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    Peak winds at 1 hPa over the winters (December–February) of 1990–2010 from the ERA-Interim reanalysis (gray shaded in kt as indicated on the grayscale bar; 1 kt = 0.5144 m s−1). Mean winds over the period are plotted with short barbs, long barbs, and pennants representing 5, 10, and 50 kt, respectively. This plotting convention for winds is used in all figures. Barbs are plotted in black and white for readability only.

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    Schematic representation of the UBN technique applied in the context of Charney and Phillips (1953) vertical discretization and the GEM state variables. The upper and lower model boundaries are represented by heavy solid lines, with “momentum” levels in dashed lines and “thermodynamic” levels in solid lines. The nesting zone (dark gray shading) extends above the model domain using a similar discretization strategy, and the optional blending zone (light gray shading) is used to relax the model state variables to the nesting fields within the domain close to the nested boundary. The levels at which P is evaluated by the solver are indicated in the right-hand column along with the model state variables present at each level. Only Vh, T, and w are explicitly included as nesting variables in this schematic, but any field that influences the model’s state can be nested using the UBN technique, including chemical and microphysical tracers.

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    Time series of 120-h RMSE against Northern Hemisphere radiosondes from 20 Dec 2006 to 19 Jan 2007 in the Global LOW (solid line) and Global HIGH (dashed line) GDPS configurations. Errors at (a) 100, (b) 250, and (c) 500 hPa are shown. The initialization time of each forecast is shown along the abscissa at 12-h intervals. The standard deviation of the Global LOW and Global HIGH differences over the period is plotted in gray and light gray shading, respectively, with dark gray representing regions of overlap. A separation of the shading therefore implies a minimum 2 standard deviation difference in errors (95% confidence interval).

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    Time series of daily AO (solid line), NAO (dashed line), and stratospheric NAM [dotted line, computed at 10 hPa by for the NCEP reanalysis by Martineau and Son (2010)] indices from 1 Dec 2006 to 31 Jan 2007. Indices are plotted as standardized anomalies so that values of ±1 represent 1 standard deviation above and below the daily long-term mean (1980–2009), respectively. The 25 Dec–4 Jan period is highlighted by gray shading.

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    (a)–(f) Analyses of θDT [(e),(f) color filled in kelvin as indicated on the color bars], DT winds, and mean 925–850-hPa relative vorticity (solid contours at intervals of 0.5 × 10−4 s−1 above 0.5 × 10−4 s−1) from ERA-Interim at 48-h intervals as indicated. Annotations are “R” for the European ridge and “T” for the cyclonically breaking upper-tropospheric wave. In (a), “R” is replaced by outlines of the northern (red) and southern (blue) regions used for the blocking index shown in Fig. 6.

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    Time series of the daily Pelly and Hoskins (2003) blocking index, using θDT centered at (55°N, 0°) with a width of 10° and a height of 20° for each region as shown in Fig. 5a. A 3-day running mean smoother has been applied to the time series to remove subsynoptic-scale noise. Positive values of the blocking index indicate a reversal of the mean meridional gradient of θDT. The 25 Dec–4 Jan period is highlighted by gray shading.

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    Analyses of (a),(c),(e) 850-K PV [color filled in PVU as indicated on the color bar in (e)] and winds and (b),(d),(f) 850-K pressure [color-filled in hPa as indicated on the color bar in (f)], winds and pressure-coordinate vertical motion [ω, plotted at intervals of 40 × 10−2 Pa s−1, with dashed negative (upward motion) and no 0 contour] from ERA-Interim for the same dates as shown in Fig. 5. Annotation “W” identifies the low-PV feature associated with the anticyclonically breaking wave: (top to bottom) 0000 UTC 25, 27, and 29 Dec 2006. (g)–(l) As in (a)–(f), but for 31 Dec 2006, and 02 and 04 Jan 2007.

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    Time series of wave-1 (solid) and wave-2 (dashed) zonal harmonic component contributions to θDT averaged between 40° and 70°N. The 25 Dec–4 Jan period is highlighted by gray shading.

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    Time series of (a) wave activity and (b) E–P flux vectors for December 2006 and January 2007. Wave activity is defined as the meridional eddy heat flux (FH) at 100 hPa averaged between 45° and 75°N as specified by Waugh et al. (1999). The E–P flux vector consists of an eddy heat flux vertical component (FP) and an eddy momentum flux horizontal component (FY) at 60°N in (b). The 25 Dec–4 Jan period is highlighted by gray shading in (a) and the definitions of mathematical symbols can be found in appendix B.

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    Time series of (left) AC and (right) RMSE at (a),(b) 10; (c),(d) 100; (e),(f) 250; and (g),(h) 500 hPa. All scores are computed for the northern hemispheric LAM domain against ERA-Interim.

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    Forecasts of 10-hPa PV (PVU, plotted as in Fig. 7 but on an isobaric surface) and winds from the (left) LOW-LAM and (right) HIGH-LAM at 24-h intervals valid at the times indicated.

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    Forecasts of 10-hPa θ (kelvin, plotted as in Fig. 7 but on an isobaric surface) and winds from the (left) LOW-LAM and (right) HIGH-LAM at 24-h intervals valid at the times indicated. Pressure-coordinate vertical motion (ω, as in Fig. 7) is shown for the HIGH-LAM integrations, but is 0 by definition for LOW-LAM at the model top.

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    Trajectory paths from the (b) LOW-LAM, (c) HIGH-LAM, and (d) UBN-LAM integrations. Trajectories are released in the black boxes at 30 hPa after 36 h of integration (1200 UTC 31 Dec) and are tracked back to 0 h and forward to 120 h (96 h in HIGH-LAM). (a) The 36-h forecast of θ and winds at 30 hPa in the HIGH-LAM is shown for reference, plotted as in Fig. 12 [ω contoured at intervals of 80 × 10−2 pa s−1 with dashed negative (upward motion) and no 0 contour] with the parcel release zone outlined with a blue box. Parcel pressure is plotted along the trajectories using the coloration indicated on the color bars.

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    Differences in the geopotential height fields UBN-LAM – LOW-LAM (color-filled in decameters as indicated on the color bar) after 120 h of integration throughout the depth of the model domain. Heights from ERA-Interim are shown in solid black contours for reference at intervals of (a) 48, (b)–(e) 24, and (f) 12 dam. Height differences that reduce forecast errors relative to the reanalysis are solid filled, while those that increase errors are dotted.

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    (a)–(c) Tropospheric height differences induced by the stratospheric flow after 120 h of integration, as in Figs. 14d–f. The difference in PV between the integrations is used as a PV perturbation in the piecewise inversion framework of Davis (1992a). The boundary temperature perturbation at 200 hPa [chosen for consistency with Hartley et al. (1998) and as the isobaric surface largely above the midlatitude winter tropopause] and interior PV differences in regions with stratospheric PV values induce the height perturbations shown here. Tests with different boundaries and PV thresholds yield qualitatively similar results.

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The Utility of Upper-Boundary Nesting in NWP

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  • 1 Numerical Weather Prediction Research Section, Environment Canada, Dorval, Quebec, Canada
  • | 2 Development Division, Canadian Meteorological Centre, Meteorological Service of Canada, Dorval, Quebec, Canada
  • | 3 Numerical Weather Prediction Research Section, Environment Canada, Dorval, Quebec, Canada
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Abstract

The importance of stratospheric influences for medium-range numerical weather prediction (NWP) of the troposphere has led to increases in the heights of global model domains at operational centers around the world. Grids now routinely extend to 0.1 hPa (approximately 65 km) in these systems, thereby covering the full depth of the stratosphere and the lower portion of the mesosphere. Increasing the vertical extent of higher-resolution limited-area models (LAMs) nested within the global forecasts is problematic because of the computational cost of additional levels and the possibility of inaccuracy or instability in the high-speed stratospheric jets. An upper-boundary nesting (UBN) technique is developed that allows information from high-topped driving grids to influence the evolution of a lower-topped (~10 hPa) LAM integration in a manner analogous to the treatment of lateral boundary conditions.

A stratospheric vortex displacement event in the winter of 2007 is used to study the effectiveness of the UBN technique. Tropospheric blocking over Europe leads to the development of an amplifying planetary-scale wave in the lower stratosphere that culminates in an anticyclonic wave break over Asia and a marked increase of wave-1 asymmetry. The rapid evolution of stratospheric potential vorticity (PV) is poorly represented in low-topped models, resulting in PV-induced forecast height errors throughout the depth of the troposphere on time scales as short as 2–5 days. Application of the UBN technique is shown to be an effective way for low-topped configurations to benefit from stratospheric predictability without the problems associated with the inclusion of the stratospheric flow in the higher-resolution model domain. The robustness and relative ease of implementation of the UBN technique may make this computationally inexpensive strategy attractive for a wide range of NWP applications.

Corresponding author address: Ron McTaggart-Cowan, Numerical Weather Prediction Research Section, Environment Canada, 2121 Trans-Canada Highway, Floor 5, Dorval QC H9P 1J3, Canada. E-mail: ron.mctaggart-cowan@ec.gc.ca

Abstract

The importance of stratospheric influences for medium-range numerical weather prediction (NWP) of the troposphere has led to increases in the heights of global model domains at operational centers around the world. Grids now routinely extend to 0.1 hPa (approximately 65 km) in these systems, thereby covering the full depth of the stratosphere and the lower portion of the mesosphere. Increasing the vertical extent of higher-resolution limited-area models (LAMs) nested within the global forecasts is problematic because of the computational cost of additional levels and the possibility of inaccuracy or instability in the high-speed stratospheric jets. An upper-boundary nesting (UBN) technique is developed that allows information from high-topped driving grids to influence the evolution of a lower-topped (~10 hPa) LAM integration in a manner analogous to the treatment of lateral boundary conditions.

A stratospheric vortex displacement event in the winter of 2007 is used to study the effectiveness of the UBN technique. Tropospheric blocking over Europe leads to the development of an amplifying planetary-scale wave in the lower stratosphere that culminates in an anticyclonic wave break over Asia and a marked increase of wave-1 asymmetry. The rapid evolution of stratospheric potential vorticity (PV) is poorly represented in low-topped models, resulting in PV-induced forecast height errors throughout the depth of the troposphere on time scales as short as 2–5 days. Application of the UBN technique is shown to be an effective way for low-topped configurations to benefit from stratospheric predictability without the problems associated with the inclusion of the stratospheric flow in the higher-resolution model domain. The robustness and relative ease of implementation of the UBN technique may make this computationally inexpensive strategy attractive for a wide range of NWP applications.

Corresponding author address: Ron McTaggart-Cowan, Numerical Weather Prediction Research Section, Environment Canada, 2121 Trans-Canada Highway, Floor 5, Dorval QC H9P 1J3, Canada. E-mail: ron.mctaggart-cowan@ec.gc.ca

1. Introduction

The potential for communication between the stratosphere and troposphere has been largely neglected in numerical weather prediction (NWP) systems until quite recently (Hartley et al. 1998); however, an increasing number of operational systems now include much of the stratosphere in their domains. The extension of higher-resolution limited-area models (LAMs) into the middle stratosphere carries a prohibitively high cost in terms of both computational volume and time-step reduction required for reliable simulation of the stratospheric jets. Using a nesting technique similar to that employed at the lateral boundaries, this study shows that it is possible for LAM applications to benefit from the enhanced predictability associated with well-represented interactions between the stratosphere and troposphere, resulting in improved numerical guidance under certain flow conditions.

The troposphere has long been treated as a wave generator for numerical studies of stratospheric sudden warming (SSW) events (Matsuno 1971; Robinson 1988; and others); however, attention has recently been focused on identifying the tropospheric features that lead to these large-scale rearrangements of the stratospheric flow. Martius et al. (2009) show that tropospheric blocking precedes nearly all SSW events in the 1958–2001 period. Furthermore, they show that the block location has an impact on the evolution of the stratospheric flow, with blocking in the North Atlantic sector preferentially generating “vortex displacements” (O’Neill 2003) while blocking over the North Pacific—or simultaneous blocking in both basins—leading to “vortex splits.” This view of a blocking-induced stratospheric response is supported by a detailed analysis of the January 2006 SSW event by Coy et al. (2009). They demonstrate that an anticyclonic Rossby wave break in the upper troposphere redirects wave activity upward, and hypothesize that a resonant cavity (McIntyre 1982) could be responsible for rapid growth of the stratospheric perturbation.

Communication across the tropopause occurs in both directions. A series of mechanisms for stratospheric influence on the troposphere are investigated by Song and Robinson (2004), who find that a deceleration of the high-latitude upper-tropospheric flow triggers a transient-eddy feedback that projects onto the annular modes of the troposphere. Hartley et al. (1998) propose a direct pathway to tropospheric control, and use potential vorticity (PV) inversion to show that almost 35% of the geopotential height perturbations on the tropopause are attributable to stratospheric PV during polar vortex disturbance events. Extending these findings, a diagnostic height tendency equation is developed by Colucci (2010), and used to show that stratospheric warm advection can have an impact on tropospheric cyclogenesis, while adiabatic cooling in the stratosphere can assist with the development of tropospheric blocking anticyclones.

The effects on tropospheric predictability of a numerical model’s ability to simulate the stratospheric flow were first demonstrated by Boville (1984). Since that time, a number of studies (Polvani and Kushner 2002; Taguchi 2003; Norton 2003; Sassi et al. 2010) have shown that modeled tropospheric circulations are sensitive to perturbations of the stratospheric state, particularly as they relate to disturbances of the polar vortex. In light of these results, most operational centers have increased the height of the upper boundary in their modeling and analysis systems to approximately ~0.1 hPa [Untch and Simmons 1999; (the National Centers for Environmental Prediction) NCEP 2003; Met Office 2005]. In 2009, the Canadian Meteorological Center (CMC) also raised the top level of the operational Global Environmental Multiscale (GEM) model (Côté et al. 1998) in the Global Deterministic Prediction System (GDPS) to this level. A limited-area version of the GEM model is used for other applications at CMC; however, a pair of practical limitations precludes the extension of these domains into the middle and upper stratosphere to benefit from its improved representation. First, wind speeds in the winter stratospheric jet can exceed 350 kt (180 m s−1, Fig. 1), which leads to large Courant numbers that may result in instability in Eulerian advection schemes and reduced accuracy in semi-Lagrangian advection schemes (Héreil and Laprise 1996; Semazzi et al. 2005). Technical problems such as nesting-zone exceedances may also arise for long back trajectories computed in implementations using semi-Lagrangian techniques. Second, the computational costs associated with such an extension are prohibitive for operational LAMs with forecast ranges of several days at most, for which stratospheric influences through wave-induced feedbacks on the mean circulation (Song and Robinson 2004 and references therein) are not thought to be of primary importance.

Fig. 1.
Fig. 1.

Peak winds at 1 hPa over the winters (December–February) of 1990–2010 from the ERA-Interim reanalysis (gray shaded in kt as indicated on the grayscale bar; 1 kt = 0.5144 m s−1). Mean winds over the period are plotted with short barbs, long barbs, and pennants representing 5, 10, and 50 kt, respectively. This plotting convention for winds is used in all figures. Barbs are plotted in black and white for readability only.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

This study documents the development of an upper-boundary nesting (UBN) technique that allows a low-topped LAM to be nested at the upper boundary within a high-topped dataset—usually one supplied by driving global model predictions. A description of the UBN technique is provided in section 2 and appendix A. An analysis of the dynamics associated with a winter 2007 polar vortex disturbance is presented in section 3 in order to develop an understanding of the influence of the stratospheric PV rearrangement on the tropospheric flow. This knowledge is then applied to an analysis of forecast errors made by low-topped (10 hPa), high-topped (0.1 hPa), and UBN-enabled model integrations. In section 4, the robustness of the UBN technique is investigated in the context of a full forecast and analysis system integrated for an extended period. The study concludes with a discussion of the findings in section 5. A list of symbols and acronyms is provided in appendix B for reference.

2. Model and data descriptions

This study makes use primarily of two independent gridded datasets. For all diagnostic calculations and model evaluations, the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim reanalysis (ERA-Interim) pressure-level data with a 1.5° grid spacing are used. All model initializations employ the model-level operational final analysis from CMC at 0000 UTC 29 December 2006. This dataset extends to 0.1 hPa as required for the high-topped model configurations described below.

The GEM model uses implicit time-stepping and a semi-Lagrangian advection scheme to solve the Euler equations on the sphere [Côté et al. (1998); Yeh et al. (2002); with a modified set of basic equations and an updated vertical discretization be described by Girard et al. (2010)]. The model operates in both global and limited-area configurations and contains a full set of physical parameterizations applicable at grid spacings varying from several degrees to several kilometers (Mailhot et al. 1998). A description of the model configurations used in this study is provided in Table 1.

Table 1.

Configurations of the GEM model used for this study. The LAM domains for HIGH-LAM, LOW-LAM, and UBN-LAM are centered on the North Pole and cover the Northern Hemisphere north of 20°N, while the HIGH-REG and UBN-REG domains are centered on northern Canada and cover the Arctic Ocean, western North Pacific, and the North American continent.

Table 1.

The objective evaluations of model performance used in this study consist of root-mean square errors (RMSE) compared to radiosonde observations, and anomaly correlation (AC) and RMSE computed against ERA-Interim. While RMSE is one of the standard metrics used for tracking model performance between operational centers, the AC score is less sensitive to extreme error values. Instead, the AC coefficient responds to the error pattern’s deviation from climatology, here taken to be the NCEP–National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al. 1996) daily long-term mean. An AC score of less than 0.6 is generally accepted to represent useless forecast, while a coefficient value of less than 0.5 is indicative of a prediction that is worse than a pure climatological estimate.

Implementation of upper-boundary nesting

Most operational centers now include the stratosphere in the domain of their global analysis and prediction systems as noted in section 1. In general, the LAM systems that are driven by these global grids run for shorter forecast ranges and have their top levels in the lower stratosphere. The analysis to be presented in section 3 shows that these LAM systems can also benefit from an improved representation of the stratosphere. This section outlines the development of the UBN technique, which uses a nesting strategy analogous to that employed at the lateral boundaries to obtain the predictive benefit of the global model’s stratospheric forecast without increasing the height of the LAM domain. Additional details specific to the GEM model are contained in appendix A.

Implementation of the UBN technique can be broken into three distinct stages: nesting mechanics, open boundary advection, and solver boundary conditions. All three of these steps have a common goal: to specify the flow normal to the top model boundary, thereby eliminating the material treatment of the model’s topmost level. In the context of a LAM, the nesting and blending mechanics can be readily implemented following the design for the lateral boundary conditions (Thomas et al. 1998). This generally consists of determining which predictive variables to nest (a selection that will become clear in the forthcoming discussion) and ensuring that the external data is made available in the nesting and blending zones (Fig. 2). Although it would be possible to extend the UBN approach to the upper boundary of a global model, the mechanics required for this type of nesting has not yet been implemented in GEM.

Fig. 2.
Fig. 2.

Schematic representation of the UBN technique applied in the context of Charney and Phillips (1953) vertical discretization and the GEM state variables. The upper and lower model boundaries are represented by heavy solid lines, with “momentum” levels in dashed lines and “thermodynamic” levels in solid lines. The nesting zone (dark gray shading) extends above the model domain using a similar discretization strategy, and the optional blending zone (light gray shading) is used to relax the model state variables to the nesting fields within the domain close to the nested boundary. The levels at which P is evaluated by the solver are indicated in the right-hand column along with the model state variables present at each level. Only Vh, T, and w are explicitly included as nesting variables in this schematic, but any field that influences the model’s state can be nested using the UBN technique, including chemical and microphysical tracers.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

Permitting advection across the model’s upper boundary is possible once the nesting mechanics have been implemented. In the semi-Lagrangian context of the GEM model, the upstream points of subsiding advection trajectories are allowed to fall within the nesting zone, thus permitting the advection of state variables and tracers into the domain from above (Fig. 2). Conversely, air is implicitly evacuated from the domain when ascent occurs at the top model level. Predictive equations have the canonical form:
e1
where F represents a state variable—or combination thereof—and G encompasses all source terms related to F. Using implicit time discretization, the finite-difference form of the generalized equation becomes
e2
in which subscripts A and D correspond to the “arrival” (position r and time t) and “departure” (position rδr and time tδt) points, respectively. The coefficient b is a free parameter that can be used to implement off-centering (Ritchie and Tanguay 1996). Defining, τ = b δt and β = [(1 − b)/b], and regrouping arrival and departure terms yields
e3
where the left-hand side is valid at (r, t), and the right-hand side (defined as ) is the advected quantity from the departure point at the previous time step (rδr, tδt). By providing nonzero coordinate-normal vertical motion and sufficient nesting data to compute for each predictive equation above the top level of the model (Fig. 2), the UBN technique allows rδr to lie outside the model domain. Therefore, unlike the traditional material boundary treatment that implies the truncation of back trajectories at the model’s upper-boundary, nested coordinate-normal vertical motions in the UBN strategy transport state variables and tracers across the top level of the domain.

The use of implicit time discretization means that a simultaneous solution of the model’s predictive equations is required. A series of substitutions allow for the reduction of the system to a Helmholtz equation with a single dependent variable (P, the “generalized pressure”) as described in more detail in appendix A. As required for the closure of this problem, the motions normal to the boundaries in three dimensions are supplied (horizontal winds Vh at lateral boundaries and the coordinate displacement, , at the upper and lower boundaries). In the traditional framework, is specified at the upper boundary; allowing nonzero values of forms the essence of the UBN technique. However, the specification of directly from nesting information is problematic because of the possibility of tilted nesting surfaces and the need for accurate vertical interpolation in a region with potentially widely spaced levels. Instead, the relationship between temperature T and P in the thermodynamic equation is exploited such that a nested Ttop serves as the upper-boundary condition for the solver. These forms of upper-boundary specification are mathematically identical and either could be used to implement the UBN technique in other modeling systems.

3. Stratospheric perturbation during the winter of 2007

The period between 25 December 2006 and 4 January 2007 will be studied in detail here to demonstrate the importance of upper-troposphere–lower-stratosphere (UTLS) interactions in the context of NWP, even on a relatively short time scale. This interval is chosen because forecast height errors differ dramatically in an intercomparison of GDPS cycles running in a pair of similar configurations: one with a model top at 10 hPa (Global LOW) and one with a model top at 0.1 hPa (Global HIGH, Fig. 3). Over the period of interest, 120-h Northern Hemisphere geopotential height RMSE values at 100 hPa in Global LOW remain above 8 dam (1 dam = 10 m) and attain a maximum of 14 dam in the forecast initialized at 0000 UTC 29 December. Scores from Global HIGH are consistently near 6 dam throughout the period. The temporally coherent nature of the error in Global LOW suggests that something about the flow makes the presence of the model boundary at 10 hPa particularly problematic for the system. An analysis of the evolution of the UTLS flow is therefore required to identify the processes responsible for the decrease in guidance quality in the low-topped model configuration.

Fig. 3.
Fig. 3.

Time series of 120-h RMSE against Northern Hemisphere radiosondes from 20 Dec 2006 to 19 Jan 2007 in the Global LOW (solid line) and Global HIGH (dashed line) GDPS configurations. Errors at (a) 100, (b) 250, and (c) 500 hPa are shown. The initialization time of each forecast is shown along the abscissa at 12-h intervals. The standard deviation of the Global LOW and Global HIGH differences over the period is plotted in gray and light gray shading, respectively, with dark gray representing regions of overlap. A separation of the shading therefore implies a minimum 2 standard deviation difference in errors (95% confidence interval).

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

a. Upper-tropospheric evolution

The latter half of December 2006 is characterized by the establishment and destruction of a large-scale blocking pattern over the North Atlantic. Both the Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO; Wallace and Gutzler 1981) indices reach local minima shortly after 22 December and rise to +4 and +1 standardized anomalies, respectively, by the end of the month (Fig. 4). A change in the NAO index from −1 to +1 standardized anomalies within a 1-week period is identified as a regime transition by Archambault et al. (2010), an event that occurs once on average each boreal winter. The upper troposphere is therefore undergoing rapid restructuring and zonal acceleration over the period of interest.

Fig. 4.
Fig. 4.

Time series of daily AO (solid line), NAO (dashed line), and stratospheric NAM [dotted line, computed at 10 hPa by for the NCEP reanalysis by Martineau and Son (2010)] indices from 1 Dec 2006 to 31 Jan 2007. Indices are plotted as standardized anomalies so that values of ±1 represent 1 standard deviation above and below the daily long-term mean (1980–2009), respectively. The 25 Dec–4 Jan period is highlighted by gray shading.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The presence of large-scale blocking over the North Atlantic and Europe confirmed by the 0000 UTC 25 December analysis of potential temperature on the dynamic tropopause [θDT, as shown in Fig. 5 where the dynamic tropopause (DT) defined as the 2-PVU (1 PVU 10−6 K m2 kg−1 s−1) surface of Ertel (1942) PV (Morgan and Nielsen-Gammon 1998)]. A large ridge over western Europe extends to 80°N at this time (labeled “R” in Fig. 5). The presence of easterly flow over southern Europe and a reversal of the meridional θDT gradient (Pelly and Hoskins 2003) shown in Fig. 6 suggests that the block has a dipole structure (Rex 1950a,b).

Fig. 5.
Fig. 5.

(a)–(f) Analyses of θDT [(e),(f) color filled in kelvin as indicated on the color bars], DT winds, and mean 925–850-hPa relative vorticity (solid contours at intervals of 0.5 × 10−4 s−1 above 0.5 × 10−4 s−1) from ERA-Interim at 48-h intervals as indicated. Annotations are “R” for the European ridge and “T” for the cyclonically breaking upper-tropospheric wave. In (a), “R” is replaced by outlines of the northern (red) and southern (blue) regions used for the blocking index shown in Fig. 6.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

Fig. 6.
Fig. 6.

Time series of the daily Pelly and Hoskins (2003) blocking index, using θDT centered at (55°N, 0°) with a width of 10° and a height of 20° for each region as shown in Fig. 5a. A 3-day running mean smoother has been applied to the time series to remove subsynoptic-scale noise. Positive values of the blocking index indicate a reversal of the mean meridional gradient of θDT. The 25 Dec–4 Jan period is highlighted by gray shading.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The block remains in place from 19 to 25 December (Fig. 6) and the meridional temperature difference remains weak (>−10 K) until a Rossby wave begins to break cyclonically over the eastern North Atlantic at 0000 UTC 29 December (labeled “T” in Fig. 5). The European block tilts negatively and becomes indistinguishable from the surrounding θDT as the wave break is completed and the zonal component of the flow is reestablished over Europe on 2 January (Fig. 5). The effects of the block on the North Atlantic jet and associated climate indices are clear; moreover, Martius et al. (2009) show that blocking in the North Atlantic sector can have a substantial impact on the evolution of the stratospheric flow across the Northern Hemisphere.

b. Tropospheric–stratospheric interactions

The UTLS interactions over the period of interest must be understood in order for model performance to be properly assessed and interpreted. These interactions are bidirectional, with the European blocking event described in section 3a effecting an anticyclonic planetary wave break in the midstratosphere, a feature whose evolution in turn affects the tropospheric flow through large-scale PV rearrangement. The impact of these tropospheric adjustments will be discussed in more detail in section 3c.

The dynamics associated with SSW events have been the subject of numerous studies since the advent of regular stratospheric monitoring by satellites (Quiroz 1975). Although no major warming (defined as a reversal of the 10-hPa flow at 60°N) occurs between late December 2006 and early January 2007, 10-hPa circumpolar winds drop to below 30 kt (15 m s−1), the stratospheric northern annular mode (NAM) index reaches a local minimum [Fig. 4 and Martineau and Son (2010)], and a dramatic rearrangement of the stratospheric flow can be seen in the 850-K isentropic PV and pressure maps shown in Fig. 7 (Hoskins et al. 1985). This suggests that an application of existing theories for SSW may help to elucidate the evolution of the flow over the period of interest.

Fig. 7.
Fig. 7.

Analyses of (a),(c),(e) 850-K PV [color filled in PVU as indicated on the color bar in (e)] and winds and (b),(d),(f) 850-K pressure [color-filled in hPa as indicated on the color bar in (f)], winds and pressure-coordinate vertical motion [ω, plotted at intervals of 40 × 10−2 Pa s−1, with dashed negative (upward motion) and no 0 contour] from ERA-Interim for the same dates as shown in Fig. 5. Annotation “W” identifies the low-PV feature associated with the anticyclonically breaking wave: (top to bottom) 0000 UTC 25, 27, and 29 Dec 2006. (g)–(l) As in (a)–(f), but for 31 Dec 2006, and 02 and 04 Jan 2007.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The Aleutian high displaces the polar vortex toward the Eastern Hemisphere, close to its climatological position, in early December (not shown). The elongated vortex rotates cyclonically around the Pole between 25 and 27 December without appreciable distortion (Figs. 7a,c). However, on 29 December, a tongue of low-PV air appears over northern Europe and Asia (labeled “W” in Fig. 7e). Over the following 48 h, this incipient wave-1 disturbance grows in amplitude and undergoes an anticyclonic wave break over eastern Asia (Fig. 7g). The climatological study of Baldwin and Holton (1988) shows that is the preferred region in the Northern Hemisphere for such wave break events to occur.

The result of the wave break is a dramatic increase in the wave-1 asymmetry of the flow by 2 January (Fig. 7i), with a large cutoff anticyclone centered over eastern Asia consistent with the vortex displacement evolution identified by O’Neill (2003). This feature is actively eroding PV from the polar vortex as evidenced by the extrusion and equatorward advection of high-PV air downstream of the anticyclone center [the “potential enstrophy cascade” of Rhines (1979)]. By 4 January (Fig. 7k), a robust dipole structure in the isentropic PV field has been established, with a strong Aleutian high and a retracted polar vortex centered over northern Europe. As noted by McIntyre (1982) for the wave-1 precursor to the 1979 SSW, the net effect of this wave breaking event appears to be the sharpening of the PV gradients defining the polar jet. The similarity of the 1979 displacement event and the one currently under investigation is particularly evident through a comparison of Fig. 7 with the results of Hsu (1980). Further parallels between the 1970 event (Baldwin and Holton 1988) and vortex disturbances observed in each of the last four Boreal winters (2007–2010; O. Martius personal communication 2010) suggest that the evolution of the stratospheric flow documented here constitutes an important mode of variability rather than isolated incident, thereby enhancing the need to understand and correct systematic model errors associated with this type of flow rearrangement.

An important component of the tropospheric influence on the stratospheric circulation in this case is related to the development of the low-PV stratospheric feature in late December (“W” in Fig. 7). The tropospheric block over Europe (“R” in Fig. 5) represents a “blocking precursor” in the climatologically preferred North Atlantic jet exit region as described by Martius et al. (2009). Combined with troughing over the North Pacific (Fig. 5), the amplitude of wave-1 asymmetry is increased as wave-2 activity decreases over the blocking period (Fig. 8), behavior originally noted by Labitzke (1978). Martius et al. (2009) show that such a tropospheric pattern tends to precede stratospheric vortex displacement events, whereas conditions of strong wave-2 asymmetry appear to favor vortex splitting. This planetary-scale wave 1 is capable of penetrating the stratosphere despite the increasing refractive index that reflects wave 3 and above (Charney and Drazin 1961). Tung and Linzen (1979) show that such a stationary longwave pattern can lead to a resonant amplification of stratospheric waves that signals the onset of vortex perturbation and SSW events.

Fig. 8.
Fig. 8.

Time series of wave-1 (solid) and wave-2 (dashed) zonal harmonic component contributions to θDT averaged between 40° and 70°N. The 25 Dec–4 Jan period is highlighted by gray shading.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

A peak in wave activity transfer between the troposphere and stratosphere (Fig. 9a), and in the upward- and poleward-directed Eliassen–Palm (E-P) flux (Fig. 9b; Eliassen and Palm 1961) occur on 26–27 December as the European block tilts negatively and begins to retrogress (Figs. 5 and 6). This implies that Rossby wave activity is converging into the polar stratospheric cap and that UTLS interaction is maximized at this time (Edmon et al. 1980). The stratospheric response to this wave forcing is increasing subsidence over Europe between 25 and 29 December (Figs. 7b,d), a hallmark of wave amplification during SSW events (McIntyre 1982). The resulting tilted (wave 1) 850-K isentropic surface rotates cyclonically between 29 December and 4 January with the sharpest baroclinic gradient covering 60° of latitude across the Pole (Fig. 7f,h,j). Adiabatic descent occurs over Asia and ascent over North America by 4 January in association with the swirling flow of the remnant polar vortex. The vertical motions associated with the tilted isentropic surface near 10 hPa are the root cause of the model errors in this case.

Fig. 9.
Fig. 9.

Time series of (a) wave activity and (b) E–P flux vectors for December 2006 and January 2007. Wave activity is defined as the meridional eddy heat flux (FH) at 100 hPa averaged between 45° and 75°N as specified by Waugh et al. (1999). The E–P flux vector consists of an eddy heat flux vertical component (FP) and an eddy momentum flux horizontal component (FY) at 60°N in (b). The 25 Dec–4 Jan period is highlighted by gray shading in (a) and the definitions of mathematical symbols can be found in appendix B.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

c. Model performance

With an understanding both of the processes responsible for the rapid stratospheric flow rearrangement and of the morphology of the event itself, it is now possible to meaningfully assess the model performance over the period of interest (Fig. 3). It will be shown in this section that the UBN strategy dramatically improves model performance during the event; moreover, it does so in a way that is consistent with the dynamic description developed in the previous sections.

Regime transitions are well known to affect both observed extreme weather (Thompson and Wallace 2001) and predictability in NWP systems (Namias 1983). It is therefore to be expected that forecast skill should be reduced in association with the European blocking event (Figs. 5 and 6). Indeed, the cycling Global HIGH forecast system—an experimental configuration that is now operational at CMC—shows a modest increase in upper-tropospheric RMSE that is sustained from 25 to 29 December as the block withdraws (Fig. 3b). More surprising, however, is the fact that Global LOW [Table 1, described in detail by Bélair et al. (2009) and operational at the time of the event] develops very large errors at 100 hPa from 25 December to 4 January (Fig. 3a). The RMSE in this cycle reaches a peak of 14 dam (cf. 5 dam in Global HIGH) in the 0000 UTC 29 December initialization. This error appears to influence tropospheric predictability as RMSE values in Global LOW exceed those produced by Global HIGH by 1–2 dam throughout the period (Figs. 3b,c). Since the primary difference between the forecast systems is the height of the upper model boundary (10 hPa in Global LOW and 0.1 hPa in Global HIGH), it appears that the representation of the stratosphere has a large impact on model performance in this case.

Since the mechanics of the UBN strategy are implemented only for limited-area configurations of the model, the 0000 UTC 29 December forecasts from each of the Global HIGH and LOW configurations are rerun on a limited-area grid (HIGH-LAM and LOW-LAM, respectively, as described in Table 1). The domain is centered at the Pole and is designed to encompass the full stratospheric polar vortex by extending to at least 20°N in all directions. The grid spacing is adjusted to account for the differing map scale factors on the global and LAM domains and the time step is adjusted accordingly. All other configurations are left unchanged between the respective global and limited-area integrations. To isolate differences in evolution from those associated with the initial state, both the HIGH-LAM and LOW-LAM simulations are initialized with data from the Global HIGH forecast cycle (initializing HIGH-LAM from Global LOW data is impossible since no information exists above the 10-hPa model top). The result is a pair of limited-area control forecasts whose guidance quality resembles that obtained from the global integrations (not shown).

1) High- and low-top model comparison

An initial assessment of model performance is provided by AC and RMSE scores against ERA-Interim (Fig. 10). The AC scores from the HIGH-LAM forecast are consistently high, with values above 0.9 throughout the 120-h integration. The LOW-LAM AC scores drop off after 48 h of simulation, especially in the upper troposphere and lower stratosphere (Fig. 10, left column). The conventional “useless” value of the AC score (0.6) is reached at 72 h at 10 hPa in the LOW-LAM guidance, indicating that the flow at this level bears little resemblance to the analyzed fields. The RMSE, highly sensitive to the large errors at the top of the LOW-LAM domain, rises rapidly to over 12 dam at 10 hPa within 12 h of the initialization (Fig. 10b) and reaches almost 35 dam by 72 h (not shown). In the midtroposphere, RMSE values in LOW-LAM reach 6 dam, 1 dam higher than the hemispheric average of the high-topped integrations. This RMSE difference is approximately one standard deviation above normal as shown in Fig. 3c.

Fig. 10.
Fig. 10.

Time series of (left) AC and (right) RMSE at (a),(b) 10; (c),(d) 100; (e),(f) 250; and (g),(h) 500 hPa. All scores are computed for the northern hemispheric LAM domain against ERA-Interim.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The dramatic differences in the quality of the LOW-LAM and HIGH-LAM forecasts of the stratospheric flow are apparent upon comparison of Figs. 7 and 11 (the 850-K surface employed in Fig. 7 cannot be used to display the model fields since it lies above parts of the LOW-LAM model domain). The evolution of the 10-hPa PV field in the LOW-LAM integration confirms that the flow is poorly represented at all forecast ranges in terms of both amplitude and structure (Fig. 11, left column). The region of low PV initially over Asia (Fig. 11a) rotates cyclonically around the Pole and undergoes only a weak anticyclonic wave break on 31 December (cf. Figs. 7g and 11c). In general, the PV features in the LOW-LAM integration are strained out by the polar vortex and are unable to maintain their positions in the swirling flow despite evidence of ridging over the North Pacific. This results in a weakened Aleutian high in LOW-LAM by 2 January (Fig. 11g) that is mislocated near the date line in comparison to its HIGH-LAM and analyzed position over eastern Asia (Figs. 11h and 7i, respectively). Robinson (1988) shows that the lack of nonlinearity during the life cycle of stratospheric perturbation events leads to an inaccurate representation of the equilibrated stratospheric state following the wave break, consistent with the poor prediction of the PV features evident in LOW-LAM by the 96–120-h forecast range.

Fig. 11.
Fig. 11.

Forecasts of 10-hPa PV (PVU, plotted as in Fig. 7 but on an isobaric surface) and winds from the (left) LOW-LAM and (right) HIGH-LAM at 24-h intervals valid at the times indicated.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The key to understanding the root cause of the model’s error in representing the stratospheric flow lies in the isentropic pressure maps of Fig. 7 (right column). The wave-1 tilt of the 850-K surface engendered by the breaking planetary wave results in an isentropic surface that is steeply sloped at the 10-hPa level. Assuming the dominance of adiabatic processes, strong adiabatic ascent is implied over northern Canada and descent over Europe by 2 January (Rossby et al. 1937). This wave-1 pattern is evident in both the analyzed vertical motion fields and at the 10-hPa level in the 96-h forecast from the HIGH-LAM integration (Figs. 7j and 11j), but is necessarily absent from the LOW-LAM configuration in which the upper-boundary condition of Xtop = 0 s−1 (no generalized vertical motion) is applied as discussed in appendix A.

The imposition of an isobaric material upper model boundary eliminates all terms in the adiabatic form of the thermodynamic equation save the one representing quasi-horizontal temperature advection. The enhanced cyclonic rotation and straining-out of the PV features noted in the LOW-LAM results (Fig. 11) are both a direct result of this limitation at the top boundary of the model. Still more striking is the difference in 10-hPa potential temperature (θ) between LOW-LAM and HIGH-LAM (Fig. 12). The dominance of quasi-horizontal advection of the initial structures (similar to those shown in Fig. 7f) is immediately clear in the LOW-LAM results, in which θ bears little resemblance to either the analyzed or HIGH-LAM fields throughout the forecast period (cf. Figs. 7 and 12). Vertical displacements at 10 hPa are evident in HIGH-LAM, where a broad region of descent occurs over Europe and ascent dominates over the North Pacific and northern Canada (Fig. 12, right column). The flow near 10 hPa follows the 850-K isentropic surface in HIGH-LAM as opposed to the isobaric upper model boundary in LOW-LAM, leading to a wave-1 θ pattern that rotates only slowly around the Pole in the former. As the flow descends over Europe, parcel temperatures increase adiabatically and the resulting thickness increase enhances the ridging associated with the low-PV values over Asia.

Fig. 12.
Fig. 12.

Forecasts of 10-hPa θ (kelvin, plotted as in Fig. 7 but on an isobaric surface) and winds from the (left) LOW-LAM and (right) HIGH-LAM at 24-h intervals valid at the times indicated. Pressure-coordinate vertical motion (ω, as in Fig. 7) is shown for the HIGH-LAM integrations, but is 0 by definition for LOW-LAM at the model top.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

A set of trajectory analyses are shown in Fig. 13 to demonstrate the effects of the isobaric material upper boundary on air parcels in the LOW-LAM integration. The parcels are released at 30 hPa at 1200 UTC 30 December (36 h after initialization) over northern Russia in the region of maximum baroclinicity (Fig. 13a). They are tracked backward and forward in time throughout the integrations. The LOW-LAM trajectories (Fig. 13b) descend over Europe, but very few of them turn anticyclonically into the Aleutian high compared to the HIGH-LAM parcels (Fig. 13c). This is consistent with the weakened and poorly located low-PV feature noted in Fig. 11. Furthermore, the LOW-LAM trajectories do not begin to ascend again until they reach northern Canada, unlike the HIGH-LAM parcels that rise along the θ gradient over the western Siberia. The dominance of the quasi-horizontal swirling flow enforced by the model’s upper-boundary condition is evident in the LOW-LAM trajectories, despite the fact that the 30-hPa parcel release altitude is well below the topmost model level. Clearly, the LOW-LAM simulation is incapable of accurately representing the stratospheric flow during this vortex perturbation event.

Fig. 13.
Fig. 13.

Trajectory paths from the (b) LOW-LAM, (c) HIGH-LAM, and (d) UBN-LAM integrations. Trajectories are released in the black boxes at 30 hPa after 36 h of integration (1200 UTC 31 Dec) and are tracked back to 0 h and forward to 120 h (96 h in HIGH-LAM). (a) The 36-h forecast of θ and winds at 30 hPa in the HIGH-LAM is shown for reference, plotted as in Fig. 12 [ω contoured at intervals of 80 × 10−2 pa s−1 with dashed negative (upward motion) and no 0 contour] with the parcel release zone outlined with a blue box. Parcel pressure is plotted along the trajectories using the coloration indicated on the color bars.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

2) UBN performance

Without increasing the vertical extent of the model domain, a viable solution to the problems identified in the LOW-LAM integration for this case is to relax the upper-boundary condition that treats the 10-hPa level as a material surface. This reformulation is outlined in section 2a, wherein it is shown that both the pressure solver and the advection scheme need to be modified to account for flow across the upper model boundary. The results from the UBN-LAM integration (identical to LOW-LAM but with the UBN strategy implemented, Table 1) show that the UBN strategy is highly effective at improving the AC scores of a low-topped model (Fig. 10). Throughout both the troposphere and the lower stratosphere the UBN-LAM scores follow the target HIGH-LAM scores very closely, indicating that the evolution of the stratospheric flow and its impact on the troposphere are well represented in both integrations.

The quality of the stratospheric flow forecast in UBN-LAM is evident from the parcel trajectories shown in Fig. 13d. The realistic strength of the Aleutian anticyclone is evident from the curvature of the southern trajectories. In addition, the wave-1 distribution of vertical motion structures is well represented using the UBN technique.

By design, the 10-hPa PV field of the UBN-LAM integration is very similar to that of HIGH-LAM (Fig. 11, right column) since the former employs nesting data derived from the Global HIGH integration. It is therefore more interesting to compare the geopotential height fields at various levels in the UBN-LAM, HIGH-LAM, and LOW-LAM forecasts. Height differences (defined as UBN-LAM–LOW-LAM) and errors (defined relative to ERA-Interim) after 120 h of integration are shown in Fig. 14. A similar comparison for HIGH-LAM–LOW-LAM yields qualitatively identical results as suggested by the correlation of the HIGH-LAM and UBN-LAM scores (Fig. 10). Throughout the depth of the domain, the height differences display a strong wave-1 pattern. In the lower stratosphere, the advectively induced over-rotation of the height field around the Pole in LOW-LAM is corrected in UBN-LAM (Figs. 14a–c). This pattern is consistent with the PV structures shown in Figs. 11i,j, where the low-PV values associated with the Aleutian anticyclone are 60° longitude farther upstream in UBN-LAM than in the low-topped integration. The improved prediction of lower-stratospheric heights leads directly to reduced height errors throughout the troposphere as shown in Figs. 14d–f. Reduced heights over eastern Asia combine with increased heights over North America to create an equivalent barotropic dipole pattern in the troposphere.

Fig. 14.
Fig. 14.

Differences in the geopotential height fields UBN-LAM – LOW-LAM (color-filled in decameters as indicated on the color bar) after 120 h of integration throughout the depth of the model domain. Heights from ERA-Interim are shown in solid black contours for reference at intervals of (a) 48, (b)–(e) 24, and (f) 12 dam. Height differences that reduce forecast errors relative to the reanalysis are solid filled, while those that increase errors are dotted.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

The downward influence of the stratospheric flow errors in the LOW-LAM is evident in Figs. 10 and 14. This is consistent with the analyzed maintenance of upward-directed E–P flux vectors (Fig. 9) during the integration period; however, studies that identify wave fluxes from the stratosphere to the troposphere as the primary form of control associate a time scale of 10 days to this process (Haynes et al. 1991; Baldwin and Dunkerton 2001; Polvani and Waugh 2004). Clearly, this time scale is too long for the current situation, in which a tropospheric response is seen within the 5-day integrations. Hartley et al. (1998) and Colucci (2010) show that the restructuring of the stratospheric PV field can have a direct and immediate impact on the tropospheric flow by PV induction.1 A piecewise inversion (Davis, 1992a,b) of the lower-stratospheric PV difference between the LOW-LAM and UBN-LAM integrations (Figs. 11i,j) demonstrates that the errors in the stratospheric flow have an important impact on the tropospheric circulation (Fig. 15). The height perturbations shown in Fig. 15 are purely a result of the differences in the representation of the stratospheric flow between the two integrations since only this component of the PV difference field is used for the inversion. The remarkable similarity between the height perturbations in Fig. 15 and the tropospheric height differences shown in Fig. 14 (right column) suggests that PV induction is the leading order mechanism for stratospheric influence on the troposphere in this case. This demonstrates the potential for rapid communication of errors from the model stratosphere to the model troposphere and illustrates the need for an adequate representation of the stratospheric flow, even on the relatively short time scales considered here.

Fig. 15.
Fig. 15.

(a)–(c) Tropospheric height differences induced by the stratospheric flow after 120 h of integration, as in Figs. 14d–f. The difference in PV between the integrations is used as a PV perturbation in the piecewise inversion framework of Davis (1992a). The boundary temperature perturbation at 200 hPa [chosen for consistency with Hartley et al. (1998) and as the isobaric surface largely above the midlatitude winter tropopause] and interior PV differences in regions with stratospheric PV values induce the height perturbations shown here. Tests with different boundaries and PV thresholds yield qualitatively similar results.

Citation: Monthly Weather Review 139, 7; 10.1175/2010MWR3633.1

4. Evaluation of the robustness of the UBN technique

The detailed evaluation of the winter 2007 stratospheric vortex perturbation presented in the previous section has shown the potential for serious forecast degradation resulting from a poor representation of the stratospheric flow. However, it is clear from the similar performance of the Global HIGH and LOW model configurations for predictions outside the period of interest (Fig. 3) that most forecasts are not subject to appreciable magnitudes of the error described above. The climatological study of Charlton and Polvani (2007) shows that an average of less than one SSW event occurs per boreal winter (not including the final spring breakdown of the polar vortex). While that study does not assess the frequency of minor warmings or stratospheric perturbation events such as the one studied here, it suggests that planetary-scale rearrangements of the stratospheric night jet occur relatively infrequently. It is therefore important to show that the UBN solution, in addition to limiting the extent of stratospheric flow errors during perturbation events, does not degrade overall forecast performance.

A high-topped limited-area regional deterministic prediction system (RDPS) is currently under development at CMC to replace the existing stretched-grid regional model (HIGH-REG). Developed in parallel, a cycling version of the RDPS that employs the UBN strategy has been integrated for both winter and summer 2009. The only differences between HIGH-REG and UBN-REG are the use of the UBN technique and the heights of the top model level, which are 0.1 and 10 hPa, respectively (Table 1).

A series of 48-h integrations are run at 36-h intervals over January and February 2009 (40 initializations). The forecasts from UBN-REG and HIGH-REG are compared against all radiosonde stations within their North American domain for heights, winds, temperatures, and humidity. Neither the bias nor the RMSE metrics are adversely affected in the UBN-REG at any altitude after 48 h of integration (not shown), indicating that the UBN technique does not induce any systematic error in the RDPS. Combined with the potential for problems in stratospheric jets noted in section 1, the neutral overall impact of the UBN strategy and the demonstration of its effectiveness during stratospheric wave-breaking events are sufficient justification for its planned inclusion in future versions of the RDPS (Fillion et al. 2010).

5. Discussion

It is becoming increasingly clear that planetary-scale rearrangements of the stratospheric flow can have an important impact on tropospheric circulations and predictability in NWP models (Hartley et al. 1998; Song and Robinson 2004; Colucci 2010). Most operational centers have increased the height of their global model domains to 0.1 hPa or above, thereby including the full depth of the stratosphere in their medium- and extended-range predictions. A similar increase in the height of the upper boundary of the LAM systems driven by the data from these global models is problematic for two reasons: strong stratospheric wind speeds can cause numerical problems both in the free domain and at the LAM boundaries, and the computational cost of the additional levels is likely unreasonable in these higher-resolution systems. Although stratospheric influences over the short integration periods of typical LAM systems have traditionally been considered unimportant, Colucci (2010) shows that stratospheric features can have a direct and immediate influence on the evolution of the synoptic scales in the troposphere. The UBN technique developed in this study allows low-topped LAM models to benefit from the stratospheric guidance produced by a driving model with an extended vertical domain.

To implement the UBN technique in the GEM model, three distinct steps are required. First, the infrastructure to place nesting and blending data at the top of the LAM domain is developed. Second, modifications are made to the semi-Lagrangian advection scheme to allow back trajectories to extend into the nesting region so that air may enter and exit the domain through the top boundary. Third, the boundary conditions required to solve the model’s Helmholtz problem are reformulated to avoid the traditional treatment of the uppermost level as a material surface. In the GEM model, the specification of the temperature perturbation at the top model level is sufficient to allow for a hydrostatic specification of the upper-boundary condition. To include nonhydrostatic effects at the top of the LAM domain, the nonhydrostatic pressure perturbation (q) must also be specified during the recomputation of the model’s state vector (appendix A). Since the application of the UBN technique does not involve the implementation of any additional operations in the model, performance scales directly with the reduction in the number of model levels and increase in model time step. The execution time of UBN-LAM is reduced by 28% compared to HIGH-LAM (Table 1) as a result of the reduction of model levels from 80 to 58 (28%). A similar relationship for time step increases is expected, although all LAM integrations for this study were run with 450-s time steps to restrict the number of degrees of freedom present in the experimental design.

A stratospheric polar vortex displacement event that took place in late December 2006 is used as a case study to evaluate the effectiveness of the UBN technique. A period of enhanced wave activity flux upward from the troposphere results from blocking over Europe. A stratospheric planetary-scale wave amplifies in the climatological resonant cavity associated with the jet exit region, then breaks anticyclonically over eastern Asia and displaces the core of the stratospheric vortex from the Pole. This dramatic increase in the wave-1 asymmetry results in a tilted 850-K surface over the polar region and the establishment of a strong Aleutian anticyclone in the lower stratosphere.

An evaluation of high-topped (0.1 hPa) and low-topped (10 hPa) model performance over the period of interest shows that an accurate representation of the stratospheric flow is beneficial for tropospheric predictions on a 2–5-day time scale in this case. Such sensitivity to stratospheric evolution is consistent with the findings of a climate model-based study described by Sassi et al. (2010); however, the errors that develop in their low-topped (3.5 hPa) model appear to arise from wave reflection at the material upper boundary. In this case, the amplification of the upward-propagating planetary-scale wave is suppressed in the low-topped model without UBN because the generation of lower-stratospheric subsidence over eastern Europe in association with the wave’s development is prevented by the model’s isobaric material upper boundary. The evolution of the flow is dominated by quasihorizontal advection and isentropic surfaces are strained out around the polar vortex rather than tilted by the breaking wave. A rapid decrease in predictive skill occurs in the lower stratosphere and results in tropospheric errors that increase with height.

A low-topped model using the UBN technique is shown to reproduce the driving model’s solution very closely at all levels. A strong wave-1 asymmetry develops in the model’s lower stratosphere and parcels enter and exit the domain as they circulate around the Pole on the tilted 850-K surface. The differences in stratospheric PV evolution between the low-topped integrations with and without UBN induce tropospheric height perturbations that match the observed forecast discrepancies. This indicates that UTLS communication takes the form of direct PV induction rather than relying on downward controls acting on much longer time scales. A reliable depiction of stratospheric flow evolution may therefore be beneficial for even short- and medium-range NWP systems during vortex perturbation events.

The success of the integrations using the UBN technique for the winter 2007 case is complimented by forecast cycles of UBN-based LAM integrations for both winter and summer 2009. A comparison of these results with those of high-topped version of the same system shows that the UBN technique reliably reproduces the guidance of the more computationally expensive and potentially unstable integrations. Given the relative ease of implementation of the UBN technique in existing LAM systems, this approach provides an effective way to obtain the benefits of accurate representation of the stratospheric flow without the problems associated with the vertical extension of the LAM domain.

Once the upper boundary of the model is no longer treated as a material surface, it is possible to imagine other potential applications for the UBN technique (Mahalov et al. 2009). A nested global modeling system could be developed in which stratospheric information from a coarse-resolution high-topped model is used as the upper-boundary condition for a higher-resolution global model of the troposphere, thereby making optimal use of computational resources. Similarly, a very high-resolution LAM could focus on the boundary layer, with full nonhydrostatic UBN used to provide information about the upper-tropospheric flow. However, the inclusion of physical parameterizations complicates this picture dramatically since most schemes are designed to work through a deep layer of the atmosphere. Regional climate models may also benefit from the UBN technique since the long integration times of these systems both increase the chances of simulating a stratospheric perturbation event and provide ample time for UTLS interactions to occur. Finally, a mirror of the UBN technique could readily be applied to the model’s lower boundary, thus allowing the bottom level to be lifted from the surface. This could lead to the development of a flexible system applicable to a broad range of problems from boundary layer investigations to regional climate and middle-atmospheric modeling given appropriate physical parameterizations.

The success of the UBN technique implemented in the GEM model, shown through both the December 2006 case study and the seasonal UBN-REG cycle, has led to its adoption in a number of modeling systems under development at CMC. The predictive benefits of well-represented UTLS communication can be obtained through a set of relatively minor changes to existing LAM systems, allowing the UBN technique to offer an attractive alternative to increasing the vertical extent of model domains. Continued investigation of alternative formulations of upper- and lower-boundary conditions may allow for the extension of this technique and for the development of new applications that benefit from the passage of information across model boundaries.

Acknowledgments

The authors thank Michel Roch and Alain Patoine for their help in generating and analyzing some of the GEM model data used for this investigation. Comments from Olivia Martius led to important improvements to the study, as did the suggestions of two anonymous reviewers. Earlier versions of this work also benefited from discussions with Abdessamad Qaddouri, Lance Bosart, and Eyad Atallah. Patrick Martineau provided NAM index values for the period. The ERA-Interim reanalysis datasets used for this study were obtained from the ECMWF data server, and the climate index data used in section 3a were obtained from online catalog of the Climate Prediction Center.

APPENDIX A

Detailed Description of the UBN Technique in GEM

The GEM model equations are described here in order to demonstrate the application of the UBN technique in greater detail than that provided in section 2a. Appendix B contains a list of the symbols used here for reference. A complete description of the dynamical core of recent GEM versions is provided by Girard et al. (2010).

The derivation of the GEM model equations for a terrain-following hydrostatic pressure coordinate (Z) is described by Yeh et al. (2002). The primary difference between the Yeh et al. (2002) governing equations and those employed in more recent model versions is the transition to a log-hydrostatic pressure coordinate (ζ). In the Yeh et al. (2002) formulation,
ea1
as shown in Eq. (2.4) of Yeh et al. (2002). The updated ζ coordinate in the GEM model used for this study is instead based on
ea2
where pref is a constant reference pressure. The relationship between ζ and pressure (p) depends also on the coordinate metric and nonhydrostatic terms:
ea3

The governing equations then become

article image

References in these equations specify corresponding equation numbers in Yeh et al. (2002), and the symbols in parentheses in the first column will be used as subscripts for corresponding equations throughout this section.

These equations are separated into linear (L) and nonlinear (N) components of the canonical form:
ea11
where represents the right-hand side terms as defined in Eq. (3). Note that the “linearization” of the equations proceeds by splitting the equations into fast (linear) and slow (nonlinear) components rather than adhering to the pure mathematical sense of the term. The N components of each equation are handled iteratively, and are therefore considered known values in Eq. (A11), as are the advected quantities from the previous time step .
Following the temporal discretization strategy described in section 2a, the linearly treated components become
ea12
ea13
ea14
ea15
ea16
ea17
ea18
The diagnostic equations in (A17) and (A18) are then readily eliminated from this system, leading to modified forms of the vertical momentum and thermodynamic equations:
ea19
ea20
Following these substitutions, the system can be reduced to a set of three equations with three unknowns (w, P, and X) using the definitions P = ϕ′ + RT*(Bs + q) and for the generalized forms of pressure and vertical motion, respectively:
ea21
ea22
ea23
These equations can be further combined to yield a Helmholtz equation with a single dependent variable (P):
ea24
ea25
The presence of terms involving derivatives with respect to the vertical coordinate in this elliptic equation necessitates the application of boundary conditions for P at the highest and lowest model levels.
The standard closed top boundary condition defines the uppermost level as an isobaric material surface such that Btop = 0 and qtop = 0. This implies that Xtop = 0 s−1 and that Eq. (A21) can immediately be reduced to
ea26
ea27
which provides Ptop directly.
The UBN technique is designed to avoid this material treatment of the upper boundary by allowing (and thus Xtop) to vary in both space and time. Although this could be accomplished directly by providing the value of , this implementation is problematic for two reasons. First, different coordinate slopes—common in nesting applications where orographic fields are treated at different resolutions—would require projection of the three-dimensional wind onto the coordinate-normal component. Second, finescale structures common in the vertical motion fields could be poorly represented if vertical interpolation is necessary in the upper levels, where vertical resolution tends to be low. Instead, a recasting of the linear terms of the thermodynamic equation [Eq. (A14)] yields a result that relates P and :
ea28
ea29
The presence of in this boundary condition necessitates the specification of this value from the nesting data and forms the foundation of the UBN technique from the perspective of the model solver.
The foregoing discussion assumes that nonhydrostatic perturbations at the top model level are small enough to be ignored (qtop = 0). The hydrostatic form of the UBN technique can be applied even in the context of a nonhydrostatic model since it does not eliminate q at levels below the upper boundary. Indeed, when is specified, qtop is only required during the recalculation of the state variables after the solver has been used to update P. During this back-substitution step, q is found by combining Eqs. (A11) and (A19) to yield the following:
ea30
All quantities on the right-hand side of this equation are known either from previous conditions or from prior back substitutions (w). Since the vertical derivative of q is needed during the solution process, a boundary condition must be supplied. Although the application of qtop = 0 is likely sufficient under most conditions, the value of qtop could instead be supplied by the same nesting data used to specify . Such an implementation of the UBN technique would nest both hydrostatic and nonhydrostatic components of the flow, and might be necessary for models with very low tops of the type discussed briefly in section 5. Throughout this study, however, the hydrostatic form of UBN is used because of the relatively low horizontal resolution, the elevated (10 hPa) upper model boundary, and the fact that the GDPS configuration is hydrostatic.

APPENDIX B

List of Symbols and Acronyms

article image

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1

As noted by Hartley et al. (1998), the word “induction” here is used in the context of the electrostatic analogy of PV inversion and is not intended to imply causality.

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