A limited-area spatio-temporal stochastic pattern generator for simulation of uncertainties in ensemble applications

214

250

Members in ensemble forecasts differ due to the representations of initial uncertainties and model uncertainties. The inclusion of stochastic schemes to represent model uncertainties has improved the probabilistic skill of the ECMWF ensemble by increasing reliability and reducing the error of the ensemble mean. Recent progress, challenges and future directions regarding stochastic representations of model uncertainties at ECMWF are described in this article. The coming years are likely to see a further increase in the use of ensemble methods in forecasts and assimilation. This will put increasing demands on the methods used to perturb the forecast model. An area that is receiving greater attention than 5–10 years ago is the physical consistency of the perturbations. Other areas where future efforts will be directed are the expansion of uncertainty representations to the dynamical core and other components of the Earth system, as well as the overall computational efficiency of representing model uncertainty.

Section: Unrepresented Uncertainties In the Earth Systemmentioning

confidence: 99%

“…Even with the current spectral random field generator, it may be possible to explore some non‐seperable covariance models, e.g. ones that obey the ‘proportionality of scales’ advocated by Tsyrulnikov and Gayfulin (2016).…”

Section: Future Directionsmentioning

confidence: 99%

Stochastic representations of model uncertainties at ECMWF: state of the art and future vision

Leutbecher

Lock

Ollinaho

et al. 2017

214

250

“…It can be shown (e.g. Tsyrulnikov and Gayfulin, , appendix A.4) that

{\overset{α}{false}}_{m} false(t false)

are independent standard complex‐white‐noise processes ω m ( t ) with the common intensity

a = 1 false/ \sqrt{2 π R}

{\overset{α}{false}}_{m} false(t false) = a ω_{m} false(t false) .

Now, we substitute Equations – into Equation , getting

\frac{normald {\overset{ξ}{false}}_{m}}{normald t} + ((), ρ + \frac{ν}{R^{2}} m^{2}) {\overset{ξ}{false}}_{m} = a σ ω_{m} false(t false) .

This is the spectral‐space form of the model Equation . It is easily seen that if ρ + ( ν / R 2 ) m 2 > 0, the solutions to Equation for different m become, after an initial transient, mutually independent stationary zero‐mean random processes.…”

Section: Stochastic Advection‐diffusion‐decay Model With Constant Coementioning

confidence: 99%

“…larger wavenumbers m ) correspond to smaller time‐scales τ m . This feature of space‐time correlations (“proportionality of scales”) is physically reasonable – as opposed to the simplistic and unrealistic separability of space‐time correlations – and widespread in the real world (Tsyroulnikov, , Tsyrulnikov and Gayfulin, , and references therein).…”

Section: Stochastic Advection‐diffusion‐decay Model With Constant Coementioning

confidence: 99%

“…In this setting, the model forcing ε k becomes the model error (e.g. Tsyrulnikov and Gayfulin ()), with its covariance matrix Q k also available to the filters. We reiterate that in each experiment, the secondary fields (which determine the forecast operator and the model‐error statistics), once generated, were kept fixed.…”

Section: Performance Of the Three Covariance‐blending Techniques Undementioning

confidence: 99%

See 1 more Smart Citation

Impact of non‐stationarity on hybrid ensemble filters: A study with a doubly stochastic advection‐diffusion‐decay model

Tsyrulnikov

Rakitko²

2019

Self Cite

Effects of non‐stationarity on the performance of hybrid ensemble filters is studied. (By hybrid filters we mean those which blend ensemble covariances with some other regularizing covariances.) To isolate effects of non‐stationarity from effects due to nonlinearity (and the non‐Gaussianity it causes), a new doubly stochastic advection‐diffusion‐decay model (DSADM) is proposed. The model is hierarchical: it is a linear stochastic partial differential equation whose coefficients are random fields defined through their own stochastic partial differential equations. DSADM generates conditionally Gaussian spatiotemporal random fields with a tunable degree of non‐stationarity in space and time. DSADM allows the use of the exact Kalman filter as a baseline benchmark. In numerical experiments with DSADM as the “model of truth”, the relative importance of the three kinds of covariance blending is studied: with static, time‐smoothed, and space‐smoothed covariances. It is shown that the stronger the non‐stationarity, the less useful the static covariance matrix becomes and the more beneficial the time‐smoothed covariances are. Time‐smoothing of background‐error covariances proved to be systematically more useful than their space‐smoothing. Under non‐stationarity, a filter that extends the (previously proposed by the authors) Hierarchical Bayes Ensemble Filter and accommodates the three covariance‐blending techniques is shown to outperform all other configurations of the filters tested.

Impact of land surface stochastic physics in ALADIN‐LAEF

Wang

Belluš

Weidle

et al. 2019

To deal with the land surface physics uncertainties, a stochastic scheme based on stochastic perturbation of physics tendencies is implemented and tested. The impact of land surface physics uncertainties and their relative importance to land surface initial uncertainties are investigated in the regional ensemble forecasting system ALADIN‐LAEF (Aire Limitée Adaptation Dynamique Développement InterNational – Limited Area Ensemble Forecasting). The land surface initial perturbation is generated by using an ensemble of land surface data assimilation; and the land surface physics uncertainties by applying the idea of stochastically perturbed parametrization tendencies (SPPT) scheme. Three experiments are conducted and compared with the reference ensemble over a 2‐month period. The results show the introduction of land surface stochastic physics increases the ensemble spread, reduces the ensemble bias, and keeps neutral in deterministic forecast skill of the ensemble, its impact strongly depending on the quality of ensemble initial conditions. The ensemble land surface data assimilation has stronger positive impact on the ALADIN‐LAEF than the land surface stochastic physics for screen‐level temperature and humidity. There is not much impact on 10 m wind and precipitation. Best results are obtained when both the ensemble land surface data assimilation and land surface stochastic physics are used simultaneously; it gives a more reliable and statistically consistent forecast, which is contributed mainly by ensemble land surface data assimilation in the first forecast hours and largely by land surface stochastic physics in the later forecast hours.