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  • View in gallery
    Fig. 1.

    The rmse of the 500-hPa geopotential height over the northern extratropics (north of 20°N) depicted separately for the mean of the eight SEF (thin line) and eight GEM (thick line) forecasts. These results are based on forecasts initiated at 36-h intervals in January 2006, for a total of 21 cases. The verifying analyses are from a 4DVAR data assimilation cycle, which uses GEM to generate the background fields.

  • View in gallery
    Fig. 2.

    Mean over 15 days and four members of the global power spectrum of the SKEB wind forcing. The arrows indicate the wavenumber values of Lmin and Lmax; i.e., 40 and 128, respectively.

  • View in gallery
    Fig. 3.

    Solid lines: ensemble standard deviation for UEPS (black circles) and FEPS (no circle). Dashed lines: ensemble mean error for UEPS (black circles) and FEPS (no circle). The total energy norm is used and calculated over (a) the northern extratropics, (b) the tropics, and (c) the southern extratropics.

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    Fig. 4.

    (left) CRPS as a function of forecast lead time for temperature (K) at (a) 925 hPa, (c) geopotential height (m) at 500 hPa, and (e) zonal wind (m s−1) at 250 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of CRPS, with 5%–95% confidence intervals (CIs), between UEPS and FEPS for (b) temperature at 925 hPa, (d) geopotential height at 500 hPa, and (f) zonal wind at 250 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

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    Fig. 5.

    (left) Dispersion as a function of forecast lead time of (a) temperature at 925 hPa, (c) geopotential height at 500 hPa, and (e) zonal wind at 250 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of dispersions, with 5%–95% CIs, between UEPS and FEPS for (b) temperature at 925 hPa, (d) geopotential height at 500 hPa, and (f) zonal wind at 250 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

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    Fig. 6.

    (left) Bias as a function of forecast lead time for (a) temperature at 925 hPa, and (c) dewpoint depression at 925 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of biases, 5%–95% CIs, between UEPS and FEPS for (b) temperature at 925 hPa, and (d) dewpoint depression at 925 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

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    Fig. 7.

    (left) BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of BSS, with 5%–95% CIs, between UEPS and FEPS for accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

  • View in gallery
    Fig. 8.

    (left) Reliability component of the BSS of precipitation as a function of forecast lead time for 12 h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. (right) Resolution component of the BSS of precipitation as a function of forecast lead time for 12 h accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Solid lines are from UEPS, dashed lines from FEPS.

  • View in gallery
    Fig. 9.

    (a) Dispersion, (c) CRPS (m), and (e) reliability component as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-PTP. (b) Difference of dispersion, (d) CRPS, and (f) reliability component, 5%–95% CIs, between UEPS and UEPS-PTP for geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-PTP) performs better than UEPS-PTP (UEPS).

  • View in gallery
    Fig. 10.

    (a) Bias of temperature at 925 hPa, (c) dispersion of zonal wind at 850 hPa, and (e) CRPS of geopotential height (m) at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-SKEB. (right) Difference, 5%–95% CIs, between UEPS and UEPS-SKEB for (b) bias of temperature at 925 hPa, (d) dispersion of zonal wind at 850 hPa, and (f) CRPS of geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-SKEB) performs better than UEPS-SKEB (UEPS).

  • View in gallery
    Fig. 11.

    Mean power spectra of the 500-hPa geopotential height difference between UEPS and UEPS-SKEB (solid lines), and the difference between DIV and UEPS-SKEB (dashed lines). The mean is calculated over the 20 members and over the 21 cases of January 2006. The 20 × 21 = 420 differences are obtained by subtracting corresponding members which differ only with regard to the SKEB algorithm. Curves are shown for 1-, 3-, and 10-day forecasts. Arrows in the lower right indicate the main spectral range at which energy is injected when SKEB is applied.

  • View in gallery
    Fig. 12.

    (a) Bias of temperature at 925 hPa, (c) dispersion of zonal wind at 850 hPa, and (e) CRPS of geopotential height (m) at 500 hPa. Solid lines are from UEPS, dashed lines from DIV. (b) Difference, 5%–95% CIs, between UEPS and DIV for bias of temperature at 925 hPa, (d) dispersion of zonal wind at 850 hPa, and (f) CRPS of geopotential height at 500 hPa. Negative (positive) values indicate UEPS (DIV) performs better than DIV (UEPS).

  • View in gallery
    Fig. 13.

    (a) CRPS (in m), and (c) reliability component as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-4D. (b) Difference of CRPS, and (d) reliability component, 5%–95% CIs, between UEPS and UEPS-4D for geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-4D) performs better than UEPS-4D (UEPS).

  • View in gallery
    Fig. 14.

    (a) Dispersion and (c) CRPS (m) as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS-SKEB, dashed lines from RES. (b) Difference of dispersion and (d) CRPS, 5%–95% CIs, between UEPS-SKEB and RES for geopotential height at 500 hPa. Negative (positive) values indicate UEPS-SKEB (RES) performs better than RES (UEPS-SKEB).

  • View in gallery
    Fig. 15.

    (a) Bias, (c) dispersion, and (e) CRPS (K) as a function of forecast lead time for temperature at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-CONV. (b) Difference of bias, (d) dispersion, and (f) CRPS, 5%–95% CIs, between UEPS and UEPS-CONV for temperature at 500 hPa. Negative (positive) values indicate UEPS (UEPS-CONV) performs better than UEPS-CONV (UEPS).

  • View in gallery
    Fig. 16.

    (left) BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. Solid lines are from UEPS, dashed lines from UEPS-CONV. (right) Difference of BSS, 5%–95% CIs, between UEPS and UEPS-CONV for accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Negative (positive) values indicate UEPS (UEPS-CONV) performs better than UEPS-CONV (UEPS).

  • View in gallery
    Fig. 17.

    (left) Reliability component of BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. (right) Resolution component of the BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Solid lines are from UEPS, dashed lines from UEPS-CONV.

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Toward Random Sampling of Model Error in the Canadian Ensemble Prediction System

Martin CharronMeteorological Research Division, Environment Canada, Dorval, Québec, Canada

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Gérard PellerinCanadian Meteorological Centre, Environment Canada, Dorval, Québec, Canada

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Lubos SpacekMeteorological Research Division, Environment Canada, Dorval, Québec, Canada

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P. L. HoutekamerMeteorological Research Division, Environment Canada, Dorval, Québec, Canada

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Normand GagnonCanadian Meteorological Centre, Environment Canada, Dorval, Québec, Canada

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Herschel L. MitchellMeteorological Research Division, Environment Canada, Dorval, Québec, Canada

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Laurent MichelinÉcole Polytechnique, Paris, France

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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.

Corresponding author address: Dr. Martin Charron, Recherche en prévision numérique, Environment Canada, 2121, route Transcanadienne, Dorval, QC H9P 1J3, Canada. Email: Martin.Charron@ec.gc.ca

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.

Corresponding author address: Dr. Martin Charron, Recherche en prévision numérique, Environment Canada, 2121, route Transcanadienne, Dorval, QC H9P 1J3, Canada. Email: Martin.Charron@ec.gc.ca

1. Introduction

The Meteorological Service of Canada (MSC) operationally produces global ensemble forecasts since 1998 (Houtekamer et al. 1996). The Canadian ensemble prediction system (EPS) participates in a joint project with the National Centers for Environmental Prediction (NCEP) called the North American Ensemble Forecast System (NAEFS). These two centers operationally combine their ensemble forecasts to generate multiensemble-based products (see Candille 2009).

Both the multimodel and multiparameterization approaches were used until recently in the Canadian EPS (Pellerin et al. 2003). It has the appealing characteristic of representing the model error of the EPS in an efficient manner. Between 1999 and 2007, two different dynamical cores were utilized in the operational global EPS at MSC: the grid point Global Environmental Multiscale (GEM) model (Côté et al. 1998a,b) and the Spectral aux Élements Finis (SEF) model (Ritchie 1991; Ritchie and Beaudoin 1994). The 16-member ensemble consisted of 8 GEM members at a uniform grid spacing of 1.2° and 8 SEF members at a triangular truncation TL149. This former system will be referred to hereinafter as the former ensemble prediction system (FEPS).

However, in recent years, the level of development of the SEF model has been significantly less intensive than that of the GEM model, which is also used for the operational deterministic global and regional forecasts at MSC. It became apparent that the quality of the SEF members was lower than the quality of the GEM members, as shown in Fig. 1. In this figure, the January 2006 root-mean-square error of the 500-hPa geopotential height (Z500) over the northern extratropics is depicted separately for the means of the eight SEF and eight GEM forecasts. The error is calculated with respect to the four-dimensional variational data assimilation (4DVAR) analyses (Gauthier et al. 2007) from a data assimilation cycle, which uses GEM to generate the background fields. For forecasts in the 4–6-day range, the SEF models lag in quality by 12–24 h.

The problem of representing model error in an EPS is very often addressed by using a multimodel approach and/or a random sampling approach (i.e., random perturbations of otherwise identical members, each having an a priori equal probability of occurrence). With the former, different models can have different biases leading to clustered forecasts with little day-to-day variability in the predicted uncertainty. On the other hand, the random sampling approach is expected to be more robust to artificial multimodality, although it is not clear that the phase–space volume it encompasses is necessarily sufficient to adequately represent model error. For example, it is not certain that perturbing a given set of subgrid-scale parameterizations in a numerical forecast model will ever provide an adequate representation of the type of forecast error generated by that model. Note that this also applies to the multiparameterization approach. At this stage, model error representation in operational EPSs remains relatively empirical and choices are often based on practicality. The EPS of the European Centre for Medium-range Weather Forecasts (ECMWF) uses perturbations of model physical tendencies (Buizza et al. 1999; Palmer et al. 2009), as well as a stochastic kinetic energy backscatter (SKEB) algorithm (Shutts 2004, 2005; Berner et al. 2009). At NCEP, research is being performed to include a stochastic forcing on the total model tendencies—the forcing is sampled from the differences between perturbed members and a control run (Hou et al. 2006, 2008). At the Met Office (UKMO), model error is represented with the SKEB algorithm, random perturbations of some model parameters, and by stochastically injecting vorticity in regions of high convective available potential energy (Bowler et al. 2008, 2009).

In a first stage aimed at reducing artificial forecast multimodality and simplifying the development and maintenance of the Canadian EPS, the choice was made to reduce as much as possible the number of components and to introduce random sampling in the system.

On 10 July 2007, an important upgrade to the Canadian EPS was made (see Houtekamer et al. 2009; Gagnon et al. 2007; Houtekamer et al. 2007). The use of the SEF model in the global EPS was abandoned; the system is now based solely on the GEM dynamical core. The multiparameterization approach is still in use, and stochastic perturbations have been introduced into the EPS to partly account for model error representation. Stochastic perturbations of the tendencies of the physical parameterizations (inspired by Buizza et al. 1999) and the SKEB algorithm (Shutts 2005) are now used. These two stochastic components compensate for the loss of ensemble spread due to the use of a single dynamical core instead of two. The number of ensemble members has been increased from 16 to 20, and the uniform horizontal grid spacing is reduced from 1.2° to 0.9°.

The ensemble initial conditions are provided by an ensemble Kalman filter (EnKF) with first guess at appropriate time and a coherent use of time in the computation of the Kalman gain (Houtekamer and Mitchell 2005). In the EnKF, it is necessary to account for model error (Houtekamer et al. 2009). In both the old and the new configuration of the EnKF, an ensemble of isotropic random perturbation fields, with a prescribed covariance structure, is added every 6 h to the ensemble of estimated states to maintain sufficient spread in the ensemble. In the new EnKF configuration, model error is also simulated by the use of different parameterizations of unresolved processes by different members of the short-range forecast ensemble. This, in conjunction with the general reduction of the model error in the improved EnKF, permitted a reduction of the amplitude of the isotropic perturbations in the EnKF.

As will be shown below, the representativeness of the initial condition errors has been significantly improved. A multiplicative inflation procedure, used previously to increase the ensemble spread at the beginning of the medium-range forecasts, is no longer needed.

This paper describes the Canadian global EPS operational since 2007 [referred to as the updated EPS (UEPS)], documents its performance compared with the FEPS, and evaluates the impacts on probabilistic scores of some specific components of the new system. Section 2 describes the forecast models as well as the multiparameterization arrangements of the FEPS and the UEPS. Section 3 describes the stochastic parameterizations that are used in the UEPS. The EnKF used to generate the ensemble of initial conditions for the EPS is outlined in section 4. Comparisons between the previously operational suite and the current one are performed with a variety of probabilistic measures in section 5. The specific impacts of introducing stochastic physical tendency perturbations, the SKEB algorithm, time interpolation in the EnKF, reduced horizontal grid spacing, and the impact of using four different deep convection parameterizations are evaluated in section 6. Conclusions are drawn in section 7.

2. Model configurations

At MSC, 16-day forecasts with the global EPS are run operationally twice daily. In the following subsections, the former and the updated EPSs are described.

a. Former EPS

The former EPS (FEPS) is a multimodel forecast system with two dynamical cores: the grid point GEM model (Côté et al. 1998a,b) and the SEF model (Ritchie 1991; Ritchie and Beaudoin 1994). This system is described in Candille et al. (2007). A 16-member ensemble is formed by using 8 GEM members at a uniform grid spacing of 1.2° and 8 SEF members at a triangular truncation TL149. Different physical parameterizations or parameters are employed for convection, condensation, surface processes, and gravity wave drag (see Table 1a). Three different parameterized deep convection schemes are utilized by the different members: a Kuo scheme (Kuo 1974; Geleyn 1985), a modified Kuo-type scheme (called Kuo symmetric; Wagneur 1991), and the relaxed Arakawa–Schubert scheme (RAS; Moorthi and Suarez 1992). Two different planetary boundary layer (PBL) cloud schemes are used: 1) one called Turwet dealing with turbulence in partially saturated air (see Mailhot et al. 1998, section 7.1); and 2) another called Conres developed by C. Girard based on local instability (Mailhot et al. 1998, section 7.2). To represent shallow convection and clouds just above the PBL, a scheme called Kuo transient, which is based on the Kuo (1965) deep convection scheme, is used (Bélair et al. 2005). Two different surface parameterizations are used by different members: the Force-Restore (FR; Mailhot et al. 1997) and the Interaction Soil–Biosphere–Atmosphere (ISBA; Noilhan and Planton 1989) schemes. Different versions of the Sundqvist condensation scheme are employed: the standard Sundqvist scheme (Sundq.; Sundqvist et al. 1989), and a modified Sundqvist scheme (Mod. Sundq.; Dastoor 1994). Different values of a tunable parameter of the McFarlane (1987) orographic gravity wave parameterization [e/2; see McFarlane (1987), Eq. (2.30)] are also used. Different SEF models employ a two- or three-time-level semi-Lagrangian advection scheme, while GEM solely employs a two-time-level scheme.

b. Updated EPS

In the UEPS, all members employ the same gridpoint dynamical core (GEM) with a uniform latitude–longitude horizontal grid spacing of 0.9°. For all members, the number of vertical levels is 28, and the model vertical domain extends from the surface to 10 hPa. The terrain-following vertical coordinate (η) is described in Laprise and Girard (1990). As in FEPS, different combinations of a set of subgrid-scale physical parameterizations are employed in order to partly represent the model error component of the forecasts.

For convection, four different schemes are used: the three from the FEPS and the Kain and Fritsch (1993) scheme. Mixing lengths in the turbulent boundary layer are parameterized using the Blackadar (1962) scheme (as in FEPS; see also Delage and Girard 1992) as well as the Bougeault and Lacarrère (1989) scheme. Two different values for a parameter β linking the temperature (and humidity − ϕT) and the momentum (ϕM) stability functions of the parameterized vertical turbulent diffusion are employed. The stability functions are related to each other following (Delage and Girard 1992; Mailhot 1992; Delage 1997; Mailhot et al. 1998, section 2.1):
i1520-0493-138-5-1877-eq1
Table 1b provides an overview of the different versions of parameters/parameterizations used for each member in the updated MSC global EPS. The UEPS also uses two stochastic parameterizations that are described in the following sections.

3. Stochastic processes

Most ensemble systems suffer from insufficient spread. In FEPS, the use of different physical parameterizations/parameters does not provide sufficient ensemble spread to match the ensemble mean error of medium-range forecasts. Buizza et al. (1999) showed that a simple approach based on stochastically perturbing the total tendency provided by the physical parameterizations can improve probabilistic scores of ensemble forecasts. The approach of stochastically perturbing the physical tendencies is used in the UEPS and will be described in subsection 3b.

Global numerical models generally tend to overdissipate near the truncation limit. Shutts (2005, and references therein) argues that part of the kinetic energy that is overdissipated would, at sufficiently high resolution, be backscattered in turbulent inverse cascade processes. These processes are thought to influence, in a stochastic way, the larger scales. Shutts (2005) also argues that global models with current horizontal grid spacing of the order of 100 km do not capture this backscattering effect and that it could be beneficial to parameterize it, especially for ensemble forecasts. A version of the SKEB algorithm (Shutts 2005) is described in section 3c.

a. Generation of random fields on the sphere

The Buizza et al. (1999) and Shutts (2005) algorithms necessitate the use of random functions on the sphere. A simple method to generate such functions with specified space and time decorrelation scales is presented in Li et al. (2008). It consists of producing Markov chains that are the spectral coefficients of an expansion of spherical harmonics. An autocorrelated random field ψ is obtained from:
i1520-0493-138-5-1877-e31
with
i1520-0493-138-5-1877-e32
The independent variables λ, ϕ, and t are longitude, latitude, and time, respectively. The Yl,m are spherical harmonics, with l being the total horizontal wavenumber, and m the zonal wavenumber. The parameters Lmin and Lmax specify the spectral range of the random function. The parameter τ is the decorrelation time scale of the spectral coefficients, and Δt is a specified time interval (in this case, the model time step of 45 min). In the present paper, τ is chosen to be constant and independent of wavenumber. However, it would be possible to use τ = τ(l, m) in order to generate random fields with decorrelation times depending on spatial scales. The complex Rl,m are uncorrelated random processes with mean zero and variance, , unity. In the experiments shown in this paper, the Rl,m are Gaussian processes. To obtain a real ψ, one imposes al,m = (−1)ma*l,−m. With Lmin > 0, the global mean of the random function ψ(λ, ϕ, t) is μ. The constant σ is the specified global standard deviation of ψ. As is described in Li et al. (2008), a stretching can be applied to ψ (to get Ψ, the final perturbation factor of the physical tendencies) to ensure that the random field lies within specified bounds (say, Ψmin and Ψmax), and to modify its probability density function (PDF). The function Ψ is given by
i1520-0493-138-5-1877-e33
with Ψmaxμ = μ − Ψmin and β = −1.27. The reader is referred to Li et al. (2008) for further details. The same stretching as in Li et al. (2008) is applied here. The global standard deviation of Ψ is then close to 1.7σ.

b. Tendency perturbations of physical parameterizations

Buizza et al. (1999) showed that even a rather radical approach for representing model error in ensemble forecasting can contribute to improved probabilistic scores. They stochastically perturb the total tendency produced by all the subgrid-scale physical parameterizations. Tendencies on tiles of 10° × 10° are uniformly perturbed, and each tile is perturbed independently of the others with a constant multiplicative factor over a specified period of time.

In the present paper, the total momentum and temperature tendencies produced by all the subgrid-scale physical parameterizations of each ensemble member are stochastically perturbed by multiplying each member by different realizations of Ψ. The global mean of Ψ is μ = 1, and Ψ lies in the range [0.5, 1.5]. The other parameters in Eqs. (3.1) and (3.2) are: Lmin = 1, Lmax = 8, τ = 3 h, and σ = 0.135. Note that σ is the standard deviation of the unstretched field ψ, while the standard deviation of the stretched field Ψ is close to 0.23. The spectral range at which these perturbations are applied lies in the planetary and synoptic range. These scales are somewhat larger than what is used in Buizza et al. (1999). Perturbing only the planetary and synoptic scales seemed to maximize the impact. Tests also showed that results are relatively insensitive to a choice of τ in the range [3, 12] h. The approach described here has the advantage of providing a relatively smooth space–time perturbation method, and is essentially just a variant of Buizza et al. (1999). More recently, Palmer et al. (2009) introduced into the ECMWF EPS a perturbation approach for parameterized physical tendencies with random scaling patterns similar to that used for parameter perturbations in Li et al. (2008).

c. Stochastic kinetic energy backscatter algorithm

It is a well known fact that, in comparison to the real atmosphere, global numerical weather prediction (NWP) models overdissipate kinetic energy near their truncation scale. Numerical processes such as explicit and implicit dissipation inhibit energy upscaling. Also, parameterized subgrid-scale gravity wave tendencies due to breaking and parameterized deep convection are, in their current implementation status, unlikely to produce energy upscaling. As pointed out by Shutts (2005), a nonnegligible part of the turbulent inverse cascade process is likely inhibited because of this overdissipation. Shutts (2005) estimates that limitations in simulating inverse cascade processes in current NWP models could amount to a tendency error of the order of 5 m s−1 day−1 on the horizontal winds. He proposed the use of an SKEB algorithm to compensate for reduced energy upscaling due to overdissipation.

A stochastic representation of this upscaling of energy appears well suited for probabilistic predictions. Energy can be injected randomly near the model truncation scale to compensate for the absence of inverse cascade coming from the unresolved and highly dissipated scales (Shutts 2005). One could argue that simply reducing the explicit numerical diffusion would provide a simpler alternative. However, a nonnegligible part of the numerical diffusion present in the GEM model could be inherent in the off-centered time stepping and, maybe to a lesser extent, the interpolation procedure in the semi-Lagrangian advection scheme.

A variant of the SKEB algorithm is used in this paper. Shutts (2005) employs cellular automatons for generating random fields on the sphere. The present study employs the method described in section 3a which gives sufficient control over the characteristics of the random functions, especially the wavenumber spectral range and the decorrelation time scale of the SKEB forcing. Another difference pertains to the temperature forcing. Shutts (2004) defines a temperature forcing through an estimated available potential energy loss rate from the quasigeostrophic definition. In the present implementation, a more prosaic temperature forcing is employed for which no particular balance is assumed. This can be justified considering the relatively small scales of the forcing.

The horizontal wind (u, υ) and temperature (T) fields are stochastically forced through an added tendency term according to
i1520-0493-138-5-1877-e34
i1520-0493-138-5-1877-e35
i1520-0493-138-5-1877-e36
The small-scale forcing Su and Sυ can be chosen to directly excite selected modes. To force rotational modes, one can choose
i1520-0493-138-5-1877-e37
i1520-0493-138-5-1877-e38
Alternatively, one can choose to force divergent modes only:
i1520-0493-138-5-1877-e39
i1520-0493-138-5-1877-e310
Both types of forcing have been tested for this paper, but the UEPS uses forcing on the rotational modes (see section 6b for an explanation). Following Shutts (2005), the potential FΨ is given by
i1520-0493-138-5-1877-e311
where Δx = 100 km and Δt = 2700 s are a typical model grid length and time step, respectively. The constant α is a tuning parameter of order unity, Ψ is a random function defined in section 3a. The parameters used to obtain Ψ are Lmin = 40, Lmax = 128, τ = 36 h, μ = 0, and σ = 0.27. Note that although the model has 400 × 200 horizontal grid points, Lmax < 199 is chosen to control the noise at the truncation limit. All the realizations of Ψ lie within the bounds [−1, 1] and have a global standard deviation of 0.46.

The term (λ, ϕ, η, t) (m2 s−3) is an estimate of the local rate of change of kinetic energy resulting from explicit numerical horizontal diffusion and parameterized subgrid-scale gravity wave drag. It is estimated by taking the modulus of the inner product of the vectorial tendencies and the horizontal wind. Since the model longitudinal grid spacing decreases when approaching the poles, this field is smoothed using a Gaussian filter with full width at half maximum of 240 km.

A time mean global spectrum of the SKEB horizontal wind forcing averaged between 100 and 300 hPa is shown in Fig. 2. The spectral elements are mostly located within the range [Lmin, Lmax], indicating that the forcing is exerted on the small scales.

The stochastic temperature forcing ST is defined without assuming a specific balance:
i1520-0493-138-5-1877-e312
where αT = 2 and cp is 1004 J kg−1 K−1.

4. Global initial conditions from an ensemble Kalman filter

Since 2005, an ensemble Kalman filter has been operational at MSC to provide the initial conditions used to initialize the EPS. Significant improvements to the EnKF were implemented on 10 July 2007 at the same time as the EPS modifications described in the current paper. The main modifications were:

  1. a decrease of the model horizontal grid spacing from 1.2° to 0.9° as in the EPS (Houtekamer et al. 2007 and Gagnon et al. 2007);

  2. the use of different configurations of the GEM model instead of a unique one to produce the trial fields (Houtekamer et al. 2009); and

  3. the introduction of time interpolation into the forward operator (Houtekamer and Mitchell 2005).

Hereafter, this new assimilation system will be referred to as EnKF2007. In our current study, the UEPS was initialized using analyses coming from EnKF2007; while the FEPS used the operational analyses produced by the EnKF version implemented in December 2005 (hereafter EnKF2005; see the descriptions in Houtekamer et al. 2005; Houtekamer and Mitchell 2005). It should be noted that in an operational context, both systems use either a short cutoff of 3 h (to provide initial conditions to the medium-range ensemble forecasts) or a long cutoff of 12 h (for continuous data assimilation cycles) for data ingestion. In this study, the EnKF2007 system long cutoff analyses are used for UEPS initialization while the EnKF2005 short cutoff analyses are the initial conditions for the FEPS. Therefore the UEPS benefits from superior initial conditions coming from a more recent assimilation system using a longer data cutoff. This can be expected to affect the results presented in section 5, but not those in section 6.

5. Relative performance of UEPS versus FEPS

A comparison between the performance of the UEPS (including all the above mentioned changes) and the FEPS has been made using a variety of measures for January 2006. Fifteen-day ensemble forecasts were initiated every 36 h starting at 0000 UTC 1 January 2006. The resulting 21 ensemble forecasts have been objectively verified for each system. The ensemble standard deviation and root-mean-square (rms) error of the ensemble mean, averaged over the northern extratropics (north of 20°N), the southern extratropics (south of 20°S), as well as the tropics (20°S to 20°N), are shown for both EPSs in Fig. 3. The so-called total energy norm (), where
i1520-0493-138-5-1877-e51
is used as a metric (see, e.g., Errico 2000). The normalization factor K equals Ω ln(100/1000) (with Ω being the area of a specified domain). The fields ue and Te denote the horizontal wind and temperature departures, respectively. The constants cp = 1004 J kg−1 K−1, and Tr = 300 K, are the air heat capacity at constant pressure, and a reference temperature, respectively. The vertical integral is performed from 1000 to 100 hPa, and the horizontal integral is done over the above specified domains. When calculating rms errors, the departure fields are calculated using the difference between the members (or the ensemble mean) and the Canadian 4DVAR analyses. These analyses at a horizontal grid spacing of 0.9° (400 × 200 grid points) are interpolated to the appropriate grid spacing (300 × 150 grid points) when used to evaluate the FEPS. When calculating ensemble standard deviations, the departure fields are the difference between the realizations and the ensemble mean. All the results presented in this paper are based on giving equal weight to all ensemble members.

Figure 3 shows that the amplitude of the initial perturbations in the UEPS is noticeably reduced compared with those of the FEPS. The initial decrease in spread over the first 24 h in FEPS, particularly evident in the tropics but also present in the northern and southern extratropics, is not observed in UEPS (solid lines). This indicates that the initial perturbations in UEPS are not unrealistically large nor do they decay over the first 24 h, as seems to be the case in FEPS.

The quality of the ensemble mean (dashed lines) in UEPS is in general increased for forecast lead times up to 5 days in the northern extratropics, up to around 8 days in the southern extratropics, and up to 15 days in the tropics where the quality of the ensemble mean has been particularly improved. The forecasted spread of UEPS is greater than that of FEPS after day one, leading to a closer correspondence between the ensemble mean error and ensemble spread.

The mean rms error of the individual ensemble members (not shown) is somewhat greater in UEPS than in FEPS after day one. In part because of the increase in resolution and in part because of the use of stochastic forcing, it is expected that the internal variability of UEPS should be larger than that of FEPS. This is consistent with a larger rms error for the individual members and with the larger ensemble standard deviation for UEPS.

A detailed global validation against observations from radiosondes (instead of analyses as done above) also shows similar improvements for most of the dynamical variables. Observations at 374 stations (leading to more than 6000 profiles over a month when sampled each 36 h) distributed over the globe are employed. Using the bootstrap method with temporal blocks of 36 h and tools described in Candille et al. (2007), the statistical significance of the differences between the output of UEPS and FEPS for a variety of probabilistic scores can be assessed.

The continuous ranked probability score (CRPS; see Hersbach 2000) of the temperature at 925 hPa (T925), geopotential height at 500 hPa (Z500), and the zonal wind at 250 hPa (U250) in January are shown in Fig. 4 for UEPS and FEPS. An improved quality of about 12 h is observed in UEPS for lead times less than 10 days for Z500 and U250. For T925, an improvement is observed up to day 7, but a degradation occurs beyond day 12. Figure 4 also depicts the difference of the scores with 5%–95% confidence intervals using the bootstrap method. It shows that the improvements for Z500 and U250 are significant for forecast lead times ranging from 1 to 10 days (even greater for U250). For T925, the improvements up to day 7, as well as the degradation beyond day 12, are significant. The CRPS can be decomposed into a resolution and a reliability component. Both are significantly improved for Z500 in UEPS over FEPS up to day 10 (not shown). The reliability of U250 is significantly improved in UEPS up to day 15, while the resolution is significantly improved up to day 10 (not shown). For T925, the improvements in reliability and resolution are significant up to day 7 (not shown).

The reduced centered random variable y is defined as
i1520-0493-138-5-1877-e52
For each realization (any observation of any radiosonde at a given pressure level), there is one observation o, one ensemble mean m, and one ensemble standard deviation σf . The observation error σo is taken to be the same for all realizations and depends on the instrumentation error and includes representativeness errors. Candille and Talagrand (2008) further discuss the impact of observational error in the verification of an EPS. The bias is defined as the average of y over all the realizations, and the dispersion is defined as the standard deviation of y. A perfectly reliable ensemble system has zero bias and a dispersion of 1. The dispersion of T925, Z500, and U250 in UEPS shows significant improvements over FEPS for forecast lead times up to 8, 9, and 15 days, respectively (Fig. 5). The biases of geopotential height fields and winds are not significantly changed (not shown), but Fig. 6 shows that warmer forecasts at T925 appear in UEPS and significantly worsen (improve) the bias compared to FEPS for lead times greater than five days (less than three days). Figure 6 also shows that UEPS has a significantly improved humidity (dewpoint depression) bias at 925 hPa for forecasts up to day 15.

Verification of precipitation forecasts over Canada has been performed at observation points for 200 synoptic stations. Accumulations over 12 h have been evaluated using the Brier skill score (BSS; see, e.g., Jolliffe and Stephenson 2003) for UEPS and FEPS. Figure 7 shows that for the 1-mm threshold, the skillful forecast range has been extended from 2 days in FEPS to 4 days in UEPS, and the improvement is mostly significant over the 15-day forecast range. For the 5- and 10-mm thresholds, the improvements are clearly significant for forecasts shorter than four days, but results are noisier because of the smaller sample size at these thresholds. No significant improvements have been detected for thresholds larger than 10 mm (not shown). The BSS can be decomposed into its reliability (negatively oriented) and resolution (positively oriented) components provided that all samples are drawn from the same distribution (see Hamill and Juras 2006). The reliability measures the ability of a system to reproduce the sample climatology, while the resolution measures the ability of a system to correctly forecast distinguished events. Figure 8 shows that for small rain amounts (1-mm threshold), the reliability of UEPS is clearly improved over FEPS for the whole forecast range, and the resolution is improved up to day 6. For larger rain accumulations (5 and 10 mm), the reliability and resolution improvements in UEPS over FEPS are mainly apparent up to 4–5-day forecasts.

6. Impact of some system subcomponents on scores

To better understand the specific impacts of some of the new elements introduced into the Canadian global EPS, sensitivity experiments were performed for January 2006 in which a single component was removed from the system. This procedure allows the contribution of specific elements of UEPS to its general behavior to be isolated. The reader is referred to Table 2 for a summary of the performed experiments.

a. Tendency perturbations of physical parameterizations

Removing the stochastic perturbations of the total tendencies of horizontal winds, temperature, and humidity generated by all the physical parameterizations from UEPS (referred to as experiment UEPS-PTP) produces significant changes to some probabilistic scores. The Z500 bias is significantly deteriorated in UEPS-PTP for forecast lead times shorter than 5 days, while the T850 bias seems marginally improved during the second forecast week (not shown). In UEPS-PTP, the dispersion of most upper-air dynamical variables is significantly degraded compared to UEPS for most of the forecast lead times (see Fig. 9 for the geopotential height at 500 hPa). The CRPS of Z500 is marginally, but significantly, degraded up to 4–5-day forecasts in UEPS-PTP, and is significantly degraded during the second week of forecast (Fig. 9). The reliability component of the CRPS for Z500 until day 13 is significantly degraded in UEPS-PTP compared to UEPS (Fig. 9). The resolution component of the CRPS is also significantly degraded in UEPS-PTP during the week two forecasts for U250 and Z500 (not shown). This last result implies that stochastically perturbing the tendencies produced by the model parameterizations increases the ability of the EPS to distinguish and represent events during the second week of the forecasts. It must be noted however that the performance of the system for week two remains relatively low.

b. Stochastic kinetic energy backscatter algorithm

Another sensitivity experiment was performed in which the SKEB algorithm was not used (referred to as UEPS-SKEB). Results for January 2006 indicate that the T925 bias is significantly degraded when using the SKEB algorithm (Fig. 10). In the current SKEB implementation, low-level temperature biases are introduced, but the physical mechanism leading to these biases is still unclear. It is known, however, that stochastically perturbing a nonlinear system can change its mean state (see, e.g., Palmer 2003). The dispersion is significantly degraded in UEPS-SKEB with respect to UEPS for 850-hPa zonal winds at all lead times (see Figs. 10c,d), Z500 up to a lead time of 9 days (not shown), and T850 (lead times ranging from day 2 to 7, not shown). The CRPS for Z500 is slightly but significantly degraded in UEPS-SKEB up to a lead time of 6 days, and even more degraded for early week two forecasts (for lead times ranging from 9 to 12 days; Figs. 10e,f). The reliability component of the CRPS is significantly degraded in UEPS-SKEB up to lead times of 10 days for U250 and Z500 (not shown). The U250 resolution component is improved in UEPS-SKEB over UEPS for short-term forecasts (less than 3 days), but degraded for early week two forecasts (not shown). This week two degradation in UEPS-SKEB occurs for Z500 as well (not shown). The same type of behavior was observed in UEPS-PTP, indicating that both types of stochastic perturbations contribute to improve week two ensemble forecasts. However, it appears that the resolution component of the CRPS for short-range forecasts can be degraded for some fields when stochastic forcing is employed. This behavior can become problematic in a data assimilation context when trying to represent very short-range model error with such stochastic forcing (Houtekamer et al. 2009).

The experiment UEPS employs the SKEB algorithm with forcing on the rotational component of the horizontal winds. To test the impact of that specific choice over forcing the divergent component of the winds, a sensitivity experiment (DIV) has been performed in which the wind component of the SKEB forcing is applied to the divergent modes. One can visualize the backscattering effect of the algorithm on dynamical fields by plotting the power spectrum of the difference of each individual member with and without SKEB, the rest being identical. Figure 11 depicts the ensemble mean of such spectra for 1-, 3-, and 10-day forecasts, averaged over the 21 cases of January 2006. It shows that forcing the divergent component of the winds (DIV experiment) has a very weak impact for lead times of 3 days and less, compared to forcing the rotational component (UEPS). For longer lead time periods (10 days), forcing the rotational component of the winds still has more impact than forcing the divergent component, but the difference is not as strong as for the shorter lead times. This result is in accordance with the well-known principle that rotational modes are more likely to inverse cascade than divergent modes (see, e.g., Pedlosky 1987, section 3.27). In UEPS, the backscattering effect of forcing winds at total wavenumbers ranging from 40 to 128 takes about 3 to 10 days to impact the synoptic wavenumber range.

Figure 12 compares T925 biases, U850 dispersion, and Z500 CRPS for the experiments using rotational forcing (UEPS) and divergent forcing (DIV). It appears that UEPS is significantly warmer than DIV at 925 hPa. This leads to a smaller bias in UEPS for short-range forecasts (1 to 2 days) and a larger bias for longer-range forecasts (4 to 15 days). For reasons still unclear, rotational SKEB forcing generates warmer low-level temperatures than divergent SKEB forcing. The U850 dispersion is significantly more realistic with rotational SKEB forcing (UEPS) than with divergent SKEB forcing (DIV), consistent with spectra of the 500-hPa geopotential height differences shown in Fig. 11. Figure 12 also shows that the CRPS of Z500 is slightly better in UEPS until days 5–6, and that week two is also improved over the DIV experiment. In summary, the stochastic physical tendency perturbations and SKEB mostly improve the reliability of the forecast by acting on the ensemble dispersion.

c. Four-dimensional handling of observations in the EnKF

To produce the analyses for the UEPS, time interpolation of the trial fields is done to assimilate the observations at their time of validity. The length of the assimilation time window in EnKF2007 is 6 h as in EnKF2005, however the trial field values at 3, 4.5, 6, 7.5, and 9 h are linearly interpolated in time to match the observation time. This allows assimilation of more observations inside the 6-h window because the restriction of EnKF2005 regarding the assimilation of some data types [aircraft, satellite winds (satwind), Advanced Microwave Sounding Unit (AMSU), wind profilers] to the central 3-h window can be abandoned. It should be noted that in the previous assimilation system (EnKF2005), all selected observations were assumed to be valid in the middle of the assimilation window (central analysis time).

The impact on the medium-range forecasts of improving the temporal handling of observations was evaluated. An assimilation cycle was done with EnKF2007 but with time interpolation deactivated and with a corresponding more restrictive selection of observations (hereafter UEPS-4D). In Fig. 13, the CRPS and reliability of 500-hPa geopotential height forecasts initialized with and without 4D observation handling (UEPS and UEPS-4D, respectively) are shown. A small improvement, significant up to day 3, is noted when 4D handling is employed. The improvement in the short range is also noted at all levels for geopotential heights and temperature (not shown). For longer lead times, the signal is relatively neutral for both fields. No significant improvement is noted for winds and humidity (not shown).

d. Horizontal resolution

The horizontal grid spacing of the Canadian global operational EPS went from 1.2° to 0.9° in July 2007. The impact of this specific change can be evaluated by comparing experiments UEPS-SKEB with RES (see Table 2). This comparison has been performed without employing the stochastic kinetic energy backscattering algorithm whose behavior is resolution dependent. The increase in horizontal resolution leads naturally to an increase in ensemble standard deviation (or dispersion) because of the larger internal variability it produces at the high end of the spectrum. Figure 14 shows that this increase in dispersion for Z500 takes place over the entire period of the 15-day forecasts. It is clearly statistically significant until day 10, and marginally significant afterward. This figure also shows that the increase in horizontal resolution results in a significant gain in CRPS for Z500 up to day 7 of the forecasts. After day 7, this change is mostly not statistically significant.

e. Using four different parameterizations for deep convection

The UEPS employs four deep convection parameterizations: Kuo (Kuo 1974; Geleyn 1985), Kuo symmetric (Wagneur 1991), relaxed Arakawa–Schubert (Moorthi and Suarez 1992), and Kain–Fritsch (Kain and Fritsch 1993). The Kain–Fritsch scheme is the only deep convection scheme used by the operational deterministic global (Bélair et al. 2009) and regional GEM models run at the MSC. It has been shown (H. Lin 2008, personal communication) that the use of four schemes for deep convection significantly improves the representation of the tropical Madden–Julian oscillation (MJO). For MJO forecasts, individual member scores are best using the relaxed Arakawa–Schubert scheme, then in order of MJO forecast quality, Lin ranked the schemes as follows: Kain–Fritsch, Kuo, and Kuo symmetric. The impact of using this multiparameterization approach for deep convection can be assessed by employing a single scheme in a test experiment. Experiment UEPS-CONV employs solely the Kain–Fritsch/Conres/Kuo–Trans triplet (see Table 1b). In terms of forecast scores of dynamical fields against observations, the main impact of this change is on temperature in the midtroposphere. Figure 15 shows that the mean temperature at 500 hPa is colder in UEPS than in UEPS-CONV. This leads to a degraded mean bias for UEPS until day 5, and an improved mean bias after day 7. In UEPS, the use of different deep convection schemes causes bias compensation by systematic clustering, especially in the tropics (not shown), a feature not necessarily desirable in an EPS regarding the dispersion. The forecast dispersion should be representative of the uncertainty regarding the future state of the atmosphere, and this uncertainty is poorly sampled with different biases of individual deep convection parameterizations. However, objective scores are nevertheless generally improved when using this approach. Figure 15 also depicts the gain in dispersion at T500 when using four convection schemes instead of one. This gain is significant over the entire forecast range. The CRPS for T500 is marginally improved for the first four forecast days in UEPS over UEPS-CONV, and significantly improved after day nine (see also Fig. 15).

The impact on precipitation scores over Canada of using a single convection scheme instead of four is slightly, but consistently, negative, up to about 4–5-day forecasts. This degradation is statistically significant for 12-h accumulations with thresholds at 1, 5, and 10 mm, as can be seen in Fig. 16. For forecast ranges larger than five days, the differences are not statistically significant. When decomposing the BSS into its reliability and resolution components, it is seen (Fig. 17) that it is mainly the reliability for “moderate” (5-mm threshold) to “high” (10-mm threshold) rain fall rates that is degraded when using a single convection scheme. The quality of the resolution component seems mostly unchanged.

7. Summary and conclusions

Since 10 July 2007, the operational global EPS at the Meteorological Service of Canada produces medium-range forecasts using a single dynamical core (GEM) at 0.9° horizontal grid spacing. A new multiparameterization arrangement has been set up for 20 ensemble members (see Table 1b). This updated system employs two types of stochastic physical perturbations to partly represent the effect of model errors in forecasts. The subgrid-scale physical tendencies produced by each member are multiplied by a realization of a global random field with amplitude in the range [0.5, 1.5] and with specified spatial and temporal decorrelation scales. In addition, a stochastic kinetic energy backscatter algorithm that injects energy in the total wavenumber range [40, 128] has been implemented. These two stochastic algorithms contribute significantly, in particular, to improving the system’s dispersion and reliability.

When compared with the previous operational global EPS, gains in global predictive skill of dynamical fields are significant. For example, there was a 16-h gain in predictive skill for 6-day temperature forecasts at 925 hPa, as measured by the CRPS. Similarly, there was a 12-h gain in predictive skill for geopotential height at 500 hPa, and a 9-h gain for the zonal wind at 250 hPa. Initial condition perturbations in the updated EPS are smaller by about 30% in the tropics and 20% in the extratropics when measured by the total energy norm. The former EPS also suffered from a decrease in ensemble spread over the first 24 h of integration, especially in the tropics. This initial decrease in spread does not happen in the updated EPS. Precipitation forecasts, verified over Canada with the BSS, are also significantly improved for 12-h accumulations up to 10 mm for forecasts of 5 days or less (larger amounts are not significantly improved). Both the reliability and resolution components of the BSS are improved compared to the former EPS. On the negative side, the low-level temperature bias is mostly degraded in the updated EPS because of overly warm forecasts beyond day 5.

Both stochastic algorithms (physical tendency perturbations and stochastic kinetic energy backscattering) contribute in a similar fashion to the behavior of the updated EPS. They improve the system’s dispersion and reliability for most of the forecast range. Their use also improves the CRPS for geopotential height at 500 hPa up to about day 5 (because of a better reliability) and for week two (because of both better reliability and resolution). However, the backscattering algorithm accounts for about half of the degraded low-level temperature bias compared with the former EPS. On the other hand, the tendency perturbations of physical parameterizations have a positive impact on the Z500 bias for relatively short-range forecasts. The role of these two stochastic algorithms on forecast biases needs to be studied further.

The updated EPS is initialized with an EnKF whose forward operator includes time interpolation, thus permitting a fully 4D assimilation of observations. This has a positive impact on the CRPS of the 500-hPa geopotential height (mainly its reliability component) and is felt up to days 3–4.

The decrease in horizontal grid spacing from 1.2° to 0.9° also contributes significantly to the improvement in 500-hPa geopotential height scores. When tested at a grid spacing of 1.2°, the updated EPS performed significantly worse during the first forecast week, and suffered from worsened underdispersion problems. It is expected that as resolution continues to increase, the need for stochastic physical processes, in particular SKEB, will be reduced, since model variability will increase at the high end of the spectrum.

As was the case for the former EPS, the updated EPS utilizes a multiparameterization approach for deep convection. The former EPS used two Kuo-type schemes, and the relaxed Arakawa–Schubert scheme, while the updated EPS uses these three and the Kain–Fritsch scheme. The impact of this multiparameterization choice on the system’s quality has been evaluated by comparing the updated EPS with one using only the Kain–Fritsch scheme. The impact of the multiparameterization approach on dynamical fields is most apparent on midtropospheric temperatures. The CRPS of the 500-hPa temperature is significantly improved for a forecast range larger than 8 days, and is marginally improved up to day 5 when using several convection schemes instead of a single one. The precipitation scores, measured by the BSS, are slightly improved up to day 4 for 12-h accumulation amounts of 10 mm or less when using several deep convection schemes. The reliability component is improved, while the resolution component is mostly unchanged.

For an overview of the main results presented in this paper, the reader is referred to Tables 3 and 4 describing respectively, the variations of Z500, T850, and U850 CRPS and dispersion for 5-day forecasts and for all the experiments. It can be seen that the increase in horizontal resolution is an important element that contributes to improving the CRPS and dispersion for Z500 and T850. The SKEB algorithm is the main element contributing to the improvement of U850 dispersion. Note that for the CRPS (Table 3), the contribution of the sum of all the tested subcomponents accounts for slightly more than half of the total improvement of the system. The rest of the improvement could be attributed to, among other things, the removal of the SEF model, the use of 20 members instead of 16, and a longer cutoff for data assimilation. Note however that for the dispersion (Table 4), the sum of the contributions of all the tested subcomponents accounts for almost the entire improvement.

For future versions of the Canadian global EPS, efforts will be made to reduce biases and improve the resolution component of the forecast quality. This will imply replacing aging parameterizations at our center that are considered not state of the art, including the radiation parameterization, the force-restore surface scheme, and Kuo-type convection schemes. Work is in progress to introduce a Charney–Phillips vertical staggering. In addition, the vertical domain of the model will be extended into the middle atmosphere to improve the stratospheric and tropospheric model dynamics.

From a practical perspective, having to maintain different state-of-the-art dynamical cores and several subgrid-scale parameterizations in a single medium-size research division has proven to be extremely challenging. The adoption of a single dynamical core in the Canadian EPS configuration allows the consolidation of resources. However, the quality of the system could not be improved, and was in fact degraded, when a single set of subgrid-scale parameterizations was employed (with and without stochastic perturbations). Hence, it has not so far been possible to avoid the multiparameterization approach in the Canadian EPS. This use of statistically nonidentical ensemble members can lead to potential problems such as artificial multimodality (clustering) of the forecasts due to different parameterizations having different biases and more generally different performance. To alleviate this problem, one could argue that the use of some form of stochasticity in conjunction with a single set of parameterizations could be beneficial, provided that ensemble dispersion remains sufficient. In most ensemble prediction systems, the approach followed when stochastically perturbing forecast models is still relatively crude and deserves a great deal of attention. In the longer term, the use of physical parameterizations conceived and built to incorporate the notion of probability and random realization (see, e.g., Plant and Craig 2008) would seem more satisfying than the ad hoc perturbations of the total tendencies produced by deterministic subgrid-scale parameterizations.

Acknowledgments

The authors thank Guillem Candille for several of the verification tools used in this paper, and for fruitful discussions related to objective verification. They also thank two anonymous reviewers and Thomas M. Hamill, the editor, for comments that resulted in improvements to the manuscript.

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Fig. 1.
Fig. 1.

The rmse of the 500-hPa geopotential height over the northern extratropics (north of 20°N) depicted separately for the mean of the eight SEF (thin line) and eight GEM (thick line) forecasts. These results are based on forecasts initiated at 36-h intervals in January 2006, for a total of 21 cases. The verifying analyses are from a 4DVAR data assimilation cycle, which uses GEM to generate the background fields.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 2.
Fig. 2.

Mean over 15 days and four members of the global power spectrum of the SKEB wind forcing. The arrows indicate the wavenumber values of Lmin and Lmax; i.e., 40 and 128, respectively.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 3.
Fig. 3.

Solid lines: ensemble standard deviation for UEPS (black circles) and FEPS (no circle). Dashed lines: ensemble mean error for UEPS (black circles) and FEPS (no circle). The total energy norm is used and calculated over (a) the northern extratropics, (b) the tropics, and (c) the southern extratropics.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 4.
Fig. 4.

(left) CRPS as a function of forecast lead time for temperature (K) at (a) 925 hPa, (c) geopotential height (m) at 500 hPa, and (e) zonal wind (m s−1) at 250 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of CRPS, with 5%–95% confidence intervals (CIs), between UEPS and FEPS for (b) temperature at 925 hPa, (d) geopotential height at 500 hPa, and (f) zonal wind at 250 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 5.
Fig. 5.

(left) Dispersion as a function of forecast lead time of (a) temperature at 925 hPa, (c) geopotential height at 500 hPa, and (e) zonal wind at 250 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of dispersions, with 5%–95% CIs, between UEPS and FEPS for (b) temperature at 925 hPa, (d) geopotential height at 500 hPa, and (f) zonal wind at 250 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 6.
Fig. 6.

(left) Bias as a function of forecast lead time for (a) temperature at 925 hPa, and (c) dewpoint depression at 925 hPa. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of biases, 5%–95% CIs, between UEPS and FEPS for (b) temperature at 925 hPa, and (d) dewpoint depression at 925 hPa. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 7.
Fig. 7.

(left) BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. Solid lines are from UEPS, dashed lines from FEPS. (right) Difference of BSS, with 5%–95% CIs, between UEPS and FEPS for accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Negative (positive) values indicate UEPS (FEPS) performs better than FEPS (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 8.
Fig. 8.

(left) Reliability component of the BSS of precipitation as a function of forecast lead time for 12 h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. (right) Resolution component of the BSS of precipitation as a function of forecast lead time for 12 h accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Solid lines are from UEPS, dashed lines from FEPS.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 9.
Fig. 9.

(a) Dispersion, (c) CRPS (m), and (e) reliability component as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-PTP. (b) Difference of dispersion, (d) CRPS, and (f) reliability component, 5%–95% CIs, between UEPS and UEPS-PTP for geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-PTP) performs better than UEPS-PTP (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 10.
Fig. 10.

(a) Bias of temperature at 925 hPa, (c) dispersion of zonal wind at 850 hPa, and (e) CRPS of geopotential height (m) at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-SKEB. (right) Difference, 5%–95% CIs, between UEPS and UEPS-SKEB for (b) bias of temperature at 925 hPa, (d) dispersion of zonal wind at 850 hPa, and (f) CRPS of geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-SKEB) performs better than UEPS-SKEB (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 11.
Fig. 11.

Mean power spectra of the 500-hPa geopotential height difference between UEPS and UEPS-SKEB (solid lines), and the difference between DIV and UEPS-SKEB (dashed lines). The mean is calculated over the 20 members and over the 21 cases of January 2006. The 20 × 21 = 420 differences are obtained by subtracting corresponding members which differ only with regard to the SKEB algorithm. Curves are shown for 1-, 3-, and 10-day forecasts. Arrows in the lower right indicate the main spectral range at which energy is injected when SKEB is applied.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 12.
Fig. 12.

(a) Bias of temperature at 925 hPa, (c) dispersion of zonal wind at 850 hPa, and (e) CRPS of geopotential height (m) at 500 hPa. Solid lines are from UEPS, dashed lines from DIV. (b) Difference, 5%–95% CIs, between UEPS and DIV for bias of temperature at 925 hPa, (d) dispersion of zonal wind at 850 hPa, and (f) CRPS of geopotential height at 500 hPa. Negative (positive) values indicate UEPS (DIV) performs better than DIV (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 13.
Fig. 13.

(a) CRPS (in m), and (c) reliability component as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-4D. (b) Difference of CRPS, and (d) reliability component, 5%–95% CIs, between UEPS and UEPS-4D for geopotential height at 500 hPa. Negative (positive) values indicate UEPS (UEPS-4D) performs better than UEPS-4D (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 14.
Fig. 14.

(a) Dispersion and (c) CRPS (m) as a function of forecast lead time for geopotential height at 500 hPa. Solid lines are from UEPS-SKEB, dashed lines from RES. (b) Difference of dispersion and (d) CRPS, 5%–95% CIs, between UEPS-SKEB and RES for geopotential height at 500 hPa. Negative (positive) values indicate UEPS-SKEB (RES) performs better than RES (UEPS-SKEB).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 15.
Fig. 15.

(a) Bias, (c) dispersion, and (e) CRPS (K) as a function of forecast lead time for temperature at 500 hPa. Solid lines are from UEPS, dashed lines from UEPS-CONV. (b) Difference of bias, (d) dispersion, and (f) CRPS, 5%–95% CIs, between UEPS and UEPS-CONV for temperature at 500 hPa. Negative (positive) values indicate UEPS (UEPS-CONV) performs better than UEPS-CONV (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 16.
Fig. 16.

(left) BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. Solid lines are from UEPS, dashed lines from UEPS-CONV. (right) Difference of BSS, 5%–95% CIs, between UEPS and UEPS-CONV for accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Negative (positive) values indicate UEPS (UEPS-CONV) performs better than UEPS-CONV (UEPS).

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Fig. 17.
Fig. 17.

(left) Reliability component of BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (a) 1, (c) 5, and (e) 10 mm, respectively. (right) Resolution component of the BSS of precipitation as a function of forecast lead time for 12-h accumulation greater than (b) 1, (d) 5, and (f) 10 mm, respectively. Solid lines are from UEPS, dashed lines from UEPS-CONV.

Citation: Monthly Weather Review 138, 5; 10.1175/2009MWR3187.1

Table 1.

(a) Parameterizations/parameters for the former EPS. Members 1 to 8 employ SEF, and members 9 to 16 employ GEM. (b) Parameterizations/parameters for the updated EPS. All members employ GEM. Kain–Fritsch has been shortened to KF and Bougeault–Lacarrère has been shortened to BL.

Table 1.
Table 2.

Main characteristics of the experiments.

Table 2.
Table 3.

Summary of the CRPS variation between the different experiments for Z500, T850, and U850 at day 5.

Table 3.
Table 4.

Summary of the dispersion variation between the different experiments for Z500, T850, and U850 at day 5.

Table 4.
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