Diurnal variations of the Great Plains low-level jet (GPLLJ) and vertical motions have been related to the development of summer precipitation individually, but their underlying connection and consequences for the nocturnal and afternoon precipitation peaks are less discussed. This paper examines how together they help explain the spatial pattern of the frequency of summer convective precipitation over the Great Plains. A one-layer linearized boundary layer model is used to reproduce the diurnal cycle of the GPLLJ. Its periodic rising and sinking motions compare favorably with those of the North American Regional Reanalysis (NARR) climatology.
Its development of rising motion is also consistent with the enhanced occurrence of nocturnal convective precipitation over the central and eastern Great Plains (90°–100°W) and afternoon maximum over the western Great Plains (100°–105°W). The diurnal phasing of the vertical motions can be captured by the model only if the diurnal oscillation of the jet is forced by both near surface geopotential gradients and friction with observed diurnal variability.
The diurnal variation of the vertical velocity (or boundary layer convergence and divergence) is explained by local vorticity balance; that is, following the diurnal oscillation of the jet, the zonal gradient of the meridional wind oscillates and, thus, relative vorticity and its tendency. The slowing down of the jet after midnight decreases the anticyclonic (cyclonic) vorticity and consequently gives a positive (negative) vorticity tendency to the east (west) of the jet core; anomalous rising (sinking) motions occur to balance these positive (negative) vorticity tendencies. The pattern reverses when the jet is relatively weak.
Convective precipitation has been one of the processes in climate models most difficult to model. Over continental areas, it can have a large diurnal variation, most commonly peaking in the afternoon, as expected from local column thermodynamics. However, it also has nocturnal maxima in some locations, most notably over the U.S. Great Plains and Midwest in summer (Wallace 1975), which are commonly not reproduced by climate models (e.g., Dai et al. 1999). Strong daytime maxima are found to the west and southeast of this area of nocturnal maxima. Various interpretations of the nocturnal maximum precipitation have been proposed. Carbone et al. (2002) identified mesoscale storm systems that developed over the Rockies in the afternoon and propagated across the Great Plains into the Midwest (cf. also Jiang et al. 2006). This currently prevailing interpretation is nicely summarized by Ruane (2010): “As the sun rises in the sky, the Rockies act as an elevated heating source that sets up a large-scale mountain–lowland circulation pattern with subsidence over the Great Plains—inhibiting convection during the afternoon.... Moist instabilities...initiate convection in rising air over the lee of the Rockies, propagating to the east.... The moisture supply for these storms is...by the low-level jet, aiding in the setup of convective ‘corridors’ for intense storms” (p. 1231). Various authors have identified processes in models responsible for their lack of success in reproducing the nocturnal peak or, in a few cases, success—for example, Liang et al. (2004), who found that in their fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5)-based regional climate model the Grell scheme for convection could produce the nocturnal peak but not the Kain–Fritsch scheme. Lee et al. (2007, 2008, 2010) has extensively examined the occurrence or absence of Great Plains nocturnal peaks in climate models. The gist of their study is that large-scale upward motion and associated moisture advection precondition nocturnal convection, high-cloud radiative cooling may initiate deep convection, and convection schemes sensitive to upward motion produce the nocturnal maximum, but those responding primarily to surface heating simulate only afternoon peaks.
This study does not address further the issue of convection schemes. Rather, it provides an explanation for the patterns of upward and downward motion (or convergence and divergence) indicated by various authors (e.g., Bleeker and Andre 1951; Pitchford and London 1962; Hering and Borden 1962; Wallace 1975; Dai et al. 1999) as related to the observed diurnal patterns of precipitation over the central United States. What has not been answered is: why do these patterns of upward motion occur? The crux of this explanation is that the diurnal patterns of the Great Plains low-level jet (GPLLJ) require diurnal patterns of convergence and divergence from boundary layer winds to satisfy conservation of vorticity. The diurnal variability of the GPLLJ has previously been studied by many authors (e.g., Bleeker and Andre 1951; Blackadar 1957; Hering and Borden 1962; Holton 1967; Bonner and Paegle 1970; Paegle and Rasch 1973; Jiang et al. 2007). Paegle and McLawhorn (1973) connected simulated vertical velocities to be consistent with 11 nocturnal thunderstorms in 1972, and Astling et al. (1985) suggested that deceleration ahead of the GPLLJ also produced convergence and rising motions. As summarized by Carbone and Tuttle (2008) the nocturnal maximum of summer precipitation can be related to wave propagation (e.g., Carbone et al. 2002), mountain–plains solenoidal circulation (Wolyn and McKee 1994), associated differential heating, and the GPLLJ. Here we focus on understanding the dynamical connection between the GPLLJ and spatial pattern of summer convective precipitation over the Great Plains.
For explanatory clarity, we construct a model of the GPLLJ that is simpler than those used in previous studies. Its primary simplification is the use of prescribed geopotential height gradients to force a boundary layer slab model. The diurnal variability of the GPLLJ is then reproduced by the diurnal variation of this geopotential gradient and surface drag coefficient.
We will show that one key for understanding its vertical motions is the local vorticity, primarily ∂υ/∂x and its tendency, where υ is the northward velocity and x is the eastward coordinate. This term is maximum (cyclonic) west of the jet core and minimum (anticyclonic) to the east. We will show that, after reaching a maximum speed around midnight, the jet slows down, with upward motion on its eastern side responding to the decrease of the anticyclonic shear. Figure 1 illustrates the dynamical processes to be established. We now develop the simple model, and different parametric assumptions to examine further these balances.
The North American Regional Reanalysis (NARR) (Mesinger et al. 2006) provides 3-hourly meteorological variables from 1979 to 2012 at a high spatial resolution (i.e., about 32 km horizontally and 45 layers vertically), thus suitable for studying the diurnal oscillation of the GPLLJ. Precipitation in the NARR is assimilated from gauge and satellite analysis and captures the diurnal cycles (Ruane 2010) and interannual variations (Ruiz-Barradas and Nigam 2006) of rainfall over the United States quite well. Climatological 3-hourly variables, averaged from 1979 to 2012 for June and July when both the GPLLJ and summer precipitation over the Great Plains reach maximum, are used to examine the diurnal cycle of boundary layer flow and convective precipitation.
b. Model simulation
A linearized one-layer model based on the work of Lindzen and Nigam (1987) is used to examine the diurnal oscillation of boundary layer circulation, as obtained from the following:
where and υ are zonal and meridional winds, f ≡ 2Ω sinφ is Coriolis parameter, Ω=7.292 × 10−5 s−1 is the angular speed of rotation of Earth, φ is latitude, H =1 km is the layer depth, and are zonal and meridional geopotential gradients, and h′ is height of the layer top, the interactive component of forcing. The bulk aerodynamic formula simulates the friction due to surface viscosity, where Cd is surface drag, and = 5 m s−1 is a prescribed magnitude of the horizontal winds, which is close to the domain-averaged wind speeds calculated from the NARR. Nonlinear terms of horizontal advection in the horizontal momentum [Eqs. (1a) and (1b)] and continuity [Eq. (1c)] equations are ignored. Since the model only contains one layer, possible influences from high-level jet streaks (Uccellini and Johnson 1979) and feedbacks from cloud, latent heating of condensation (Nicolini et al. 1993), and land surface (McCorcle 1988) are also ignored. Controls by the land surface are implicit in the assumed forcing. As a slab model, it refers to some depth of atmosphere above the local surface; however, the additional gradient terms implicit in such a model are not needed here since the forcing gradients were evaluated in pressure coordinates.
We follow the assumption of Lindzen and Nigam (1987) that convergence is taken up by the upper layer in regions with strong convection. However, the inclusion of this term is controversial. In particular, Battisti et al. (1999) argue for a “reduced gravity” at the interface and Stevens et al. (2002) leave it out entirely, taking the observational pressure gradients as the only forcing. Here we take τ = 3 s, small enough that the free-surface term is likely not to have an effect. Its primary effect is a smoothing of sharp gradients. Geopotential gradients and surface drag are prescribed as forcing to the model in a domain from 15° to 49.5°N and from 59° to 135.5°W. This study focuses on the region 25°–45°N, 90°–105°W where the core of the GPLLJ is located and rainfall variability is relatively high (Ruiz-Barradas and Nigam 2013) and positively correlated with the strength of the GPLLJ (Weaver and Nigam 2008).
Three simulations were conducted (labeled in Table 1), showing the effect of Cd and diurnal variations separately and together. The diurnal components of and were omitted in the VDFG simulation with its idealized pattern mimicking the near surface summer mean geopotential gradients over the Great Plains derived from the NARR. Figure 2a displays these zonal geopotential height gradients (shading) and associate geostrophic winds (vectors) interpolated to 500 m above the surface in the NARR June–July climatology. The following fitting functions were developed to mimic the pattern and magnitudes of the geopotential gradients:
where X1 = (x − x1)/a + m, X2 = (x − x2)/b + m, Y1 = (y − y1)k, Y2 = (y − y2)k, x1 = 259.7, x2 = 267.7, y1 = 22.3, y2 = 43.3, a = 3.35, b = 4.90, k = 0.5, m = 0.82, α = 3.5, β = 2.65, γ = 0.20, c1 = 0.075, c2 = 0.02, d1 = 0.75, and d2 = 0.60. The second derivatives of the geopotential gradients [Eqs. (2a) and (2b)] are designed to equal each other, that is, ∂ϕx/∂y = ∂ϕy/∂x, in order to keep the daily-mean geostrophic winds nondivergent. Figure 2b displays the prescribed zonal geopotential height gradient and geostrophic winds. The geostrophic meridional wind centered between 97° and 102°W is slightly greater (by about 1 m s−1) than that of the NARR over central Texas but weaker to the south along the east coast of Mexico at 23°–27°N (by about 2–3 m s−1). The zonal geopotential gradient is uniformly positive while the meridional geopotential gradient has noticeable meridional variations (i.e., positive south of 30°N and negative to the north). The so-constructed meridional geopotential gradient and, thus, zonal geostrophic winds are less realistic than the meridional winds since they have little zonal mean component over the jet core.
A diurnal cycle of Cd with shape shown in Fig. 2c simulates the oscillation of surface drag coefficient of Fig. 7 of Jiang et al. (2007) from their AGCM output but was scaled to near-surface level. A daily maximum of 0.0144 in the afternoon around 1330 local time (LT) and minimum of 0.004 from 2100 to 0600 LT along with a fixed were uniformly prescribed to the whole domain. Spatial heterogeneity of surface friction was not considered.
In the FDVG simulation, the surface drag coefficient was fixed at the daily mean of 0.0081, while sinusoidal diurnal cycles of and were prescribed. Variations of (shown in Fig. 2d) mimic those in the NARR, with an afternoon maximum around 1700 LT and a minimum at 0530 LT in the morning. The prescribed also has a diurnal cycle similar to that in the NARR, although the magnitude is a bit greater and thus results in stronger westerly winds. As shown in Fig. 2d, the variations of the westerly winds in the outflow area are largely consistent with the NARR. Sensitivity tests suggest that the contribution of to the diurnal cycle of the jet and patterns of vertical wind is relatively small but may slightly affect the magnitude of vertical winds.
Diurnal cycles of Cd, , and were all considered in the VDVG simulation. A horizontal resolution of 1.5° latitude by 1.5° longitude was used and the model was integrated for 4 days with a time step of 5 min. It reached equilibrium after 1 day with stable periodically oscillating winds; the results of the last day are presented.
a. Covariations of the GPLLJ and vertical motions
Figure 3 shows the diurnal cycles of vertical (shading) and meridional (contours) winds averaged over 35°–40°N from the three simulations and the NARR climatology. Modeled vertical velocities (w) at the top of boundary layer are calculated from w = h′/τ, which is equal to the vertical integration of the horizontal convergence over the depth of 1 km [Eq. (1c)], while simulated horizontal winds represent the mean flow of the whole layer. All three simulations produce diurnal oscillations of meridional winds comparable to those observed but the observed phase is best captured by the VDVG simulation. The simulated jet peaks around 0000 LT when both variations of geopotential height and surface friction are considered (Fig. 3c), but later (i.e., 0000–0300 LT, Fig. 3a) if only the diurnal variation of surface friction is considered and earlier (i.e., 2100 LT, Fig. 3b) if only varying geopotential gradients are prescribed. These phase differences are consistent with results of Bonner and Paegle (1970) and are related to similar time lags between the maxima of geopotential gradients and surface friction prescribed in the models, about 3 h here and 2 h by Bonner and Paegle (1970). The simulated jet core is located around 100°W (Fig. 3c), consistent with that in the NARR (Fig. 3d). The occurrence of the minimum of the jet speed near noon is also captured by the model. The timing and location of the jet maximum may slightly change owing to different averaging period and area; however, the results here are within the range found by previous studies, that is, the jet peaks around 0000–0300 LT between 95° and 100°W (Bonner 1968; Bonner and Paegle 1970; Paegle and Rasch 1973; Jiang et al. 2007).
Occurring with the diurnal variations of the jet are diurnal variations of vertical winds, with opposite phases on the western and eastern sides of the jet. In the VDFG and FDVG simulations, rising motions are mainly located to the west of the jet core, while sinking motions are to the east (Figs. 3a,b). When both forcings are included (Fig. 3c), periodic rising and sinking motions occur on both side of the domain; that is, rising motion develops over the western side of the domain from about 0900 LT to midnight along with a sinking motion to the east, with a maximum at 1800–2100 LT, about 3 h earlier than the nocturnal peak of the jet. From 0300 to 0900 LT, the directions of vertical winds are shifted, with sinking motion to the west and rising motion to the east. This diurnal cycle of the vertical winds is very similar to that of the NARR in terms of their phasing (Fig. 3d) but with magnitudes of simulated vertical winds that are somewhat greater (except those over the western boundary in the early morning due to topography), consistent with an overestimation of the jet speed. In the afternoon, from 1200 LT to midnight, the rising motion in the NARR covers a larger area than that simulated by the slab model, while from midnight to the early morning the eastward extension of the rising motion is also not as smooth as that in the model. The discrepancies between the model results and the NARR climatology may be related to the linearization of the slab model and a neglect of upper-level influences and feedbacks from the precipitation field.
In short, the simple model reproduces the major features of diurnal oscillation of the horizontal and vertical winds. Previous studies found that both the variations of geopotential gradients and surface friction are needed to reproduce the timing of the diurnal variability of the jet (Bonner and Paegle 1970; Jiang et al. 2007). The simulations here establish that both forcing terms are also required to obtain the observed diurnal phase shift of vertical velocities.
b. Frequency of convective precipitation and its association with boundary winds
Boundary layer rising motion can lift a low-level air mass and so contribute to triggering convective precipitation (Paegle and McLawhorn 1973; Astling et al. 1985). Here we revisit this topic to clarify the connections between the diurnal oscillations of boundary layer vertical winds and the spatial variability of the summer convective precipitation over the Great Plains and their relationship with the GPLLJ.
Figures 4 and 5 are designed to show for June–July how the nighttime (Fig. 4) and daytime (Fig. 5) patterns of the frequency of convective precipitation and vertical winds progress over 3-h periods near their peaks, that is, from 0000 to 0300 LT and from 1200 to 1500 LT, for the initial decay of peak nocturnal precipitation at night and the buildup to maximum afternoon precipitation, respectively. The frequency of convective precipitation is calculated by dividing the number of 3-hourly accumulated convective precipitation events greater than 1 mm day−1 for June and July from 1979 to 2012 by the total number of 3-hourly data being evaluated.
Figures 4a,b show that the nighttime maximum of precipitation frequency propagates from Kansas and Nebraska in the central Great Plains toward Iowa and Missouri to the east. Moisture convergence is located over 90°–97°W to the east of the jet core (Figs. 4c,d), generally collocated with the precipitation maxima (white contours), while near 100°W moisture divergence dominates. The magnitude of moisture convergence increases from midnight to 0300 LT, consistent with the enhanced precipitation frequency in the area. Along with the eastward propagation of the convective precipitation (and its frequency), the rising motion over the western plains, residual from the daytime, translate to the east (Figs. 4g,h). The pattern of vertical wind in the model is generally similar to that in the NARR, showing an eastward extension of the rising motion but is much smoother.
From noon to 1500 LT (Figs. 5a,b), convective precipitation develops over the western Great Plains between 100° and 105°W, while to the east over 90°–97°W afternoon precipitation is also frequent with the greatest occurrence along the Gulf Coast. This afternoon maximum has been related to the sea breeze (e.g., Carbone and Tuttle 2008) but may also include other mechanisms as the nighttime onshore winds are greater than in daytime.
The enhanced surface convective available potential energy (CAPE) is consistent with convection in both regions but with a greater increase on the eastern side than that of the western side because of higher boundary layer humidity. Convective inhibition (CIN) is reduced, that is, positive anomaly, mainly to the west (Figs. 5c,d) where rising motion intensifies from 1200 to 1500 LT in both NARR and the simple model (Figs. 5e–h), consistent with the enhanced precipitation occurrence (Figs. 5a,b). The magnitudes of simulated subsidence are slightly greater than those in the NARR while the area of the rising motion is smaller. One possible reason for these discrepancies is that feedbacks from precipitation to the low-level vertical motions are also included in the reanalysis and thus enhance the rising motion. Although the afternoon subsidence on the eastern side of the domain (96°–90°W) from low-level divergence weakens its daytime decrease of CIN and so is unfavorable for the development of convective precipitation, a secondary peak in precipitation still occurs, likely from the daytime enhancement of convective instability (i.e., more CAPE and less CIN).
c. Diurnal oscillation of vertical winds related to the dynamics of the jet
To complement the night and day snapshot just discussed, the full diurnal variation of the frequency of convective precipitation is summarized in Fig. 6a by averaging it between 35° and 40°N. Its maximum on the western side from noon to the evening matches the maximum of rising motion (Figs. 3c,d), as does the eastward extension of precipitation occurrence from midnight to the early morning. In sum, the development of low-level rising motion is important for supporting the afternoon precipitation over the western Great Plains and the nocturnal peak over the central Great Plains. Although precipitation is closely coupled with the low-level circulation and can enhance convergence, our simple model suggests that its diurnal variability is largely driven by the diurnal oscillation of the near-surface pressure gradients and friction and the physical mechanism behind these forcing terms.
The diurnal cycle of the vertical velocities (or the low-level convergence and divergence) can be explained through a vorticity budget analysis. In the one-layer model [Eq. (1)], changes of convergence are related to the variations of vorticity through the following equation:
where ζ = ∂υ/∂x − ∂u/∂y is relative vorticity and β = df/dy. The convergence term is on the lhs of the equation. The first term on the rhs is the vorticity tendency, the second term is the meridional transport of planetary vorticity, and the last is the drag term.
Anomalous convergence develops in the afternoon on the western side of the jet between 100° and 105°W and extends toward the central Great Plains on the eastern side of the jet from midnight to about 0900 LT. The two maxima of anomalous convergence at 0600 and 1900 LT (Fig. 6b) are consistent with the maxima of precipitation frequency on the eastern and western sides of the domain, respectively (Fig. 6a). The anomalous divergence to the west from midnight to noon inhibits convective precipitation and is consistent with the minimum occurrence of convective precipitation. The large-scale subsidence from 0900 LT to midnight in the eastern plains inhibits deep convection. The maximum of precipitation frequency around 1500 LT (Fig. 6a) is mainly related to enhanced convective instability associated with the relatively high daytime CAPE and CIN (Figs. 5c,d). The development of the anomalous convergence and divergence is mainly balanced by the tendency of vorticity (Fig. 6c), with anomalous positive (negative) vorticity tendency corresponding to the anomalous rising (sinking) motions. The diurnal oscillation of planetary vorticity transport is about one magnitude smaller but can become dominant with space and time averaging (e.g., Pu et al. 2012), and the drag term is less than one-half of the tendency term and so contributes less to the diurnal variations of convergence (but determines the daily mean). Changes of vorticity tendency can be inferred from the diurnal cycle of relative vorticity (Fig. 6d); for example, the positive tendencies from midnight to 0300 LT on the eastern side are related to the switching from negative vorticity anomalies to positive anomalies.
Decomposition of the vorticity variations into the changes from meridional and zonal winds (Figs. 6e,f) shows that the primary contribution is that of the diurnal oscillation of ∂υ/∂x, that is, the zonal gradient of the meridional wind, as forced by the variations of near-surface pressure gradient and friction. In the early evening, the eddy viscosity associated with turbulent mixing quickly decreases after sunset, while the positive zonal pressure gradient associated with the surface heating is still relatively high (Figs. 2c,d), so that the GPLLJ intensifies overnight from 1800 to 0600 LT. Positive anomalies of the zonal gradient of meridional wind (∂υ/∂x) and thus anomalous positive vorticity to the west of the jet core and anomalous negative ∂υ/∂x and vorticity to the east are established. The strength of the jet as well as that of the vorticity reaches maxima around midnight. The intensification of the jet decreases from midnight to the early morning as the near-surface pressure gradient weakens. Around 0600 LT, the magnitude of zonal pressure gradient reaches its minimum when the surface friction starts to increase after sunrise (Figs. 2c,d), and the jet weakens. The pattern of vorticity shifts accordingly following the variations of ∂υ/∂x. From about 0600 to 1800 LT negative vorticity anomalies occur on the western side when the strength of the jet is below its daily mean, while positive vorticity anomalies are established to the east. As the jet reaches minimum around noon, the anomalies of negative (positive) vorticity to the west (east) also peak. Changes of the meridional gradient of zonal wind (i.e., −∂u/∂y) slightly enhance the vorticity anomalies to the east, but weaken the vorticity anomalies to the west.
In short, a vorticity analysis shows how in response to the diurnal variations of near-surface pressure gradient and drag patterns of rising/sinking motion to the west and east of the jet core are developed to balance the anomalous vorticity tendencies produced by the zonal gradient of meridional wind related to the diurnal cycle of the GPLLJ.
4. Discussion and conclusions
We have examined the relationship between the spatial pattern of the convective precipitation occurrence and the diurnal cycle of boundary layer winds over the Great Plains. The dynamics of the GPLLJ and associated vertical winds are shown using a linearized slab model.
Boundary layer vertical winds are found to covary with the diurnal cycle of the GPLLJ with periodic rising and sinking motions with opposite phase on the western and eastern sides of the Great Plains. These oscillations are best reproduced by the model when it includes diurnal variations of both near-surface pressure gradient and surface drag.
The eastward propagation of the boundary layer rising motion from day to night is consistent with the development of summer nocturnal precipitation shown in the NARR climatology. The afternoon peak of the rising motions on the western side of the domain between 35° and 40°N and between 100° and 105°W is also collocated with the maximum frequency of convective precipitation, while the subsidence on the eastern side (35°–40°N, 90°–100°W) weakens the daytime precipitation that is mainly triggered by convective instability.
Although past studies have indicated that the nighttime maximum in precipitation over the eastern Great Plains is related to patterns of convergent wind, they have not previously identified its underlying dynamic cause. This dynamical basis is implicit in past studies that related dynamical wind variability to the diurnal patterns of surface drag and pressure gradients. Forced with these terms, our model confirms that the jet peaks at midnight and slows down over the rest of the night and shows that, with this deceleration, the vorticity tendency east of the jet maximum is positive after midnight and convergence and upward vertical motion are developed. The same mechanism acts on the western side during the afternoon, and, conversely, downward motion is forced on the western side after midnight and on the eastern side in the afternoon.
The analysis and conclusions above are based on the climatological diurnal cycle of the jet and convective precipitation. We realize that there are day-by-day and interannual variability such that the timing of jet and rainfall maxima and their locations may at any given time differ from the results presented here. For instance, Hu et al. (2013) found that the jet increased between 0000 and 0600 LT based on site observations for a few days in July 2003, while Song et al. (2005) found in their 6 years of observations at a site in Kansas that 28% of the time, the nocturnal low-level jet was northerly.
The vertical winds/convergence and precipitation are closely coupled with each other. Thus, the covariations of the two do not necessarily imply causality. However, the similarity between the reanalysis climatology and slab model simulation results suggest that the diurnal oscillation of the large-scale rising and sinking motion is mainly forced by diurnal cycle of near-surface pressure gradients and friction. Also, the analysis of Ruiz-Barradas and Nigam (2013) found that moisture flux convergence leads precipitation on a pentad scale, consistent with this hypothesis.
The connection shown here between the vertical winds and convective precipitation suggests that obtaining correctly the nocturnal peak of the summer convective precipitation over the Great Plains requires accurate modeling of the various contributions to the diurnal variations of the GPLLJ.
This work is supported by a grant from the U.S. Department of Energy (DOE) (Grant DE-FG02-09ER64746).