error Budget ◽  
Initial Errors ◽  
External Time

Abstract. The behaviour of the error growth is analyzed in several simple examples of systems with external time-dependent forcings. in some systems oscillations of the error around the saturation level can be observed. A common feature of these examples is the error growth dependence on initial time. In the examples here considered the improvement in the predictability derived from an adequate choice of the Initial time is comparable to those obtained by reducing the initial errors.

scholarly journals “Jumpiness” of the ECMWF and Met Office EPS Control and Ensemble-Mean Forecasts

2009 ◽  
Vol 137 (11) ◽  
pp. 3823-3836 ◽  
Author(s):  
Ervin Zsoter ◽  
Roberto Buizza ◽  
David Richardson
Keyword(s):  
Time Series ◽  
Weak Link ◽  
Forecast Error ◽  
Forecast Uncertainty ◽  
Flip Flop ◽  
Lower Error ◽  
Ensemble Mean ◽  
Analysis Error ◽  
Ensemble Systems

Abstract This work investigates the inconsistency between forecasts issued at different times but valid for the same time, and shows that ensemble-mean forecasts are less inconsistent than corresponding control forecasts. The “jumpiness” index, the concepts of different forecast jumps—the “flip,” “flip-flop,” and “flip-flop-flip”—and the inconsistency correlation between time series of inconsistency indices are introduced to measure the consistency/inconsistency of consecutive forecasts. These new measures are used to compare the behavior of the ECMWF and the Met Office control and ensemble-mean forecasts for an 18-month period over Europe. Results indicate that for both the ECMWF and the Met Office ensembles, the ensemble-mean forecast is less inconsistent than the control forecast. However, they also indicate that the ensemble mean follows its corresponding control forecast more closely than the controls (or the ensemble means) of the two ensemble systems following each other, thus suggesting weaknesses in both ensemble systems in the simulation of forecast uncertainty due to model or analysis error. Results also show that there is only a weak link between forecast jumpiness and forecast error (i.e., forecasts with lower inconsistency do not necessarily have, on average, lower error).

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.

scholarly journals Soil Moisture Assimilation Using a Modified Ensemble Transform Kalman Filter Based on Station Observations in the Hai River Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Guocan Wu ◽  
Bo Dan ◽  
Xiaogu Zheng
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Water Budget ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Surface Model ◽  
Common Land Model ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Ensemble Transform

Assimilating observations to a land surface model can further improve soil moisture estimation accuracy. However, assimilation results largely rely on forecast error and generally cannot maintain a water budget balance. In this study, shallow soil moisture observations are assimilated into Common Land Model (CoLM) to estimate the soil moisture in different layers. A proposed forecast error inflation and water balance constraint are adopted in the Ensemble Transform Kalman Filter to reduce the analysis error and water budget residuals. The assimilation results indicate that the analysis error is reduced and the water imbalance is mitigated with this approach.

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