Introduction

Most of the urban areas in the southwestern United States are located in complex terrain (e.g., El Paso, Texas, Las Vegas, Nevada, and Phoenix and Tucson, Arizona), and the wind patterns in these areas are influenced by numerous factors. As shown in Fig. 1, upper-level synoptic winds (with velocity scale U_p) “dip” down into the terrain, causing pressure-gradient-driven flows within (U_Δp). Mesoscale thermal circulation induced by a diurnal heating–cooling cycle consists of valley (U_υ) and slope (U_s) flows, with downslope/downvalley flows occurring at night and upvalley/upslope flows appearing during the day. These synoptically induced and mesoscale flows are perturbed by a continuum of orographic perturbations such as obstructions and canyons, and they are superimposed on a variety of smaller-scale flows induced by thermal and mechanical inhomogeneities. These include local urban-scale circulations driven by land-use inhomogeneities such as lake–land breeze (U_L), urban-heat-island (U_H) flows, and small-scale flows such as those through urban canyons, microfronts (e.g., slope breezes), and shear and convective turbulence.

Approximately 70% of the time, the southwestern urban areas of the United States are dominated by high pressure systems (Wang and Angell 1999), which are characterized by weak synoptic flows (U_p < 4–5 m s⁻¹, U_Δp < 1–2 m s⁻¹) and clear skies conducive for slope flows (U_s ∼ 2–5 m s⁻¹). In the Phoenix area, land-use inhomogeneities do not create significant winds, the most important in this context being urban-heat-island flows with U_H ∼ 1–3 m s⁻¹ (Fernando et al. 2001; Lucas et al. 1998). There are periods with monsoonal activity in the summer, tropical storms in autumn, or frontal storms in the winter (Douglas and Li 1996; Jurwitz 1953; Sellers and Hill 1974), but they are the exception rather than the rule for the Phoenix area. It is the typical periods with (U_Δp, U_υ, U_L, U_H) < U_s, where the slope flows play an important role in a multiscale situation, that are of interest in this paper.

The usual situation is that the effects of geographically varying features are more pronounced in the autumn and in early winter before the onset of frontal storms and again in the spring and early summer before the beginning of the North American monsoon (Comrie 1996; Brazel and Ellis 2003). However, at any time of the year, days to weeks of mesoscale and locally related variations are evident in the Phoenix area (estimated over 50% of the time for the period from June of 2002 to May of 2003). Several research papers on the area have included analyses of flows (e.g., Comrie 2000; Ellis et al. 2000; Frenzel 1963; Kirby and Sellers 1987; Fast et al. 2000; Stewart et al. 2002). In this paper, the focus is on thermally driven circulation in the urban basin of Phoenix. The emphasis is on evening transition between the up- and downslope flows that have received little attention in the past, in the context of which some interesting phenomena have been noted during recent observations and for which some theoretical descriptions have also been advanced.

The topography of metropolitan Phoenix area is shown in Figs. 2a and 2b, together with monitoring sites operated by various agencies. In this area, variations in terrain inclination near abrupt slopes typically are greater than 1° to the north, east, and southeast, but, on average, the slopes are not steep (<0.5°) in most of the areas, with major river channels draining from the southeast, east, and north to the northwest, west, and south. As a result of this orientation and terrain configuration, the only first-order weather station in the region (located at Sky Harbor International Airport) experiences annual wind regimes dominated by slope winds aligned with the Salt River channel (e.g., Frenzel 1963). A pronounced shift in local wind regimes typically occurs between day and night. Note that the nature of the basinlike topography does not allow clear distinctions between slope/valley winds in the idealized sense described by Whiteman (1990, 2000, and valleylike features can be discernible in all directions. Under low synoptic winds, the daytime winds are mainly westerly toward eastern/northeastern mountains and can be considered as upslope winds, and the flow reverses at night. Given that it is difficult to define the slopes and valleys in the Phoenix area, the terms slope winds and valley winds have been interchangeably used in describing flow in this valley. Whiteman (1990) defines the term slope winds to describe thermal circulation in basins, but in our case, the topography is neither a pure basin nor a slope–valley configuration. Further discussions on thermal circulations in the Phoenix and Tucson areas can be found in Balling and Cerveny (1987), Berman and Delaney (1975), Comrie (2000), Ellis et al. (2000), Fast et al. (2000), Fernando et al. (2001), Stewart et al. (2002), and Lee and Fernando (2004).

As mentioned, some interesting features pertinent to the evening transition have been noted in recent Phoenix area observations. One of these is the lag between the time of wind shift at greater heights and that of the reversal of solar radiation from heating to cooling (which will be referred to as the transition lag). This lag can be as high as 3–6 h and is not correlated with synoptic variability (Stewart et al. 2002). The nighttime pattern of cooling and subsequent drainage flows on the lower slopes and at the bottom of the valley are great challenges for analysis and modeling, because they vary continuously and are not necessarily in equilibrium. In addition, they depend on a variety of other factors such as topographic setting, exposure, land use, and other urban influences.

The purpose of this paper is to investigate the nature of the transition lag and the flow development in early to midevening using selected surface weather sites in the Phoenix area. Although most of the paper is about the evening transition, flow patterns for the entire evening and nighttime period are illustrated for one winter period (1800–0600 LST 14–15 January 2003), considering that winter periods are more conducive for high pressure conditions (U_Δp ≪ U_s). Note that the days selected for our analysis are characteristic of the days with high pressure conditions for the seasons concerned, and hence conclusions to be made have general applicability. Given that the transition occurs within a few hours with initial characteristic velocity and length scale at the beginning of transition that are on the order of 5 m s⁻¹ and 10 km, respectively, the Rossby number tends to be greater than 1. Therefore, the effects of the earth’s rotation are neglected for the transition-period analysis. As the winds weaken during transition, however, Coriolis effects ought to become important, but it is assumed that the sidewalls of the urban basin act as a constraint for wind rotation that may occur because of Coriolis forces.

Evening transition on a slope—Theoretical concepts

Evening transition on sloping boundaries involves a sequence of processes. At about sunset or about 0.5–1.5 h before it, the generation of convective turbulence ceases, with the air layer within the lowest few tens of meters starting to cool (typically 1°–4°C h⁻¹, depending on the location and season). This condition causes the positively buoyant air layer near the ground to lose buoyancy, finally becoming negatively buoyant to initiate the downslope flow (Defant 1949). Although the evening transition over flat terrain has been studied using field experiments (Acevedo and Fitzjarrald 2001), numerical simulations (Nieuwstadt and Brost 1986), and theoretical analysis (Goulart et al. 2003), evening transition on complex topography has not been considered in detail until recently. Hunt et al. (2003) conducted a theoretical analysis in this regard by considering the idealized problem of Lagrangian movement of fluid parcels over a uniform slope, with the surface air layer subjected to gradual cooling of the form Δθ = −Δθ₀(t/Δt_θ), where Δθ is the perturbation to the undisturbed background potential temperature profile at the boundary layer height, Δt_θ is the time scale of cooling, t is the time, and the buoyancy jump is defined in terms of the reference temperature θ_r as Δb = −gΔθ/θ_r, with g being gravitational acceleration (Note that Δb > 0 for a negatively buoyant fluid). This cooling was imposed on an already established upslope flow, the velocity scale of which was derived theoretically as U_M = λ_uα^1/3w∗, where α is the slope angle, w∗ is the Deardorff convective velocity, defined in terms of the surface buoyancy flux q₀ as w∗ = (q₀h)^1/2, h is the upslope flow (boundary layer) height, and λ_u is a constant. The velocity of a fluid parcel starting at x = 0 at time t = 0 with a velocity U₀(z) was shown to decrease with time (i.e., with the distance along the slope x) as

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where the subscript 0 indicates an initial value at t = 0. Note that the last term dominates the penultimate term, and thus the prescribed cooling leads to the formation of a stagnation front at a distance

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as illustrated generally in Fig. 3. After the front forms, a downslope current is initiated upslope of the front (a transition front), and its downslope movement causes the lifting up of colder fluid from near the ground (much like a paint stripper). The dense air above the warmer air so generated causes convective instability, and hence the region around the front is characterized by intense turbulent mixing. A laboratory demonstration of this phenomenon was also presented by Hunt et al. (2003).

Using the above expressions, we may estimate the time for the transition t_d, which can also be considered as the time delay of transition t_d after the buoyancy reversal. Using U(z, t) = dx/dt, and upon substituting for U(z) from (1) and for x_F from (2),

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This expression, which is valid for the entire radiational cooling layer, predicts larger transition times at lesser (gentler) slopes, slower cooling rates, and larger initial heat fluxes (before the cooling begins). Note that (3) is independent of the horizontal extent of the circulation system, given that the boundary conditions for the flow deceleration are specified at the slope break.

Another important aspect is the variations that occur above the cooling layer. The upslope flow therein is not directly subjected to negative buoyancy forces, and hence inertia of this air mass (of thickness on the order of h ∼ 0.5–4 km) continues to propel it upslope, only to be retarded by shear stresses propagating upward from the reversed flow (i.e., initial phase of the katabatic flow) beneath. The reversed flow sustains only small Reynolds stresses because of the suppression of turbulence by stable stratification. Thus the ground-level flow tends to disconnect from the upper-level upslope flow, wherein the latter is retarded by the shear stresses within. The time scale of the upper-level flow retardation can be estimated using the dominant terms of the momentum equation, namely,

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where h is the convective layer depth of the upslope flow (velocity U_s), σ is the rms velocity, and the factor 0.5 in (4) represents the correlation coefficient (Townsend 1976). Using typical values (Monti et al. 2002) σ ≈ 1 m s⁻¹, U_s ∼ 5 m s⁻¹, and h ∼ 2 × 10³ m, it is possible to evaluate the time scale of transition of the entire convective layer as T_d ∼ 6 h. Of course, this estimate varies from site to site, and specific estimates for the cases in point are given in Table 1. The heuristic estimates given above suggest that transition occurs in two phases, very near the ground in a thin layer (<100 m) dominated by radiational cooling (associated with a mixing front and time delay t_d, as in Fig. 3) and a slower (frictional) deceleration of the air mass aloft the cooling layer (with a time scale T_d) that tends to decouple from the lower layer because of stable stratification.

Note that the low-level transition front drains down the slope, much like a gravity current. When it reaches the bottom of the valley, which has a gentler slope, the flow hydraulically adjusts to the new topography (e.g., through a hydraulic jump). Transition fronts reaching low-elevation slopes also can cause sudden wind gusts. Additional complications are introduced in urban valleys, for example, because of local variations in slopes associated with washes, small hills, freeways, artificial water sources (e.g., lakes), land-use changes and other natural and built-up features. Such inhomogeneities may either induce or alter local flow patterns.

Observations from the Phoenix Air Flow Experiment

Although data from long-term operational networks form the basis of this study, they are mostly available in hourly averaged form and hence are often insufficient to obtain a detailed understanding. Therefore, as background material, here we discuss high-time-resolution data obtained during a field campaign conducted during 14 January–4 February 1998, known as the Phoenix Air Flow Experiment (PAFEX-1). In this project, vertical virtual potential temperature and wind data were collected at a central urban Phoenix location in winter (Grachev et al. 1999; Fernando et al. 2001; Lee and Fernando 2004) to study the urban boundary layer during calm atmospheric conditions (the PAFEX-1 site is indicated as a star in Fig. 2a).

PAFEX-1 included observations of atmospheric conditions from the surface to 200-m altitude for a set of winter days, especially over the night and including morning and evening transition periods. The results illustrate a very shallow layer of air as a part of the initial evening drainage flows that develop over the slopes. Figure 4 shows a typical progression of vertical virtual potential temperature prior to and for an early evening transition period on 31 January. Figure 5 shows the u, υ, and w wind components and air temperature for this same period and site. Note the passage of a downslope front emanating near the site for the same period. Downslope wind started with stable stratification (and cooling) at about 1740 LST, followed by warming (mixing), and then further cooling in the lower layers throughout the evening. The lower layer is shallow (∼40 m), often below the lowest levels of current observations of the radar profiler system (115 m). A stagnation point is identified by 1738–1741 LST, prior to the downslope front passage at this location, possibly caused by the mechanism discussed in section 2. We note that key variations to look for in the standard weather observational system records (and in the absence of actual u, υ, and w data) associated with the early evening transition period would be the slowing down of the upslope flow to near zero, followed by reversal in wind direction and the onset of increased winds of the downslope/downvalley regime. In addition, we should observe associated alterations in temperature cooling rates (perturbations associated with the transition fronts—either cooling or warming and intense mixing) and possible rapid fluctuations or changes in dewpoint temperatures.

Data analysis and methods

For this paper, we analyze the early evening transition for four selected periods in 2002–03 in different seasons for sites shown in Fig. 2. In recent years, there have been several automated weather networks put in place for various purposes in the Phoenix region. In addition, the Arizona Department of Environmental Quality has established a radar profiler system in the midst of the urban area (labeled VEL in Fig. 2), which includes recording of air temperature, wind direction, horizontal wind speed, and vertical wind starting at a level of 110 m up to 1 km (Fast et al. 2000).

A full analysis of the entire historical record for all of these data is beyond the scope of this paper. We have determined that the number of days of potential local thermal circulation range from 13% (July) to over 70% (June) for the period June 2002–May 2003. This was determined by analyzing the Sky Harbor record with the criteria of noting sharp evening wind shifts from west to east coincident with clear nights and winds of less than 5 m s⁻¹. Examples of the usefulness of some of these data to study the evening transition phenomenon are illustrated for four selected seasonal periods—6–7 June and 8–9 October 2002 and 14–15 January and 8–9 March 2003. During these specific months, many days experienced local circulations (i.e., June 2002, 70%; October 2002, 41%; January 2003, 58%, and March 2003, 52%). These periods were chosen based on identifying weak regional pressure gradients, low synoptic winds (U_S > U_p or U_S ≪ U_Δp; see Table 1) and low specific humidities for the respective times of year of June (premonsoon), October (postmonsoon), January (midwinter), and March (spring). We used the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis daily composite interactive Web site to choose exact dates based initially on identifying clear, calm periods. A detailed inspection showed that these days are representative of high pressure days in these months [the NCEP–NCAR reanalysis is the result of a project that is described in Kalnay et al. (1996)]. During the four periods chosen, for example, 850-hPa geopotential height anomalies from monthly normals were +10, +10, +30, and +15 hPa for the region centered over central Arizona for the June, October, January, and March sample days, respectively. Zonal, meridional, and vector winds (U_Δp) at 850 hPa depicted for these dates from the reanalysis database were less than 2 m s⁻¹ in all cases. These periods were generally conditions of ridging in the western United States, with weak regional pressure gradients in the Southwest and along the West Coast. We also analyzed the typical meteorological year 2s (TMY2s) data (National Renewable Energy Laboratory 1995) for Phoenix in relation to the times of year we chose for 2002–03 to compare with the long-term hourly patterns revealed in the 1961–90 TMY2s database. The days we chose for analysis in this paper resemble very closely typical diurnal patterns of wind speed and, in particular, wind direction evident in the TMY2s data profile for the Phoenix Sky Harbor Airport for those times of the year for clear weather. Although our general discussion for these periods highlights the timing and spatial aspects of the evening transition, we further focus on the 14–15 January 2003 period in some detail in this paper by illustrating the maps of 1800–0600 LST wind directions because of the persistent high pressure conditions in the winter and their implications in local air quality.

Surface wind records used for the four periods are as follows: (a) on-the-hour and 5-min data (for identifying more closely the stagnation time) from the Phoenix Real-Time Instrumentation for Surface Meteorological Studies (PRISMS) network (Pon et al. 1998), (b) Sky Harbor’s Automated Surface Observing System hourly data, (c) three Maricopa County Air Quality (MCAQ) sites’ hourly data (both winds and low-level delta temperature in the first 10 m), and (d) data from an automated weather station (5-min resolution) atop a dam of a lake in the channel of the Salt River (near star for other sites in Fig. 2a). In addition, as indicated earlier, we accessed hourly records of the VEL radar profiler system (data for 8–9 March are not available). For this work, we only resolve data on an hourly basis, because the Sky Harbor station information is only available routinely on that basis. No sounding data are available for the Phoenix region, other than soundings conducted by the Salt River Project, a power/energy company, during severe weather conditions (J. Skindlov, Salt River Project, 2004, personal communication).

The PRISMS network consists of recently installed propeller/vane anemometer systems, which recently replaced older National Weather Service large 3-cup anemometer and separate wind vane systems (prone to having too high a starting speed of over 1 m s⁻¹). This change provides further justification for analyzing more recent archives for 2002–03, because we have more confidence in the data for low wind speed conditions in using the PRISMS and MCAQ results than for historical periods prior to this time. PRISMS data are communicated in real time to a central hub of the Salt River Project through their microwave communications system linking electrical energy substations throughout the metropolitan area. In cooperation with Arizona State University’s Office of Climatology, the state climatologist (archival function), and the National Weather Service, these data become available for a variety of applications. Sometimes there are sporadic communication problems that produce data gaps. The periods we chose were also selected to minimize these data problems. However, even for the periods chosen, there were a few 5-min segments of missing records for some sites. In those cases, we produced simple linear interpolations between time periods. No periods of missing records spanned longer than 10 min of time. The MCAQ sites use instrumentation similar to that of PRISMS, and there were no missing records for our periods. The dam-site weather station was a complete Campbell Scientific, Inc., automated weather station (sensitive Met One Instruments, Inc., 034A wind vane and 3-cup anemometers) set for 5-min intervals and had no missing records; this station was operated by the authors. Although our focus is on the near-surface wind field, we made note of the lower levels of the profiler data to illustrate the upvalley/upslope flow strength and flow stagnation above the 110-m level in comparison with that estimated for 10-m level from surface weather sites.

For all sites, a determination was made of the local slope and aspect (250-m radius around a site) from a digital elevation terrain map of the region using ESRI Company ArcView GIS. Using the hourly records, an estimate was made of the stagnation time and switch to downslope/downvalley flow. This estimate was accomplished by analyzing for when the upvalley/upslope winds were considerably reduced after sundown (in some cases dramatically, to near zero), when the wind direction was first rapidly changing from upvalley/upslope directions toward downslope/downvalley, (in some cases) when obvious temperature cooling rates were accelerating, or when temperature and dewpoint “jumps” were occurring. The PAFEX-1 project results suggest this local wind shift may be rapid (over minutes), indicating frontal features. We cannot resolve with the historical data this kind of accuracy, and so we estimated the timing of transition to the nearest hour. We checked the 5-min-resolution data of the PRISMS network and determined the hourly estimates were reasonable, because there was considerable variability well exceeding an hour among the sites.

Results

The 14–15 January 2003 period

To illustrate the spatial progression of transitions after sundown across the sites, the 14–15 January 2003 hourly sequence (1800–0600 LST) is shown in Fig. 6. Several features can be noted: (a) general maintenance of upvalley/upslope flow after 1800 LST, in particular for some sites west of the urban area in lower elevations (e.g., the Collier, Sheely, and Kay sites); (b) opposing directions of wind in many small areas at locations likely experiencing the transition (e.g., Pringle and NP at time 1900–2100 LST); (c) initiation of downslope/downvalley flow over larger subareas starting at about 2000 LST and progressing forward (e.g., apparent in the eastern upper sections of the terrain); (d) a possible heat-island cyclonic circulation or a convergence phenomenon relative to the urban center commencing at 2100 LST and more pronounced toward midnight [when the katabatic flow is still weak, with U_S/U_H ∼ O(1)]; and (e) fully established downslope/downvalley flow after midnight, when U_S/U_H is greater than 1. All of these observations are in agreement with the theoretical framework discussed in section 2 and the multiscale flow features alluded to in section 1.

The possibility of a heat-island circulation in early evening is consistent with temperature-progression differences between two rural sites (Collier and Falcon) in comparison with Sky Harbor hourly air temperatures from 1800 to 0600 LST (Fig. 7). The airport, close to the city center, is often assumed to be representative of an urban site (Balling and Cerveny 1987; Brazel et al. 2000). The heat island, as determined in this manner, peaks at 2200 LST and is over 5°C. If we assume we have appropriately characterized a heat island using the two rural sites against Sky Harbor’s data, it appears to be diminishing once a more well-defined downvalley/downslope flow commences, and it is considerably reduced by 0300 LST but is reestablished toward the minimum temperature time of 0600 LST. Doran et al. (2003), in their experiment of the Phoenix area that focused on the morning transition period, raised a question for future researchers regarding apparent vertical mixing that seems to occur 1–3 h earlier than might have been anticipated from the nature of potential temperature profiles and the development of conditions conducive to convective mixing. Whether we have confirmed a heat-island circulation or a series of flows that are converging on entering the valley bottom from differing directions remains for more detailed assessment using numerical modeling together with detailed field data.

Multiscale effects of the heat-island flow and downslope/downvalley flows can further be quantified using the appropriate idealized expressions for the katabatic winds and urban-heat-island circulation. According to Princevac et al. (2004, manuscript submitted to J. Atmos. Sci., hereinafter PFH), the layer-averaged velocity of the katabatic winds can be written as U_s = λ_K(ΔbL_s sinα)^1/2 where λ_K is a constant and L_S is the along-slope length scale. Lucas et al. (1998) presented laboratory results on flow induced by an urban heat island of width W and a horizontal buoyancy jump across it of Δb_H as U_H = λ_H (Δb_HW)^1/2, where λ_H is a constant. Thus the parameter determining the relative importance of the urban heat island and the slope (katabatic) flows becomes

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where Δθ is the corresponding temperature differential. Laboratory and field-derived characteristic values for the constants are λ_K = 0.6 (PFH) and λ_H = 0.06 (Lucas et al. 1998). In the period following evening transition, the temperature deficit of the slope flows is Δθ ∼ 2°C and for heat island Δθ_H ∼ 5°C, and with L_S = 100 km (for the flow drainage from northeastern and northern mountains) and W = 50 km (valley width), it is possible to estimate U_s/U_H ≈ 0.9, indicating that the urban-heat-island effect plays an equally important role as the katabatic flow. Here the average slope for all stations (0.642°) has been used. For the late evening and early morning, the temperature deficit of the katabatic winds becomes larger, Δθ ∼ 10°C, and, assuming the same heat-island influence, it is possible to estimate U_s/U_H ≈ 2, implying that the slope flows have an overriding influence over the heat-island-induced flow.

Another comparison (Table 3) highlights the variable timing and the shallow nature of the air that is in transition in the early evening for this date, confirming the theoretical descriptions of section 2 and the comments of Fast et al. (2000). The Superstition (Sup) site is in the higher elevations to the east, upslope from the urban area, Sky Harbor (SH), and the urban VEL site. VEL 110–275-m-level wind directions are shown for comparison with the surface wind directions of the Sup and SH sites. The easterly flow across the city center to depths over 110 m does not occur until midnight and thereafter, whereas the extreme easterly part of the region experiences downslope surface flow from the east at 2000 LST and Sky Harbor’s transition occurs 2 h later at 2200 LST. Given that the area-averaged slopes (over 10 km, slope flow scales) of the SH and Sup sites are approximately 0.2° and 1.42°, respectively, the time lags of near-surface transitions can be evaluated as (t_d)_SH/(t_d)_SUP = (α)^1/3_SUP/(α)^1/3_SH ≈ 1.8. This is broadly consistent with the observed delay times of approximately 4.5 h at the SH site and approximately 2 h at the Sup site. Table 3 also shows that the transition at higher altitudes (VEL 1–4) occurs much later than near the surface, consistent with larger values of T_d, as estimated in section 2.

Conclusions

Evening transition in the Phoenix metropolitan area was investigated for sample days for various times around the year under weak synoptic conditions that favor local thermal circulation. Clear thermal circulation patterns and their diurnal variability were evident from the data taken from routine monitoring stations, as well as a wind profiler operated by a local agency. These data, as well as those taken from a 1998 field campaign, showed that the evening transition is sensitive to numerous factors, such as the exposure, the elevation, and the magnitude of slope. The data were consistent with a recent proposal by Hunt et al. (2003) that the first transition occurs in a thin layer near the ground, on the order ot tens of meters, as a well-defined front, which then propagates downward as a gravity current head and creates “slope breezes” in low-elevation slopes. While this thin colder air layer flows downslope, the existing upslope flow aloft continues to flow while weakening gradually and reversing after some time. Therefore, the transition is height dependent, but the work reported herein mainly addressed the surface-level phenomena, and further work is called for to study the vertical variability of the transition process.

The dynamical basis of the Hunt et al. (2003) formulation was borne out well by the observations. The theory assumes that, because of radiational cooling, the surface layer decreases its positive buoyancy and become negatively buoyant after some time. When the inertia forces are too feeble to overcome this negative buoyancy, the transition to the downslope flow occurs. We extended the Hunt et al. (2003) formulation to calculate the time period during which the upslope flow can continue against the buoyancy forces due to cooling, which is an indicator of the delayed transition over the slopes. The observational data taken at various slopes agree reasonably well with the delay time scale proposed.

Another issue of interest was the multiscale flow in urban areas, which needs to be considered in interpreting slope-flow observations. The study periods were devoid of major synoptic effects, but the urban-heat-island effects were evident in the early evening, soon after the transition occurs. Simple quantitative estimates were given to delineate the conditions under which the heat-island effects become important, which was consistent with the observations. Another contributor is the Coriolis effect, which may become important as the flow weakens during the evening transition. This effect was not considered in the data analysis; it was assumed that the sidewalls of the valley prevent Coriolis-induced turning of the flow (e.g., formation of inertial oscillations). This assumption needs to be investigated further in future work.