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Martin Charron
,
P. L. Houtekamer
, and
Peter Bartello

Abstract

The ensemble Kalman filter (EnKF) developed at the Meteorological Research Branch of Canada is used in the context of synthetic radial wind data assimilation at the mesoscale. A dry Boussinesq model with periodic boundary conditions is employed to provide a control run, as well as two ensembles of first guesses. Synthetic data, which are interpolated from the control run, are assimilated and simulate Doppler radar wind measurements.

Nine “radars” with a range of 120 km are placed evenly on the horizontal 1000 km × 1000 km domain. These radars measure the radial wind with assumed Gaussian error statistics at each grid point within their range provided that there is sufficient upward motion (a proxy for precipitation). These data of radial winds are assimilated every 30 min and the assimilation period extends over 4 days.

Results show that the EnKF technique with 2 × 50 members performed well in terms of reducing the analysis error for horizontal winds and temperature (even though temperature is not an observed variable) over a period of 4 days. However the analyzed vertical velocity shows an initial degradation. During the first 2 days of the assimilation period, the analysis error of the vertical velocity is greater when assimilating radar observations than when scoring forecasts initialized at t = 0 without assimilating any data. The type of assimilated data as well as the localization of the impact of the observations is thought to be the cause of this degradation of the analyzed vertical velocity. External gravity modes are present in the increments when localization is performed. This degradation can be eliminated by filtering the external gravity modes of the analysis increments.

A similar set of experiments is realized in which the model dissipation coefficient is reduced by a factor of 10. This shows the level of sensitivity of the results to the kinetic energy power spectrum, and that the quality of the analyzed vertical wind is worse when dissipation is small.

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Xiaoli Li
,
Martin Charron
,
Lubos Spacek
, and
Guillem Candille

Abstract

A regional ensemble prediction system (REPS) with the limited-area version of the Canadian Global Environmental Multiscale (GEM) model at 15-km horizontal resolution is developed and tested. The total energy norm singular vectors (SVs) targeted over northeastern North America are used for initial and boundary perturbations. Two SV perturbation strategies are tested: dry SVs with dry simplified physics and moist SVs with simplified physics, including stratiform condensation and convective precipitation as well as dry processes. Model physics uncertainties are partly accounted for by stochastically perturbing two parameters: the threshold vertical velocity in the trigger function of the Kain–Fritsch deep convection scheme, and the threshold humidity in the Sundqvist explicit scheme. The perturbations are obtained from first-order Markov processes. Short-range ensemble forecasts in summer with 16 members are performed for five different experiments. The experiments employ different perturbation and piloting strategies, and two different surface schemes. Verification focuses on quantitative precipitation forecasts and is done using a range of probabilistic measures. Results indicate that using moist SVs instead of dry SVs has a stronger impact on precipitation than on dynamical fields. Forecast skill for precipitation is greatly influenced by the dominant synoptic weather systems. For stratiform precipitation caused by strong baroclinic systems, the forecast skill is improved in the moist SV experiments relative to the dry SV experiments. For convective precipitation rates in the range 15–50 mm (24 h)−1 produced by weak synoptic baroclinic systems, all experiments exhibit noticeably poorer forecast skills. Skill improvements due to the Interactions between Soil, Biosphere, and Atmosphere (ISBA) surface scheme and stochastic perturbations are also observed.

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Abdelaziz Beljadid
,
Abdolmajid Mohammadian
,
Martin Charron
, and
Claude Girard

Abstract

In this paper, theoretical and numerical analyses of the properties of some complex semi-Lagrangian methods are performed to deal with the issues of the instability associated with the treatment of the nonlinear part of the forcing term. A class of semi-Lagrangian semi-implicit schemes is proposed using a modified TR-BDF2 method, which is the combination of the trapezoidal rule (TR) and the second-order backward differentiation formula (BDF2). The process used for the nonlinear term includes two stages as predictor and corrector in the trapezoidal method and one stage for the BDF2 method. For the treatment of the linear term, the implicit trapezoidal method is employed in the first step, the explicit trapezoidal method in the second step, and the implicit BDF2 method in the third step. The combination of these techniques leads to a family of schemes that has a large region of absolute stability, performs well for the purely oscillatory cases, and has good qualities in terms of accuracy and convergence. The use of the explicit method for the linear term in the second step makes the proposed class of schemes competitive in terms of efficiency compared to some well-known schemes that use two steps. Numerical experiments presented herein confirm that the proposed class of schemes performs well in terms of stability, accuracy, convergence, and efficiency in comparison with other, previously known, semi-Lagrangian semi-implicit schemes and semi-implicit predictor–corrector methods. The potential practical application of the proposed class of schemes to a weather prediction model or any other atmospheric model is not discussed and could be the subject of other forthcoming studies.

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Christophe Lavaysse
,
Marco Carrera
,
Stéphane Bélair
,
Normand Gagnon
,
Ronald Frenette
,
Martin Charron
, and
M. K. Yau

Abstract

The aim of this study is to assess the impact of uncertainties in surface parameter and initial conditions on numerical prediction with the Canadian Regional Ensemble Prediction System (REPS). As part of this study, the Canadian version of the Interactions between Soil–Biosphere–Atmosphere (ISBA) land surface scheme has been coupled to Environment Canada’s numerical weather prediction model within the REPS. For 20 summer periods in 2009, stochastic perturbations of surface parameters have been generated in several experiments. Each experiment corresponds to 20 simulations differing by the perturbations at the initial time of one or several surface parameters or prognostic variables. The sensitivity to these perturbations is quantified especially for 2-m temperature, 10-m wind speed, cloud fraction, and precipitation up to 48-h lead time. Spatial variability of these sensitivities over the North American continent shows that soil moisture, albedo, leaf area index, and SST have the largest impacts on the screen-level variables. The temporal evolution of these sensitivities appears to be closely linked to the diurnal cycle of the boundary layer. The surface perturbations are shown to increase the ensemble spread of the REPS for all screen-level variables especially for 2-m temperature and 10-m wind speed during daytime. A preliminary study of the impact on the ensemble forecast has shown that the inclusion of the surface perturbations tends to significantly increase the 2-m temperature and 10-m wind speed skill.

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P. L. Houtekamer
,
Herschel L. Mitchell
,
Gérard Pellerin
,
Mark Buehner
,
Martin Charron
,
Lubos Spacek
, and
Bjarne Hansen

Abstract

An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used.

It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment, it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling, fairly stable global filter statistics are obtained with no sign of filter divergence.

The quality of the ensemble mean background field, as verified using radiosonde observations, is similar to that obtained using a 3D variational procedure. In part, this is likely due to the form chosen for the parameterized model error. Nevertheless, the degree of similarity is surprising given that the background-error statistics used by the two procedures are rather different, with generally larger background errors being used by the variational scheme.

A set of 5-day integrations has been started from the ensemble of initial conditions provided by the EnKF. For the middle and lower troposphere, the growth rates of the perturbations are somewhat smaller than the growth rate of the actual ensemble mean error. For the upper levels, the perturbation patterns decay for about 3 days as a consequence of diffusive model dynamics. These decaying perturbations tend to severely underestimate the actual error that grows rapidly near the model top.

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Martin Charron
,
Gérard Pellerin
,
Lubos Spacek
,
P. L. Houtekamer
,
Normand Gagnon
,
Herschel L. Mitchell
, and
Laurent Michelin

Abstract

An updated global ensemble prediction system became operational at the Meteorological Service of Canada in July 2007. The new elements of the system include the use of 20 members instead of 16, a single dynamical core [the Global Environmental Multiscale (GEM) model], stochastic physical tendency perturbations and a kinetic energy backscatter algorithm, an ensemble Kalman filter with four-dimensional data handling, and a decrease from 1.2° to 0.9° in horizontal grid spacing. This system is compared with the former operational one using a variety of probabilistic measures. For global upper-air dynamical fields, the improvement in predictive skill for equivalent forecast quality is from 9 to 16 h around day 6. Precipitation forecasts, verified over Canada, are also significantly improved. The impact of each of the abovementioned new elements of the ensemble prediction system is also evaluated separately in a series of sensitivity experiments for which one given element is removed from the system.

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Ron McTaggart-Cowan
,
Leo Separovic
,
Martin Charron
,
Xingxiu Deng
,
Normand Gagnon
,
Pieter L. Houtekamer
, and
Alain Patoine

Abstract

The ability of a stochastically perturbed parameterization (SPP) approach to represent uncertainties in the model component of the Canadian Global Ensemble Prediction System was demonstrated in Part I of this investigation. The goal of this second step in SPP evaluation is to determine whether the scheme represents a viable alternative to the current operational combination of a multiphysics configuration and stochastically perturbed parameterization tendencies (SPPT). An assessment of the impact of each model uncertainty estimate in isolation reveals that, although the multiphysics configuration is highly effective at generating ensemble spread, it is often the result of differing biases rather than a reflection of flow-dependent error growth. Moreover, some of the members of the multiphysics ensemble suffer from large errors on regional scales as a result of suboptimal configurations. The SPP scheme generates a greater diversity of member solutions than the SPPT scheme in isolation, and it has an impact on forecast performance that is similar to that of current operational uncertainty estimates. When the SPP framework is combined with recent upgrades to the model physics suite that are only applicable in the stochastic perturbation context, the quality of global ensemble guidance is significantly improved.

Significance Statement

The stochastically perturbed parameterization (SPP) technique was introduced in Part I to represent model uncertainties in forecasts generated by an operational global ensemble prediction system. We focus here on the viability of this technique as a replacement for the system’s current uncertainty estimates: multiphysics and stochastic perturbations of physics tendencies. Despite the practical success of this combination, it suffers from physical inconsistencies and poor conservation properties. The adoption of SPP allows the ensemble to benefit from a recent set of model updates that couple with this new representation of model uncertainty to yield significant improvements in the quality of forecasts generated by the system.

Open access
Hai Lin
,
Normand Gagnon
,
Stephane Beauregard
,
Ryan Muncaster
,
Marko Markovic
,
Bertrand Denis
, and
Martin Charron

Abstract

Dynamical monthly prediction at the Canadian Meteorological Centre (CMC) was produced as part of the seasonal forecasting system over the past two decades. A new monthly forecasting system, which has been in operation since July 2015, is set up based on the operational Global Ensemble Prediction System (GEPS). This monthly forecasting system is composed of two components: 1) the real-time forecast, where the GEPS is extended to 32 days every Thursday; and 2) a 4-member hindcast over the past 20 years, which is used to obtain the model climatology to calibrate the monthly forecast. Compared to the seasonal prediction system, the GEPS-based monthly forecasting system takes advantage of the increased model resolution and improved initialization.

Forecasts of the past 2-yr period (2014 and 2015) are verified. Analysis is performed separately for the winter half-year (November–April), and the summer half-year (May–October). Weekly averages of 2-m air temperature (T2m) and 500-hPa geopotential height (Z500) are assessed. For Z500 in the Northern Hemisphere, limited skill can be found beyond week 2 (days 12–18) in summer, while in winter some skill exists over the Pacific and North American region beyond week 2. For T2m in North America, significant skill is found over a large part of the continent all the way to week 4 (days 26–32). The distribution of the wintertime T2m skill in North America is consistent with the influence of the Madden–Julian oscillation, indicating that a significant part of predictability likely comes from the tropics.

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Ron McTaggart-Cowan
,
Leo Separovic
,
Rabah Aider
,
Martin Charron
,
Michel Desgagné
,
Pieter L. Houtekamer
,
Danahé Paquin-Ricard
,
Paul A. Vaillancourt
, and
Ayrton Zadra

Abstract

Accurately representing model-based sources of uncertainty is essential for the development of reliable ensemble prediction systems for NWP applications. Uncertainties in discretizations, algorithmic approximations, and diabatic and unresolved processes combine to influence forecast skill in a flow-dependent way. An emerging approach designed to provide a process-level representation of these potential error sources, stochastically perturbed parameterizations (SPP), is introduced into the Canadian operational Global Ensemble Prediction System. This implementation extends the SPP technique beyond its typical application to free parameters in the physics suite by sampling uncertainty both within the dynamical core and at the formulation level using “error models” when multiple physical closures are available. Because SPP perturbs components within the model, internal consistency is ensured and conservation properties are not affected. The full SPP scheme is shown to increase ensemble spread to keep pace with error growth on a global scale. The sensitivity of the ensemble to each independently perturbed “element” is then assessed, with those responsible for the bulk of the response analyzed in more detail. Perturbations to surface exchange coefficients and the turbulent mixing length have a leading impact on near-surface statistics. Aloft, a tropically focused error model representing uncertainty in the advection scheme is found to initiate growing perturbations on the subtropical jet that lead to forecast improvements at higher latitudes. The results of Part I suggest that SPP has the potential to serve as a reliable representation of model uncertainty for ensemble NWP applications.

Significance Statement

Ensemble systems account for the negative impact that uncertainties in prediction models have on forecasts. Here, uncertain model parameters and algorithms are subjected to perturbations representing impact on forecast errors. By initiating error growth within the model calculations, the equally skillful members of the ensemble remain physically realistic and self-consistent, which is not guaranteed by other depictions of model error. This “stochastically perturbed parameterization” technique (SPP) comprises many small error sources, each analyzed in isolation. Each source is related to a limited set of processes, making it possible to determine how the individual perturbations affect the forecast. We conclude that SPP in the Canadian Global Ensemble Forecasting System produces realistic estimates of the impact of model uncertainties on forecast skill.

Open access
Claude Girard
,
André Plante
,
Michel Desgagné
,
Ron McTaggart-Cowan
,
Jean Côté
,
Martin Charron
,
Sylvie Gravel
,
Vivian Lee
,
Alain Patoine
,
Abdessamad Qaddouri
,
Michel Roch
,
Lubos Spacek
,
Monique Tanguay
,
Paul A. Vaillancourt
, and
Ayrton Zadra

Abstract

The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

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