The effects of a progressively enhanced Asian summer monsoon on the mean zonal wind are examined in a series of experiments using the Community Atmosphere Model version 4 (CAM4). The response of the barotropic mean zonal wind varies in a linear fashion with the forcings of 5, 10, and 20 W m−2 in net radiation over South Asia. The authors increase the strength of the monsoon by making the South Asian land surface hotter (via lower soil albedo). This leads to an enhanced Rossby wave source region over the Balkan Peninsula at 45°N, northwest of the upper-level Tibetan high (TH). Equatorward propagation of Rossby waves causes stationary eddy momentum flux divergence (SEMFD) to the south of this source region. This local area of SEMFD produces easterly tendencies of the barotropic part of the mean zonal wind in the subtropics. As the easterly mean flow strengthens, so do low-level easterlies across the subtropical Atlantic, leading to a westward displacement of the North Atlantic subtropical high (NASH) on its equatorward flank. The western intensification of the NASH causes drying in the west Atlantic and neighboring land masses primarily because of near-surface wind divergence in the anticyclone. These modeling results confirm the mechanisms deduced in the authors’ recent observational analysis of the mean seasonal cycle’s midsummer drought.
Monsoon dynamics driven by ocean–atmosphere–land interactions impact the large-scale circulation and seasonal climate in the tropics and subtropics enormously. In Northern Hemisphere summer, the South Asian monsoon is particularly dominant with far-reaching impacts and teleconnections across the globe (e.g., Lau and Peng 1992; Lau and Weng 2002; Ding and Wang 2005). Diabatic heating associated with monsoon convection over Southeast Asia forces a planetary-scale high pressure system in the upper troposphere (~200 hPa) known as the Tibetan high (TH). The TH is seen in Fig. 1 that shows observed geopotential height and winds at 200 hPa and precipitation for June–August (JJA). The TH is such a prominent anticyclonic flow that it makes closed contours of the total geopotential height (or streamfunction) field (Fig. 1). In longitude, the TH stretches all the way from the Greenwich meridian on its western edge to around 150°E to the east. The displacement of the upper-level TH anticyclone to the west of convection is consistent with the equatorial, β-plane linear theory of the westward spreading of a long Rossby wave pattern due to an off-equatorial heat source (Matsuno 1966; Gill 1980).
One implication of the TH for the global circulation may be through its crucial role in the mean zonal momentum budget in the northern subtropics. The pressure-weighted mean (i.e., barotropic) zonally averaged zonal wind (simply called “barotropic zonal wind” here) tendency equation obeys
where angled brackets indicate a vertical average, square brackets indicate a zonal average across the globe, and asterisks denote zonal deviations. The overbar indicates a time average from June to August computed using monthly outputs. We focus on the barotropic zonal wind budget for simplicity, since zonal momentum is rapidly redistributed, both in the zonal direction by pressure forces and in the vertical by slight but very efficient Hadley cell adjustments (see also Shaw and Boos 2012). These efficient adjustment processes make the zonal and barotropic (mass) mean 〈[u]〉 the only zonal flow quantity whose budget is tractable. To cast the statement more physically, 〈[u]〉 is not readily changed and may be an important “flywheel” flow component in seasonal climate akin to annular modes (Thompson and Wallace 2001). The first term on the right-hand side of (1) is stationary eddy momentum flux convergence (SEMFC). For convenience, we denote the other terms in (1) symbolically as transient eddy momentum flux convergence (TEMFC), mountain torques (MT), and surface friction (SF). While these terms are not necessarily small, their annual cycle is inconsistent with the easterly maximum of 〈[u]〉 as the monsoon develops, suggesting that SEMFC holds the key to the midsummer easterlies in the subtropics (Kelly and Mapes 2011, hereafter KM011).
This study is motivated by the hypothesis from KM011 that the onset of the Asian monsoon causes the observed midsummer drying in the western Atlantic, by driving near-surface easterlies in the subtropics via SEMFC on the western edge of the TH. The geographical distribution of total (stationary and transient) EMFC in summer is shaped by stationary eddies and the particular importance of the western edge of the TH is seen in Fig. 2, which shows the horizontal distribution of SEMFC [first term on right-hand side of Eq. (1)]. The JJA climatology of stationary eddy momentum flux (; Fig. 2a), its convergence in latitude (Fig. 2b), and the longitudinal distribution of the latter averaged between 20° and 35°N in the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective Analysis for Research and Applications (MERRA) dataset (Rienecker et al. 2011) is shown in Fig. 2. We focus on SEMFC at 200 hPa, as its magnitude is greatest at upper levels where meridional gradients of absolute vorticity are large (the vertical mean pattern is very similar).
The largest local contribution to the zonal mean SEMFC in the subtropics is from around 30° to 40°E (Fig. 2c), which corresponds to the western edge of the TH (Figs. 2a,b). The southwesterly flow around the TH interacts strongly with the oncoming westerlies on its northwest corner (~40°N), causing an area of enhanced positive momentum flux over the eastern Mediterranean due to strong southwesterlies. To the south (~20°N), there is negative eddy momentum flux on the southwest corner of the TH as southeasterlies transport negative momentum poleward. Hence, near 30°N, there is a large meridional divergence of zonal momentum (or northward transport of vorticity) as southwesterlies flux positive zonal momentum to the north and southeasterlies flux negative zonal momentum to the north. There is also a secondary contribution to SEMFC from the tropical upper-tropospheric troughs (TUTTs) in the Atlantic and Pacific. TUTTs are positively tilted cold-core lows that reside above the subtropical anticyclones (White 1982) and are thought to be maintained by subsidence driven by local land–sea contrasts (Miyasaka and Nakamura 2005) as well as from remote Rossby waves emitted from deep monsoon heating (Rodwell and Hoskins 2001). Basinwide averages of SEMFC are relatively small, however (Fig. 2c), leaving the western part of the subtly asymmetric TH as the key to the zonal mean (KM011).
Using observational composite and correlation analysis, KM011 found an out of phase relationship between summer rainfall over South Asia and the western Atlantic, which are connected by variations in 〈[u]〉. Their findings, summarized in the schematic repeated here as Fig. 3, point to the leading role of the Asian monsoon TH in this chain of correlations. To reiterate, the western edge of the TH acts as momentum sink on the barotropic zonal mean wind 〈[u]〉, driving easterlies at all levels in the subtropics in summer. In particular, near-surface easterlies in the Atlantic advect the North Atlantic subtropical high (NASH) westward, thereby suppressing convection in the western Atlantic around July. Here we test this causality interpretation with global modeling experiments using external monsoon forcings. This paper is organized as follows: section 2 details the modeling techniques used, section 3 discusses the impact of a stronger monsoon on SEMFC and the momentum budget, section 4 discusses the effects on precipitation in the west Atlantic, and a summary is given in section 5.
2. Model and methods
General circulation model (GCM) experiments using the Community Atmosphere Model version 4 (CAM4) are used to probe the observed linkages presented in KM011 and summarized in Fig. 3. CAM4 is the atmosphere component of the Community Climate System Model, version 4 (CCSM4), a fully coupled state-of-the-art climate model for simulating the earth’s climate system (Gent et al. 2011). CAM4 is configured using a finite-volume dynamical core with a 1.9° × 2.5° horizontal resolution and 26 vertical levels. Observed climatological SSTs (Hurrell et al. 2008) act as boundary forcing over ocean grid points, while over land CAM4 is coupled to the Community Land Model version 4 (CLM4; Oleson et al. 2010).
The effects of forcing to the Asian monsoon are explored through a suite of four simulations in which the land surface heating over South Asia is steadily increased by changing the soil color. Together with soil wetness, soil color acts to determine the snow-free ground albedo in CLM4. Soil color ranges from 1 to 20, with higher numbers indicating lower reflectance (for more details, see Oleson et al. 2010). Note that the total surface albedo is only partially determined by the soil albedo and, in regions of dense vegetation, soil color is essentially ignored in the model. The soil color value is adjusted over the region 5°–40°N, 50°–100°E (Fig. 4). Control values of soil colors in the model (not shown) are quite heterogeneous, ranging from 1–2 (high albedo) over the Middle East to 18–19 (low albedo) in the eastern edge of the domain over eastern India/western China. Rather than using this observed color as control, we examine high soil color (low albedo) minus low soil color (high albedo) for clarity. A total of four simulations were carried out in which the soil color is set consistently throughout the boxed domain to a value of 1, 3, 5, and 20 (SOIL_01, SOIL_03, SOIL_05, and SOIL_20). Each simulation was integrated for 22 yr, and the first 2 yr were discarded to account for any transient spinup effects.
We use SOIL_20 as the reference simulation that most closely resembles CAM4’s control simulation using its native soil color distribution (not shown). The differences between SOIL_05, SOIL_03, and SOIL_01 subtracted from SOIL_20 are called WEAK, MEDIUM, and STRONG. Note that these differences all represent positive enhancements to the monsoon of varying magnitude. The biggest change in surface albedo is preferentially on the northwest corner of the domain (Fig. 4), where vegetation is relatively scarce and hence soil color plays a more significant role. The domain-averaged (land points only) surface albedo, net surface radiation, and surface temperature for WEAK, MEDIUM, and STRONG are shown in Table 1. Forcings of +5, +10, and +20 W m−2 in net radiation are the net result of these boundary condition experiments.
3. Rossby waves, eddy momentum fluxes, and mean easterlies
Following Sardeshmukh and Hoskins (1988), the vorticity equation for a single level in the upper troposphere (200 hPa here) can be approximated as
where the Rossby wave source (RWS) is defined as
The notation here is standard and the total wind vector has been decomposed into its rotational () and divergent () components. The first term on the right of (3) is the advection of absolute vorticity by the divergent wind, and the second term is the stretching or divergence term. Hence, the evolution of the vorticity field that describes Rossby waves is driven by the action of the divergent wind that generates them. RWS at 200 hPa is shown in Fig. 5 along with the 500-hPa omega field for WEAK, MEDIUM, and STRONG cases.
As heating over South Asia is ramped up, there is increasing upward motion near the Indian subcontinent, particularly over the Arabian Sea and the Tibetan Plateau (Figs. 5b,d,f). As expected, there is a broad area of negative RWS and upper-level vorticity divergence (Figs. 5a,c,e) associated with this midlevel ascent. Interestingly, there is a robust area of positive RWS to the northwest of these convective centers, particularly over the Mediterranean near 45°N. The midlevel subsidence over the Mediterranean (Figs. 5b,d,f) corresponding to this upper-level convergence is the “monsoon-desert mechanism” Rodwell and Hoskins (1996) showed on the 325-K isentrope. They argue this isentropic downglide occurs as the equatorward flank of the midlatitude westerlies interacts with the warm thermal structure of the westward-propagating stationary Rossby wave response to heating. The positive RWS over the Mediterranean corresponds to the northwest corner of the upper-level TH anticyclone (Figs. 1, 2). Extratropical convergence forms here as the TH extends westward and interacts with the background westerlies as heating is increased. This finding is consistent with previous studies that examined the RWS response to Asian monsoon-like heating in a 3D baroclinic atmosphere (Lin 2009; Jin and Hoskins 1995; Qin and Robinson 1993). Although total RWS is shown here, the positive RWS response in Fig. 5 is mainly due to the divergence term in (3). This contrasts to the original emphasis by Sardeshmukh and Hoskins (1988) on vorticity advection by the divergent wind. The main distinction is that their barotropic model imposed a divergence perturbation a priori, not allowing for extratropical convergence to develop outside of the specified area of tropical divergence (heating).
The wave activity flux formulated by Plumb (1985) is an extension of the classic Eliassen–Palm relation (Edmon et al. 1980) to three dimensions, giving insight into the propagation of longitudinally varying stationary waves. We use wave activity flux following Plumb (1985) to highlight the propagation of upper-level Rossby waves away from their source on the northwest corner of the TH. The horizontal Plumb flux for stationary waves on a sphere is defined as
In Eq. (4), denotes streamfunction; is pressure normalized by 1000 hPa; a is the earth’s radius; and (λ, φ) denote longitude and latitude, respectively. Subscripts and asterisks signify partial derivatives and zonal asymmetries associated with planetary waves, respectively. The flux is parallel to the local group velocity of planetary waves and is independent of wave phase, as in the zonally averaged form given by Eliassen–Palm. Figure 6 shows the mean summer eddy vorticity (color) and streamfunction (gray contours) at 200 hPa for each model simulation overlain with (arrows), where the convergence (divergence) of indicates the import (export) of wave activity. Note that here we examine total fields, not differences, since interpreting vector differences can be ambiguous. Increasing land surface heating (soil_01 → soil_20) forces a stronger upper-level anticyclone centered near 30°N, 40°E as seen in the eddy streamfunction field, with a corresponding increase in positive vorticity on its poleward edge near 45°N. There is a clear flux of wave activity diverging out of this vorticity maximum (around 45°N, 20°E) to the southeast over the Middle East. This vorticity maximum corresponds to the maximum in RWS identified in Fig. 5. There is also a secondary area of wave activity diverging out of the northeastern flank of the eddy anticyclone north of India, converging over Southeast Asia. This wave activity flux is weaker than that over the Middle East because the y component of epends heavily on the eddy meridional wind component [see Eq. (4)]. The eastern part of the TH (over Tibet) is zonally elongated, whereas its western part near the eddy streamfunction maximum has a greater phase tilt in the meridional plane as the anomalous anticyclone interacts with the oncoming westerlies (Figs. 1, 2). The meridional propagation of Rossby waves away from their source on the northwest corner of the TH implies momentum convergence there (westerly acceleration), since Rossby waves transport zonal momentum in the opposite direction of their wave activity flux. By the same token, momentum divergence (easterly acceleration) is generated over the Middle East near 30°N as Rossby waves are absorbed near the middle of the TH anticyclone (Fig. 6).
This connection between Rossby wave propagation and momentum transport is directly confirmed in Fig. 7, which shows the impact of increased monsoon heating on stationary eddy momentum fluxes (u*υ*; left panels) and their convergence (right panels). The biggest eddy momentum flux changes (Figs. 7a,c,e) are again on the northwest corner of the TH, where the contours of the anomalous anticyclone are tilted almost at 45° (Fig. 6), maximizing the product u*υ*. As monsoon heating is increased, the magnitude of momentum convergence (westerly acceleration; red in right panels) and divergence (easterly acceleration; blue in right panels) is increased on the poleward and equatorward flanks of this u*υ* maximum, respectively (Figs. 7b,d,f). Momentum convergence around 45°N corresponds to the Rossby source region identified in Fig. 5, and the area of momentum divergence near 30°N over the Middle East is consistent with the propagation of Rossby waves away from this source (Fig. 6).
The global response of stationary eddy momentum fluxes is not just confined to the longitudes of the monsoon. Considerable changes in the form of a nearly fixed pattern with amplitude proportional to the forcing are also seen over the eastern oceanic TUTTS, for instance. However, as summarized in Fig. 8, local Rossby wave forcing of the mean flow on the western margin of the TH (~25°E) is the most prominent feature driving the zonal mean. The background reference climatology (SOIL_20 run) of SEMFC is also shown in Fig. 8 in addition to the response to monsoon heating experiments. Interestingly, the model’s response is largely an amplification of its basic state: the SEMFC response to heating (lines in Fig. 8) closely follows the reference climatology phase (colors in Fig. 8), both for the Asian TH as well as for the Atlantic and Pacific TUTTS. The entire global stationary wave pattern appears to resonate with local forcing centered over South Asia. This reinforces the conclusion of previous studies using simpler models that local heating from the Asian monsoon is the primary control of the global stationary wave pattern in summer (e.g., Ting 1994; Hoskins and Rodwell 1995; Chen et al. 2001). CAM4’s mean reference climatology of SEMFC is also quite similar to MERRA observations (cf. Fig. 8 and bottom panel of Fig. 2) as the western TH is crucial to zonal mean SEMFC in both. One distinction, however, is that CAM4’s TH circulation (and associated u*υ*) is shifted too far west by about 10°–20°, consistent with its westward-shifted monsoon precipitation bias (Meehl et al. 2012).
Since ultimately it is changes in the zonal mean of Fig. 8 that matters to 〈[u]〉 [Eq. (1)], Figs. 9a,c,e show the zonally averaged response of SEMFC to steadily increasing monsoon forcing. The main feature is the area of negative SEMFC (i.e., divergence) around 30°N in the upper troposphere, which drives an easterly acceleration of increasing magnitude as monsoon heating is increased. Also evident is the low-level eddy dipole between 10° and 20°N, corresponding to the intensification of the famous Indian monsoon southwesterlies or Somali jet (Findlater 1969a,b), which brings warm, humid air onshore to South Asia. However, Rodwell and Hoskins (1995) show potential vorticity constraints dictate that this meridional flow drags along East Africa highlands with lateral friction a vorticity sink. Thus, eddy [u*υ*] may be partly balanced by frictional and perhaps mountain torques, making low levels less influential in driving the column mean SEMFC in the subtropics. Transient momentum fluxes (not shown) are also affected by these heating experiments, but their influence is minor compared to the role of stationary eddies.
Eddy-induced acceleration of the mean zonal wind at any one level will drive a mean meridional circulation (MMC) to rebalance the mass field to ensure geostrophic (and thermal wind) balance is maintained. Hence, we show changes in the mean meridional streamfunction field alongside SEMFC in Figs. 9b,d,f. An enhancement of the cross-equatorial thermally direct Hadley cell in the tropics (see, e.g., Dima et al. 2005) is clearly seen in Figs. 9b,d,f, with circulation changes centered near 10°N and maximum ascent near 20°N. The Coriolis force acting on this Hadley response in the deep tropics drives equatorward flow aloft (easterlies) and poleward flow near the surface (westerlies). In the subtropics (centered near 30°N), the summer hemisphere Hadley cell also exhibits changes proportional to the forcing but, in contrast to the cross-equatorial cell, eddy momentum fluxes play a more important role than diabatic heating in driving the summer hemisphere MMC (Schneider and Bordoni 2008). The easterly torque at upper levels near 30°N (negative SEMFC) in Figs. 9b,d,f drives mean meridional motions (clockwise circulation) with poleward-flowing air aloft offset by equatorward-flowing air near the surface. The Coriolis deflection of the equatorward-flowing air at subtropical latitudes (Figs. 9b,d,f) implies an easterly response of the zonal wind at low levels.
Changes in 〈[u]〉 and [u] can be seen in Fig. 10. There is a robust equivalent barotropic response of the mean zonal wind in the subtropics centered around 25°–30°N, with easterlies increasing in a monotonic (with height) and linear fashion with increased monsoon heating. Peak changes are in the upper troposphere where the maximum in SEMFC forcing acts (Fig. 9), but with a deep easterly response extending all the way down to the surface in the subtropics. The compensating midlatitude westerly response of the mean flow (near 45°N) is also evident, which corresponds to the Rossby wave source region on the northwest corner of the TH (Fig. 5).
4. Drying in the west Atlantic subtropics
The downstream impacts of a stronger Asian monsoon and zonal mean easterlies on west Atlantic climate are examined here. As seen above, increasing the Asian land–sea temperature contrast creates a more vigorous South Asian monsoon with increased onshore moisture flow and precipitation. The near-surface monsoon cyclone and upper-level anticyclone are enhanced (Fig. 11) over the Middle East, to the northwest of precipitation (Fig. 12), as suggested by the Gill (1980) mechanism. Near-surface anticyclonic anomalies over the Mediterranean and northern Sahara are also consistent with the monsoon-desert mechanism (Rodwell and Hoskins 1996) discussed previously. Maximum rainfall changes (Fig. 12) are collocated in regions where the mean rainfall is (excessively) large in CAM4’s control climatology: namely, over the Arabian Sea and the steep foothills of the Tibetan Plateau (Meehl et al. 2012).
The western Atlantic and neighboring land masses systematically become drier (Fig. 13) as the Asian monsoon gets wetter (Fig. 12).1 Consistent with this drying is the development of near-surface anticyclonic anomalies around the Gulf of Mexico (Figs. 11, 13). Meanwhile, near-surface cyclonic anomalies envelop the subtropical east Atlantic (east of ~60°E), an east–west vorticity dipole pattern that resembles the midsummer change in the NASH seen in observed climatology (KM011). In accord with changes in 〈[u]〉 (Fig. 10), the low-level wind over the subtropical Atlantic [~(20°–30°N)] becomes increasingly easterly (Fig. 13) as the monsoon is enhanced, advecting the southwest corner of the NASH westward (Fig. 11). The western enhancement of the NASH and drying in the western Atlantic subtropics with increased monsoon forcings supports the causal mechanisms suggested in the correlation analysis of KM011 (Fig. 3). While not shown here, the western edge of the Pacific anticyclone also dries the subtropics where easterly anomalies have been induced but less.
In the eastern Pacific ITCZ, there is an (erroneous) increased rainfall response (Fig. 13) due to low-level wind convergence (Fig. 14) along the Pacific coast of Mesoamerica. This contradicts observations that show a pronounced drying here in July and August associated with an enhancement of easterly trade winds (Magaña et al. 1999). Kelly (2012) demonstrates that this model error is due to the lack of coupled air–sea interactions when CAM4 is driven by fixed SSTs. When the present model experiments are repeated using CAM4 coupled to a slab ocean model, evaporative cooling of SSTs dries the eastern Pacific (and the western Atlantic) as the easterlies trades of the NASH intrude (Kelly 2012).
Another robust change is the increase in rainfall in the east Atlantic ITCZ around 10°N as the monsoon forcing is steadily increased (Fig. 13). As the trade winds decrease in the tropical east Atlantic, anomalous westerlies converge in the eastern basin at 10°N. This east–west rain dipole in the tropical Atlantic is also in the same sense of its observed climatology, which shows a rainfall decrease (increase) in the western (eastern) basin from early to midsummer, so onset and magnitude of the Asian monsoon may also be an important factor in explaining the rainfall climatology of the Atlantic ITCZ.
A simple moisture budget is analyzed here to diagnose the source of drying in the western Atlantic. The relevant balance equation assuming a steady state can be estimated as
where is the horizontal wind vector, ρw is liquid water density, g is gravity, and q is specific humidity. The first term in the parentheses is the vertically integrated advection of humidity by the horizontal wind. The second term is the vertically integrated product of moisture and convergence. Together, these two terms constitute moisture flux convergence (MFC). Changes in the total MFC as well as the contribution from low-level wind divergence () are shown in Fig. 14, where negative values indicate a drying tendency. The large-scale drying in the western Atlantic is predominantly due to the low-level wind divergence term () in the westward displaced NASH (Fig. 11), as its pattern closely resembles the total MFC. However the advective component () of MFC by northeasterlies (Fig. 13) is a contributing factor locally: for instance, the enhancement of dry anomalies in the Bahamas and off the southeastern United States, as well as over central Mexico (~20°N, 100°W), where orographic effects matter.
5. Summary and closing remarks
In a series of experiments with the Community Atmosphere Model version 4 (CAM4), a soil color (albedo) boundary condition is progressively darkened in South Asia (Fig. 4), causing net surface radiation changes (including all feedbacks) of about 5, 10, and 20 W m−2 for each forcing magnitude. As a result, rainfall is enhanced in South Asia (Fig. 12), while the western Atlantic is progressively dried (Fig. 13), in a pattern indicative of a westward shift of the NASH circulation system (Fig. 11), with its dry fine weather, by the monsoon-driven zonal mean wind differences (Fig. 10). These changes in the vertically averaged (or barotropic) mean zonal wind are due to changes in eddy momentum fluxes (1), which act primarily at upper levels near 30°N (Fig. 9). Changes in the zonal mean SEMFC at upper levels are primarily due to eddy divergence on the western edge of the upper-level TH (Figs. 7, 8), which in turn are due to the southeastward flux of upper-level Rossby waves out of their source in eastern Europe (Figs. 5, 6). In summary, monsoon forcing of the upper-level TH anticyclone is a key mechanism governing the enhancement of mean subtropical easterlies in summer.
These modeling results substantiate the mechanistic hypothesis of KM011. Figure 3 (published by KM011 based on observations before these model results were obtained) shows a schematic of this causal connection, from right to left, from Asian monsoon convection, through the zonal mean, and culminating in the NASH pressing into the far western Atlantic causing drier weather in the western Atlantic in midsummer. This causal chain is thought to be active in both mean climatology and in interannual variability (KM011) and may also explain the JJA mean bias of CAM4. Asian monsoon precipitation in CAM4 is biased westward (Meehl et al. 2012), which drives a TH that extends too far west into the Atlantic. Mean subtropical easterlies are also too strong in CAM4 and the NASH is displaced westward, all consistent with its monsoon-based errors (see diagnostic figures at http://www.cesm.ucar.edu/). The experimental results shown here indicate that these mean biases may be connected through subtle yet significant mean flow changes, emphasizing that the whole Northern Hemisphere climate system may be viewed as a unified whole. Such a view might affect priorities in model development or research directions.
This work was funded by the National Science Foundation under Grant 0731520. A question raised by Ben Kirtman motivated a good portion of this analysis. The authors are also grateful for the technical advice of Dave Lawrence and comments by several anonymous reviewers.