intercomparison of three urban climate models

INTERCOMPARISON OF THREE URBAN CLIMATE MODELS

PAUL E. TODHUNTER* and WERNER H. TERJUNG

Department of Geography, Universiry of Calfonda. Los Angeles, CA 90024, U.S.A.

(Received in final form 19 June, 1987)

Abstract. An intercomparison of the surface energy budgets from three urban climate models was made to assess the comparability of results, and to evaluate the surface energy fluxes from each model. The three models selected spanned the continuum of approaches currently employed in the treatment of the effects of urban geometry. The first model was an urban canopy-layer model which explicitly examined urban canyon geometry. The second model treated the city as a warm, rough, moist plate but included greatly simplified parameterizations of urban geometry. Neither model included a dynamic link to the urban boundary-layer. The third model was a one-dimensional urban boundary-layer model which utilized a simple warm, rough, moist plate approach but included a dynamic coupling of the urban surface layer to the urban boundary-layer.

Results showed considerable disagreement between the three models in regards to the individual energy fluxes. Average rankings of the energy Buxes in terms of comparability from high-to-low similarity were: (1) solar radiation, (2) sensible heat flux, (3) conduction, (4) latent heat flux, (5) longwave re-radiation, and (6) longwave radiation input. In general, the urban canopy-layer model provided more realistic results, although each model demonstrated strong and weak points. Results indicate that current urban boundary- layer models may produce surface energy budgets with lower sensible heat fluxes and substantially higher latent heat fluxes than is supported by field evidence from the literature.

1. Introduction

Current research in urban climatology focuses upon the measurement of surface and atmospheric processes and states, and their relationships through numerical models of the urban surface and boundary layers. These two research foci are closely connected since numerical models integrate field observations into a holistic framework while process studies lead to model validation data sets and the development of more physically realistic model parameterizations. The adoption of a modeling paradigm has led to a proliferation of urban climate models which, in the recent review by Bornstein (1986), can be grouped into two broad categories: (1) urban canopy-layer models which examine microscale climate variations occurring below roof-level, and (2) urban boundary-layer models which simulate mesoscale climate variations occurring above roof-level. This division recognizes that different processes control the energetics of the urban canopy and boundary layers (Oke, 1982). Vertical and horizontal gradients of meteorological fields within the urban boundary-layer (UBL) are generally conservative and vary in response to atmospheric structure, surface roughness and energy exchanges occurring at the canopy-layer/boundary-layer interface. Urban canopy-layer (UCL) meteorological fields, however, often change abruptly because of nonhomogeneities of land cover, surface materials, building density, urban geometry, and surface-solar geometry (Taesler, 1986).

* Present address: Graduate School of Geography, Clark University, Worcester, MA 01610, U.S.A.

Boundary-Layer Meteorology 42 (1988) 18 l-205. 0 1988 by D. Reidel Publishing Company.

182 PAUL E. TODHUNTER AND WERNER H. TERJUNG

Early research in urban climatology failed to distinguish between above and below roof-level processes. The distinct urban microclimate was generally attributed to variations in surface material properties of different land-use classes (albedo, emissivity, wet fraction, thermal diffusivity, anthropogenic heat, and roughness length). Although the importance of urban geometry effects on surface energy exchanges has been recognized for some time (Parry, 1967), a more complete understanding has emerged only within the past decade. Included among these processes are multiple reflections of shortwave radiation, view factor controls on diffuse shortwave and longwave radiation exchanges, shading due to obstructions, and vertical wall-solar geometry. Results obtained from field observations (Nunez and Oke, 1976; Barring et al., 1985; Yamashita et al., 1986), numerical urban canyon models (Terjung and O’Rourke, 1980a; Arnfield, 1982) and scale-model studies (Aida, 1982) have identified urban geometry as an important determinant of urban surface energy budgets.

Because of the structural and material complexity of the urban surface, a continuum of approaches of varying sophistication and realism exists for modeling urban surface energy budgets. The most detailed approach is to represent the city by a series of rectangular blocks (Terjung and O’Rourke, 1980a). A second approach assumes that urban geometry effects are too complex to model directly but can be approximated by parameterizations based upon a limited number of land-use-specific terrain parameters (Outcalt, 1972; Jenner, 1975). The final approach disregards the detailed urban canopy- layer processes and treats the city as a flat, warm, moist plate of variable roughness, consolidating the effects of urban geometry into a single variable - roughness length. Early UBL models represented the city by a plate of uniform aerodynamic roughness (Atwater, 1972; Bornstein, 1975). Subsequent studies increased the realism by varying surface roughness in a discrete manner along a rural-urban transect, the approach adopted in essentially all current UBL models (McElroy, 1973; Gutman and Torrance, 1975). Present research in urban climate modeling is clearly skewed toward the examination of turbulence within the UBL at the expense of proper consideration of the variable and complex nature of the urban canopy-layer, despite the known variability of the urban surface temperature field (Carlson et al., 198 1; Vukovich, 1983). Bomstein and Oke (198 1) have commented that incorporation of UCL effects would result in more realistic lower boundary conditions for UBL models.

This study seeks to compare and evaluate alternative methods of modeling the effects of urban geometry upon the surface energy budget. Representative UCL and UBL models will be used to simulate the surface energy budgets of two synthetic urban sites. The intercomparison is premised upon the assumption that under controlled initial and boundary conditions, different models simulating the same physical feature should provide similar results. The intercomparison will focus upon two goals: (1) a quantitative assessment of the comparability of the surface energy budgets, and (2) a qualitative evaluation of the surface energy fluxes on the basis of reported values in the literature. The three urban climate models selected spanned the continuum of methods for parameterizing urban geometry.

The need for model intercomparison studies has only recently been recognized and

INTERCOMPARISON OF THREE URBAN CLIMATE MODELS 183

encouraged (WMO, 1981; Coakley and Wielecki, 1979; Potter and Gates, 1984). Examples of model intercomparison studies in other disciplines include Sinclair et al. (1976) Terjung and O’Rourke (1980b) and Munn et al. (1987).

2. Model Descriptions

2.1. INTRODU~ITON

The steady-state energy budget equation for an urban surface is given by:

(Q + q) (1 - a) + sItotal - mT4 - H - G - LE = 0, (1)

where Q = direct solar radiation, q = diffuse solar radiation, a = surface albedo, E = surface emissivity, Itotal = hemispherical longwave radiation, 0 = Stefan- Boltzmann constant, T = surface temperature, H = sensible heat flux, G = conduction, and LE = latent heat flux. The reader is referred to the original papers for a thorough discussion of the structure and underlying assumptions of each of the following models.

2.2. URBAN3

URBAN3 approximates the physical structure of a city by a finite number of rectangular blocks intermixed with streets, parking lots and parks (Terjung and Louie, 1974; Terjung and O’Rourke, 1980~). The structural and material characteristics of a city are approximated by specifying the properties, dimensions and distribution of each block. A solar obstruction model calculates the shadowing effects of surrounding buildings upon the receipt of shortwave radiation on each urban canyon.

Direct beam shortwave radiation explicitly accounts for horizontal surface- and vertical surface-solar geometry. Diffuse solar radiation from the sky on a horizontal surface is determined from an empirical relationship, while the vertical surface diffuse component utilizes view factors and includes isotropic diffuse radiation from the sky as well as directional diffuse radiation on the sunlit portion of each facet. A third shortwave radiative term, diffuse radiation reflected from the environment, is included for both horizontal and vertical surfaces. Two reflections were considered adequate to account for the majority of the energy exchanged in the infinite multiple reflection series. Longwave radiation includes separate inputs from the sky and from the buildihgs, streets and lots which comprise the surrounding terrain. This latter component can be a significant energy flux (Cole, 1976). The longwave emissions from nearby surfaces are multiplied by their respective view factors and then summed to determine the longwave input from the environment for a particular surface.

Conduction of energy into the urban fabric takes one of three forms depending upon whether the surface is a street, opaque wall, rooftop, parking lot or glass window. Sensible heat flux is obtained by the use of a convection coefficient, a standard procedure in mechanical engineering which eliminates the complexities involved with the use of eddy difhusivity theory in non-uniform terrain, and which has gained increased use in building climatology (Cole and Sturrock, 1977; Sharples, 1984). The evaporative flux


is solved by a multi-layered leaf energy budget model (Terjung and O’Rourke, 1980b). It is assumed that stomatal resistance is a function only of leaftemperature, ranging from maximum stomata1 resistance at minimum and maximum leaftemperatures, to minimum stomata1 resistance (r+) at optimum leaftemperature. Vegetated surfaces are assumed to be under negligible water stress (rst,, = 0.5 s cm- ‘), since urban water balances are typically augmented by considerable inputs of anthropogenic moisture.

2.3. URBD

The URBD model (Myrup, 1969; Out&, 1972) is a surface-climate simulation model which assumes that the urban surface layer is composed of such a variety of materials and surfaces that explicit modeling of individual interfaces would be either unrepresenta- tive or prohibitively expensive. A city is partitioned into a mosaic of homogeneous land-use units for which area-weighted input parameters are developed based upon a limited number of urban geometry variables. Surface energy fluxes are then computed for each land-use unit.

Although the city is treated as a flat plate, total absorbed solar radiation includes contributions from both horizontal and vertical surfaces. Diffuse radiation includes two contributions, downward scattering of attenuated direct beam and backscattering of reflected direct and diffuse radiation. A slope correction factor is applied to both ditIuse terms. The effects of urban obstructions, view factors and solar-wall geometry are treated through simple parameterizations. The fraction of the flat plate obstructed by shadows is considered a function of the solar zenith angle. Direct beam irradiance upon vertical walls is found by rotating the surface throughout the day so that its aspect is always equal to the solar azimuth angle. Total absorbed solar radiation includes unobstructed horizontal area direct and diffuse terms, a shadowed horizontal area diffuse term, and vertical surface direct and diffuse terms weighted according to a silhouette ratio which increases in magnitude with increasing building size and density. View factor effects upon the longwave radiation regimes of urban canyons are parameterized by use of the same silhouette ratio. The additional longwave radiation input from urban terrain is not considered.

Conduction is solved via the soil heat flux equation employing an eight-layer soil model and a single lower boundary condition. Sensible and latent heat transfers are obtained by eddy diffusivity theory, with the eddy diffusivities of heat and water vapor assumed to be equal and obtained from the logarithmic wind profile relationship adjusted for non-neutral stability conditions. The latent heat flux is found by multiplying the surface-air water vapor density gradient by a wet fraction, the fraction of the horizontal area covered by freely evapotranspiring surfaces.

2.4. HFLUX

The HFLUX model developed by Carlson et al. (1981) is a one-dimensional boundary- layer model in which the partitioning of radiant energy at the urban interface is dynamically linked to the temperature, wind and moisture structure of the urban mixing layer. HFLUX adopts a simple flat plate approach wherein the urban complex is


characterized by a limited number of physical properties - roughness length, thermal inertia, albedo, emissivity, and moisture availability. No attempt is made to consider directly the effects of urban geometry upon surface energy exchanges. Model structure incorporates four layers: a 1.5 m substrate layer; a transition layer of variable height in which radiant, conductive and turbulent heat exchanges coexist, from purely diffusive fluxes at the soil surface to purely turbulent fluxes at the top of the surface layer; a turbulent surface layer 50 m in height in which turbulent exchange processes dominate; and a dynamic mixing layer. HFLUX represents an improvement over other one- dimensional UBL models because the mixing-layer height is time-varying due to the addition of sensible heat from the surface and the entrainment of air from above the mixing layer (Bornstein, 1986).

Global solar radiation is determined from a one-dimensional solar radiation model (Carlson and Boland, 1978). An overall atmospheric transmission coefficient incorporates the separate path length-dependent absorption and scattering of dust, water vapor, air molecules and ozone, as well as backscattering due to dust and air molecules. Atmospheric radiation is dependent upon air temperature at the top of the surface layer and the precipitable moisture content of the boundary-layer.

Conduction within the substrate layer is governed by the soil heat flux equation. The determination of sensible and latent heat exchanges follows separate procedures for daytime and nighttime conditions. Daytime solutions, based upon boundary-layer theory, are determined from the soil surface-turbulent surface-layer temperature and moisture gradients, the integrated height-dependent eddy diffusivities for heat and vapor, and surface-layer stability. The nighttime sensible heat flux is obtained from a modified form of the critical Richardson Number approach. Nighttime latent heat transfer is solved in a similar manner as during the daytime provided the flux is directed away from the surface. Nighttime latent heat fluxes directed toward the surface are set to zero.

2.5. BOUNDARY CONDITIONS

The conceptual differences between the three models are reflected in their contrasting boundary conditions. Meteorological parameters (air temperature, surface pressure, wind speed, and relative humidity) are input at hourly time intervals for URBAN3 and URBD. These time-varying upper boundary conditions compensate, in part, for the omission of an explicit dynamic link to the UBL. The two models share a common lower boundary condition, the temperature at the base of the soil layer which is set equal to the mean daily air temperature. URBAN3 includes a second lower boundary condition, the constant interior building air temperature. Upper boundary conditions for HFLUX consist of an initial wind profile and a temperature and humidity sounding taken immediately prior to sunrise. The constant temperature at the base of the substrate layer serves as the single lower boundary condition and is set equal to the surface air temperature obtained from the sounding.


3. Data Preparation

An intercomparison of the three urban climate models requires that model integrations be performed under comparable conditions. The degree of control over the initial and boundary conditions between any two models will always be less than perfect and is an unavoidable problem resulting from differences in model structure and parameterizations. When initial and boundary conditions are controlled to the greatest extent possible model results may be compared and evaluated, bearing in mind the characteristic assumptions and structural dissimilarities of each model.

3.1. CLIMATE DATA

October 11, 1983 was selected because that day meets the synoptic conditions required by the HFLUX model, which included clear skies, low humidity, high pressure, light-to-moderate winds, and the absence of a low ceiling height to impair the development of the daytime mixing layer. Hourly climate data at Los Angeles Airport were obtained by cubic spline interpolation from three-hour observations. The pre-sunrise air and dew point temperature soundings near Los Angeles Airport revealed well-developed thermal and moisture inversions created by nocturnal surface radiative heat loss and dew deposition. All climate data required for model simulations are provided in Todhunter (1986).

3.2. URBAN GEOMETRY SCENARIOS

A synthetic city was created to evaluate the response of each model to the controlled environmental inputs. The use of a synthetic city has precedence in urban climatology (Terjung and O’Rourke, 1980a) and has several advantages. First, for geographic applications it can be ‘relocated’ and thus used to analyze the influence of climate and latitude. Second, model assumptions can be more closely met by a synthetic city. Third, regional land-use homogeneity can be insured by design. Two urban density scenarios (a medium- and a low-density case) are shown in perspective view in Figure 1. Each circular-shaped region consisted of twenty-four blocks surrounded by streets and/or open lots. The north-south and east-west aligned streets range in width from 7.6 to 32.0 m. The twenty-four blocks are arranged in two concentric zones: a central core of taller blocks and a peripheral zone of shorter structures. Block widths varied in length from 42.7 to 91.4 m and are the same for both scenarios. Complete block and street dimensions and building heigths are provided in Todhunter (1986). Medium-density (M) scenario building heigths ranged from 6.1 to 36.6 m with an average height of 18.7 m. Low-density (L) scenario building heights ranged from 0.0 to 12.2 m with an average height of 5.7 m. The ratio of total surface area (horizontal and vertical) to horizontal surface area was 1.45 and 1.14 m* m - * for the medium- and low-density cases, respectively. This ratio, a ‘building area index’, provides a simple and unbiased measure of urban structural density. Fifty percent of all building walls were covered by windows with drawn drapes. Wet fractions of 14.1 y0 (M) and 18.0% (L) were obtained by dividing the total vegetated area (street level parks and rooftop gardens) by the total


Fig. 1. Perspective view of medium-density (left) and low-density (right) urban scenarios. The low-density scenario appears different because three of the blocks were assigned a height of 0.0 m.

combined horizontal and vertical area. This method for determining the wet fraction takes into account all of the surface area involved in energy exchange processes, and resulted in more realistic latent heat fluxes than a method based only upon horizontal surface area (Todhunter, 1986). Surface roughness lengths were estimated by the empirical method of Lettau (1969) and were calculated directly from the synthetic city dimensions. The aerodynamic roughness length obtained for the medium-density case (138.0 cm) agreed with observed values for downtown areas reported in the literature (Oke, 1974). The low-density scenario roughness length (13.0 cm) was also derived from the Lettau formula.

Although urban net radiation input is a relatively conservative term (White et al. (1978) report intra-urban variations of < 5 %), the disposition of urban net radiation is highly dependent upon land-use type (Ching et al., 1983; Ching, 1985). The results obtained from these simulations, therefore, apply to only a subset of all possible urban land-use types. The medium-density scenario is most representative of a commercial or central business district zone in a medium-to-large city. The low-density scenario most closely resembles a small city central business district, a warehouse district, or a high density residential sector. Other urban land-use types exist but are not approximated by either of the two described scenarios (Auer, 1978).

3.3. MISCELLANEOUS DATA

Building interior air temperature in URBAN3 was held at a constant temperature of 26.7 “C, corresponding to a modest expenditure of energy for domestic/commercial space heating and cooling. The inclusion of anthropogenic energy in the URBAN3 surface energy budgets requires that a similar magnitude energy term be added to URBD and HFLUX. Methods for estimating the domestic and commercial anthropogenic energy sectors contain numerous subjective elements and were not used (Harrison et al.,


1984). An objective approach was taken which estimated the anthropogenic flux directly from the URBAN3 output. Two sets of URBAN3 simulations were made for the medium- and low-density scenarios, hrst with the building interior temperature set to 26.7 “C and the substrate temperature set to 23.3 “C, and second, with both lower boundary conditions set to 23.3 “C. Conduction fluxes were summed over a diurnal period for each urban density scenario for the two interior air temperature values. The absolute value of the difference between the daily summed conduction for each pair of cases was considered to represent the effect of building space heating and cooling. The constant anthropogenic energy temrs obtained were only 5.1(M) and 3.4(L) W m-*.

The value of the urban thermal inertia used in HFLUX (P = 2.08 x lo3 J m - 2 K - ’ s l/*) was obtained from the maximum downtown values given in Carlson et al. (1981). Values for other thermal properties - thermal conductivity (A = 2.3 W m -* K-‘), heat capacity (C, = 1.88 x lo6 J me3 K-l) and thermal diffusivity ( IC = 1.2 x 10 - ’ s - ‘) -were taken from Myrup and Morgan (1972), subject to the relationships P = (IC,)“’ and IC = n/C,. Minimum zenith angle-dependent albedos of 0.13(L) and 0.16(M) were employed in all model simulations.

4. Model Evaluation Procedures

4.1. INTRODU~ION

No generally accepted criteria exist for determining the selection of model intercomparison variables. Model design complicates the selection process because separately conceived and structured models have different types and numbers of possible output variables from which to choose. The approach of Potter and Gates (1984) was adopted which compared the most physically signitkant variables common to each model, which were clearly the diurnal components of the individual terms in the surface energy budget equation (l), along with related derived parameters.

In order to facilitate comparisons with the URBD and HFLUX models, the energy fluxes from the sixty three-dimensional air-surface interfaces in URBAN3 were converted into comparable flux densities for a two-dimensional surface, utilizing a simple linear two-step weighting scheme. First, new energy fluxes were obtained from the sixty urban canyon systems by transforming the individual fluxes from the five urban canyon interfaces into a single flux over an equivalent horizontal area. The weighting equation was of the form

Fx. = Fl, Wl + F2,TH, + F3,TD + F4iTH2 + F5i W2 2 ,

Wl+TD+W2

where FX, = equivalent energy flux of the ith energy term over a horizontal distance equal to Wl + TD + W2, Wl and W2 = roof lengths of opposing buildings, TD = street width, THl and TH2 = wall lengths of opposing buildings, and Fn, = the ith energy term for each of the five (n) urban canyon interfaces. Second, the sixty sets of new


horizontal area energy budgets were weighted according to the surface area of each urban canyon. The second weighting equation was

FLUX, = 5 FX, j=l

where FLUX, = the energy flux density for the jth energy term for the horizontal area of the synthetic city, FX, = the energy flux density for the jth energy term for each of the sixty (i) urban canyon system horizontal equivalent areas, 2 = the average horizontal equivalent area of the sixty urban canyon systems, and Ai = the horizontal equivalent area of the ith urban canyon system. This weighting scheme enabled the energy flux densities from the sixty urban canyon systems in URBAN3 to be aggregated and expressed as an energy flux density comparable to the flat plate method used in URBD and HFLUX.

4.2. EVALUATION OF MODEL COMPARABILITY

Evaluating the similarity of results between separate modeling efforts is conceptually similar to determining the level of accuracy of model predictions versus observed values. Significant progress has been made in recent years in developing suitable statistical methods for the quantitative evaluation of model performance for scalar quantities (Willmott, 1982). The scalar quantity model comparison guidelines proposed by Willmott (1982) test the level of agreement between observed values and model- predicted estimates. In such comparisons the choice of the independent (observed) and dependent (predicted) variables is clear. In this application, pairs of model-predicted values are compared, thus the selection of independent and dependent variables is somewhat arbitrary. Although the use of 0 and P for the observed and predicted values was retained, they now refer to the independent and dependent variables rather than to observed and predicted fluxes. Only the index of agreement (d) developed by Wilhnott will be presented here. Its value is computed by

d=l- (4)

where Pi = Pi - 0, O,! = Oi - 0, 0 = mean of the independent variable, and N = 24 (except for the solar radiation flux where N = the number of hours of sunlight). The index of agreement is an easily interpreted non-dimensional descriptive statistic which facilitates cross-comparisons of model results. A value of 1.0 corresponds to perfect comparability between model fluxes and a value of 0.0 indicates perfect disagreement.

4.3. EVALUATION OF MODELPERFORMANCEVERSUS FIELD OBSERVATIONS

Since the three models encompass the spectrum of urban geometry treatment in urban climate modeling, it is important to make some assessment of the relative accuracy of


the surface energy flux densities obtained from each respective approach. An independent field validation program to measure all of the energy balance terms over a diurnal period for a large number of downtown urban canyons, although desirable, was beyond the scope of this study. Instead, use is made of a select number of independent field studies reported in the literature to provide an assessment of the three sets of simulation results. While such an approach has limitations, it does give an independent first-order appraisal of the direction, form and magnitude of the model results. Obvious departures from realistic energy flux densities are readily apparent based upon physical reasoning. Attention was paid to insure that the site conditions of the reported studies closely matched the scenario conditions used, particularly with respect to wet fraction and time of year. The most useful validation data sets are derived from tower-based measurement programs within homogeneous land-use units with adequate fetch conditions in all directions. Such data sets present spatially integrated values unconstrained by site-specific conditions. Street-level observations also provide high quality measurements but are of more limited value due to their site-specific nature. Complete energy budgets can be obtained from either method. A more limited number of variables can be measured from low-altitude aircraft and satellite-based sensors, the final source of validation data.

5. Model Results

The energy budgets from the three models are presented in Figures 2 and 3 for the medium- and low-density scenarios, respectively. Maximum and minimum values for the six individual energy terms and net radiation (R,) are provided in Table I along with a series of parameters derived from the average daytime energy fluxes. Individual radiant term traces are shown in Figures 2 and 3 in lieu of the composite net radiation trace because the former method provides greater insight into the dynamics of the urban radiation regime. In the discussion which follows, positive values denote surface energy sources while negative totals indicate surface energy sinks.

5.1. URBAN3

The absence of significant cloud cover results in global solar radiation curves which follow a unimodal pattern. Peak ii-radiances differ very little between the medium- and low-density cases: 595(M) and 607(L) W m-‘. A minor noontime depression occurs in both sets of URBAN3 output at solar noon because of the extreme wall-solar azimuths (90.0 ” ) experienced by both opposing walls along north-south aligned urban canyons (half of all urban canyon systems). At all other hours, one of the two opposing walls has a wall-solar azimuth less than 90.0’) thus eliminating the depression. Too few field studies of urban canyon radiation regimes have been observed to determine whether this apparent depression is a real phenomenon or a unique feature of the model formulation or urban street orientations. In any case, the magnitude of the depression is small by both absolute and relative standards.

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TABLE I

Summary of the energy balance comparisons and parameters derived from the average daytime values. Positive values indicate energy flux densities directed toward the surface; negative values indicate energy flux densities directed away from the surface. Maximum and minimum energy flux densities (W m - 2, are given by the upper and lower numbers in each pair of totals, respectively. By definition, fi = H/LE, -- - -- - --

j = (H/R” I, t$ = 1 LE/R, 1, 3, = 1 G/R, 1 and R, = net radiation.

(a) Medium-density

URBAN3 596 493 -685 393 -300 -67 -57 3.34 0.65 0.20 0.15 415 -475 -110 84 35 -1

URBD 637 302 -380 568 -124 -76 -371 0.19 0.14 0.75 0.11 257 -313 -55 101 84 0

HFLUX 634 396 -502 526 -165 -217 - 190 0.72 0.26 0.36 0.38 319 -381 -83 19 10 8

(b) Low-density

URBAN3 607 406 -599 410 -312 -72 -63 3.54 0.65 0.19 0.16 344 -393 - 100 78 26 - 1

URBD 603 339 -438 510 - 110 - 185 -215 0.36 0.17 0.47 0.36 288 -350 -64 35 85 0

HFLUX 656 395 -500 548 -156 -216 -222 0.58 0.23 0.40 0.37 319 -381 -82 16 4 6

of air temperature and relative humidity, daytime heating of the urban environment by solar radiation, nighttime cooling of the urban environment by re-radiation, and structural differences between the urban density scenarios. On a daily basis, the input

of energy via longwave radiation from the environment is the principal source of energy, rivaling solar radiation in terms of peak energy flux densities for the medium-density

scenario. Total longwave radiation input averages 17 y0 less for the low-density scenario than for the medium-density case. Longwave radiation from the surrounding urban terrain supplies 22% (M) and 9% (L) of the total longwave input. Thus the reduced total longwave input for the low-density scenario is primarily attributable to the decreased longwave flux from the surrounding buildings arising from increased sky view factors. Peak ZJ occurs at 1200 LST for both urban density scenarios, while the highest air temperatures are present at 1100 LST, illustrating the critical role played by the surrounding urban terrain.

Longwave re-radiation is the dominant energy sink at all hours for both scenarios. The longwave output diurnal amplitude is considerably greater than that of the longwave input because of the surface temperature-dependence of the former as it responds to the daytime solar forcing. The reduction in ZT from the medium- to low-density scenarios is due to decreased building surface area rather than surface temperature contrasts since the method by which the five urban canyon interface energy fluxes are converted into equivalent horizontal energy fluxes utilizes the same horizontal area for both urban density scenarios (2 and 3). Large longwave re-radiation losses result in modest net radiation totals with maximum daytime values of 393(M) and 410(L) W mp2. A


pre-noon peak in longwave re-radiation is observed for both urban scenarios and arises from the convection coefficient approach to sensible heat flux parameterization, in concert with the prevailing synoptic weather conditions. Higher air temperatures and lower wind velocities in the pre-noon period suppressed sensible heat flux, thereby increasing surface temperature (and Zt). Post-noon surface-air temperature gradients and wind velocities were favorable to forced convection, resulting in enhanced sensible heat flux and lower surface temperatures.

The dissipation of daytime net radiation via sensible heat flux, conduction and latent heat flux follows consistent proportions between the two urban density scenarios. About 65 % of daytime net radiation is disposed of by sensible heat, approximately 20 % by latent heat flux and the remaining 15% by conduction into the street, lot and building fabric. Conduction is less than might have been anticipated because the maintenance of a constant building interior air temperature reduces the exterior/interior wall temperature gradient. Sensible heat flux and conduction provide daytime energy sinks and nighttime energy sources, whereas latent heat flux is a continuous energy sink. The conduction and latent heat fluxes exhibit pre-noon maximums (1000 and 1100 LST, respectively), while peak sensible heat flux occurs in the early afternoon (1300 LST). Average daytime Bowen ratios are between 3.0 and 4.0.

5.2. URBD

The URBD results contain numerous differences with URBAN3 (Figures 2 and 3, Table I). Global solar radiation is symmetric about noon and comparable in magnitude to the URBAN3 fluxes, with peak flux densities of 637 (M) and 603 (Z,) W m- ‘. The small reduction in global radiation for the low-density case is attributable to the smaller silhouette ratio used in weighting the vertical surface contributon of the total absorbed solar radiation term.

Longwave radiation inputs are significantly less than for URBAN3, peaking at 1100 LST, the hour of maximum air temperature. Average ZJ totals are 38% (M) and 16%(L) less than for URBAN3 because of the omission of radiation from the surrounding urban terrain and the view factor parameterization scheme employed. The increase in peak ZJ values for the low-density case results from the view factor parameterization scheme as well. Average longwave re-radiation values are 38 z(M) and 18% (L) less than for URBAN3, and exhibit more restricted daily amplitudes. The more conservative net longwave radiation regime results in net radiation totals which are greater than in URBAN3, with peak daytime totals of 568(M) and 5 10(L) W m- ‘. A slight pre-noon peak in Zt also occurs in URBD but is much less pronounced due to the role of evaporative cooling in reducing the surface-air temperature gradient.

The partitioning of daytime net radiation into the turbulent and molecular fluxes follows a much different pattern. The percentage division of net radiation into sensible heat flux/conduction/latent heat flux is 14%/11%/75%(M) and 17%/36%/47%(L). The two points which stand out are the primacy of latent heat flux, and the sensitivity of energy partitioning to the surface roughness length estimate. The first observation is demonstrated by Bowen ratios less than 0.50 for both urban density cases. The sharp


decrease in the surface roughness length from 138.0(M) to 13.0 cm(L) results in a large reduction in the latent heat flux, a small increase in the relative importance of the sensible heat flux, and a substantial relative and absolute increase in molecular diffusion. All three modes of energy transfer experience peak flux densities at 1200 LST.

5.3. HFLUX

The HFLUX results (Figures 2 and 3, Table I) are generally intermediate in value between the URBAN3 and URBD totals. Global solar radiation is marginally higher than in the other models, and increases slightly from the medium- to low-density scenarios because of the average albedo reduction from 0.16(M) to 0.13(L). The omission of view factor and urban terrain considerations results in inputs of longwave radiation that are essentially unchanged between the two urban density scenarios. The more realistic boundary-layer structure led to enhanced atmospheric emissivity and vertically integrated air temperature values, and therefore larger atmospheric radiation totals than did the simpler shelter height-based approach used in URBD and URBAN3. Average values of ZJ are only 18%(M) and l%(L) less than for URBAN3, with the boundary-layer structure compensating, in part, for the omission of longwave radiation from the surrounding urban terrain. Peak longwave radiation inputs lag until 1400 LST due to the same boundary-layer considerations. Longwave re-radiation is quite similar between the two urban density scenarios, and peaks at 1300 LST in contrast to the pre-noon peak in the other two models. Average Zt totals are 19% (M) and 3 % (L) less than for URBAN3, with a more subdued diurnal amplitude.

HFLUX demonstrates a relatively even division of daytime net radiation into the various energy sinks. The total energy lost via sensible heat flux/conduction/latent heat flux was 26%/38%/36%(M) and 23%/37%/40%(L). The dynamic structure of HFLUX results in decreased turbulent fluxes and an increased soil heat flux in comparison to URBD, even though the governing equation for molecular diffusion is identical. In going from the medium- to low-density scenarios, a reduction occurs in the relative importance of sensible heat flux and conduction and a corresponding increase in the relative importance of the latent heat flux. Latent heat flux is the primary means of energy dissipation, with average daytime Bowen ratios between 0.50 and 1.00 for both scenarios. Peak energy flux densities for sensible heat flux, conduction and latent heat flux occur at 1200, 1000, and 1300 LST, respectively.

6. Discussion

6.1. COMPARABILITY OF MODEL FLUXES

The model intercomparison results are summarized in Table II which presents the d statistic for each energy term, urban density scenario and model pairing. The statistics were averaged to obtain a mean for each urban density scenario, as’well as an overall value. Average d statistics for each model pair were computed by taking the mean of the six energy terms. The overall rankings of the individual energy fluxes in terms of


TABLE II

Summary of intercomparison statistics. Numbers in the table are the d statistic, or index of agreement, between the model pairs indicated in the left column.

IV-DV” (Q+q) II It H LE G Average

(a) Medium-density

URBAN3-URBD URBAN3-HFLUX HFLUX-URBD Average

(b) Low-density

URBAN3-URBD URBAN3-HFLUX HFLUX-URBD Average Overall

0.99 0.22 0.37 0.98 0.38 0.53 0.99 0.23 0.30 (0.99) (0.28) (0.40)

0.99 0.44 0.61 0.98 0.73 0.62 0.98 0.31 0.38

(0.98) (0.49) (0.54) (0.99) (0.39) (0.47)

0.85 0.26 0.87 0.43 0.88 0.68 (0.87) (0.46)

0.75 0.50 0.84 0.37 0.93 0.85

(0.84) (0.58) (0.85) (0.52)

0.87 (0.60) 0.68 (0.65) 0.72 (0.63) (0.76)

0.75 (0.67) 0.68 (0.70) 0.87 (0.72)

(0.77) (0.76)

a IV = independent variable, DV = dependent variable.

comparability was identical for both urban density scenarios and is as follows (from high-to-low): (1) Q + q - 0.99, (2) H- 0.85, (3) G - 0.76, (4) LE - 0.52, (5) It - 0.48, and (6) IL- 0.39. The average d statistics provide a quantitative measure of the sensitivity of each energy term to the different urban geometry and boundary-layer parameterizations.

The high solar radiation average d statistic is especially noteworthy considering the very different approaches taken by the models. Although the surface receipt of solar radiation varies enormously within the city along the individual facets of an urban canyon, these microscale effects are apparently lost when the fluxes from a large number of buildings are spatially aggregated. This can be explained by scale considerations: within urban canyons, the receipt of solar radiation is principally determined by shading effects and surface-solar geometry, while at a regional scale, individual urban canyons compensate for one another thereby making mesoscale variations in global solar radiation the critical determinant. A moderately high average d statistic is also obtained for the sensible heat fluxes from each model; however, significant deviations are found in the remaining energy terms. Conduction demonstrates only a modest level of agreement since URBAN3 shares the same lower boundary condition with URBD and HFLUX in only 56% (M) and 63% (L) of the horizontal surface area. The lower boundary condition for the remaining 44% (M) and 37% (L) of the horizontal surface area is the constant indoor air temperature. Those conduction flux variations not attributable to boundary-value considerations are due to divergent equilibrium surface temperatures since the same diffusion equation is used in all of the models. Turbulent latent heat fluxes generally exhibit low levels of agreement. The energy terms with the lowest average d statistics were the two longwave radiation fluxes. Poor agreement between 1~ totals arise from either building longwave emission factors or urban


boundary-layer considerations. Lack of agreement between longwave re-radiation fluxes is caused by equilibrium surface temperature inequalities arising from substantial contrasts in the magnitude of conduction and latent heat loss.

The mean d statistic of the medium-density pairings (0.63) was noticeably lower than for low-density pairings (0.70). Three of the energy terms (11, It, and LE) show an increase in the d statistic in going from the medium- to low-density scenario, while the remaining energy terms (Q + q, H, and G) show little change. The similarity of the energy budgets of the three models clearly improves as urban density complexity decreases, or as the flat plate assumption is approached. Thus, as structural dissimilarities between the models are reduced, their results converge, although considerable disagreement still occurs between the models due to other factors.

6.2. EVALUATION OF MODEL RESULTS VERSUS FIELD OBSERVATIONS

Surface energy flux evaluation was based upon a limited number of high quality field studies reported in the literature which closely approximate the model scenario boundary conditions. Little experimental data exist on the solar radiation regimes of urban complexes. Individual building surfaces are known to receive highly variable solar irradiances because of the combined effects of surface aspect, solar azimuth, view factors, and building obstructions (Tuller, 1973; Sagara and Horie, 1978). Nunez and Oke (1977), however, have shown that the composite solar radiation flux of a symmetri- cal urban canyon volume resembles a unimodal curve. The similarity between the URBAN3, HFLUX, and URBD results (Figures 2 and 3) implies that the accuracy of the solar radiation fluxes will primarily depend upon the solar transmission model and urban albedo values used. The conservative nature of the composite solar radiation fluxes suggests that regional solar irradiance may be effectively parameterized by a solar transmission model in combination with an effective urban albedo scheme. Urban albedos are generally lower than rural values because of surface spectral properties and multiple reflection effects; they have been efficiently parameterized by Sievers and Zdunkowski (1985).

Insufficient data exist to evaluate the magnitude of the total (atmosphere and terrain) longwave radiation input. Terjung and O’Rourke (1980d) present modeling results which show that under extreme urban geometric configurations, longwave radiation from buildings can exceed 50% of urban canyon longwave radiation inputs. Field measurements by Cole (1976) revealed increases of 25% in the longwave radiation incident upon vertical surfaces because of the additional ground component alone. The presence of surrounding buildings would only further augment the increase. Nunez and Oke (1976) and Barring et al. (1985) have shown that longwave radiation regimes of urban canyon systems differ markedly from horizontal rooftop and rural surfaces because of reduced sky view factors. On the basis of these qualitative considerations the larger II values for URBAN3 indicated in Table I seem preferable.

Measurements of longwave re-radiation from downtown urban surfaces are available from White et al. (1978), Ching (1985) and Vukovich (1983). White et al. (1978) report surface radiant temperatures over St. Louis for two land-use types relevant to this study


- a commercial zone (C) with a wet fraction < 15%) and an industrial zone (Z) with a wet fraction < 5 %. Assuming an emissivity of unity, peak Zt values of approximately

- 580 W m-“(Z) and - 570 W m-*(C) were recorded. Ching (1985) cites maximum longwave emissions of - 535 and - 550 W m-* over downtown St. Louis. Vukovich (1983) reported surface radiant temperatures over St. Louis during the summer with measurements confined to the times of satellite overpass. Downtown longwave emissions at 1330 LST generally exceeded - 535 W rnm2, while nighttime emissions (0230 LST) were at least - 390 W m- 2. On the basis of these limited data sets, the URBAN3 results seem tenable for the low-density scenario but perhaps too high for the medium-density case. The URBD fluxes are consistently low, especially for the medium- density scenario. HFLUX totals are reasonable for both scenarios, although the maximum daytime emissions are perhaps too conservative.

The scarcity of information on the individual radiant energy terms is mitigated by a larger body of net radiation data. Reported observations of net radiation and accom- panying energy balance fluxes are summarized in Table III for various appropriate land-use types, as well as two suburban studies. These latter two sites clearly do not match the boundary conditions of the two urban scenarios, but are included to provide upper and lower bounds for comparison. Peak daytime net radiation totals in Table III range from 400 to 620 W m- *, with most values between 440 and 570 W m - 2. Minimum reported nighttime net radiation fluxes vary between - 50 and - 80 W m - *. The URBAN3 net radiation fluxes appear to be too low during the daytime and too large at night because of the large longwave radiation emissions discussed earlier. The URBD totals are within the range of measured values since small longwave inputs are balanced by small longwave outputs. The HFLUX daytime and nighttime net radiation fluxes are within the range of reported values.

The partitioning of net radiation into the turbulent fluxes of sensible and latent heat has been observed to be dependent upon the horizontal area fraction composed of evapotranspiring surfaces, and the availability of moisture within those moist surfaces. Traditionally, urban boundary-layer models have incorporated one and omitted the other of these two dominant physical processes in their parameterizations of surface moisture exchanges. Moist surface area fraction has an obvious control on the partitioning of net radiation and, since it can easily be determined from remotely-obtained imagery, has long been included in surface parameterizations. Kalanda et al. (1980), however, report average daytime Bowen ratios ranging between 0.48 and 2.35 for the same suburban site because of different degrees of surface dryness caused by varying time intervals between rainfall or urban irrigation events. As a result, the observed sensible and latent heat fluxes in Table III and the derived Bowen ratios show considerable range in values. Peak sensible heat fluxes between - 220 to - 320 W m - * and peak latent heat fluxes between - 50 to - 125 W m - * are indicated in Table III for urban environments composed of minimal vegetated surface area, although sensible heat fluxes as high as -530 W m-* (Ching, 1985) and as low as - 185 W m-* (Kerschgens and Hacker, 1985) have been recorded for similar environments. Measured daytime sensible heat flux peaks have been found to be in phase with net radiation or

TABL

E III

Su

mm

ary o

f app

roxi

mat

e m

axim

um a

nd m

inim

um e

nerg

y flu

x de

nsiti

es (W

m-‘)

an

d de

rived

par

amet

ers

for u

rban

sur

face

s rep

orte

d in

the

liter

atur

e. P

ositi

ve v

alue

s re

pres

ent e

nerg

y flu

x de

nsiti

es d

irect

ed t

owar

d th

e su

rface

; neg

ativ

e va

lues

ref

er to

ene

rgy

flux

dens

ities

dire

cted

aw

ay fr

om t

he s

urfa

ce.

Ref

eren

ce

Loca

tion

WF’

D

ate

R,”

H

G

LE

83

14

cp5

16

Whi

te e

t al.

(197

8)

Chi

ng e

t nl

. (1

983)

St.

Loui

s, M

O

38”4

0’

<0.1

5

0.10

Chi

ng (1

985)

Kers

chge

ns a

nd H

acke

r (1

985)

Ya

p an

d O

ke (

1974

)

Nun

ez a

nd O

ke (

1977

)

Bon

n, F

.R.G

. 50

”42’

Va

ncou

ver,

BC

49”1

3’

(urb

an c

anyo

n)

cent

ral

city

0.

18

0.30

<O.lO

Kala

nda

et a

l. (1

980)

(s

ubur

ban)

0.

64

Cle

ugh

and

Oke

(19

86)

(sub

urba

n)

0.64

Oke

(19

82)

Idea

l m

idla

titud

e ur

ban

site

18 A

ug.,

1976

7 19

Aug

., 19

76’

Aug.

19

76

Aug.

19

76’

18 A

ug.,

1976

’ 19

Aug

., 19

76’

13 Ju

ly,

1982

5 Ju

ly,

1972

17

July

, 19

72

9-11

Sep

t., 1

973

9-11

Sep

t., 1

973

10 S

ept.,

77”

13 S

ept.,

77”

30 d

ay s

umm

er

aver

age

1983

su

mm

er

368

359

440

-65 473

425

409

465

- 29

5 10

-2

44

- 11

5 -1

10

- 12

5 -

80

- 12

5 -

190

- 17

59

615

620

500

-70 6.8”

’ 49

0 -

80

470

-75 57

0 -1

10

- 22

5 -

295

-80

- 32

0 -

130

so

- op

& -

280

- 11

09

25

559

- 14

0 -

1o59

30

45

9 -

230

- 13

59

15

659

2.00

-115

2.

12

- 10

0 1.

10

- 20

0 0.

70

- 18

5 1.

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- 25

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20

- 50

6.

40

l.%

5.17

-

120

2.35

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-

295

0.48

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-2

10

1.28

40

1.

50

0.78

0.52

0.

24

0.24

0.

33

0.37

0.

30

0.20

0.

50

0.30

0.

37

0.37

0.

279

0.37

0.

47

0.40

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0.64

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= w

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net

radi

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3 B

= H

/LE;

4

x =

1 HIR

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, I;

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/R,l;

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1300

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atio

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lag slightly behind it, whereas maximum latent heat fluxes are usually found to be in phase with R,. Sensible heat fluxes in downtown urban regions have been observed to account for 40 to 60% of daytime net radiation, while latent heat percentages have varied between 10 and 30%. Average daytime Bowen ratios between 1.5 and 6.0 have been reported. Small positive sensible heat fluxes normally occur at night although small latent heat fluxes directed away from the downtown surface generally occur for all hours.

The simulation results exhibit important inter-model variations and significant dis- crepancies from the reported observations. The URBAN3 figures are within the expected range of values, with the daytime energy budget dominated by the sensible heat flux. URBAN3 is sensitive, however, to the minimum stomatal resistance value used in the determination of canopy transpiration. Earlier use (Todhunter, 1986) of a minimum stomata1 resistance of 2.0 s cm- ’ produced LE totals only half as large and Bowen ratios twice as large as the present study (which is based upon a minimum stomata1 resistance of 0.5 s cm- ‘). Peak daytime sensible and latent heat fluxes are recorded as expected at 1300 and 1100 LST, respectively. Nighttime turbulent fluxes are of the proper magnitude and direction. The URBD totals are characterized by unrealistically large daytime latent heat fluxes accounting for 75 y0 (M) and 47 y0 (L) of daytime net radiation. Daytime sensible heat fluxes appear too small, comprising only 14%(M) and 17% (L) of net radiation; thus average daytime Bowen ratios are excessively low. Physically inconsistent results are obtained between the medium- and low-density energy budgets as evidenced by the sharp drop in $ and the large increase inp in Table I. The model displays a strong sensitivity to wet fraction, thermal diffusivity and especially the surface roughness length values. Nighttime energy fluxes are more realistic as LE is always directed away from the surface and H is of proper magnitude, although a peak nighttime H of 100.0 W m - ’ seems too large. Both daytime turbulent fluxes are in phase with solar noon. The HFLUX energy budgets are more reasonable than the URBD results but present many of the same sensitivities. Too much net radiation is dissipated by latent heat flux and too little is lost via sensible heat flux. The average daytime Bowen ratios of 0.72(M) and 0.58(L) would be appropriate for suburban land-use zones but are too small for downtown environments. Nighttime sensible heat fluxes also appear to be too small, although the latent heat flux is directed away from the surface at night. Daytime turbulent fluxes of sensible heat are in phase with net radiation, while maximum daytime latent heat exchanges occur at 1300 LST.

Considerable uncertainty surrounds the nature of the conductive heat flux within the urban canopy-layer because of its complex composition and structure and the uncertainty regarding proper boundary conditions. Modeling studies by Terjung and O’Rourke (1980d) and Goward (198 l), which incorporate the explicit structure of the urban canopy-layer, indicate reduced urban conduction in contradistinction to the enhanced thermal inertia which has been a basic assumption in urban climatology for over one hundred years. Field studies of a single building by Sagara and Horie (1978) demonstrate the importance of individual wall aspect and interior wall temperatures in determining the magnitude and direction of the conductive heat flux. Rooftop observations determined from soil heat flux plates by Yap and Oke (1974) also found reduced


daytime conduction values. Because of the enormous di@culty in directly measuring conduction within the urban canopy-layer, it is usually determined either as a residual in the energy balance equation or as a parameterized function of net radiation. This latter approach emphasizes the effects of surface materials and either ignores the unique features of the urban canopy-layer (Doll et al., 1985), or is non-ideal with respect to its structure (Oke et al., 1980/81).

Because of these uncertainties, the field studies in Table III indicate probable daytime conductive heat fluxes ranging between - 50 to - 150 W rnp2, accounting for 10 to 30% of the energy budget, and nighttime values between 50 to 75 W m-2. The daytime URBAN3 conduction fluxes are within the expected range, accounting for approximately 15% of net radiation in both urban density scenarios. Nighttime fluxes were somewhat less than expected. The significant difference between daytime conduction for the medium- and low-density cases in URBD is unrealistic. Daytime URBD conduction totals for the medium-density scenario are acceptable, but the low-density values are too large. Both nighttime peak fluxes are somewhat larger than expected. The maximum daytime conduction fluxes from HFLUX for both scenarios are excessively large while the peak nighttime fluxes are too small. Peak daytime conduction fluxes for both urban density scenarios were recorded at 1000 LST for URBAN3 and HFLUX, and at 1200 LST for URBD, with the earlier time preferred.

7. Concluding Remarks

A model intercomparison of three distinct type of urban climate models for two synthetic city scenarios under comparable initial and boundary conditions revealed substantial differences in surface energy budgets. The models selected were representative of the spectrum of approaches currently used in the treatment of surface geometry effects, and the divergent surface energy budgets were found to be largely attributable to the different surface parameterization schemes. A quantitative evaluation of the similarity between the results indicated a considerable range of agreement between the models that varied according to individual energy flux. Rankings of the individual energy flux d statistics averaged for the two urban density scenarios were: (1) Q + q, (2) H, (3) G, (4) LE, (5) Zt, and (6) ZJ. These figures provide a measure of the flux-dependent sensitivity of omitting explicit urban canyon geometry. Thus, omission of urban geometry considerations has a minimal impact upon urban regional solar radiation regimes, but a profound impact upon longwave radiation regimes. Average flux comparability showed modest improvements with decreasing urban density and was relatively independent of model pairings.

An evaluation of individual model fluxes based upon reported values in the literature showed that the urban canopy-layer model energy budgets were generally the most realistic. Highest Zl values were obtained in URBAN3 because of the additional emission of longwave radiation from the surrounding building terrain. R, totals, however, were low because of high IT losses arising from surface area considerations. The high Zt fluxes could be ameliorated, somewhat, by selection of a larger value for


the thermal conductivity and a smaller value for minimum stomatal resistance. Net radiation was primarily disposed of via sensible heat, followed by smaller and comparable-sized conduction and latent heat fluxes. Physically consistent changes in energy fluxes were obtained in going from the medium- to low-density scenarios. Although the urban canyon model allowed precise specification of the percent evapotranspiring area, it did exhibit a sensitivity to the minimum stomataI resistance, a variable expressing the degree of moisture availability. Severe problems were found with nearly all of the energy fluxes from the URBD model. The R, totals, although of proper magnitude, masked longwave radiation terms that were too small. The energy budget terms exhibited a strong sensitivity to the specification of the wet fraction and roughness length which produced excessively high latent heat fluxes and physically inconsistent changes between the two urban density scenarios. Energy fluxes from the HFLUX model provided a mixed set of results. The three radiant energy terms were physically acceptable despite the omission of longwave inputs from the surrounding buildings. Dissipation of net radiation via sensible heat, conduction and latent heat was problematic, however, with H totals being too small and G and LE totals too large. Physically consistent changes occurred between the medium- and low-density scenarios. HFLUX lacked a way of specifying the wet fraction and proved to be most sensitive to the prescribed surface thermal inertia.

This work suggests that significant errors may be present in the surface energy fluxes that provide the lower boundary forcings in urban boundary-layer and pollution dispersal models, particularly with respect to the surface input of sensible and latent heat. It must be re-emphasized, however, that these results are based only on those urban land-use classes having minimal vegetative surface area. The surface energy budgets of other land-use classes (urban parks, low- and medium-density residential, institutions, roads) which make up a large percentage of the urban environment were not considered. In a related study, Loudon (1984) compared the energy budgets from three flat-plate models against the measured fluxes from a low-density residential neighborhood in Vancouver, B.C., and arrived at similar conclusions regarding the probability of signiticant errors in urban climate models. She also noted the difficulty in prescribing, a priori, appropriate values for the model terrain parameters. Although not based upon direct measurements, as was the Loudon study, this work independently arrived at the same conclusions for a much different set of urban environments, based upon a broader range of urban climate models with respect to the parameterization of urban geometry.

The effectiveness of each urban surface parameterization scheme must also be considered in light of the computational demands of each model. URBAN3 required 122.2 s of execution time (on an IBM 3033) for each synthetic city, in contrast to only 1.2 s for URBD, and 5.2 s for HFLUX. Thus approximately a five-fold increase in execution time resulted from incorporating a more realistic link to the urban boundary- layer, while inclusion of explicit urban geometry effects resulted in nearly a hundred-fold increase. These considerations strongly suggest that urban canopy-layer processes will have to be parameterized within urban boundary-layer models on the basis of a limited


number of urban land-use categories rather than upon explicit consideration of citywide urban canyon geometry. The land-cover scheme proposed by Auer (1978) may be varied enough to characterize the urban complex in sufficient detail.

This study confirms the warning raised by Bomstein and Oke (198 1) that the field of urban climate modeling may have exceeded present insights into the processes governing the urban-atmosphere system, particularly with respect to the parameterization of the surface sensible and latent heat fluxes, subsurface heat storage and the role of urban geometry upon surface energy budgets. The simple treatment of the urban surface in present UBL models appears inadequate. Our review of the literature revealed only one attempt to incorporate urban canopy-layer effects within an urban boundary- layer model (Sorbjan and Uliasz, 1982). Since the structure of the UBL is determined, in part, by the forcing of the surface energy budget, progress in urban climate modeling will be closely linked to our understanding of the effects of urban geometry upon canopy-layer energetics and the coupling between the urban canopy and boundary layers.

Acknowledgements

We would like to thank Dr Samuel Outcalt of the Department of Geosciences, University of Michigan, for providing a copy of the URBD model, and also Dr Toby Carlson of the Department of Meteorology, Pennsylvania State University, for supply- ing a version of his boundary-layer model. The cooperation of the South Coast Air Quality Management District, El Monte, California, in providing the necessary sounding data was appreciated. The use of the computer facilities of the UCLA Office of Academic Computing is acknowledged.

References

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Auer, A. H., Jr.: 1978, ‘Correlation of Landuse and Cover with Meteorological Anomalies’,J. Appl. Meteorol. 17,636-643.

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intercomparison of three urban climate models

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