Introduction

Meteorological models have been used in studying and assessing the effects of urbanized regions on the meteorological fields in their vicinity. Examples include assessing convective activity, precipitation, heat islands, and wind-flow patterns in and around urban areas (e.g., Vukovich et al. 1976; Bornstein 1975; Vukovich and Dunn 1978; Seaman et al. 1986; Nicholls et al. 1995). More recently, mesoscale models have been used in assessing the magnitudes of urban heat islands and their impacts on energy use and ozone production (Taha 1996, 1997; Lyons et al. 1995; Cardelino et al. 1993). In this sense, a more accurate estimation of the magnitude of urban heat islands (e.g., through meteorological modeling) is important in assessing related meteorological conditions, utility loads, temperature-dependent emissions of biogenic and anthropogenic precursors of ozone, and ozone production. It is also critical for estimating region-specific patterns of energy use. Furthermore, mesoscale models are being used in assessing the air quality impacts of land-use and land-cover (LULC) changes and large-scale surface characteristics modifications (e.g., Taha 1996, 1997).

However, mesoscale models were not explicitly designed to distinguish between boundary layer and canopy layer phenomena, for example, boundary layer versus canopy layer heat islands, nor those between urban and nonurban areas. At best, distinction of the latter is handled by differentiating the values of appropriate model input parameters. But the effects of the complex active surface and associated myriad of energy fluxes in urban areas are not treated explicitly in mesoscale models since these are considered subgrid-scale or microscale processes and can only be indirectly parameterized.

This leaves something to be desired, particularly when attempting to extend mesoscale model results to assess near-surface heat islands and their potential effects in urban areas, for example, energy use and air quality. A better accounting for urban land-use effects, that is, model modification, is thus needed. From a practical point of view, it is also desirable that whatever scheme be adopted in modifying a model be a function of LULC since detailed information of microscale dimensions is seldom available for large regions. And even if it was (e.g., geometry, building-by-building specification, thermophysical properties, etc.) it would be an overwhelming task to specify all these as input to mesoscale models and would not be warranted for the additional reason that detail will be lost when averaging back to coarse model grid. Thus a “bulk” parameterization of the effects of urban canopy layer fluxes (e.g., heat storage) that is a function of LULC is deemed as the most suitable scheme for this purpose.

This paper describes preliminary modifications to a mesoscale model to better account for urban heat storage. The approach involves integrating the Objective Hysteresis Model (OHM) of Grimmond et al. (1991) with the Colorado State University Mesoscale Model (CSUMM) of Pielke (1974).

The CSUMM is a hydrostatic, primitive-equation, three-dimensional Eulerian model. It assumes incompressible flow and employs a σ_z coordinate system. It uses a first-order turbulence closure scheme in treating subgrid-scale terms of the governing differential equations. The model solves a set of coupled equations representing the conservation of mass (continuity), potential temperature (heat), momentum, and water vapor. In this application, the model’s domain top is at 9 km with 22 atmospheric grid levels and an underlying soil layer 50 cm deep. The CSUMM generates three-dimensional fields of prognostic variables as well as a mixing height field.

The integration of OHM with CSUMM is discussed in this paper and the application of the resulting version (MM) to the Atlanta, Georgia, region is presented. The models will be referred to as CSUMM [or alternatively Boundary Layer Model (BLM)], OHM, and MM, the latter being the resulting modified model.

Approach

It is thought that thermal storage in urban areas is an important factor in the genesis of urban heat islands (Oke 1987; Grimmond et al. 1991; Goward 1981), particularly in warm climates. Thus, there is an interest in better estimating this parameter. A better representation of thermal storage in numerical models should result in better accounting for the energetics related to urban land uses and the effects of canopy layer fluxes on the overlying boundary layer.

For example, Tso et al. (1990) suggested a simple approach that involved modifying the surface energy balance calculations by introducing an urban heat storage term to account for urban/building mass effect. Kerschgens and Kraus (1990) suggested that the total storage heat flux (S) for an urban area of interest be computed as

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meaning that the contribution of the canopy layer fluxes to an area A at the bottom of the boundary layer is the weighted sum of the contribution of fluxes from individual surfaces (S_i). In Eq. (1), ρ is density, C is specific heat, T is depth-integrated temperature of surface i, υ is volume, and t is time.

It seems possible to estimate the equivalent of Σ S_i in Eq. (1) through a bulk parameterization, such as OHM. “Bulk” here is interpreted to mean that the effects of various surfaces and canopy layer fluxes are not explicitly and individually computed. Rather, it is assumed that their overall integrated effect is accounted for by OHM. This is also more amenable to computation since an exact and detailed description of all surface components in the canopy layer would not be required as the case would be if Eq. (1) were used. Thus, OHM is more appropriate for use in conjunction with available LULC information as is the objective of the preliminary modeling described in this paper. Note that OHM’s merits are simplicity and ease of integration with mesoscale models. However, there exist more sophisticated methods for modeling urban energetics and heat islands, for example, Kimura and Takahashi (1991).

Oke et al. (1981) discuss the earlier formulation of OHM, including several linear relationships between the storage heat flux term (ΔQ_s) and net all-wave radiation (Q*). The relationships, of the form ΔQ_s = a(Q* + b), did not account for thermal time lag or “hysteresis.” That effect was introduced by Camuffo and Bernardi (1982), integrated in OHM by Oke and Cleugh (1987), and refined by Grimmond et al. (1991) so that the updated form of OHM is

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where a, b, and c are empirical coefficients corresponding to land use (or surface type) i; n is the number of land uses in a grid cell or area of interest; and A is the area fraction of surface type i. On the other hand, CSUMM calculates soil heat flux with the last term of the left-hand side in Eq. (3)

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where Q* is the net all-wave radiation, ρ is density, C is specific heat, u* is friction velocity, θ* is friction potential temperature, L_υ is latent heat of evaporation, q* is friction specific humidity, k is thermal diffusivity, and z is height (or depth). The subscript s refers to surface. In implementing OHM in MM, Q* is taken as

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where α is albedo, R is incoming solar radiation, L is incoming longwave radiation, σ is the Stefan–Boltzmann constant, ε is emissivity, and T_s is surface temperature. In Eqs. (3) and (4), the overbars simply denote terms that can be modified to account for urban effects and this notation is not to be confused with average or vector notations (these “modifiable” terms will also be referred to in section 6). In addition, the following finite-difference approximation is made:

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where τ and τ − 1 refer to current and previous time steps and Δt is the time step interval. Furthermore, the soil heat flux in MM is weighted by area; the soil heat flux in Eq. (3) is prorated by the fraction of nonurban land uses so that

GA_uG,(6)

where G′ is the modified soil heat flux term, G is the BLM-calculated soil heat flux, and A_u is the urbanized fraction of a computational grid cell. In this paper, A_u is the sum of fractions of OHM categories “roofs” and “paved surfaces.” For cells that contain at least one urban land use, a surface potential temperature tendency term is added to the BLM model’s equations so that

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where the additional tendency term is weighted by A_u. In this equation, ΔZ_s is the thickness of the uppermost soil layer.

Grimmond et al. (1991) suggest that Eq. (2) be used for daylight hours. In this study, MM is allowed to revert to Eq. (3) to calculate G during nighttime conditions.

In MM, anthropogenic heat flux (Q_f) is added to the sink/source term (S_θ) in the potential temperature conservation equation for the first level of the model

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The time-dependent anthropogenic heat flux is computed as

Q_ftQ_fmaxFt(9)

where Q_fmax is a maximum heat flux and is assumed to be a function of land use and F(t) is a fraction of Q_fmax and is given by a Fourier series (Taha et al. 1992; Sailor 1993) as

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where γ = 0.557, λ₁ = −0.227, λ₂ = −0.006, λ₃ = −0.084, ϕ₁ = −0.384, ϕ₂ = 0.016, and ϕ₃ = −0.012.

Equations (2)–(10) describe the modifications implemented in MM. It is appropriate to mention here that the magnitudes of ΔQ_s [from Eq. (2)] and terms in Eq. (3) were compared to ensure that they are within reasonable bounds. They were examined out of concern that the empirically based storage heat flux term in OHM may be of different magnitude than other terms calculated in Eq. (3) by BLM. Specifically, the magnitude of ΔQ_s for bare land was compared to the term G (in the BLM) for the same surface type. The comparison suggests that ΔQ_s is comparable to the BLM-computed soil heat flux (both range from about −80 to +80 W m⁻² diurnally) and, thus, the proposed bulk parameterization approach does not seem unreasonable.

It is to be understood that the discussion and equations apply to each grid cell of the modeling domain. For simplicity, however, the indical notation (e.g., i, j, k) was dropped.

Application

The nonmodified CSUMM was run first to simulate northern Georgia (large domain) for model validation purposes. The large-domain simulations were initialized at 1200 UTC (0700 LST) 28 July and terminated at 2400 LST 1 August. A single-station initialization was done using representative soundings from Peachtree City, near Atlanta. The northern Georgia modeling domain, covering an area of 365 km × 320 km, shown in Fig. 1, was simulated with a mesh of 5 km × 5 km. On the other hand, MM was run to simulate the Atlanta vicinity from 25 through 27 July. The MM simulations were focused on an area of 60 km × 60 km surrounding urban Atlanta (as shown by the inner square in Fig. 1) with a mesh of 2 km × 2 km. Because the original OHM was formulated for smaller scales (on the order of 1–2 km), it was necessary to reduce the grid size in MM to 2 km × 2 km. In addition, 2 km × 2 km CSUMM simulations were also performed on the smaller domain for comparison with MM.

Two sets of simulations were performed with each of the original and modified models: one to represent the base-case conditions during the selected episode and another to represent a scenario in which the albedo of paved surfaces and roofs was increased. In the latter scenario, it was assumed that the albedo of residential LULC was increased from 0.16 to 0.29, that of commercial from 0.14 to 0.30, of industrial from 0.20 to 0.34, of transportation/communication from 0.16 to 0.30, of industrial/commercial from 0.18 to 0.34, of mixed urban from 0.16 to 0.25, and of built-up areas from 0.14 to 0.21. These area-averaged increases were computed based on estimated increases in albedo of individual roofs and paved surfaces. In this modeling study, it is assumed that LULCs other than those listed above were not affected by albedo changes.

As a first step in this application, the OHM coefficients for each computational grid cell in the MM modeling domain were computed based on averaging of OHM categories in each cell. Table 1 shows the OHM LULC categories and their corresponding coefficients (based on Grimmond et al. 1991). The 200 m × 200 m U.S. Geological Survey (USGS) LULC data for the Atlanta region were remapped into the available OHM categories and averaged over the model’s grid size (in this case, 2 km × 2 km). The coefficients a, b, and c for each cell were then computed by area-weighting the OHM coefficients according to the LULC fractional distribution in each cell. Built-up USGS LULCs were remapped into “roof” or “paved” OHM categories, forest land into “mixed forest,” vegetated into “grassland,” and so forth, based on the best possible match between the two systems of surface characterization.

There are 37 LULCs in the USGS database that were remapped into seven OHM categories listed in Table 1. Obviously, there is a gap between these two systems that needs to be narrowed in future work. Note that the coefficients in Table 1 were developed for various regions (Grimmond et al. 1991; Oke et al. 1981). Their applicability to Atlanta cannot be determined at this time, but the assumption made here is that there is a certain extent of similarity among North American cities to justify use of OHM for Atlanta.

For those cells in the modeling domain that have no urban LULC at all (i.e., roofs or pavements), the model uses the original BLM formulation in calculating soil heat flux, as in Eq. (3). But if there is at least one urban OHM category in a particular cell, then the storage heat flux term is computed using Eq. (2). This storage term is then weighted by the urbanized fractional area of the cell. The soil heat flux of the rest of the cell, that is, the nonurban LULCs, is computed by Eq. (3) and weighted by the fractional area of nonurban OHM LULC in each cell, as in Eq. (6).

Results

This discussion of results will focus on the air temperature field since it is the main aspect of interest being investigated, that is, the urban heat island. For this purpose, the 2-m air temperature simulated by the MM and CSUMM for the smaller domain is discussed. It is appropriate to mention here that air temperature per se is not directly modified by the model modifications described in this paper. Surface heat fluxes are the parameters being directly modified, and changes in air temperature are only second-order effects resulting from the changes in surface heat fluxes. A direct comparison of simulated and observed heat fluxes was not performed in this study because of a lack of observational data for Atlanta. However, observational meteorological data, including air temperature, were available, and thus were used in model performance evaluation. Air temperature, as a test variable, has also been used by other researchers, for example, Kimura and Takahashi (1991).

Figures 2 and 3 show the simulated air temperature field at 2 m for 1400 LST 27 July. Note that the heat island around central Atlanta is larger in MM (Fig. 3) than in CSUMM (Fig. 2), indicating an increased differentiation between the storage heat flux of urban and nonurban land uses in the modified model. The CSUMM-simulated heat island in this domain is about 1°–1.25°C at 1400 (Fig. 2) and is consistent with the heat island obtained from the large-domain simulations (not shown). The heat island simulated by MM (Fig. 3) is about 2.5°C. Georgia Institute of Technology (GIT), Clark Atlanta University (CAU), and downtown Atlanta are within the warmest parts of the heat island, and so is Marietta, to the northwest.

Figures 4 and 5 show simulated urban heat island time series for 1000–1700 LST 27 July. The temperature difference is that between points (758, 3750 km) representing urban conditions and (770, 3726 km) representing rural LULC (see Figs. 2 and 3 for locations of these two points, shown with plus signs as “urban” and “rural”). These locations were selected to coincide with OHM categories of interest for comparison. Cell (758, 3750 km) is 97% roofs and paved surfaces, whereas cell (770, 3726 km) is 20% grassland and 80% forest. In Fig. 4 (base case), the CSUMM-simulated heat island (solid line) is on the order of 1°C and is relatively constant throughout the daytime. The MM-simulated heat island (broken line), on the other hand, is about 1°–1.5°C larger than simulated with CSUMM and is larger between 1200 and 1400 (∼2.5°C) than earlier or later during the daytime.

In the high-albedo case seen in Fig. 5 (see section 3 for an explanation of this case), the heat island is decreased by about 0.5°C in CSUMM and about 1°C in MM (compare with Fig. 4). In other, urban-core locations within the 60 km × 60 km domain (not shown in the figures), CSUMM predicts a decrease of up to 1.1°C in air temperature at 1400 LST following increasing albedo, whereas MM predicts a decrease of up to 1.6°C. Examination of simulated heat fluxes (not shown) suggests that the effects of increased albedo on air temperature occur mostly through reduction of the sensible heat flux component, but there is a small additional contribution from the change in storage heat flux that helps keep the air slightly cooler (the additional 0.5°C cooling), as simulated by MM compared to that by CSUMM. The mechanism for this additional cooling can be explained by differentiating Eq. (2) with respect to albedo (for a particular land use)

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Expanding Q* as per Eq. (4), substituting, and with a little algebra, one can arrive at

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which simply is a statement that the rate of change in storage heat flux with respect to albedo depends on OHM coefficients a and b and is larger when R and/or its rate of change are largest.

In this algebra, the coefficients a, b, and c were assumed independent of albedo, which may be incorrect since the empirical determination of these coefficients in the first place must have been some function of the local albedo. Although that dependence could be small, it is unknown at this time. Thus the fidelity of Eq. (12) in explaining the additional cooling effect in the real world is somewhat limited in extent, however, it is exact in explaining the MM calculations since the coefficients in the modeling are unchanged from the base case to the high-albedo case.

Model base-case performance evaluation

Two tests for model performance evaluation are briefly presented: 1) CSUMM model performance for the large-domain simulations and 2) MM performance for the smaller, Atlanta domain. In either case, 2-m air temperature was selected as the test variable. This is the height at which temperature is measured (at the Mesonet referred to in this paper) and is also the height of the first level at which it is calculated in the model (first level for thermodynamic variables). For the large-domain simulations validation, data from 18 Mesonet stations were used in testing the model performance (stations are identified in Figs. 1 and 2); for the MM test, data from three stations were used: 1) a weather station at GIT was used to represent “urban” conditions; GIT is not in urban-core Atlanta but may be the most “urban” of the stations closest to the core; 2) a weather station at CAU, to the west of downtown, is relatively more meshed within residential neighborhoods and could be considered as a suburban site for MM validation purposes; and 3) a weather station in the Gainesville region, to the northeast of Atlanta, which is remote enough to be considered rural.

The Mesonet meteorological data were obtained from the Georgia Automated Environmental Monitoring Network (Hoogenboom 1996). Data from urban-core Atlanta were not available (no monitoring station is located in the area) and thus, observational data from nearby stations are used to give a general assessment for the MM performance.

For the large-domain model performance evaluation of CSUMM, the indices used include root-mean-square error (ε) of the simulation, unbiased root-mean-square error (ε′) of the simulation, standard deviations of simulated and observed parameters (σ, σ_o), and the mean unsigned relative error (E) of the simulation. Here, ε, ε′, and E are defined as

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and

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where V_i and V_io are simulated and observed values at station i, respectively; V* is average value of V_i; and V^*_o is average value of V_io; all are defined at 2 m. Here, N is the number of available observed/simulated data pairs. Note that E is typically used in evaluating photochemical model simulations (e.g., Urban Airshed Model), but the concept is extended here for use in conjunction with a meteorological model. Table 2 lists the values of these indices as computed for this episodic simulation.

According to Pielke (1984), Keyser and Anthes (1977), and EPA (1991), model skill is demonstrated if 1) σ ≈ σ_o, 2) ε < σ_o, 3) ε′/σ_o ⩽ 0.6, and 4) E < 35%. Thus, Table 2 suggests that the model’s performance is acceptable on clear days (such as day of year 211, 1996), which is expected since the model does not include cloud or phase-change physics.

Validating or testing the OHM performance, that is, its original formulation, is beyond the scope of this study because the empirical coefficients were developed for various regions and that related observational data is unavailable for Atlanta. However, OHM has been independently validated by Oke and Cleugh (1987), Grimmond et al. (1991), and Roth and Oke (1994) for other regions.

With regard to MM performance evaluation, Fig. 6 shows observational data (on day of year 211, 1996) plotted as heat island time series at GIT and CAU with respect to Gainsville. During the daytime, GIT is about 1°C warmer than CAU and up to 2°C warmer than Gainesville between 1300 and 1500 LST. One needs to bear in mind that GIT is somewhat vegetated and is not part of the Atlanta core area (downtown), which is devoid of vegetation and has many tall buildings. Thus the temperature in the core area could be higher than observed at GIT, and the 2.5°–2.9°C heat island (simulated with MM) may be realistic for downtown Atlanta. While the lack of observational data from downtown Atlanta precludes making a reliable statement about MM performance, the observational data from GIT, CAU, and Gainesville suggest reasonable MM performance for the simulated episode.

Other possible approaches

Conceptually, several other approaches may be possible for model modification for the purpose of better accounting for urban heat storage. At the minimum, the energy balance equation may be modified [through modification of the terms with overbars in Eqs. (3) and (4)] to better simulate urban areas. In this case, an improved surface characterization, for example, through use of remote-sensed data (satellite and aircraft), may be a good way to modify some terms of the equations. This approach has been taken, for example, in Pielke et al. (1995), Taha (1996, 1997), Hoyano (1984), and in this study.

A second approach could involve coupling canopy layer models with boundary layer models. This coupling, with or without feedback (e.g., one- or two-way nesting), would allow telescoping down onto areas of interest, for example, urban regions. Several canopy layer models have been developed in the past, for example, those of Terjung and Louie (1974), Terjung and O’Rourke (1980), Arnfield (1982), Swaid and Hoffman (1990a,b), Sharlin and Hoffman (1984), and Elnahas and Williamson (1997). These radiative models were examined in the context of this study and evaluated for the purpose of coupling with mesoscale models. Another category of canopy layer models, for example, canyon flow, dispersion, and turbulence models, can also improve the resolution of mesoscale simulations in urban areas. Models of Kotake and Sano (1981) and Yamartino and Wiegand (1986) are examples of this category.

A third approach could consist of modifying the friction terms (e.g., u*, θ*) used in the surface layer formulation of BLMs, based on empirical or theoretical relations. These and other possible approaches will be examined in more depth in future efforts.

Conclusions

A mesoscale meteorological model (CSUMM) was modified by incorporating a semiempirical formulation for storage heat flux in urban areas. The modified version (MM) uses OHM by Grimmond et al. (1991) and adds a weighted temperature tendency term to the surface energy balance equation of the boundary layer model.

The MM is used in simulating Atlanta, Georgia, as a case study. The MM simulates larger heat islands around the urban core, suggesting an increased differentiation between the soil heat fluxes in urban and nonurban land uses in MM compared to the nonmodified CSUMM. The simulated heat island reaches up to about 2.5°C in MM but only about 1.4°C in CSUMM. Increasing the albedo of urban Atlanta results in decreasing the simulated heat island at 1400 LST by about 0.5°C in CSUMM and about 1°C in MM. In other locations within the modeling domain, the original CSUMM predicts a decrease of up to 1.1°C in air temperature following increasing albedo, whereas MM predicts a decrease of up to 1.6°C. All these numbers are for 2 m above ground.

The larger simulated urban heat islands and more pronounced effects of albedo changes will have several ramifications in terms of energy use and photochemical (air quality) modeling. Larger heat islands mean larger cooling energy use and also larger temperature-dependent emissions of anthropogenic and biogenic volatile organic compounds and nitrogen oxides. It also means enhanced production of photochemical smog. On the other hand, larger cooling of the air (due to increased albedo for example) would result in reversing these effects, that is, energy use, emission, and ozone production. Thus, if the model modifications suggested in this paper are further evaluated and found to be reasonable, MM will be used in other applications such as estimating the photochemical impacts of urban heat islands and the benefits of cool communities in saving energy and improving air quality. In addition, other regions and urban areas will be simulated and studied in the future.