Search Results

You are looking at 1 - 10 of 12 items for :

  • Author or Editor: Zoltan Toth x
  • Monthly Weather Review x
  • All content x
Clear All Modify Search
Zoltan Toth

Abstract

An empirical predictability study is presented based on 7OO-hPa Northern Hemispheric circulation analogs. A linear relationship between the initial root-mean-square difference of analog pairs and the time taken for the error to reach a certain limit value is used to extrapolate the predictability with initial errors considerably smaller than those in the present database. The relationship, first used in predictability experiments with the NMC numerical weather prediction (NWP) model, conforms to the experimental data in that the effor growth depends not only on the magnitude of the error but also, to a lesser extent, on the initial error.

Despite the fact that earlier error growth studies did not reflect this dependence on the initial error predictability results with two state-of-the-art numerical models using different analysis methods, and those derived here by the linear relationship mentioned above from circulation analogs are gratifyingly similar. These estimates indicate that given the present observational error (about 12 m rms) and spatial resolution of the data, in the NH winter, the atmosphere seems to have 17-18 days of predictability before the initial difference reaches 95% of the saturation Revel (random error). In present models, the forecast error reaches the same 95% level at around ten and a half days. Since the climate mean as a forecast has considerably less error than a random forecast, from a forecaster's point of view it is more appropriate to use the climate mor as a reference level (71% of the saturation level). With the same conditions as above and using this alternative error reference level, the atmosphere might have a predictability of nine days, while the two models considered currently exhaust predictability at close to six days, leaving considerable room for improvement. Note that these atmospheric predictability estimates were obtained without considering a possible enhancement of predictability due to interactions with the slowly changing ocean and other geospheres. Hence, these estimates can be considered as lower limits to atmospheric predictability.

Comparing the predictability estimates gained from twin model experiments to those from observational data is a special, complex method of model verification. Keeping in mind the uncertainties in the observational studies, one can ascertain that the models produce quite similar error growth characteristics to those of the real atmosphere. Hence, the NWP models are quite good on the tirne and spatial scales for which they were designed. However, there are some indications that they probably could not be reliably used to answer the theoretical questions regarding the gain in predictability with very small initial errors or with very high spatial resolution. Some kind of dynamic-empirical approach based on the interactions between different scales of motion is required to enhance current knowledge on these topics.

Full access
Zoltan Toth

Abstract

Most circulation studies use the root-mean-square difference (RMSD) or correlation (COR) (or both) as a toot for comparing different (observed or forecast) circulation patterns. However, there are some other measures introduced into the literature (e.g., mean absolute error, rms vector error, S1 score) and one might easily construct other measures of circulation similarity. The question of the appropriate choice among possible similarity measures rarely arises. In this paper an objective intercomparison of nine different similarity measures (also called distance functions) is presented. The similarity measures were evaluated through the 7OO-hPa hemispheric analog forecasts obtained by them. In the indirect evaluation, the analogs to the base cases found by each individual distance function were checked whether they were identical with the best analogs (selected by all nine functions) to the circulation pattern that actually followed. The number of coincidences is an indication of the quality of the similarity measures and is found, both for daily and pentad data, to be largest for a dynamically oriented distance function that measure the difference between the gradient of height of two maps. For daily data, RMSD also appears to be significantly better than COR. However, in a direct assessment, where analog forecasts by each distance function were compared to the analysis fields using one of the distance functions to measure the difference, practically no performance differences were found among the functions that performed differently in the indirect evaluation.

It should be noted that the results of both intercompaiison methods are, in a strict sense, valid only for forecast situations. For other purposes, other distance functions might be more appropriate. However, there are some indications that the similarity measure that performed best in the forecast experiments (difference in the gradient of height) remains superior in other applications, too.

Full access
Zoltan Toth

Abstract

In this paper daily wintertime extratropical Northern Hemisphere (NH) circulation analogs are studied. First the analog forecasts are compared to various common benchmark methods such as random or persistence forecasts and the climate mean as a forecast. In line with earlier work, it is concluded that beyond a few days lead time the analogs offer no advantage over any of these benchmark methods. The same is true for derivative analogs (where only the time derivative of the analogs is used and added to the base case), although they perform considerably better than the traditional analogs on the first time step(s).

Even though the circulation analogs have no extended-range forecast capability, they nevertheless offer a convenient way of studying the gross structure of the phase space of circulation patterns. A thorough study of the root-mean-square distances (rmsd) between the best circulation analogs, considered as an indicator for the relative frequency in the phase space, has been performed. It was shown that in a phase-average sense, when the density characteristics are considered only as a function of distance from the climate mean, the distribution of circulation patterns is statistically indistinguishable from a multinormal distribution.

This simple but previously unobserved fact has a series of consequences, some of which are presented here. First, since the density of the distribution of circulation patterns is increasing with decreasing distance from the climate mean, the best analog to a particular circulation pattern is more likely to be closer to the climate mean than the base case. A second observation is that the persistence of the flow increases with decreasing distance from the climate mean. A double stratification of the analogs according to their initial difference and the persistence of the flow showed no enhanced predictability in persistent cases; the forecast error depends only on the initial error of the analogs. This is an indication that the higher numerical forecast skill in persistent cases (reported in earlier studies) may be related to the fact that those cases are relatively close to the climate mean, where even random forecasts have smaller rms error. A third point is that analog predictability does not depend on the initial flow's distance from the climate mean either.

The phase-average multinormality of the wintertime extratropical NH circulation phase space discussed in this study does not rule out the possibility of a fine structure with several local maxima (multiple equilibria) embedded in the overall gross structure of approximate normality. Indeed, a refined methodology revealing the existence of such “dense” areas will be reported in a later paper.

Full access
Mozheng Wei and Zoltan Toth

Abstract

Most existing ensemble forecast verification statistics are influenced by the quality of not only the ensemble generation scheme, but also the forecast model and the analysis scheme. In this study, a new tool called perturbation versus error correlation analysis (PECA) is introduced that lessens the influence of the initial errors that affect the quality of the analysis. PECA evaluates the ensemble perturbations, instead of the forecasts themselves, by measuring their ability to explain forecast error variance. As such, PECA offers a more appropriate tool for the comparison of ensembles generated by using different analysis schemes.

Ensemble perturbations from both the National Centers for Environmental Prediction (NCEP) and the European Centre for Medium-Range Weather Forecasts (ECMWF) were evaluated and found to perform similarly. The error variance explained by either ensemble increases with the number of members and the lead time. The dynamically conditioned NCEP and ECMWF perturbations outperform both randomly chosen perturbations and differences between lagged forecasts [used in the “NMC” (for National Meteorological Center, the former name of NCEP) method for defining forecast error covariance matrices]. Therefore ensemble forecasts potentially could be used to construct flow-dependent short-range forecast error covariance matrices for use in data assimilation schemes.

It is well understood that in a perfectly reliable ensemble the spread of ensemble members around the ensemble mean forecast equals the root-mean-square (rms) error of the mean. Adequate rms spread, however, does not guarantee sufficient variability among the ensemble forecast patterns. A comparison between PECA values and pattern anomaly correlation (PAC) values among the ensemble members reveals that the perturbations in the NCEP ensemble exhibit too much similarity, especially on the smaller scales. Hence a regional orthogonalization of the perturbations may improve ensemble performance.

Full access
Zoltan Toth and Eugenia Kalnay

Abstract

The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day.

For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first-guess forecasts, is “scaled down” at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth.

The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred vectors from independent breeding cycles.

Experimental runs with a 10-member ensemble (five independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium-range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04–0.11 in pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool.

The two methods used so far to produce operational ensemble forecasts—that is, breeding and the adjoint (or “optimal perturbations”) technique applied at the European Centre for Medium-Range Weather Forecasts—have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.

Full access
Malaquias Peña, Zoltan Toth, and Mozheng Wei

Abstract

A variety of ad hoc procedures have been developed to prevent filter divergence in ensemble-based data assimilation schemes. These procedures are necessary to reduce the impacts of sampling errors in the background error covariance matrix derived from a limited-size ensemble. The procedures amount to the introduction of additional noise into the assimilation process, possibly reducing the accuracy of the resulting analyses. The effects of this noise on analysis and forecast performance are investigated in a perfect model scenario. Alternative schemes aimed at controlling the unintended injection of noise are proposed and compared. Improved analysis and forecast accuracy is observed in schemes with minimal alteration to the evolving ensemble-based covariance structure.

Full access
Roberto Buizza, P. L. Houtekamer, Gerald Pellerin, Zoltan Toth, Yuejian Zhu, and Mozheng Wei

Abstract

The present paper summarizes the methodologies used at the European Centre for Medium-Range Weather Forecasts (ECMWF), the Meteorological Service of Canada (MSC), and the National Centers for Environmental Prediction (NCEP) to simulate the effect of initial and model uncertainties in ensemble forecasting. The characteristics of the three systems are compared for a 3-month period between May and July 2002. The main conclusions of the study are the following:

  • the performance of ensemble prediction systems strongly depends on the quality of the data assimilation system used to create the unperturbed (best) initial condition and the numerical model used to generate the forecasts;
  • a successful ensemble prediction system should simulate the effect of both initial and model-related uncertainties on forecast errors; and
  • for all three global systems, the spread of ensemble forecasts is insufficient to systematically capture reality, suggesting that none of them is able to simulate all sources of forecast uncertainty.
The relative strengths and weaknesses of the three systems identified in this study can offer guidelines for the future development of ensemble forecasting techniques.

Full access
Istvan Szunyogh, Zoltan Toth, Aleksey V. Zimin, Sharanya J. Majumdar, and Anders Persson

Abstract

The propagation of the effect of targeted observations in numerical weather forecasts is investigated, based on results from the 2000 Winter Storm Reconnaissance (WSR00) program. In this field program, nearly 300 dropsondes were released adaptively at selected locations over the northeast Pacific on 12 separate flight days with the aim of reducing the risk of major failures in severe winter storm forecasts over the United States. The data impact was assessed by analysis–forecast experiments carried out with the T62 horizontal resolution, 28-level version of the operational global Medium Range Forecast system of the National Centers for Environmental Prediction.

In some cases, storms that reached the West Coast or Alaska were observed in an earlier phase of their development, while at other times the goal was to improve the prediction of storms that formed far downstream of the targeted region. Changes in the forecasts were the largest when landfalling systems were targeted and the baroclinic energy conversion was strong in the targeted region.

As expected from the experience accumulated during the 1999 Winter Storm Reconnaissance (WSR99) program, downstream baroclinic development played a major role in propagating the influence of the targeted data over North America. The results also show, however, that predicting the location of significant changes due to the targeted data in the forecasts can be difficult in the presence of a nonzonal large-scale flow. The strong zonal variations in the large-scale flow over the northeast Pacific during WSR00 did not reduce the positive forecast effects of the targeted data. On the contrary, the overall impact of the dropsonde data was more positive than during WSR99, when the large-scale flow was dominantly zonal on the flight days. This can be attributed to the improved prediction of the large-scale flow that led to additional improvements in the prediction of the synoptic-scale waves.

Full access
Jeffrey S. Whitaker, Thomas M. Hamill, Xue Wei, Yucheng Song, and Zoltan Toth

Abstract

Real-data experiments with an ensemble data assimilation system using the NCEP Global Forecast System model were performed and compared with the NCEP Global Data Assimilation System (GDAS). All observations in the operational data stream were assimilated for the period 1 January–10 February 2004, except satellite radiances. Because of computational resource limitations, the comparison was done at lower resolution (triangular truncation at wavenumber 62 with 28 levels) than the GDAS real-time NCEP operational runs (triangular truncation at wavenumber 254 with 64 levels). The ensemble data assimilation system outperformed the reduced-resolution version of the NCEP three-dimensional variational data assimilation system (3DVAR), with the biggest improvement in data-sparse regions. Ensemble data assimilation analyses yielded a 24-h improvement in forecast skill in the Southern Hemisphere extratropics relative to the NCEP 3DVAR system (the 48-h forecast from the ensemble data assimilation system was as accurate as the 24-h forecast from the 3DVAR system). Improvements in the data-rich Northern Hemisphere, while still statistically significant, were more modest. It remains to be seen whether the improvements seen in the Southern Hemisphere will be retained when satellite radiances are assimilated. Three different parameterizations of background errors unaccounted for in the data assimilation system (including model error) were tested. Adding scaled random differences between adjacent 6-hourly analyses from the NCEP–NCAR reanalysis to each ensemble member (additive inflation) performed slightly better than the other two methods (multiplicative inflation and relaxation-to-prior).

Full access
Sharanya J. Majumdar, Kathryn J. Sellwood, Daniel Hodyss, Zoltan Toth, and Yucheng Song

Abstract

The characteristics of “target” locations of tropospheric wind and temperature identified by a modified version of the ensemble transform Kalman filter (ETKF), in order to reduce 0–7-day forecast errors over North America, are explored from the perspective of a field program planner. Twenty cases of potential high-impact weather over the continent were investigated, using a 145-member ensemble comprising perturbations from NCEP, ECMWF, and the Canadian Meteorological Centre (CMC).

Multiple targets were found to exist in the midlatitude storm track. In half of the cases, distinctive targets could be traced upstream near Japan at lead times of 4–7 days. In these cases, the flow was predominantly zonal and a coherent Rossby wave packet was present over the northern Pacific Ocean. The targets at the longest lead times were often located within propagating areas of baroclinic energy conversion far upstream. As the lead time was reduced, these targets were found to diminish in importance, with downstream targets corresponding to a separate synoptic system gaining in prominence. This shift in optimal targets is sometimes consistent with the radiation of ageostrophic geopotential fluxes and transfer of eddy kinetic energy downstream, associated with downstream baroclinic development. Concurrently, multiple targets arise due to spurious long-distance correlations in the ETKF. The targets were least coherent in blocked flows, in which the ETKF is known to be least reliable. The effectiveness of targeting in the medium range requires evaluation, using data such as those collected during the winter phase of The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Field Campaign (T-PARC) in 2009.

Full access