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    Figure from Ahmadi-Givi (2002), originally adapted from Hoskins et al. (1985) showing circulations associated with three main PV features. (a) Circulations associated with the upper and surface PV anomalies, and the mechanism of mutual reinforcement. (b) Circulations induced by latent heating, which act to strengthen both the upper-level trough and the surface thermal perturbation.

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    Model domain and initial conditions for the case study at 1200 UTC 30 Dec 2001, with the blue box emphasizing the developing surface cyclone. Contours are temperature (blue and red dashed, interval 3°C), and MSLP (black, interval 4 hPa). Absolute vorticity at 300 hPa is shaded.

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    Cyclone after 32 h at 2200 UTC 31 Dec 2001 (a) 120- and (b) 20-km grid spacing. Contours are 300-hPa heights (black, interval 120 m) and MSLP (brown, interval 4 hPa). Absolute vorticity at 300 hPa is shaded.

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    (left) Minimum MSLP for 32 h of cyclogenesis period for 120- (blue) and 20-km (orange) grid spacing. Thin lines represent members of the physics ensemble, with thicker lines corresponding to the control runs. Dry 120- (violet) and 20-km (green)-grid-spacing results are also shown. (right) Scatterplot of minimum MSLP after 32 h as a function of net precipitation for 120- (crosses) and 20-km (triangles) grid spacing.

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    Diabatic heating at 700 hPa (shaded, K day−1), 24 h into simulations at 1200 UTC 31 Dec 2001. Blue dots correspond to the locations of grid points for the (a) 120- and (b) 20-km grid spacing.

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    Diabatic height tendency (shaded, m h−1), total geopotential height tendency (dashed black contours, interval 5 m h−1) at 850 hPa, and MSLP (brown contours, interval 4 hPa) for (a) 120- and (b) 20-km grid spacing, 16 h into simulation at 0400 UTC 31 Dec 2001. Cross sections through red lines for (c) 120- and (d) 20-km grid spacing, with contours and colors as in (a),(b).

  • View in gallery

    Diabatically induced wind tendency at 850 hPa (10−4 m s−2, vectors) and 850-hPa temperature (black dashed contours, interval 3 K) for (a) 120- and (b) 20-km grid spacing 16 h into simulation at 0400 UTC 31 Dec 2001.

  • View in gallery

    Tagged QGPV averaged from 850 to 750 hPa (positive values shaded, 10−4 s−1), geopotential height (black contours, interval 30 m), and temperatures at 850 hPa (blue and red dashed contours, interval 3°C) for (a) 120- and (b) 20-km grid spacing 24 h into simulations at 1200 UTC 31 Dec 2001.

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    10-season variance of high-pass-filtered meridional velocity at 300 hPa for 20-km grid spacing (m2 s−2, black contours) and difference (m2 s−2, shaded, 20- minus 120-km grid spacing).

  • View in gallery

    (a) Total diabatic temperature tendency from PBL, MP, and CP schemes (K day−1) and geopotential height (contours, interval 8 m) at 700 hPa and (b) diabatic height tendency (m h−1, shaded) and total geopotential height tendency (contours, interval 0.8 m h−1) at 850 hPa, all regressed against negative geopotential at 850 hPa (45°N, 55°W). (bottom) Vertical cross sections of (c) heating and (d) height tendency along green lines in (a) and (b), respectively. Green dots in (a) and (b) indicate the location of the base points. Contours and colors are as in (a),(b).

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    Covariance related to EAPE vertically integrated from 950 to 250 hPa at 20-km grid spacing (10−4 K2 s−1, black contours) and difference (10−4 K2 s−1, shaded, 20- minus 120-km grid spacing).

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    Meridional heat flux (K m s−1), vertically integrated from 950 to 250 hPa for 20-km grid spacing. Shaded values correspond to geostrophic heat flux, and orange contours correspond to heat flux by the diabatic wind.

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    (a) Meridional momentum flux (m2 s−2) at 300 hPa for 20-km grid spacing (black contours) and difference (shaded, 20 minus 120 km). (b) Time-mean wind speed (m s−1) at 300 hPa for 20-km grid spacing (black contours) and difference (shaded, 20- minus 120-km grid spacing).

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The Importance of Resolving Mesoscale Latent Heating in the North Atlantic Storm Track

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Abstract

Theoretical, observational, and modeling studies have established an important role for latent heating in midlatitude cyclone development. Models simulate some contribution from condensational heating to cyclogenesis, even with relatively coarse grid spacing (on the order of 100 km). Our goal is to more accurately assess the diabatic contribution to storm-track dynamics and cyclogenesis while bridging the gap between climate modeling and synoptic dynamics. This study uses Weather Research and Forecasting model (WRF) simulations with 120- and 20-km grid spacing to demonstrate the importance of resolving additional mesoscale features that are associated with intense precipitation and latent heat release within extratropical cyclones. Sensitivity to resolution is demonstrated first with a case study, followed by analyses of 10 simulated winters over the North Atlantic storm track. Potential vorticity diagnostics are employed to isolate the influences of latent heating on storm dynamics, and terms in the Lorenz energy cycle are analyzed to determine the resulting influences on the storm track. The authors find that the intensities of individual storms and their aggregate behavior in the storm track are strongly sensitive to horizontal resolution. An enhanced positive feedback between cyclone intensification and latent heat release is seen at higher resolution, resulting in a systematic increase in eddy intensity and a stronger storm track relative to the coarser simulations. These results have implications for general circulation models and their projections of climate change.

Corresponding author address: Jeff Willison, Department of Marine, Earth, and Atmospheric Sciences, Campus Box 8208, North Carolina State University, Raleigh, NC 27695. E-mail: jawill20@ncsu.edu

Abstract

Theoretical, observational, and modeling studies have established an important role for latent heating in midlatitude cyclone development. Models simulate some contribution from condensational heating to cyclogenesis, even with relatively coarse grid spacing (on the order of 100 km). Our goal is to more accurately assess the diabatic contribution to storm-track dynamics and cyclogenesis while bridging the gap between climate modeling and synoptic dynamics. This study uses Weather Research and Forecasting model (WRF) simulations with 120- and 20-km grid spacing to demonstrate the importance of resolving additional mesoscale features that are associated with intense precipitation and latent heat release within extratropical cyclones. Sensitivity to resolution is demonstrated first with a case study, followed by analyses of 10 simulated winters over the North Atlantic storm track. Potential vorticity diagnostics are employed to isolate the influences of latent heating on storm dynamics, and terms in the Lorenz energy cycle are analyzed to determine the resulting influences on the storm track. The authors find that the intensities of individual storms and their aggregate behavior in the storm track are strongly sensitive to horizontal resolution. An enhanced positive feedback between cyclone intensification and latent heat release is seen at higher resolution, resulting in a systematic increase in eddy intensity and a stronger storm track relative to the coarser simulations. These results have implications for general circulation models and their projections of climate change.

Corresponding author address: Jeff Willison, Department of Marine, Earth, and Atmospheric Sciences, Campus Box 8208, North Carolina State University, Raleigh, NC 27695. E-mail: jawill20@ncsu.edu

1. Introduction

Extratropical cyclones dominate midlatitude weather and climate. At the synoptic scale, individual storms can reach devastating intensities, while storm-track strength and position affect regional climate at seasonal time scales. Cyclones also influence the mean flow and redistribute heat, moisture, and momentum across latitudes (Peixoto and Oort 1992). Misrepresentation of cyclone frequency and intensity in climate simulations may, therefore, contribute substantial errors to the modeled global energy cycle and to regional climates. The Intergovernmental Panel on Climate Change found that many GCMs predict polar warming at the surface and tropical heating aloft under global warming (Meehl et al. 2007). These changes will act to decrease the equator-to-pole temperature gradient at the surface and increase it aloft. O'Gorman and Schneider (2008) found that the net effect of these competing large-scale changes will be to decrease eddy kinetic energy in midlatitudes [also see O'Gorman (2010) and Hernández-Deckers and von Storch (2011)]. At the same time, it is expected that specific humidity will increase in a warmer climate (e.g., Allen and Ingram 2002; Held and Soden 2006; Pall et al. 2007), making more latent energy available to storms (Watterson 2006). It remains uncertain how these competing effects will alter midlatitude cyclones (e.g., Ulbrich et al. 2008, 2009) [cf. Bengtsson et al. (2009) and Mizuta et al. (2011)]. In this work, we address the synoptic- and climate-scale importance of latent heat release from condensation, which occurs in mesoscale features that GCMs resolve poorly.

Hoskins et al. (1985) described the interaction of upper- and lower-tropospheric disturbances in a developing cyclone within a potential vorticity (PV) framework. Baroclinic instability can be envisioned as the mutual reinforcement between upper-level PV (UPV) associated with the high-PV polar stratosphere and lower-level PV (LPV) associated with a near-surface potential temperature anomaly (Fig. 1a). The cyclonic flow induced by the UPV increases warm advection and enhances the effective LPV anomaly. The cyclonic flow likewise induced by the LPV advects additional high-PV air southward, strengthening the UPV anomaly.

Fig. 1.
Fig. 1.

Figure from Ahmadi-Givi (2002), originally adapted from Hoskins et al. (1985) showing circulations associated with three main PV features. (a) Circulations associated with the upper and surface PV anomalies, and the mechanism of mutual reinforcement. (b) Circulations induced by latent heating, which act to strengthen both the upper-level trough and the surface thermal perturbation.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

The added effects of moisture and generation of diabatic PV (DPV) on cyclogenesis have since been investigated in numerous theoretical, observational, and modeling studies (Gyakum 1983; Smith et al. 1984; Emanuel et al. 1987; Snyder and Lindzen 1991; Kuo et al. 1991; Montgomery and Farrell 1991; Davis and Emanuel 1991; Davis 1992; Davis et al. 1993; Reed et al. 1993; Balasubramanian and Yau 1994; Zhu and Newell 1994; Stoelinga 1996; Huo et al. 1999; Mahoney and Lackmann 2007). Typical interactions between these PV anomalies are summarized in Fig. 1b, from Ahmadi-Givi (2002). Latent heat release generates cyclonic DPV at low levels and anticyclonic DPV aloft. Cyclonic DPV directly enhances the LPV circulation, and can even compensate for very weak LPV (Plant et al. 2003). The flow induced by cyclonic DPV advects high-PV air into the UPV, while directly strengthening the low-level jet (LLJ) and warm conveyor belt (WCB) (Lackmann 2002; Grams et al. 2011). The LLJ and WCB are mesoscale structures that transport heat and moisture ahead of the cold front and over the warm front of the cyclone (Browning and Pardoe 1973; Wernli and Davies 1997). Anticyclonic DPV aloft slows the downstream movement of the UPV maximum, which may help to maintain a constructive tilt with height and increase downstream ridging to further enhance low-level southerly flow (Ahmadi-Givi et al. 2004). Moist processes often increase cyclone strength when compared to dry simulations (e.g., Davis et al. 1993; Balasubramanian and Yau 1994; Posselt and Martin 2004; Booth et al. 2013). As diabatic effects strengthen cyclones, additional precipitation forms and more heat is released in a positive feedback. We show here that this feedback mechanism is highly sensitive to horizontal resolution.

Since much condensational heating occurs near frontal zones, underresolving these features can result in reduced DPV generation. Previous studies have shown that representation of cyclone intensity improves from about 100-km grid spacing to about 20-km grid spacing, often with little additional improvement with grid lengths below 20 km (Jung et al. 2006; Orlanski 2007; Champion et al. 2011; Jung et al. 2012). Other studies have shown that frontal gradients become sharper at higher resolution (Bauer and Del Genio 2006; Catto et al. 2010). In dry simulations, however, cyclones do not strengthen dramatically with increased resolution (e.g., Lin 2004). Here, we present a case study to demonstrate how the addition of moisture to resolution-enhanced frontal structure allows for rapid development by increasing the contributions from DPV.

Chang et al. (2002) review a variety of important processes that are relevant to storm-track dynamics. The present study, however, is focused on understanding further the importance of latent heat released in midlatitude cyclones for the behavior of the climatological storm track. Such a connection has been only partly addressed by others (e.g., Hoskins and Valdes 1990; Black 1998). For our study, 10 model-simulated winters [January–March (JFM)] over the North Atlantic storm track are analyzed within a PV framework. We also present results from linear regression analysis to determine typical diabatic structures at both resolutions. Last, eddy statistics related to terms in the Lorenz energy cycle along the storm track are presented to show the importance of DPV in the general circulation.

The competing effects of a decreased temperature gradient at the surface and an increased temperature gradient aloft, combined with the unknown influence of mesoscale latent heating in a climate with higher specific humidity, complicate projections of changes in the extratropical storm track due to climate change. We hypothesize that current climate model resolutions lead to underestimates of significant diabatic effects within the cyclones that constitute the storm tracks, and we suspect that the influence of DPV on cyclogenesis increases substantially as mesoscale features that produce condensational heating are resolved. We test this sensitivity to resolution with a cyclone case study and seasonal simulations at 120- and 20-km grid spacing.

The paper is organized as follows. The next section describes the model configuration and analysis techniques. Section 3 presents the results from a case study simulation demonstrating the sensitivity of the DPV feedback to horizontal resolution. Section 4 extends the case study analyses to the climate scale through an analysis of 10 years of winter-season simulations. Section 5 contains a summary and discussion of key findings.

2. Model and methods

a. Model description and configuration

The Weather Research and Forecasting model (WRF), version 3.2.1, is a nonhydrostatic community model developed primarily by the National Center for Atmospheric Research (NCAR) to accommodate operational and research purposes (Skamarock et al. 2008). WRF enables the direct quantification of latent heat release and allows for comparisons of simulations at different resolutions—both tasks that reanalysis datasets cannot accommodate. The full physics available in these simulations also have some advantages over idealized baroclinic wave experiments.

Both our case study and seasonal simulations use similar model configurations. The model domain for all simulations covers the North Atlantic from approximately 18° to 72°N and from 95°W to 45°E. We use two horizontal resolutions, with 120- and 20-km nominal grid spacing, valid at 52°N on a Mercator projection. The model top is located at 50 hPa, with 28 vertical levels that increase in separation with altitude. We interpolate model output to isobaric levels from 950 to 150 hPa, every 50 hPa, and we interpolate 20-km output to the 120-km grid when necessary to eliminate the effect of better sampling features on a finer grid. The case study presented in section 3 was also simulated with 60 and 100 vertical levels to test the sensitivity to vertical resolution. The effects of increased levels are found to be much smaller than those of horizontal resolution (not shown). Initial and boundary conditions are taken from the Global Forecast System (GFS) final (FNL) analysis, available at 6-h intervals on a 1° × 1° (~111 km) grid.

WRF offers a large assortment of physics options, as discussed by Skamarock et al. (2008). We present the results of a physics ensemble for the case study in section 3 to test the robustness of our results. We initialize our case study simulation 32 h before maximum cyclone intensity for a storm that began development around 1200 UTC 30 December 2001, ending the simulation at 2000 UTC 31 December 2001. This relatively short simulation time allows us to compare cyclone dynamics at different resolutions before the inherent unpredictability of the modeled atmosphere causes the solutions to diverge. Model variables are output hourly for the case study.

Section 4 describes results from simulations of 10 winters spanning the years 2001–10. Each seasonal simulation begins at 0000 UTC 24 December and runs for 105 days, ending in early April. The JFM simulation period excludes extratropical transitions of tropical cyclones that sometimes occur in early December. We use Real-Time Global (RTG) sea surface temperature (SST) analyses to update the model SST every time step, linearly interpolated from weekly values. SSTs are interpolated to the WRF grid from the 0.5° × 0.5° grid (~50 km) at which the data are available.

b. Potential vorticity framework

Both the case study and seasonal simulations make use of PV analysis. The invertibility of PV allows the balanced flow associated with a particular PV anomaly to be deduced. We follow the many previously mentioned studies that used PV and PV inversions to quantify the role of latent heat release in cyclone development. This study uses quasigeostrophic potential vorticity (QGPV), given by
e1
where represents geopotential perturbation from the reference state, f is the planetary vorticity, f0 is the reference Coriolis parameter (10−4 s−1), and is the reference-state stability—a function of pressure only. For this study, we compute the relative vorticity on isobaric levels using full model winds and the stability term using temperature anomalies. These substitutions help to remove the noise present in the high-resolution QGPV that results from the horizontal and vertical derivatives of the geopotential. Reference temperature, geopotential height, and stability profiles are taken from a 10-season average from 50° to 20°W and 40° to 55°N of the low-resolution simulations.

QGPV anomalies of diabatic origin must be separated from those of adiabatic origin. To achieve this, we tag QGPV following the method described by Lackmann (2002). QGPV at pressures greater than 500 hPa in areas of rising motion with relative humidity greater than 70% is assumed to be of diabatic origin. Levels with pressures less than 500 hPa are excluded to limit the number of stratospheric intrusions tagged. A recent study by Baxter et al. (2011) tagged all cyclonic PV perturbations at pressures greater than 500 hPa as diabatic, with no humidity or ascent criteria. We compared this method with that of Lackmann (2002), and the results are qualitatively similar. This tagging method neglects the influence of QGPV that is advected to levels with pressures less than 500 hPa and the diabatic generation of anticyclonic PV anomalies aloft. As such, this method is not useful for analyzing the effects of upper-level anticyclonic DPV. This study is primarily concerned with the role of cyclonic DPV in the lower troposphere, however, and it will be shown that it is acceptable to neglect upper-level DPV for this purpose.

Heating and cooling redistribute PV. Using model output diabatic heating we can directly compute the rate of DPV generation. In the QG framework, the diabatic PV tendency is
e2
where is the diabatic temperature tendency. Thus, below an area of heating, a cyclonic PV tendency is generated, while aloft there is anticyclonic PV generation or destruction of cyclonic PV. A caveat concerning QG assumptions must be made. Full Ertel PV is defined as
e3
and the change in full Ertel PV due to diabatic processes is
e4
where the right-hand terms are nonconservative owing to the diabatic potential temperature tendency , and friction F. The diabatic generation of Ertel PV is determined by the projection of the gradient of the diabatic temperature tendency onto the absolute vorticity vector . In frontal regions the vorticity vector tilts away from the vertical, so the QG assumption that PV generation depends only on the vertical gradient of heating may be significantly violated. Similarly, QG diagnosis of PV generation also underestimates the diabatic PV tendency in regions of strong cyclonic relative vorticity.

We compute diabatic PV tendencies from temperature tendencies obtained from the microphysics (MP), convective (CP), and planetary boundary layer (PBL) parameterizations output from WRF. We include the temperature tendencies from the PBL scheme since they are of significant magnitude and respond strongly to the behavior of the MP scheme. The relatively small temperature tendencies from the radiation scheme in the region of maximum latent heating are excluded.

Both the tagged QGPV and DPV tendencies are inverted to obtain geopotential heights and height tendencies associated with a particular PV perturbation. Inversions are performed using iterative successive overrelaxation, similar to the method used by Hakim et al. (1996). The inversion domain ranges from 950 to 150 hPa with zero diabatic geopotential perturbation at the horizontal and upper boundaries. We use temperature tendencies at 950 and 900 hPa for the lower-boundary condition when inverting DPV tendencies and Dirichlet conditions (zero values of QGPV at the lower boundary) for tagged QGPV. Dirichlet boundary conditions are used for tagged QGPV since it becomes unclear which boundary temperatures to tag and which to exclude. We set the overrelaxation coefficient at 1.5, and deem the iteration as converged when geopotential changes by no more than 10−6 m2 s−2 from the previous iteration.

c. Regression analysis

We follow previous studies that used linear regression to determine midlatitude cyclone structures (Blackmon 1976; Blackmon et al. 1977, 1984a,b; Wallace et al. 1988; Lim and Wallace 1991; Chang 1993; Orlanski and Gross 2000). Such regressions are typically performed using time-filtered data and provide a compromise between the statistical analysis of a regional climate and the synoptic analysis of a specific feature. The method is limited by the statistical blurring of relevant structures, such as those associated with fronts, and case-to-case variations, but circumvents the methodological sensitivities of feature-tracking schemes that could otherwise be used for cyclone compositing.

We compute one-point regressions following Lim and Wallace (1991), with the exception that both reference time series and the regressed field are high-pass filtered. This approach allows us to determine the typical cyclone and heating structure at a specific location. The regression coefficient b(i) of a given variable i is given by
e5
where t is time; is the high-pass-filtered reference time series at the base point; is the high-pass-filtered time series of the ith variable, which varies spatially; and N is the number of times. Dividing covariance by the standard deviation of the reference series retains the meaningful units of the dependent variable. The resulting regression patterns are those associated with a one-standard-deviation anomaly in the reference series.

Dynamics relevant to this study occur on short time scales that are excluded by traditional bandpass filtering. For example, Zhu and Newell (1994) found that the development of strong atmospheric rivers along the warm conveyor belt often occurred in the first 24 h of cyclone development. High-pass filtering retains atmospheric events that occur on all scales shorter than the cutoff period. We compute eddy and perturbation values presented in section 4 using a 7-day high-pass filter with 57 weights, for output saved every 6 h. We also present other eddy statistics, such as fluxes of heat and momentum, in section 4.

d. Lorenz energy cycle

Eddy interaction with the mean flow is an important part of the Lorenz energy cycle (Lorenz 1967). The generation of eddy available potential energy (EAPE), integrated over the mass of the atmosphere, is given by
e6
such that heating in warm areas and cooling in cold areas generates EAPE, where is high-pass-filtered diabatic temperature tendency and T′ is high-pass-filtered temperature. Eddy heat flux also contributes to the production of EAPE by conversion from zonal available potential energy (ZAPE) as warm air moves poleward or cold air moves equatorward. The rate of this conversion is given by
e7
where the rate of conversion is proportional to the geostrophic poleward eddy heat flux .
Eddy feedback on the mean flow occurs mainly through the eddy flux of zonal momentum, converting EKE to zonal mean kinetic energy (ZKE),
e8
Here, eddy momentum flux is proportional to this conversion. The influence of resolution-sensitive DPV generation on the above terms is discussed in section 4.

3. Case study

a. Synopsis

Analysis of an individual cyclone is presented as a synoptic-scale investigation of the DPV influence and its sensitivity to horizontal resolution. The cyclone in question began developing on 30 December 2001 over the western North Atlantic. This case was selected for its easily discernible frontal structures at both coarse and fine resolution. We run WRF for 32 h with hourly output and perform analysis within a PV framework.

Figure 2 shows the model domain and initial synoptic configuration. The cyclone of interest originates near the Gulf Stream as a short wave with a parent low to the north. An upper-level jet streak, providing QG forcing aloft and associated with ample baroclinicity in the lower troposphere, helps to trigger cyclogenesis (not shown). After 32 h, the surface cyclone at 120 km grid spacing deepens by 22 hPa, and the upper-level disturbance strengthens (Fig. 3a). Warm- and cold-frontal gradients appear and strengthen throughout the period. Results from the finer-resolution (20-km grid spacing) run are interpolated to the coarse grid to remove the effects of increased sampling. The cyclone intensifies more rapidly at the higher resolution, as MSLP drops 27 hPa in 32 h (Fig. 3b). Such rapid intensification is often associated with strong low-level forcing and strong SST gradients (Sanders and Gyakum 1980). The upper-level vorticity at 20-km grid spacing strengthens more than in the low-resolution run, and the frontal gradients are stronger.

Fig. 2.
Fig. 2.

Model domain and initial conditions for the case study at 1200 UTC 30 Dec 2001, with the blue box emphasizing the developing surface cyclone. Contours are temperature (blue and red dashed, interval 3°C), and MSLP (black, interval 4 hPa). Absolute vorticity at 300 hPa is shaded.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

Fig. 3.
Fig. 3.

Cyclone after 32 h at 2200 UTC 31 Dec 2001 (a) 120- and (b) 20-km grid spacing. Contours are 300-hPa heights (black, interval 120 m) and MSLP (brown, interval 4 hPa). Absolute vorticity at 300 hPa is shaded.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

Physics parameterizations may change behavior at different resolutions. To ensure that the differences between resolutions in cyclone development do not result from the particular choice of parameterizations, we perform a physics ensemble with various microphysics, convective, and boundary layer parameterizations. The evolution of MSLP over time for each ensemble member (Fig. 4a) suggests that the sensitivity to resolution is not dependent on the choice of physics. After 32 h, the surface cyclone is, on average, about 5 hPa deeper for the finer-resolution simulation. Here, the finer-grid runs are again interpolated to the coarse grid. The scatterplot of net precipitation after 32 h (Fig. 4b) indicates that total precipitation experiences a similar-resolution sensitivity, as stronger storms at finer resolution are associated with increased precipitation. We also perform a simulation of this cyclone with moisture removed. The MSLP in the dry simulations show less sensitivity to resolution. Toward the end of the dry runs, the cyclones at both the coarse and fine resolutions stop developing entirely. The importance of moisture for continued development suggests a vital role for latent heat release in this cyclogenesis.

Fig. 4.
Fig. 4.

(left) Minimum MSLP for 32 h of cyclogenesis period for 120- (blue) and 20-km (orange) grid spacing. Thin lines represent members of the physics ensemble, with thicker lines corresponding to the control runs. Dry 120- (violet) and 20-km (green)-grid-spacing results are also shown. (right) Scatterplot of minimum MSLP after 32 h as a function of net precipitation for 120- (crosses) and 20-km (triangles) grid spacing.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

The structure of 700 hPa heating after 24 h and the locations of grid points at both resolutions make clear the deficiency of the coarse grid (Fig. 5). Most heating occurs along the cold front, with substantially more heating at higher resolution. Nearly all of the heating occurs at pressures greater than 400 hPa, with a maximum near the 700-hPa level shown. Grid spacing of 20 km allows for much better representation of frontal heating. The increased heating at higher resolution shown here occurs throughout the entire period of cyclone development, in agreement with the increased net precipitation.

Fig. 5.
Fig. 5.

Diabatic heating at 700 hPa (shaded, K day−1), 24 h into simulations at 1200 UTC 31 Dec 2001. Blue dots correspond to the locations of grid points for the (a) 120- and (b) 20-km grid spacing.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

b. PV tendency

We compute DPV tendencies from the diabatic temperature tendencies and invert them to obtain geopotential height tendencies, as described in section 2. Figure 6 shows total and diabatically induced geopotential height tendencies during rapid intensification at model hour 16 for both resolutions. Low-level DPV directly enhances surface cyclogenesis, as the strongest diabatic height tendencies at 850 hPa are located between the minima of 2-h centered total height tendency and MSLP. When extending instantaneous diabatic height tendencies to 6-h totals, the magnitudes are nearly as large as the total height tendency. This is likely due to effects that are not represented by instantaneous condensational heating, such as DPV being advected away after generation, radiation effects, and other negative feedbacks that moderate the net change in QGPV. The vertically upright dipoles in Figs. 6c and 6d are expected in the QG framework, while they would be offset if considering the tilt of the relative vorticity vector. It is apparent from the cross sections how positive height tendencies aloft can help to slow the progress of the upper-level disturbance upstream, maintaining a westerly tilt with height.

Fig. 6.
Fig. 6.

Diabatic height tendency (shaded, m h−1), total geopotential height tendency (dashed black contours, interval 5 m h−1) at 850 hPa, and MSLP (brown contours, interval 4 hPa) for (a) 120- and (b) 20-km grid spacing, 16 h into simulation at 0400 UTC 31 Dec 2001. Cross sections through red lines for (c) 120- and (d) 20-km grid spacing, with contours and colors as in (a),(b).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

At upper levels the diabatic generation of an anticyclonic PV anomaly will be mitigated by its rapid advection downwind. Total and diabatic geopotential height tendencies are stronger at 20-km grid spacing, consistent with lower MSLP, increased precipitation, stronger 700-hPa heating, and stronger DPV generation. At 20 km, stronger diabatic height tendencies occur throughout the vertical column. This effect on the height tendencies confirms that the difference between the resolutions is not simply a horizontal or vertical concentration of heating, as the smoothing effects of PV inversion help to negate the effect of such concentration on the resulting geopotentials.

Additional DPV mechanisms are also sensitive to resolution. Diabatic wind tendencies at 850 hPa at model hour 16 are congruent with the positive diabatic feedback mechanism (Fig. 7a). These wind tendencies enhance temperature gradients along fronts by strengthening the transport of heat into the warm sector and by cold advection behind the cold front. Wind tendencies also lead heating along the cold front, contributing to the strength of the warm conveyor belt where moisture is transported into the region of strong convergence. Stronger 850-hPa diabatic wind tendencies at 20-km grid spacing again suggest that a stronger feedback is at work at higher resolution (Fig. 7b).

Fig. 7.
Fig. 7.

Diabatically induced wind tendency at 850 hPa (10−4 m s−2, vectors) and 850-hPa temperature (black dashed contours, interval 3 K) for (a) 120- and (b) 20-km grid spacing 16 h into simulation at 0400 UTC 31 Dec 2001.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

c. Tagged QGPV

Tagging and inverting the QGPV provides another way to determine the influence of DPV on the flow. As seen above, extending unbalanced and instantaneous DPV tendencies to 6 h results in unrealistically large height tendencies. Full QGPV is, therefore, computed and tagged using the criteria described in section 2. An example of the tagged PV distributions at both resolutions is shown in Fig. 8. The cyclone center is clearly visible in both cases, while frontal features are only weakly resolved. Tagged PV, like DPV generation, is stronger near the cyclone center at 20 km. While QGPV includes only the vertical component of vorticity, these structures are qualitatively similar to distributions of Ertel PV (not shown). It is unclear, from this analysis, to what extent stronger anticyclonic DPV aloft at 20 km may act to offset the enhanced effects of cyclonic lower-level DPV. The results of inverting the tagged QGPV are presented in section 4.

Fig. 8.
Fig. 8.

Tagged QGPV averaged from 850 to 750 hPa (positive values shaded, 10−4 s−1), geopotential height (black contours, interval 30 m), and temperatures at 850 hPa (blue and red dashed contours, interval 3°C) for (a) 120- and (b) 20-km grid spacing 24 h into simulations at 1200 UTC 31 Dec 2001.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

The above results demonstrate the ability of the model to represent a positive feedback between latent-heat release and cyclone intensification at 120-km grid spacing. The qualitative role of DPV in the lower troposphere agrees well with previous case studies (e.g., Reed et al. 1993; Stoelinga 1996). The positive feedbacks between PV anomalies and diabatic circulations are evident at 120- and 20-km-grid-spacing simulations, but the DPV influence is stronger at 20 km, resulting in more intense cyclogenesis.

4. Seasonal simulations

In this section we present the results from 10 JFM winter seasons simulated at 120- and 20-km grid spacing. These simulations extend the findings from the case study to the climatological storm track and its role in the general circulation. The variance of meridional velocity at 300 hPa is a measure of eddy kinetic energy (Fig. 9). We note a substantial increase in EKE for the storm track simulated with 20-km grid spacing. Table 1 gives additional eddy statistics at both resolutions. All variables used to compute eddy statistics are interpolated to the coarse grid prior to analysis. We find a 26.6% area-average increase in 300 hPa over the maritime storm track (area shown) at 20-km grid spacing. The 7.9% increase in net precipitation over the maritime storm track at higher resolution suggests that increased EKE may be a result of enhanced diabatic feedback.

Fig. 9.
Fig. 9.

10-season variance of high-pass-filtered meridional velocity at 300 hPa for 20-km grid spacing (m2 s−2, black contours) and difference (m2 s−2, shaded, 20- minus 120-km grid spacing).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

Table 1.

(left)–(right) Area-average EKE at 300 hPa (m2 s−2), area-average net precipitation (m), EAPE generation (10−4 K2 s−1), moisture flux by the meridional diabatic wind (kg m kg−1 s−1), moisture flux by the meridional geostrophic wind (kg m kg−1 s−1), heat flux by the meridional diabatic wind (K m s−1), and heat flux by the meridional geostrophic wind (K m s−1). Overbars represent 10-winter averages, and primes indicate high-pass-filtered values. All values except EKE at 300 hPa and net precipitation are vertically integrated from 950 to 250 hPa. All variables used in these statistics were interpolated to the coarse grid prior to analysis.

Table 1.

a. Regression analysis

One-point regressions with high-pass-filtered output reveal the average structures of cyclones and DPV. The lack of a strong upper-level height perturbation in the case study motivates the use of a geopotential base point at 850 hPa rather than 500 hPa. We regress against negative height anomalies so that the results may be interpreted as typical of a low pressure system. The base point is located in the storm-track entrance region at 45°N, 55°W. Using base points along the track, we find that the coherence of the DPV structure decreases away from the warm Gulf Stream (not shown). This could be due to a reduced role of latent heating in cyclogenesis farther downstream, or due to averaging over more variable cyclone structures and tracks there. Figure 10a shows the typical geopotential height and latent-heating structures, as estimated by the linear regression, for cyclones at 20-km grid spacing. Heating occurs ahead of the low and in a pattern consistent with the expected concentrations of frontal precipitation.

Fig. 10.
Fig. 10.

(a) Total diabatic temperature tendency from PBL, MP, and CP schemes (K day−1) and geopotential height (contours, interval 8 m) at 700 hPa and (b) diabatic height tendency (m h−1, shaded) and total geopotential height tendency (contours, interval 0.8 m h−1) at 850 hPa, all regressed against negative geopotential at 850 hPa (45°N, 55°W). (bottom) Vertical cross sections of (c) heating and (d) height tendency along green lines in (a) and (b), respectively. Green dots in (a) and (b) indicate the location of the base points. Contours and colors are as in (a),(b).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

The vertical structure of heating in Fig. 10c is consistent with the case study cyclone, with almost all of the heat released at pressures greater than 400 hPa. Cooling associated with evaporating and melting precipitation closer to the surface can be seen below the heating. Negative values behind the cyclone can be explained as artifacts of regression, rather than as a result of diabatic cooling. In the time average, this region experiences heating associated with developing cyclones. Negative deviations from the time average may, therefore, correspond simply to suppressed heating in the wake of a storm.

Greater heating occurs at all levels for 20-km grid spacing relative to 120-km grid spacing, with very similar horizontal and spatial structures (not shown). This implies that the linear regression statistically smears out various frontal features and so minimizes the structural differences between resolutions. Stronger heating directly ahead of the center of the low may result from increased moisture transport into the terminus of the WCB, as seen in our case study. Stronger cooling near the surface corresponds to enhanced evaporation as low-level winds are enhanced.

Calculating and inverting DPV tendencies computed from the heating field yields diabatic height tendencies (Fig. 10b). The strongest diabatic height tendencies are located just behind the maximum magnitude in total height tendencies, as in the case study. The vertical structure in Fig. 10d reveals a significant contribution to surface development. Again, diabatic height tendencies at 20-km grid spacing are significantly stronger than at 120 km, as are the total height tendencies (120-km-grid-spacing results not shown). This result is congruent with the enhanced deepening rate observed at higher resolution observed in the case study.

Positive height tendencies aloft again suggest a slowing of upper-level development and trough propagation. The vertical integral of the DPV tendency must vanish in the QG framework, but it is expected that anticyclonic PV aloft is advected rapidly downstream after it is generated. Therefore, the development of anticyclonic UPV is likely exaggerated in these regressions. The “typical” cyclone structure and the role of heating during its evolution are consistent with the above case study as well as those discussed in the introduction and summarized by Ahmadi-Givi (2002). Our results indicate a systematic and strongly positive feedback between diabatic effects and cyclone strength, which is sensitive to horizontal resolution.

Statistical smoothing is a weakness of the regression method, particularly in regions where cyclone structures and tracks are expected to be highly variable. Next, we present further analyses to explore the possible implications of resolution-enhanced diabatic effects along the entire storm track and implications for large-scale circulation.

b. Storm-track characteristics

As the storm track plays an important role in the general circulation, we examine the sensitivity of diabatic storm-track processes to resolution. We use the tagging and inversion methods described in section 2 to invert the 10 winters of QGPV. We then use the winds induced by tagged DPV to determine the importance of latent heating for various storm-track characteristics.

The covariance is proportional to the diabatic generation of EAPE, and is shown in Fig. 11, integrated from 950 to 250 hPa. We observe a 60.6% increase in the area-average covariance at 20 km over the maritime storm track (Table 1). The increase is most dramatic in the western half of the storm track and shows that enhanced heating at 20-km grid spacing directly contributes additional EAPE to the storm-track entrance. The sensitivity of EAPE production to moist processes is consistent with the results of Lambaerts et al. (2012).

Fig. 11.
Fig. 11.

Covariance related to EAPE vertically integrated from 950 to 250 hPa at 20-km grid spacing (10−4 K2 s−1, black contours) and difference (10−4 K2 s−1, shaded, 20- minus 120-km grid spacing).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

Another source of EAPE, the conversion C(MAPE → EAPE), is proportional to (Fig. 12). The area average of 950–250-hPa integrated geostrophic eddy heat flux over the maritime storm track increases 24.4% when simulated at 20-km grid spacing. The area-average heat flux by the diabatic winds increases even more dramatically at 52.6%. A relatively larger increase in diabatic flux suggests that the enhancement of diabatic effects with increased-resolution results from a strong positive feedback. Geostrophic and diabatic moisture fluxes ( and ) likewise increase by 4.2% and 27%, respectively. The direct radiative generation of MAPE at low and high latitudes is presumably insensitive to resolution, indicating that the enhanced conversion results primarily from increased EAPE traversing through the energy cycle. Once generated, EAPE converts to eddy kinetic energy (EKE), part of which cycles back to the zonal mean flow.

Fig. 12.
Fig. 12.

Meridional heat flux (K m s−1), vertically integrated from 950 to 250 hPa for 20-km grid spacing. Shaded values correspond to geostrophic heat flux, and orange contours correspond to heat flux by the diabatic wind.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

Eddy feedback on the mean flow [C(EKE → ZKE)] is achieved by the eddy flux of zonal momentum as shown at 300 hPa (Fig. 13a). Increased EKE at higher resolution produces a stronger flux of momentum into the jet stream in 20-km-grid-spacing simulations, which subsequently results in a stronger mean jet (Figs. 13a,b). Such a change feeds back into the eddy energy budget by generating MAPE and restoring baroclinicity as discussed in Robinson (2006). The position of the mean flow is also displaced northward and eastward.

Fig. 13.
Fig. 13.

(a) Meridional momentum flux (m2 s−2) at 300 hPa for 20-km grid spacing (black contours) and difference (shaded, 20 minus 120 km). (b) Time-mean wind speed (m s−1) at 300 hPa for 20-km grid spacing (black contours) and difference (shaded, 20- minus 120-km grid spacing).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0226.1

A dramatic increase in EAPE propagates through the energy budget and back to the mean flow. We have shown that this change is fueled by a diabatic feedback mechanism that is sensitive to horizontal resolution. The strong-resolution dependence and its consistency over 10 seasons increase our confidence in these results. As mesoscale features are better resolved, the culmination is a stronger North Atlantic storm track (Fig. 9) and a possible shift in position (Fig. 13b).

5. Summary

In recent decades the synoptic dynamics community has made great progress in understanding the role and importance of latent heating in midlatitude cyclone development. From an array of studies, the picture of a cyclogenetic and potentially significant contribution emerges (Ahmadi-Givi 2002).

Most GCM climate change simulations have been performed using models at relatively coarse horizontal resolutions, typically grid spacing of 100 km or greater, and have resulted in mixed projections of future storm-track strength (e.g., Ulbrich et al. 2009). We have investigated the role of latent heating using high-resolution simulations and a PV framework to determine the potential consequences of systematically underresolving diabatic effects. Our results suggest a significant contribution of diabatic processes to cyclogenesis, consistent with previous studies. The main contributions to development are shown to be

  1. a direct contribution to low-level cyclogenesis by the superposition of negative geopotential height perturbations near the surface cyclone (Figs. 6 and 10);
  2. strengthening of the LLJ and WCB by the diabatic wind, enhancing heat, and moisture transport (Fig. 7);
  3. generation of EAPE, directly by condensational heating in the warm sector, and by warm and cold advection ahead and behind of the cold front by the diabatic wind (Figs. 7, 11, and 12); and
  4. slowed progression of the upper-level trough, potentially preventing the loss of favorable westerly tilt with height (Figs. 6c,d and 10d).
While all of these mechanisms have been previously demonstrated in the literature, we have shown that the positive diabatic feedback is significantly enhanced when simulated with 20-km relative to 120-km grid spacing. Stronger vertical velocities along fronts result in more condensation and stronger cyclonic PV in the lower troposphere (Fig. 8). The circulation associated with DPV rapidly strengthens frontal precipitation, the LLJ, and the WCB. The stronger LLJ and WCB result in more moisture transport that terminates near the cyclone center. Height tendencies obtained by inverting PV tendencies show that the terminus of the WCB is coincident with the strongest diabatic effects, similar to the atmospheric rivers of Zhu and Newell (1994). In our case study of a generic North Atlantic cyclone, enhancement of nearly every cyclone feature culminates in an additional 5-hPa decrease of MSLP after 32 h compared to the coarse-resolution simulation (Fig. 4a).

One-point regressions and storm-track statistics indicate that the effects of latent heat release are stronger and more concentrated in the western part of the storm track. It is seen, however, that the mechanisms depicted in the case study operate throughout the storm track. The qualitative diabatic contribution to development for the typical cyclone in the regression is consistent with the mechanism seen in the case study. The combined contribution of such cyclones to the general circulation has long been recognized (Lorenz 1967). Attempts at determining the influence of cyclone-induced heating on storm tracks, however, often rely on heating computed diagnostically from reanalysis or satellite (Black 1998). To our knowledge, little attempt has been made using high-resolution nonhydrostatic simulations to quantify the effects of latent heat release on the North Atlantic storm track as done here. Fink et al. (2012) recently took steps toward developing a method that involves feature tracking for such an investigation.

Our analyses of key terms in the energy budget indicate a near doubling of EAPE generation as a result of increased horizontal resolution (Fig. 11). The enhanced diabatic heating occurs in the same western region emphasized by Hoskins and Valdes (1990). Increased EAPE then results in a stronger storm track. The difference between resolutions is dramatic and robust to the choices of physics parameterizations, which suggests that cyclone intensity at GCM resolutions may be underestimated. This deficiency may increase when simulating warmer climates with increased specific humidity. Accurately resolving storm-track characteristics and diabatic circulations results in larger eddy fluxes of heat, moisture, and momentum. The enhanced eddy energy cycle at higher resolution then feeds back on EAPE by strengthening and shifting the mean flow.

The results presented are subject to some caveats. Higher-resolution simulations presumably capture more slantwise convection and ageostrophic flow. The use of QGPV rather than Ertel PV might therefore lead to an underestimation of resolution sensitivity. Spatial structures are similar for both forms of PV, but relative magnitudes were not compared. Future studies would benefit from full EPV analysis. Most concerning is the lack of information about PV that has been advected out of the region of generation. The influence and potential canceling effects of anticyclonic PV require further investigation.

Despite these caveats, our findings have implications for climate modeling. Changes in large-scale baroclinicity have been used to explain changes in EKE in a warmer moister climate, often neglecting the effects of mesoscale latent heat release (e.g., O'Gorman and Schneider 2008; O'Gorman 2010; Hernández-Deckers and von Storch 2011). Many such studies suggest little change or a decrease in storm-track strength with global warming, with changes in large-scale baroclinicity dominating moist processes. A warmer climate with more available moisture, however, could result in systematically increased latent heat release during the cyclone life cycle, and thus consistently stronger storms or the development of storms that would not develop when simulated at coarser resolution. The result that large-scale baroclinicity is an adequate predictor of future transient eddy intensity may change as model resolution increases and simulations include important mesoscale features associated with strong latent heat release.

Necessary future work will involve global models with high-resolution nested domains over the storm track to determine if sensitivity to resolution results in storm-track behavior that is consistent with results from current GCMs. It is also of interest to see how resolving these important diabatic processes affects the general circulation and regional climate in a warmed atmosphere. The question of how GCMs are able to satisfactorily reproduce current climates without fully resolving diabatic effects must be posed. Further investigation is needed to determine whether there are competing effects that could offset resolution enhancement when not constrained by a limited domain.

Acknowledgments

This material is based upon work supported by the National Science Foundation (NSF) under Grant AGS-1007606. WRF was developed by the National Center for Atmospheric Research (NCAR). The NCAR Command Language (NCL, version 6.0) was also used for some analyses (http://www.ncl.ucar.edu/). NCAR is sponsored by NSF. FNL data for this study are from the Research Data Archive (RDA), which is maintained by the Computational and Information Systems Laboratory (CISL) at NCAR. The original data are available from the RDA (http://rda.ucar.edu) in dataset number ds083.2. SST data are from the National Centers for Environmental Prediction (NCEP; http://polar.ncep.noaa.gov/sst). Dr. Matthew Parker from North Carolina State University provided valuable feedback on this work, as did Martin Baxter from Central Michigan University and an anonymous reviewer.

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