In regional meteorological modeling, the performances of physical parameterization schemes of varying complexity are usually intercompared by simulating a weather system driven by a strong mesoscale or synoptic-scale forcing. For example, Mahfouf et al. (1987) tested different atmospheric boundary layer (ABL) schemes in simulating mesoscale circulations initiated by surface contrasts. Stull and Driedonks (1987) showed that modeled mesoscale circulations and rainfall are sensitive to the representation of subgrid-scale vertical mixing processes. However, simulation of weakly forced synoptic circulations such as those that typically exist during the summer months over the United States is of lesser interest to meteorological modelers, because of the limited weather activity during these periods.
To air pollution modelers, on the other hand, accurate simulation of these types of circulation patterns is very important. Degradation of air quality due to released and chemically transformed pollutants is very common during the summer months over the eastern and western United States. Also, convective boundary layers are present during the daytime in the summer months. In the absence of cumulus convection, these pollutants are trapped in the ABL, further deteriorating air quality. Thus, accurate specification of weakly forced synoptic circulations and of the depth of the ABL as well as realistic representations of turbulent mixing processes are very important for air quality simulation studies. Higher-order-closure boundary layer schemes (Sun and Hsu 1988; Gao and Wesely 1994) are computationally expensive, particularly for use in air quality simulation models because one must solve several equations to predict the turbulent chemical fluxes of several chemical species. Thus, given the computational speed of present and near-future vector machines, it is impractical to use these schemes for operational purposes in meteorological and air quality modeling studies. As an alternative, many research and operational models use lower-order local- and nonlocal-closure boundary layer schemes.
In this paper, our overall objective is to study the performance of computationally viable two local-closure and two nonlocal-closure mixed-layer schemes in simulating ABL processes, within the context of a one-dimensional model. Note that because a three-dimensional model is required to evaluate these schemes, a relative preference for one scheme over another will not be established. The above objective has three parts: to test each scheme’s functionality, to analyze each one’s representativeness, and to explore each one’s characteristic features in simulating the observed structures of the ABL over distinct geographical regions. For this study and other follow-on studies to be presented later, we have developed a modular, one-dimensional soil–vegetation–boundary layer model for initial testing and implementation of different mixed-layer schemes into meteorological and air pollution models. Our next study with this model will use a chemical reaction formulation to study the effects of these vertical mixing schemes on tropospheric chemical concentrations. Finally, we will move to similar studies with three-dimensional meteorological and air pollution models.
We developed a three-dimensional windowed model to study the effects of different representations of subgrid-scale vertical mixing on predicted boundary layer parameters using two local-closure and two nonlocal-closure mixed-layer schemes. The windowed model has 35 vertical sigma layers and 3 × 3 grid cells (Fig. 1a) in the horizontal. Essentially, this model is a one-dimensional soil–vegetation–boundary layer model in which predictions are made only at the central grid cell [2,2] for all vertical layers. This model can be used in two different ways. With the first option, the remaining eight horizontal grid cells (strictly, only the four grid cells [1,2], [2,1], [3,2], and [2,3]) in each layer provide lateral boundary conditions obtained from observations to the computational grid cell [2,2]. This option is the better choice when the effects of advection can be included in the model simulations. The second option can be used when observational data are available for only a single station. In this case, the eight horizontal grid cells surrounding the computational grid cell in each layer assume the same meteorological characteristics as those of the computational grid cell. Thus, the model domain (nine grid cells) in each layer becomes horizontally homogenous, so advection terms have no effect on the model calculations.
Modular models like this one offer several advantages: they can be used efficiently for one-dimensional simulation and diagnostic studies, they can be used on any computer system, and they can easily be implemented into any two- or three-dimensional model without major modifications. In our study, we use the second option (i.e., a horizontally homogenous domain) to study the performance of four mixed-layer schemes. The governing equations and the parameterization schemes used are described below.
The governing equations
The soil–vegetation model
The radiation model
A simple radiation model is used in this study. Net radiation at the surface is calculated as the sum of incoming solar radiation absorbed at the surface, atmospheric longwave backscattering radiation, and outgoing longwave surface radiation. Solar radiation reaching the surface is a function of solar zenith angle, surface albedo, and atmospheric turbidity. Surface albedo is computed as the sum of minimum albedo with a solar zenith angle of zero and albedo changes due to the variation in the solar zenith angle (Idso et al. 1975; Pleim and Xiu 1995). Upward and downward longwave radiation are calculated as suggested by Anthes et al. (1987), which are functions of soil emissivity, ground temperature, atmospheric longwave emissivity, precipitable water in the atmosphere, and atmospheric temperatures.
Boundary layer schemes
In our study, we used the two local-closure and two nonlocal-closure mixed-layer schemes described below—a K-theory-based scheme (local), a scheme based on turbulent kinetic energy and its dissipation rate (local), the transilient turbulence parameterization (nonlocal), and the asymmetric convective model (nonlocal). Figure 1b shows a schematic of eddies that can mix air among grid cells in a vertical column of air. In the local-closure schemes, K theory (BKT) and turbulent kinetic energy (TKE), vertical mixing is confined to adjacent grid cells. In the transilient turbulence parameterization (TTP) scheme, vertical mixing is determined by nonlocal mixing potentials such that mass can be transferred from any layer directly to any other layer in the entire model column. In the asymmetric convective model (ACM), a uniform amount of mass is distributed upward to all other grid cells in the ABL from the lowest grid cell. Downward transport goes from each grid cell to the adjacent lower grid cell. Thus, in the ACM upward mixing is nonlocal while the downward mixing is local.
K-theory-based scheme (BKT)
Turbulent kinetic energy scheme (TKE)
Transilient turbulence parameterization (TTP)
Asymmetric convective model (ACM)
Coupling of the surface-layer and the mixed-layer schemes
Coupling between the surface and mixed layers is different with each of the schemes. With the K-theory-based scheme, turbulent sensible heat flux, friction velocity, and virtual potential temperature of the surface layer are used to calculate the Monin–Obukhov length from which the stability parameter is calculated. Depth of the boundary layer and this stability parameter are used to estimate the eddy diffusivity values in the ABL. With the turbulent kinetic energy scheme, the convective velocity W*, the friction velocity u*, and the stability parameter are used to estimate the turbulent kinetic energy and its dissipation rate in the surface layer to provide boundary conditions. In the transilient turbulence parameterization, estimated turbulent fluxes in the surface layer are used to destabilize respective dynamic and thermodynamic parameters, which in turn are used in estimating the nonlocal TKE. In the asymmetric convective model, turbulent sensible heat flux and virtual potential temperature of the lowest two layers are used to estimate the mixing rates. Upward and downward mixing rates are used to perform the vertical mixing in the ABL.
Data and numerical simulations
The four boundary layer schemes discussed above are tested for their abilities to simulate the structures of the ABL over a densely vegetated region and a sparsely vegetated (arid) region. Numerical simulations are performed for 12 h for all cases to simulate ABL processes. For the densely vegetated region, observational data from the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) are used to perform numerical simulations. The FIFE site is located near Manhattan, Kansas, covering a 15 km × 15 km area where tall grass prairie was the predominant vegetation. Measurements during two of the five intensive field campaigns (IFCs) from the FIFE data (Sellers et al. 1992) are selected to provide initial conditions and for comparison with the model simulations. The starting times of the simulations for these two cases are 1200 UTC 11 July 1987 (0700 LT) and 1200 UTC 6 June 1987. During the IFCs, special efforts were made to measure various meteorological, hydrological, and biological parameters. During these two particular days, which Sellers et al. (1992) list as “golden days,” almost clear sky and weak advection conditions were noted. For the sparsely vegetated region, observational data from day 33 (16 August 1967) of the Wangara boundary layer experiment are used to perform simulations. Initial conditions are obtained at 2300 UTC 16 August 1967 (0900 LT).
For the FIFE simulations, single-site radiosonde profiles are used (Pleim and Xiu 1995) in estimating the geostrophic winds. For the Wangara simulations, temporally evolving geostrophic winds are derived for every 3 h from the closely spaced measurements (Mellor and Yamada 1974). The values used for various surface parameters are shown in Table 1. These values are used for all simulations and are the same as those used by Pleim and Xiu (1995).
Results and discussion
The first subsection presents simulation results from the two FIFE cases (for a densely vegetated region), and the second subsection gives results from the Wangara simulations (for a sparsely vegetated region).
Simulation of the boundary layer over the FIFE region
The 11 July 1987 case study
During this day, the second IFC of the FIFE, clear sky conditions were observed until afternoon. Cloud-camera observations indicated overcast sky conditions after 1500 LT. Because the current version of our model does not consider processes related to cloud formation and its effects on atmospheric radiation and surface processes, model predictions after 1500 LT may not be comparable to observations. The temporal variations in the net radiation reaching the ground estimated by the model and from the observations are shown in Fig. 2a. Model estimation of the net radiation is very close to the observations up to 1530 LT; after that, the model estimates deviated because the model does not consider dynamic and thermodynamic processes related to cloud formation. Since the treatment of surface layer processes is the same in all four of the mixed-layer schemes, almost the same net radiation is estimated in all cases (differences among the results are about ±5 W m−2).
Turbulent latent heat fluxes in the model are estimated using the prognostic equations for soil moisture and parameterization of vegetative transpiration (Noilhan and Planton 1989; Jacquemin and Noilhan 1990; Pleim and Xiu 1995). Figure 2b compares these predictions with surface turbulent latent heat fluxes measured using the eddy correlation method. The predicted latent heat fluxes from the four ABL schemes differ from each other by about 0–30 W m−2, even though surface processes are represented by a single set of formulations. These differences arise from the different representations of turbulent mixing processes in the four ABL schemes. In other words, turbulent mixing processes can affect surface fluxes by changing gradients across the surface atmosphere interface. Measured latent heat fluxes show a maximum of about 415 W m−2 occurring around 1300 LT. Until 1400 LT, TTP-predicted latent heat fluxes are the closest to the observations. However, the differences between the schemes are well within the uncertainty of the measurements. After 1400 LT, predicted values from each of the mixed-layer schemes deviate greatly from the measurements due to cloud effects.
Figure 2c shows the temporal variation in the measured and predicted sensible heat fluxes from the four schemes. Until 1400 LT, predicted sensible heat fluxes from all of the schemes differ from measurements. Sensible heat fluxes are lowest with the TKE scheme and highest with the BKT scheme, with a maximum difference of about 50 W m−2. This is the reverse of the trend in predicted latent heat fluxes (Fig. 2b), where the TKE scheme is highest and the BKT scheme is lowest.
In air quality modeling, accurate specification of near-surface air temperature is crucial. This is because biogenic emission rates, which can influence the formation of ozone in the lower troposphere, are strongly dependent on air temperature. Thus, differences in the predicted air temperatures can result in different estimates of biogenic emission rates. We found that the predicted ground temperature (Tg1) is highest with the TTP and lowest with the ACM, with a maximum difference of about 1.5 K. A consistent difference of about 1–2 K between measurements and predictions occurs because the measurement locations of the fluxes and soundings are different from the locations where ground temperatures are measured. Predicted air temperatures in layer 1 (∼11 m AGL) with the TKE scheme and the TTP are closer to each other and to observations. Similarly, predicted air temperatures with the BKT scheme and the ACM are very similar to each other and are about 2–3 K lower than those in the observations.
Figure 3a shows the vertical variation in “observed” virtual potential temperature Θv estimated from the observed temperature and water vapor mixing ratio for different observational periods. The presence of the superadiabatic lapse rate, a typical feature during the daytime near the surface, is evident starting from 0900 LT. The stronger vertical gradient (inversion) present at higher altitudes indicates the approximate altitude of the top of the mixed layer in each Θv profile. The Θv profiles from 1400 LT contain the influence of dynamic and thermodynamic processes related to the reported cloud activity. In the Θv profile at 1900 LT, it appears that the top of the mixed layer is pushed to an altitude (1900–2000 m) relatively higher than those in the other profiles. However, this feature cannot be simulated with the current model version.
Predicted Θv profiles from the four ABL schemes are shown for every 2 h from 0700 LT to 1900 LT in Figs. 3b–e. The vertical profiles at 0700 LT represent initial conditions in all four cases. In the BKT simulation (Fig. 3b), starting from 0900 LT the inversion is located at a lower altitude than in the observations (Fig. 3a). Also, all Θv profiles except at 1700 LT in the BKT show the presence of vertical gradients (weak unstable lapse rates) within the ABL, and the BKT scheme does not simulate well the superadiabatic lapse rates near the surface. However, the mean Θv of the predicted mixed layer (309.25 K) at 1700 LT is very close to the observed value at 1800 LT (309.5 K). Though observations indicated cloud formation after 1500 LT, predicted Θv profiles after 1500 LT are close to the observations. This may be due to the absence of warm- or cold-air advection to the observational site.
In the TKE simulations (Fig. 3c), gradual growth of the mixed layer can be seen from the Θv profiles starting from 0900 LT, similar to that in the observations. Unstable lapse rates near the surface indicate the presence of the surface layer. However, these unstable lapse rates are not as strong as in the observations. The vertically uniform predicted Θv above the surface layer indicates the presence of a well-mixed layer as found in the observations. The predicted mean Θv of the mixed layer at 1700 LT is about 0.5 K lower than the observed value. In the TTP simulations (Fig. 3d), the Θv predicted profiles up to 1300 LT show that the altitude of the inversion is still confined to about 800 m, similar to that in the BKT simulations. However, significant growth in the depth of the well-mixed layer is found after 1300 LT. The unstable lapse rates predicted in the surface layer are stronger than in the observations. The mean Θv of the mixed layer at 1700 LT is the same as in the observations. The Θv profiles in the ACM predictions (Fig. 3e) indicate relatively better growth of the mixed layer as compared to the BKT and TTP simulations. However, unstable lapse rates in the surface layer are very weak compared to observations. The mean Θv of the mixed layer at 1700 LT is similar to that in the observations at 1800 LT, with a well-mixed layer present throughout the simulation.
Prediction of stronger unstable lapse rates in the TTP may be due to underestimation of the magnitudes of mixing coefficients in the surface layer. It was also found that the negative sensible heat fluxes (due to entrainment processes) near the altitude of top of the ABL are smaller in the TTP than that in the TKE, particularly until 1300 LT. Hence, erosion of inversion near the altitude of top of ABL is weaker in the TTP as compared to that in the TKE. Thus, in the TTP simulations, neglecting vertical transport of turbulence, underestimating mixing coefficients in the surface layer, and simulating weak entrainment near the altitudes of top of the evolving ABL may have contributed to the slower growth of the ABL until 1300 LT. In a modeling study, Ayotte et al. (1996) compared the normalized turbulent fluxes obtained from a large eddy simulation model with those obtained from some local- and nonlocal-closure schemes used in general circulation models. In one of the several case studies, they also found that all of the ABL schemes (including the TTP) used in their one-dimensional model could not reproduce the entrainment fluxes as compared to those in the LES. Thus, differences in the predicted Θv among the simulations can be attributed in part to the differences in the entrainment fluxes.
In the BKT and ACM simulations, the altitude of the top of the mixed layer must be diagnosed from wind and temperature profiles. We use the bulk Richardson number criterion, similar to that used by Pleim and Xiu (1995) and suggested by Holtslag et al. (1990), in determining the depth of the ABL. On the other hand, specification of the depth of vertical mixing is not required in the TKE and TTP simulations. This is because in the absence of clear air turbulence, the turbulent kinetic energy becomes negligibly small (∼1.0 × 10−20 m2 s−2) in the TKE simulations near the top of the mixed layer. Similarly, in the TTP simulations off-diagonal elements in the transilient matrix become zero at altitudes near and above the top of the mixed layer. In the BKT simulations, the Θv profiles in the ABL indicate that the vertical mixing is underestimated in the mixed layer and overestimated in the surface layer. This is a typical characteristic of local-closure schemes in which vertical transport is proportional to vertical local gradients. Therefore, to achieve a well-mixed profile, vertical eddy diffusivity must go toward infinity. Further, the calculated altitude of the top of the mixed layer seems to be underestimated. In the ACM simulations, turbulent mixing rates in the ABL are determined by the magnitude of the sensible heat flux at the prespecified top of the surface layer and the potential temperature difference between layers 1 and 2 using an empirical formula. Therefore, the magnitude of the superadiabatic surface layer is dependent on the thickness of the lowest model layer. The main advantage of the ACM over the BKT in convective conditions is that the nonlocal mixing results in very uniform mixed layers without resorting to extraordinarily large eddy diffusivities or very short time steps in a numerical simulation.
Vertical profiles of observed horizontal winds (not shown) indicate the presence of a nocturnal jet in the stable boundary layer at 0700 LT. Thus, shear production of turbulence is probably an important factor in the growth of the ABL during the morning hours by causing mixing through the capping inversion. This process is accounted for in the TKE and the TTP simulations. While the mixing rates of the ACM and the BKT do not directly respond to vertical wind shear, the specification of the ABL top depends on the local wind shear across the interface of the inversion. Therefore, as these schemes are integrated in time, vertical wind shear at the top of the ABL increases the modeled depth of the ABL, thus including part of the capping inversion in a more rapidly mixing ABL. In this way the inversion is eroded over time allowing ABL growth. Clearly, as shown in Figs. 3 and 4, the morning ABL growth is slower for the BKT than the ACM because the local mixing in the stable entrainment zone is much less than the nonlocal convective mixing in the ACM.
In the absence of cloud formation and advection processes, the vertical distribution of trace gas species in the lower troposphere is largely controlled by ABL processes. The water vapor mixing ratio can be considered as a surrogate for the trace gas species (nonreactive) (just as latent heat fluxes at the surface can be viewed as a surrogate for surface emission fluxes). Thus, the temporal behavior and vertical distribution of the water vapor mixing ratio qv can provide some insight on the probable behavior of a surface-emitted nonreactive trace gas species. Vertical profiles of observed qv at different hours are shown in Fig. 4a. Except at 1400 and 1800 LT, qv profiles indicate a uniform distribution within the mixed layer. Larger gradients can be seen in the surface layer. These gradients in the surface layer may be due to errors in the measurements in the surface layer (0–100 m) and/or to the presence of large latent heat fluxes (∼450 W m−2) as seen in Fig. 2b. The mean qv inside the ABL changes from hour to hour, both increasing and decreasing, in ways that cannot be explained by vertical mixing and surface fluxes alone. Therefore, one-dimensional models cannot possibly replicate all of these observed features.
Vertical variation in qv at different hours of simulation with the four schemes are shown in Figs. 4b–e. In the BKT simulations (Fig. 4b), vertical gradients of qv are present in the ABL during the entire period of simulation as a result of weaker vertical mixing. For example, the qv profile at 1500 LT varies from 16.5 g kg−1 at the surface to 11 g kg−1 at 1200-m altitude while the observations (Fig. 4a) indicate a uniform value of 16 g kg−1 in the mixed layer (up to 1400-m altitude). Further, due to the availability of large latent heat fluxes and BKT’s slower growth of the mixed layer as compared to the observations, the mean qv of the mixed layer increases for the period 0700–1200 LT. Turbulence in the free atmosphere is parameterized using Eq. (13) in the BKT and ACM simulations. Variations in the BKT-predicted qv above the ABL (1500 m) are due to the free atmospheric turbulence and somewhat resemble those in the observations. In the TKE simulations (Fig. 4c), vertical variation in qv indicates almost uniform profiles within the ABL except at 0900 LT. Rapid growth of the mixed layer (shown later in Fig. 5) at 0900 LT in the TKE simulations causes overprediction of qv between the 700- and 1200-m altitudes. In the surface layer (0–100 m), the TKE simulations also show the presence of vertical gradients in qv. However, these are weaker than in the observations. Above the ABL (1500 m), the TKE scheme did not simulate free atmospheric turbulence, resulting in no changes in qv during the entire simulation period.
Vertical variation in qv in the TTP simulations (Fig. 4d) indicates slower development of the ABL until 1300 LT. After 1300 LT, predicted qv profiles also indicate a sudden growth of the ABL, which results in a decrease of the mean qv in the ABL as compared to that at 1300 LT. In the surface layer, strong vertical gradients in qv are predicted by the TTP and are very similar to the observations. Temporal variations in qv in the free atmosphere (altitudes above the ABL) are also present in the TTP simulations. Vertical variation in qv in the ACM simulations (Fig. 4e) indicates somewhat mixed results compared with the other simulations. Mean values of qv in the ABL during the entire period of simulation (except at 1900 LT) are very similar in the ACM.
Observed eastward and northward wind velocity profiles (not shown) indicate the presence of remnants of a nocturnal jet in the lower altitudes in the initial conditions (0700 LT). Presence of vertical wind shear in the ABL (an indication of weaker vertical mixing) and slower growth of the mixed layer are found in the BKT simulations. The TKE simulations (not shown) indicate that the altitude of the maximum wind in the ABL (∼1000 m) is higher than in the BKT simulations. In the TTP simulations (not shown), vertical wind shear associated with the nocturnal jet is largely reduced by 0900 LT, similar to the TKE simulations. In the ACM simulations, the wind profiles are somewhat similar to those in the BKT simulations. In general, the effects of differing growths of the mixed layer in each of the simulations are evident in the predicted u and v wind profiles.
The depth of the ABL is a key input in air quality simulation models. Errors in its specification can significantly affect the predicted concentration fields. In the TKE scheme and the TTP the top of the ABL is diagnosed from a TKE criterion, while in the BKT scheme and ACM top of the ABL is specified from the temperature and wind profiles using the bulk Richardson number as described above. Therefore, accurate specification of the ABL height is crucial to these schemes since it determines the vertical extent of the convective mixing. Figure 5 shows the temporal evolution of the depth of the boundary layer. The bulk Richardson number criterion (Holtslag et al. 1990) is used to estimate the depth of the ABL in the BKT and ACM simulations. Since measured depths of the mixed layer are not available, the above methodology is also used to estimate the actual depth of the ABL (referred to as “OBS” in Fig. 5) using the observed winds and temperature profiles. Except for 1100 LT and 1300 LT, the TTP shows higher ABL depths than the other schemes do. In general, all schemes except the TTP predict lower values for ABL depth than the “observed” values. The maximum difference among the schemes for the predicted ABL depths is about 600 m, which translates to about 33% of the maximum predicted depth. Thus, variations in the predicted/estimated depths of the ABL may influence air quality simulation results.
The 6 June 1987 case study
During our second case study, the first IFC of the FIFE, clear sky conditions were observed during the entire period of simulation. Thus, comparing the measured net radiation with the model estimates will reveal errors in the radiation formulations, initial specification of surface, and atmospheric characteristics (e.g., albedo, emissivity). We found that the model estimates are very close to the observations. This indicates the accuracy of surface input data and the model formulation of radiative processes for clear sky conditions. Next we consider model prediction of turbulent sensible and latent heat fluxes. Figure 6a shows measured and predicted sensible heat fluxes. In general, peak values of predicted sensible heat fluxes in all simulations are higher than the measurements by about 15–40 W m−2. Though the initial conditions and the formulation used to represent surface layer processes are the same in all of the simulations, the slight differences among the predictions indicate the effects of different representations of turbulent mixing processes. Analogous differences in the predicted latent heat fluxes (Fig. 6b) are smaller.
Of interest to meteorological and air quality simulation modelers is better prediction of near-surface winds, because these can affect the estimation of surface turbulent fluxes of thermodynamic parameters and chemical species. We compare surface observations of u and v winds with the model-predicted winds in the lowest layer (Figs. 7a and 7b). Since the lowest level in the model is located at about 10.9 m AGL, predicted winds can be directly compared to the measurements made at 10 m AGL. Except for the first 2 h of simulation, the trends in the predicted winds in all simulations follow the observations closely. On average, the TTP-predicted winds are closest to the observations, and the ACM predictions are the farthest from observations (overprediction).
We also compared predicted vertical variation in Θv with the observations at different hours (not shown). Compared with observations, superadiabatic lapse rates in the surface layer are lower in the BKT and ACM simulations, higher in the TTP simulations, and comparable in the TKE simulations. A feature associated only with the TKE simulations was the prediction of mixing in the residual boundary layer between 0700 and 0900 LT as observed. We also found that warming of the ABL (as indicated by the Θv profiles) is different in each of the simulations until 1300 LT, indicating the effects of different mixing schemes on the predicted ABL.
Predictions of the horizontal winds in a one-dimensional model are very sensitive to the prescribed geostrophic wind profiles. In all of our simulations we prescribe geostrophic wind profiles that were used by Pleim and Xiu (1995). Since horizontal pressure gradients are not readily available, they used a qualitative procedure to estimate temporally evolving geostrophic winds. Vertical variation in the u wind (eastward component) obtained from observations is shown in Fig. 8a. Again, the presence of a nocturnal jet at 0700 LT is evident from the u wind profile between the surface and 1000-m altitude; the core of the jet is located at about 500 m AGL. The u wind profile at 1600 LT shows the presence of a weaker vertical wind shear, indicating the effects of stronger turbulent mixing processes. Figures 8b–e show the predicted u wind profiles from the four ABL schemes. With time, all schemes except the TKE scheme show a gradual decrease in the vertical wind shear in the ABL, similar to the observations. With the TKE scheme, the coefficient of eddy diffusivity for momentum seems to be overestimated; as a result, vigorous vertical mixing leads to well-mixed u wind profiles from 0900 LT on. After 1300 LT, differences among the predicted u winds are about ±1 m s−1 in all simulations.
Vertical variation in the v wind (northward component) is shown in Fig. 9a. The presence of the nocturnal jet is somewhat evident (0700 LT) in the lower altitudes of the atmosphere. Also note that the v winds are uniform with height for all of the observational periods. Predicted v wind profiles for the four schemes are shown in Figs. 9b–e. Again, with the TKE scheme vigorous vertical mixing results in a well-mixed v profile above 200-m altitude by 0900 LT. With the other schemes, the decrease in vertical shear in the v winds is more gradual in time, similar to the observations.
Figure 10 shows the temporal variation in the depth of the ABL. As before, observed winds and temperature data were used to estimate the probable altitude of the top of the ABL utilizing the diagnostic formulation suggested by Holtslag et al. (1990). During the morning period, all of the ABL schemes underestimate the “observed” ABL depths. Among the predicted depths of the ABL, the BKT depth is the lowest in comparison with the observations and the TTP depth is the highest. The maximum difference among the predicted ABL depths is about 250 m.
Simulation of the boundary layer over the Wangara region
Because of the high density of the observational network and the availability of many meteorological parameters, the Wangara data have been used in many model comparison and evaluation studies. These data are perhaps the most widely used observational data for comparison with modeled boundary layer structures. Since the Wangara observational site is located over a sparsely vegetated region (close to a desert), errors arising from the insufficient representation of vegetation–atmosphere interactions should be at a minimum in a numerical simulation of the ABL. This feature facilitates the evaluation of other meteorological fields simulated in a numerical model. Since we have used all available observational data to specify initial values for various surface characteristics and parameters, the same soil-vegetation model that was utilized in the FIFE simulations is used for the Wangara case study.
We found that the predicted net radiation is slightly higher than observed around 1200 LT by about 30 W m−2. Predicted negative values during the nighttime are also close to the observations. We compared temporal variation in the predicted sensible heat fluxes with that derived from observations (Hicks 1981). Between 0900 and 1100 LT, differences between the derived and predicted sensible heat fluxes are found. This kind of discrepancy was also found between the values reported by Hicks (1981) and modeled by Mellor and Yamada (1974). Except between 1200 and 1400 LT, predicted sensible heat fluxes from the four ABL schemes are very similar to each other.
Figures 11a and 11b show vertical profiles of observed and predicted u and v winds at 1200 LT. Note that the differences among the predicted wind profiles are very small (less than 0.5 m s−1) and predicted winds are close to the observations. The observed and predicted wind profiles at 1800 LT shown in Figs. 11c and 11d have similar features, except the predicted v wind profiles differ from the observed. This kind of difference, which was also noticed in the simulation performed by Mellor and Yamada (1974), may be due to errors in the estimation of geostrophic winds for this hour. Figure 12a shows the vertical profiles of Θv obtained from observations for different periods. The Θv profile at 0900 LT shows the presence of a stable boundary layer, about 400 m deep. From 1200 to 1500 LT, the mean mixed layer warms up by about 2.5 K. At 2100 LT a stable boundary layer is established as indicated by a strong gradient (8 K) between the surface and 100-m altitude. Corresponding model predictions are shown in Figs. 12b–e. As indicated by the Θv profile at 1200 LT between the altitudes 800 m and 1200 m, the TKE scheme predicts an ABL depth at this hour that is lower than in the other schemes and the observations. Again, differences among the predictions from the four ABL schemes show up in the surface layer and at altitudes near the top of the mixed layer. Warming of the ABL from 0900 to 1200 LT by about 2.5 K is well predicted by all of the schemes. Development of a stable boundary layer during the nighttime (2100 LT) is also well predicted by all ABL schemes. Since the ACM cannot be used during stable conditions, K theory is used to simulate the ABL processes. Even though model simulations with the BKT scheme and the ACM use the same K theory at 2100 LT, the predicted stable boundary layer is quite different between the two schemes. This is due to differences in the predicted vertical mixing processes during daytime conditions between these two schemes.
Observed water vapor mixing ratio profiles for different hours (not shown) indicate that the growth of the ABL during the daytime results in well-mixed qv profiles except at 2100 LT. Both the Θv and the qv profiles at 2100 LT suggest advection of cold and humid air into the observational site. Since advection is not considered in the numerical simulations, predictions corresponding to this hour differ slightly from the observations. We found that the ACM-predicted profiles are closest to the observations. Again, most of the differences among the predictions occur at altitudes close to the surface and near the top of the mixed layer. Further, the TTP does not predict the changes in qv at altitudes near the top of the mixed layer that are found in the observations and in the predictions from the other ABL schemes.
Figure 13 shows the temporal variations in the predicted and observed depths of the ABL. The TTP predicts a deeper mixed layer while the TKE scheme shows weaker growth until 1500 LT. The dramatic collapse of the ABL is well predicted with all of the ABL schemes. However, the collapse in the observations occurs between 1600 and 1800 LT while in the predictions it occurs about 1–2 h earlier. Overall, the ACM shows the best agreement with the observations.
We have studied the performance of two local-closure and two nonlocal-closure boundary layer schemes in simulating the observed structures of the ABL over densely and sparsely vegetated regions using a one-dimensional soil–vegetation–boundary layer model. The local-closure schemes used in the study are (1) a K-theory-based scheme using boundary layer scaling (BKT) and (2) a scheme based on turbulent kinetic energy and its dissipation rate (TKE). The nonlocal-closure schemes are (1) the transilient turbulence parameterization (TTP) and (2) the asymmetric convective model (ACM). Two of these schemes are based on the TKE equation (TKE and TTP) and apply to the entire vertical column while the other two schemes (BKT and ACM) parameterize mixing within the boundary layer and above differently and therefore depend on the specification of ABL height. Since the TKE scheme contains the most complete physics, including both dynamic and thermodynamic effects, features such as the presence of superadiabatic lapse rates in the surface layer as well as vertical mixing resulting from strong vertical wind shear associated with the dissipating nocturnal jet are well reproduced by the TKE scheme. Thus, TKE-predicted temperature, water vapor mixing ratio, and horizontal wind profiles are generally consistent with observations. In general, the TTP-predicted depths of the boundary layer are larger than with the other schemes, and the superadiabatic lapse rates are stronger than in the observations.
In the BKT scheme and the ACM, the depth of the boundary layer has to be diagnosed using empirical formulations. Since the coefficients for vertical eddy diffusivity are strong functions of the depth of the boundary layer in the BKT scheme, errors in the specification of this depth greatly influence BKT-predicted vertical mixing. Thus, errors in the predicted temperature, mixing ratio, and horizontal wind profiles with the BKT scheme can be attributed in part to errors in the estimated ABL depth. In one of the three case studies, the presence of vertical gradients in the predicted profiles of temperature, mixing ratio, and winds indicates that mixing is weaker in the upper half of the evolving mixed layer. Further, the presence of strong vertical mixing in the lower layers close to the ground results in the prediction of weaker superadiabatic lapse rates in the surface layer with the BKT scheme.
The ACM performs upward mixing throughout the depth of the ABL, while downward mixing is gradual. The effects of this feature are clearly evident in all simulations where the predicted dynamic and thermodynamic profiles indicate a well-mixed boundary layer. However, vertical mixing in the ACM may be overestimated in the lowest layers, leading to weak adiabatic lapse rates in the surface layer. It is interesting to note that estimated depths of mixed layer are not the same in the BKT and the ACM even though we used the same formulation (Holtslag et al. 1990) in both of these simulations. This is due to the fact that the virtual potential temperature (Θv) difference between the surface layer and the top of the ABL in the BKT and the ACM simulations are not the same due to the differing representations of vertical mixing. This difference in Θv directly affects the estimation of the depth of the ABL. Also, simulated depths of the ABL in the ACM are generally closer to the observations than those in the BKT. The largest difference among the predicted depths of the mixed layer was about 33% of the maximum predicted depth.
The TTP computes the mixing fractions, using the model-simulated dynamic and thermodynamic profiles, to reflect the complex interaction among surface heating, buoyant plumes, shear across the boundary layer, and entrainment in the interfacial layer. The ACM also performs mixing from the surface level to all other levels in the boundary layer using empirically estimated mixing rates. However, the design of the mixing in the ACM is entirely different from that in the TTP. In principle, for convective conditions, these schemes should perform the best in simulating the observed structures of the convective boundary layer. However, prediction errors could arise from the uncertainty present in the prescribed constants and/or assumptions related to the simplification of the closure problem. For these reasons in part, mixing of air in the lowest layers is underestimated in the TTP, leading to the prediction of strong superadibatic lapse rates in the surface layer. Similarly, with the ACM, estimation of large mixing rates has caused excessive mixing of air in the surface layer, leading to a prediction where superadiabatic lapse rates are almost absent in the surface layer. Thus, depending upon our ability to estimate key parameters used in a closure problem, simulation results may or may not be in line with all the observed aspects.
Even though the same surface-layer parameterization scheme is used in all simulations, predicted turbulent fluxes near the surface are marginally different for each of the four schemes. This is caused by the differences in predicted vertical mixing among the schemes, which show that surface turbulent fluxes are influenced by the mixing processes in the boundary layer. Most of the differences in the predicted profiles from each of these schemes are evident during the growing stage of the boundary layer. However, prediction errors are at a minimum when the depth of the boundary layer has attained its maximum growth. We also found that for each of the four schemes, the differences between predictions and observations, which are most evident in the surface layer and near the top of the mixed layer, were consistent across the three studies throughout the simulation periods.
A comprehensive evaluation of the performance of these four mixed-layer schemes requires simulation of boundary processes and associated mesoscale circulations in a three-dimensional model. This is because boundary layer processes can affect shallow and deep cloud formation. In turn, each of these can result in feedback effects, through variations in the solar radiation and in the soil moisture, modulating the simulated mesoscale circulations. Therefore, our next step is to evaluate these schemes using the MM5 (Grell et al. 1994) modeling system.
The information in this document has been funded in part by the United States Environmental Protection Agency under cooperative agreements CR-823628 and CR-822066 to MCNC, in part by the Division of Atmospheric Sciences, National Science Foundation Grant ATM 9212636, and in part by the U.S. Department of Energy, Atmospheric Radiation Measurement Program under Contract 09157-A-Q1 with Pacific Northwest Laboratories. It has been subjected to Environmental Protection Agency review and approved for publication. It has also been approved for publication by MCNC. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. The authors thank Ms. Jeanne Eichinger for her editorial assistance and Dr. Roland Stull and Mr. Kenneth Schere for their help in this research work.
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Surface parameter values used in all numerical simulations.