## 1. Introduction

Cold-air pools (CAPs) are cold air that resides in terrain pockets surrounded by elevated topography. A CAP has weak and variable winds, is colder than overlying air, has a stable core-temperature profile, and is capped along ridge heights by a temperature inversion with varying intensity and depth (Whiteman et al. 2001). If a CAP resists a diurnal warming or synoptic displacement it can persist for up to 2 weeks, thus becoming a “persistent CAP.” Persistent CAPs suppress vertical mixing, increase ground-level air pollution, and decrease visibility to hazardous conditions in urbanized valleys and basins (Smith et al. 2010; Malek et al. 2006). Current research on CAPs has been conducted for inhabited valleys that vary from a few hundred square meters in areal coverage (Whiteman et al. 1999) to tens of square kilometers (Whiteman et al. 2001; Zhong et al. 2001; Rakovec et al. 2002) as well as for some enclosed basins or sinkholes (Clements et al. 2003; Whiteman et al. 2004; Steinacker et al. 2007). Climatological analyses of persistent CAPs in the western United States (Wolyn and McKee 1989; Reeves and Stensrud 2009) revealed that they are mainly wintertime events that are initiated either by cold-air frontal advection into terrain pockets or by a typical nighttime temperature inversion under clear skies, which is enhanced as warm air aloft advects, descending and deepening the stable layer. The persistent CAP is then efficiently destroyed when strong disturbances associated with a regional trough move over the area. The onset and maintenance of persistence CAPs have been verified by smaller observational datasets and modeling analyses (Lee et al. 1989; Whiteman et al. 1999, 2001; Zhong et al. 2001; Zängl 2005; Hoggarth et al. 2006).

Understanding the characteristics of CAPs can aid in a better understanding of this phenomenon and can possibly improve its prediction. Most of the current modeling studies address questions that target specific observational case studies, and this research has provided the current knowledge and understanding of CAP dynamics. In this study, we used a systematic numerical modeling approach to investigate the characteristics of CAPs (e.g., vertical temperature structure and cooling rates of the basin and slope environments) and their relationships to ambient stability, basin size, and slope angles. The goal is to build a framework upon which the results of high-resolution numerical modeling of the cooling process of a basin environment are assessed and are compared with relevant observations and other modeling results.

## 2. Method

### a. Model and simulation setup

For simulating a CAP under quiescent nighttime conditions in a basin environment we have chosen the Advanced Regional Prediction System (ARPS; Xue et al. 2000, 2001). ARPS is a nonhydrostatic compressible atmospheric model that is designed to perform simulations on regional scales to the microscale with a terrain-following coordinate system. ARPS has been validated in numerous studies (e.g., Chow et al. 2006; Weigel et al. 2006) and also has been cross compared with other models for different atmospheric stability conditions (Fedorovich et al. 2004; Beare et al. 2006). For this study, the ARPS simulations are strictly two dimensional (2D) with an adequate number of grid points (varying between 299 and 1043) in the west–east direction to minimize numerical contamination at the inflow boundary for different topographical scenarios. The setup has four grid points in the crosswind direction (north–south), with one central grid point on which the solution is carried out and one and one-half grid points on each side for boundary conditions (scalar and vector quantities). A wave-radiation open boundary condition (Klemp and Durran 1983) was used at the inflow boundary, and periodic conditions were applied at crosswind boundaries (north–south), which allows for an infinitely long north–south direction with no flow simulation from that direction. Coriolis force was neglected because of the 2D idealized settings and the relatively small spatial (maximum basin width of 16 km) and temporal (8 h) scales. The subgrid-scale turbulence local closure scheme used was the 1.5-order turbulent kinetic energy model. The horizontal grid spacing was 100 m, and the vertical grid is stretched following a hyperbolic tangent equation with minimum grid spacing of 10 m near the surface, increasing to 20 m at midbasin height (500 m) and to a maximum of 190 m at model top (10 km). The simulations assumed clear-sky conditions, and therefore no microphysics or cloud processes were included. The radiative schemes adopted in ARPS were after Chou (1990, 1992) and Chou and Suarez (1994) and include a full radiative transport mechanism. For further descriptions of ARPS model physics see Xue et al. (2000, 2001), and for an alternative example and performance of a 2D-ARPS model setup refer to Katurji et al. (2011).

### b. Experimental design

The topography was chosen to represent a simplified basin (1000 m deep), slope, and plateau setting as shown in Fig. 1a along with the basin widths Wb, slope angles SA, and basin cross-sectional areas *A* for the 20 different simulations (Fig. 1b) for each of the two atmospheric ambient stabilities chosen (a total of 40 simulations). The width of the basin decreases from 16 km, which scales to a medium-size populated basin such as Utah’s Salt Lake basin, to 2 km, which represents small basins/sinkholes such as Colorado’s Sinbad basin. The slope angles approximate real slope values, starting at 5.7° and reaching a steep slope of 26.5°. The initial and ambient atmospheric temperature profiles were determined on the basis of derived mean vertical profiles of temperature from climatological and experimental studies of persistent CAPs (Wolyn and McKee 1989; Reeves and Stensrud 2009; Whiteman et al. 2001). Two atmospheric stability conditions were considered: the strong-stability case with a temperature inversion of +6 K km^{−1} and the weak-stability case with near-isothermal (+0.2 K km^{−1}) conditions. Initial wind speeds for all 40 simulations were set to zero, and the simulations were run for an 8-h nighttime period in a midlatitude region.

## 3. Results

The analyses of the results are based on examination of cooling trends and evolved flow structure as a function of basin shape (in terms of its size and slope angle) and the background atmospheric stability. The basin and slope surfaces cool as a result of surface net-radiative energy loss, which leads to a negative sensible heat flux that cools adjacent air layers and results in downslope flow and convergence on the basin floor (Yoshino 1984). This process creates rising motion in the basin center and further cools the upper-air layers by adiabatic expansion. This process continues until the basin floor is covered by a strong surface-based inversion and cools considerably to allow for relatively warmer (less dense) downslope flow detrainment from the slope into and over the more stable air within the surface inversion (Baines 2001; Princevac et al. 2005). The flow that separates from the slope can also converge over the surface-based inversion and rise, further cooling the upper-basin layers.

### a. Downslope wind

We first examine the magnitude of the maximum downslope wind speed and the location of its occurrence up the slope and relate these properties to the basin area and slope angle. The maximum downslope winds were attained by inspecting the grid points over the slope at all vertical and horizontal levels, and they almost always occurred at the first model vertical level above the slope surface; a higher vertical resolution would have been required to resolve a near-surface downslope jet. The maximum wind speed (5.5 m s^{−1}) was attained for the largest basin having the weakest slope gradient, whereas the minimum wind speed (3.5 m s^{−1}) occurred for the smallest basin having the strongest slope gradient. These simulated downslope wind speeds fall within observed values of nocturnal slope flows for different slope angles (Whiteman and Zhong 2008; Zhong and Whiteman 2008; Haiden and Whiteman 2005; Monti et al. 2002).

The location of the downslope wind speed maxima up the slope, as defined by height above basin floor, and its relation to the slope angle and basin size are shown in Fig. 2. As the basin gets smaller the maximum downslope wind speed magnitude is reduced and is located farther up the slope, whereas for the larger basins (Wb = 16 km) the rate of cooling of the basin atmosphere is less (as discussed in the following section), especially for the upper area of the basin (Fig. 2a) and as a consequence the cold air flowing down the slope attains its quasi-neutral buoyancy farther down the slope.

*u*and

_{s}*w*are the along-slope and normal wind components,

_{n}*ρ*is air density,

*p*is the air pressure,

*g*is the gravitational acceleration,

*θ*is air potential temperature,

*x*is the Cartesian coordinate (Fig. 1a),

*s*is the along-slope coordinate (positive up the slope),

*n*is the normal-slope component,

*t*is time, and

*α*is the slope angle. Terms I–IV represent the downslope wind speed tendency, along-slope component of the horizontal pressure gradient force, buoyancy force, and turbulent dissipation, respectively. Points 1 and 2 represent the locations on the slope surface and the corresponding same-height location above the basin center, respectively. As shown by the dotted line in Fig. 3, which is the best fit to all data points, the maximum downslope wind speed increases linearly as the basin area increases. This is because the larger basins correspond to stronger horizontal wind speeds within the basin environment (Figs. 4e,f), suggesting that the pressure gradient force directed from the slope to the center of the basin is higher. Thus term II of Eq. (1) increases as the basin area increases. If we were to use the bulk average temperature difference between the slope environment (averaged for area

*A*in Fig. 1a) and the same height above the basin floor (averaged for area

_{s}*A*

_{uWb}) to represent the temperature differences in term II, we would also find out that the difference of this temperature gradient between the large and small basin areas also increases (taking temperatures at hour 8 in Fig. 7, discussed in detail below). Hence, terms II and III increase together as the basin area increases, yielding a higher downslope wind speed for wider basins.

A closer examination of Fig. 3 reveals that, although the linear relationship between maximum downslope wind speed and the basin size exists for all slope angles, the rate of change is slightly affected by the slope angles. For example, the rate of increase of maximum downslope wind speed with basin size along a line passing through the diamonds representing a 26.5° steep slope is faster than that along a line through the dots representing a 5.7° gentle slope. In other words, a steeper sidewall slope corresponds to a higher rate at which maximum downslope wind speed increases with the area of the basin.

For the case of varying slope angles the relationship between the maximum downslope wind speed and the slope angle remains linear (solid linear trend lines in Fig. 3), but the maximum downslope wind speed becomes less sensitive to the slope angle for larger basin areas (as shown by the increase of slope of the solid linear trend line as the basin area increases). To explain this by referring to Eq. (1), a decrease in slope angle *α* would lead to an increase in term II and a decrease in term III; also, as *α* decreases, the basin area increases (as shown in Fig. 1), resulting in a further increase of term II, as discussed in the paragraph above. Hence, a lower slope angle corresponds to an increase in downslope wind speed tendency [Eq. (1)] and therefore higher maximum downslope wind speed. As the basin area gets larger, the effect of the slope angle on terms II and III diminishes and the relationship between the maximum downslope wind and slope angle becomes weaker (as shown by the decreased tilt of trend line for larger areas in Fig. 3a).

### b. Vertical structure and evolution

Figure 4 shows the basin half-width area-averaged (*A*_{hw} in Fig. 1a) vertical profiles of temperature *T* and horizontal *U* and vertical *W* wind components for the largest and the smallest basin and for the two stability cases. We have chosen the basin half-width area average to reduce the unnecessary postprocessing computational cost because the flow fields are horizontally homogeneous and are nearly symmetric about the center (Fig. 5). The cross-sectional area of the small basin was one-sixth of the area of the largest basin, with widths and slope angles as shown in Fig. 1b. The large and small basins show very similar cooling rates for the first 200 m above the basin floor (Figs. 4a,b). The near-surface air cooled 8 K in 8 h (cooling rate of 1 K h^{−1}), with a strong temperature inversion of approximately 10 K from the surface to ~200 m at hour 8 for the large and small basins and the strong- and weak-stability cases, and with weak *U* velocities (Figs. 4e,f). Inversions of this strength are not uncommon and have been previously observed in canyons and valleys (Whiteman et al. 1999). The 8-h averaged profiles in Figs. 4a,b, also reveal similar temperature gradients near the surface, but in the strong-stability case (Fig. 4a) the upper-level air between 200 and 1000 m cools more for the smaller basin, and this is explained by the relatively higher *W* velocity for the smaller basin than for the large basin in the same height range (Fig. 4c), which results in more adiabatic expansion associated with air lifting. The weak-stability case (Figs. 4b,d) shows similar behavior, but the resulting temperature profile between 200 and 1000 m is less stable. Although the magnitudes of vertical motion are very weak, adiabatic cooling associated with the weak rising motions is enough to cool the upper-basin layers by 1 K. A capping temperature inversion is formed over the top of the basin as a result of the subsidence (negative *W* velocity; Figs. 4c,d) associated with the return flow (negative *U* velocity; Figs. 4e,f) at the height levels above the basin rim (900–1200 m). This capping inversion is stronger for the smaller basin mainly because of the stronger subsidence as depicted by the *W* velocity (Figs. 4c,d). For the large basin, the *U* velocity from the surface to ~600 m appears to be slightly greater for the weak-stability case, which may be explained by the stronger vertical momentum transfer associated with weaker stratification.

Term I represents the total potential temperature perturbation tendency or rate of change, term II represents the vertical advection of the base-state potential temperature tendency, term III is the vertical and horizontal advection tendencies, where **u** is the total wind vector, and term IV is the turbulent mixing tendency, where *ρ* and *K _{h}* are the density and thermal turbulent diffusivity of air, respectively. Term V represents the diabatic heating/cooling terms from microphysical processes and atmospheric radiative forcings or radiative flux divergence. Because microphysics was not accounted for in our simulations, term V represents solely the effect of cooling by radiative flux divergence. In our model, once the soil temperature is calculated by solving the surface energy-budget equation, thermal energy conservation of atmospheric layers is carried out. Heat is then transferred from the surface to upper-air layers by the potential temperature perturbation tendency described by Eq. (2). As shown in Fig. 6, the dominant cooling process inside the basin’s cold-air pool is the radiative flux divergence, which is greater than the advective and turbulent mixing terms by an order of magnitude and is confined to near-surface locations (<200 m high), having its strongest cooling gradient for the first three grid points above the surface (<30 m). These results illustrate the physical process responsible for the temperature profiles and its spatiotemporal evolution as discussed above and highlight the importance of longwave radiative flux divergence in the cooling process for near-surface air under very weak wind speed conditions.

### c. Basin cooling trends and minimum temperatures

To illustrate the impact of basin size, slope angle, and stability on minimum temperatures and cooling trends within the basin environment, Figs. 7 and 8 show spatial and temporal averaging of temperatures within different cross-sectional areas (or zones) of the basin as defined in Fig. 1a. The cooling trends start to differ after ~3 h, and this is when the surface-layer inversion and the slope flows begin to develop in the simulations to an extent that influences the temperatures within the basin. The smallest basin cools at a faster rate than the largest basin for all of the zones within the basin (Fig. 7a). Observations of cooling trends in valleys and basins of different sizes (De Wekker and Whiteman 2006) also suggest this relation. The largest differences occur in the upper half of the basin (*A*_{uWb}) where the smallest basin size cools faster, while the cooling rate of the lower half of the basin (*A*_{lWb}) appears to be insensitive to the basin size and ambient stability and cools at a smaller rate (−0.6 K h^{−1}; Fig. 7b) relative to the upper half of the basin. The cooling rate over the slope area *A _{s}* was less sensitive to basin size and background stability (Fig. 7d). The weaker-stability case, in general, produces smaller cooling rates when compared with the strong-stability case.

The effect of the slope angle on the spatially averaged temperatures for the entire basin area *A* is highlighted in Fig. 8. In general, the entire 8-h average of basin temperature only varied by less than 2 K for the entire range of selected slope angles and basin sizes. The weaker-stability case (Fig. 8b) exhibits a larger temperature range, but still within the 2-K limits. For a fixed slope angle the mean basin temperature decreases with decreasing basin area, as shown by the solid lines connecting the points in Fig. 8. For both stability cases, increasing the slope angle leads to a warmer basin (see the dashed lines in Figs. 8a,b) despite the fact that the basin area also decreases. This could be explained by the fact that the greater the slope angle is, the weaker are the slope winds (as discussed earlier), and thus there is weaker convergence in the basin center, which consequently leads to weaker vertical lifting and less adiabatic cooling. This effect is more pronounced for the weaker-stability case associated with a more neutral atmosphere.

## 4. Conclusions

A total of 40 two-dimensional fine-resolution numerical simulations using the ARPS model have been carried out to study the basic characteristics of a cold-air pool within basins of different sizes and slope angles and under different ambient stabilities. No complex phenomena such as low-level clouds or surface-type heterogeneity were included, but all other physical processes are accounted for in the simulations.

The main findings can be summarized as follows:

- The maximum downslope wind speed is strongly correlated with the basin size and slope angle, with stronger downslope winds corresponding to larger basin areas and lower slope angles. As basin area increases, the influence of slope angle on slope wind weakens and the maximum downslope wind is found farther down the slope.
- The cold-air pooling process appears to affect the downslope wind speed more strongly for smaller basins when more cold air is accumulated and the stable layer deepens as compared with larger basins.
- The smaller basin produces more cooling of the upper-basin layers with a vertical temperature structure that is closer to isothermal in the interior of the basin than is that in larger basins. The main physical process governing the cooling process near the basin floor (<200 m in height) was found to be longwave radiative flux divergence, whereas vertical advection of temperature dominated the cooling process for the upper-basin areas.
- As a result of the latter point, the mean cooling rates of the upper half of the basin are more sensitive to the basin size and ambient stability than are the lower half or the slope area. The lower half of the basin cooled at the slowest rate, as revealed from the deficit in temperature tendencies in that area from the heat-budget analysis, whereas the near-surface-layer cooling rate appears to be close to the upper-basin cooling rate at about 1 K h
^{−1}. - The relationships among the slope winds, basin area, and slope angle appear to be insensitive to atmospheric stability. The amount of cooling, especially in upper-basin layers, however, is affected by stability, with weaker stability allowing for more adiabatic cooling and thus a cooler basin in comparison with the stronger-stability case.

These results provide an insight into the cold-air pooling process and how the process is affected by topography and stability. Future work may include more factors such as snow cover, moisture exchanges, and low-level fog and stratus, as well as three-dimensional real case scenarios.

This research was supported by the U.S. National Science Foundation under Grants 0938401 and 0837860. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The simulations were performed partially on supercomputer BlueFern, managed and operated by the High Performance Computing Centre at the University of Canterbury, New Zealand, and partially on Bluefire, managed and operated by the Computational and Information Systems Laboratory (CISL) at the U.S. National Center for Atmospheric Research. The authors thank Mike Kiefer, Xindi Bian, Jay Charney, Warren Heilman, Sebastian Hoch, John Horel, and Dave Whiteman for useful discussions. The authors also acknowledge the time and professional dedication that the anonymous reviewers put in to refine this research.

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