A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.

Implications of model error for numerical climate prediction

Numerical climate models constitute the best available tools to tackle the problem of climate prediction. Two assumptions lie at the heart of their suitability: (1) a climate attractor exists, and (2) the numerical climate model's attractor lies on the actual climate attractor, or at least on the projection of the climate attractor on the model's phase space. In this contribution, the Lorenz '63 system is used both as a prototype system and as an imperfect model to investigate the implications of the second assumption. By comparing results drawn from the Lorenz '63 system and from numerical weather and climate models, the implications of using imperfect models for the prediction of weather and climate are discussed. It is shown that the imperfect model's orbit and the system's orbit are essentially different, purely due to model error and not to sensitivity to initial conditions. Furthermore, if a model is a perfect model, then the attractor, reconstructed by sampling a collection of initialised model orbits (forecast orbits), will be invariant to forecast lead time. This conclusion provides an alternative method for the assessment of climate models.

The predictability of extratropical storm tracks and the sensitivity of their prediction to the observing system

A new method for assessing forecast skill and predictability that involves the identification and tracking of extratropical cyclones has been developed and implemented to obtain detailed information about the prediction of cyclones that cannot be obtained from more conventional analysis methodologies. The cyclones were identified and tracked along the forecast trajectories, and statistics were generated to determine the rate at which the position and intensity of the forecasted storms diverge from the analyzed tracks as a function of forecast lead time. The results show a higher level of skill in predicting the position of extratropical cyclones than the intensity. They also show that there is potential to improve the skill in predicting the position by 1 - 1.5 days and the intensity by 2 - 3 days, via improvements to the forecast model. Further analysis shows that forecasted storms move at a slower speed than analyzed storms on average and that there is a larger error in the predicted amplitudes of intense storms than the weaker storms. The results also show that some storms can be predicted up to 3 days before they are identified as an 850-hPa vorticity center in the analyses. In general, the results show a higher level of skill in the Northern Hemisphere (NH) than the Southern Hemisphere (SH); however, the rapid growth of NH winter storms is not very well predicted. The impact that observations of different types have on the prediction of the extratropical cyclones has also been explored, using forecasts integrated from analyses that were constructed from reduced observing systems. A terrestrial, satellite, and surface-based system were investigated and the results showed that the predictive skill of the terrestrial system was superior to the satellite system in the NH. Further analysis showed that the satellite system was not very good at predicting the growth of the storms. In the SH the terrestrial system has significantly less skill than the satellite system, highlighting the dominance of satellite observations in this hemisphere. The surface system has very poor predictive skill in both hemispheres.

Regional Differences in the Prediction of Extratropical Cyclones by the ECMWF Ensemble Prediction System

A regional study of the prediction of extratropical cyclones by the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) has been performed. An objective feature-tracking method has been used to identify and track the cyclones along the forecast trajectories. Forecast error statistics have then been produced for the position, intensity, and propagation speed of the storms. In previous work, data limitations meant it was only possible to present the diagnostics for the entire Northern Hemisphere (NH) or Southern Hemisphere. A larger data sample has allowed the diagnostics to be computed separately for smaller regions around the globe and has made it possible to explore the regional differences in the prediction of storms by the EPS. Results show that in the NH there is a larger ensemble mean error in the position of storms over the Atlantic Ocean. Further analysis revealed that this is mainly due to errors in the prediction of storm propagation speed rather than in direction. Forecast storms propagate too slowly in all regions, but the bias is about 2 times as large in the NH Atlantic region. The results show that storm intensity is generally overpredicted over the ocean and underpredicted over the land and that the absolute error in intensity is larger over the ocean than over the land. In the NH, large errors occur in the prediction of the intensity of storms that originate as tropical cyclones but then move into the extratropics. The ensemble is underdispersive for the intensity of cyclones (i.e., the spread is smaller than the mean error) in all regions. The spatial patterns of the ensemble mean error and ensemble spread are very different for the intensity of cyclones. Spatial distributions of the ensemble mean error suggest that large errors occur during the growth phase of storm development, but this is not indicated by the spatial distributions of the ensemble spread. In the NH there are further differences. First, the large errors in the prediction of the intensity of cyclones that originate in the tropics are not indicated by the spread. Second, the ensemble mean error is larger over the Pacific Ocean than over the Atlantic, whereas the opposite is true for the spread. The use of a storm-tracking approach, to both weather forecasters and developers of forecast systems, is also discussed.

TIGGE: Comparison of the prediction of northern hemisphere extratropical cyclones by different ensemble prediction systems

The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) is a World Weather Research Programme project. One of its main objectives is to enhance collaboration on the development of ensemble prediction between operational centers and universities by increasing the availability of ensemble prediction system (EPS) data for research. This study analyzes the prediction of Northern Hemisphere extratropical cyclones by nine different EPSs archived as part of the TIGGE project for the 6-month time period of 1 February 2008–31 July 2008, which included a sample of 774 cyclones. An objective feature tracking method has been used to identify and track the cyclones along the forecast trajectories. Forecast verification statistics have then been produced [using the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis as the truth] for cyclone position, intensity, and propagation speed, showing large differences between the different EPSs. The results show that the ECMWF ensemble mean and control have the highest level of skill for all cyclone properties. The Japanese Meteorological Administration (JMA), the National Centers for Environmental Prediction (NCEP), the Met Office (UKMO), and the Canadian Meteorological Centre (CMC) have 1 day less skill for the position of cyclones throughout the forecast range. The relative performance of the different EPSs remains the same for cyclone intensity except for NCEP, which has larger errors than for position. NCEP, the Centro de Previsão de Tempo e Estudos Climáticos (CPTEC), and the Australian Bureau of Meteorology (BoM) all have faster intensity error growth in the earlier part of the forecast. They are also very underdispersive and significantly underpredict intensities, perhaps due to the comparatively low spatial resolutions of these EPSs not being able to accurately model the tilted structure essential to cyclone growth and decay. There is very little difference between the levels of skill of the ensemble mean and control for cyclone position, but the ensemble mean provides an advantage over the control for all EPSs except CPTEC in cyclone intensity and there is an advantage for propagation speed for all EPSs. ECMWF and JMA have an excellent spread–skill relationship for cyclone position. The EPSs are all much more underdispersive for cyclone intensity and propagation speed than for position, with ECMWF and CMC performing best for intensity and CMC performing best for propagation speed. ECMWF is the only EPS to consistently overpredict cyclone intensity, although the bias is small. BoM, NCEP, UKMO, and CPTEC significantly underpredict intensity and, interestingly, all the EPSs underpredict the propagation speed, that is, the cyclones move too slowly on average in all EPSs.

Evaluating the ability of a numerical weather prediction model to forecast tracer concentrations during ETEX 2

In this paper the meteorological processes responsible for transporting tracer during the second ETEX (European Tracer EXperiment) release are determined using the UK Met Office Unified Model (UM). The UM predicted distribution of tracer is also compared with observations from the ETEX campaign. The dominant meteorological process is a warm conveyor belt which transports large amounts of tracer away from the surface up to a height of 4 km over a 36 h period. Convection is also an important process, transporting tracer to heights of up to 8 km. Potential sources of error when using an operational numerical weather prediction model to forecast air quality are also investigated. These potential sources of error include model dynamics, model resolution and model physics. In the UM a semi-Lagrangian monotonic advection scheme is used with cubic polynomial interpolation. This can predict unrealistic negative values of tracer which are subsequently set to zero, and hence results in an overprediction of tracer concentrations. In order to conserve mass in the UM tracer simulations it was necessary to include a flux corrected transport method. Model resolution can also affect the accuracy of predicted tracer distributions. Low resolution simulations (50 km grid length) were unable to resolve a change in wind direction observed during ETEX 2, this led to an error in the transport direction and hence an error in tracer distribution. High resolution simulations (12 km grid length) captured the change in wind direction and hence produced a tracer distribution that compared better with the observations. The representation of convective mixing was found to have a large effect on the vertical transport of tracer. Turning off the convective mixing parameterisation in the UM significantly reduced the vertical transport of tracer. Finally, air quality forecasts were found to be sensitive to the timing of synoptic scale features. Errors in the position of the cold front relative to the tracer release location of only 1 h resulted in changes in the predicted tracer concentrations that were of the same order of magnitude as the absolute tracer concentrations.

A new method for evaluating regional air quality forecasts

A Kriging interpolation method is combined with an object-based evaluation measure to assess the ability of the UK Met Office's dispersion and weather prediction models to predict the evolution of a plume of tracer as it was transported across Europe. The object-based evaluation method, SAL, considers aspects of the Structure, Amplitude and Location of the pollutant field. The SAL method is able to quantify errors in the predicted size and shape of the pollutant plume, through the structure component, the over- or under-prediction of the pollutant concentrations, through the amplitude component, and the position of the pollutant plume, through the location component. The quantitative results of the SAL evaluation are similar for both models and close to a subjective visual inspection of the predictions. A negative structure component for both models, throughout the entire 60 hour plume dispersion simulation, indicates that the modelled plumes are too small and/or too peaked compared to the observed plume at all times. The amplitude component for both models is strongly positive at the start of the simulation, indicating that surface concentrations are over-predicted by both models for the first 24 hours, but modelled concentrations are within a factor of 2 of the observations at later times. Finally, for both models, the location component is small for the first 48 hours after the start of the tracer release, indicating that the modelled plumes are situated close to the observed plume early on in the simulation, but this plume location error grows at later times. The SAL methodology has also been used to identify differences in the transport of pollution in the dispersion and weather prediction models. The convection scheme in the weather prediction model is found to transport more pollution vertically out of the boundary layer into the free troposphere than the dispersion model convection scheme resulting in lower pollutant concentrations near the surface and hence a better forecast for this case study.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

Automated tertiary structure prediction with accurate local model quality assessment using the IntFOLD-TS method

The IntFOLD-TS method was developed according to the guiding principle that the model quality assessment would be the most critical stage for our template based modelling pipeline. Thus, the IntFOLD-TS method firstly generates numerous alternative models, using in-house versions of several different sequence-structure alignment methods, which are then ranked in terms of global quality using our top performing quality assessment method – ModFOLDclust2. In addition to the predicted global quality scores, the predictions of local errors are also provided in the resulting coordinate files, using scores that represent the predicted deviation of each residue in the model from the equivalent residue in the native structure. The IntFOLD-TS method was found to generate high quality 3D models for many of the CASP9 targets, whilst also providing highly accurate predictions of their per-residue errors. This important information may help to make the 3D models that are produced by the IntFOLD-TS method more useful for guiding future experimental work

Benchmarking secondary structure prediction for fold recognition

If secondary structure predictions are to be incorporated into fold recognition methods, an assessment of the effect of specific types of errors in predicted secondary structures on the sensitivity of fold recognition should be carried out. Here, we present a systematic comparison of different secondary structure prediction methods by measuring frequencies of specific types of error. We carry out an evaluation of the effect of specific types of error on secondary structure element alignment (SSEA), a baseline fold recognition method. The results of this evaluation indicate that missing out whole helix or strand elements, or predicting the wrong type of element, is more detrimental than predicting the wrong lengths of elements or overpredicting helix or strand. We also suggest that SSEA scoring is an effective method for assessing accuracy of secondary structure prediction and perhaps may also provide a more appropriate assessment of the “usefulness” and quality of predicted secondary structure, if secondary structure alignments are to be used in fold recognition.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties.