# Evaluation of the Town Energy Balance (TEB) Scheme with Direct Measurements from Dry Districts in Two Cities

Valéry Masson, C. S B Grimmond, T. R. Oke

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Valéry Masson, C. S B Grimmond, T. R. Oke. Evaluation of the Town Energy Balance (TEB) Scheme with Direct Measurements from Dry Districts in Two Cities. Journal of Applied Meteorology, 2002, 41 (10), pp.1011-1026. 10.1175/1520-0450(2002)0412.0.CO;2. hal-05325476

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# Evaluation of the Town Energy Balance (TEB) Scheme with Direct Measurements from Dry Districts in Two Cities

V. MASSON

Centre National de Recherches Météorologiques, Toulouse, France

C. S. B. GRIMMOND

Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, Indiana

T. R. OKE

Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada

(Manuscript received 31 October 2001, in final form 9 May 2002)

## ABSTRACT

The Town Energy Balance (TEB) model of Masson simulates turbulent fluxes for urban areas. It is forced with atmospheric data and radiation recorded above roof level and incorporates detailed representations of the urban surface (canyon geometry) to simulate energy balances for walls, roads, and roofs. Here the authors evaluate TEB using directly measured surface temperatures and local-scale energy balance and radiation fluxes for two “simple” urban sites: a downtown area within the historic core of Mexico City, Mexico (stone buildings five to six stories in height), and a light industrial site in Vancouver, British Columbia, Canada (flat-roofed, single-story warehouses). At both sites, vegetation cover is less than 5%, which permits direct evaluation of TEB in the absence of a coupled vegetation scheme. Following small modifications to TEB, notably to the aerodynamic resistance formulations, the model is shown to perform well overall. In Mexico City, with deep urban canyons and stone walls, almost two-thirds of the net radiation is partitioned into storage heat flux during the day, and this maintains large heat releases and an upward turbulent sensible heat flux at night. TEB simulates all of these features well. At both sites TEB correctly simulates the net radiation, surface temperatures, and the partitioning between the turbulent and storage heat fluxes. The composite wall temperature simulated by TEB is close to the average of the four measured wall temperatures. A sensitivity analysis of model parameters shows TEB is fairly robust; for the conditions considered here, TEB is most sensitive to roof characteristics and incoming solar radiation.

## 1. Introduction

Although a general understanding of the interactions between the atmosphere and urbanized areas based on carefully conducted experimental studies is emerging (see, e.g., Rotach 1995; Grimmond and Oke 1999a), the complexity and diversity of cities around the world often means observational studies are limited, either to a particular site or a single physical process. Numerical models have been developed to simulate the urban climate, but to date most of these models have been formulated either at the microscale (building and/or urban canyon) (e.g., Mills 1997; Arnfield and Grimmond 1998; Arnfield et al. 1998), or at the mesoscale (whole city), using vegetation-atmosphere transfer models originally developed for other surface types, but with parameters modified for application to the urban environment (e.g.,

Best 1998; Taha 1999). In an attempt to couple the two scales, Masson (2000) developed the Town Energy Balance (TEB) scheme, which can be used on its own for densely urbanized areas or with the Interactions between Soil, Biosphere, and Atmosphere (ISBA) model (Noilhan and Planton 1989) when vegetation is also present. TEB incorporates canyon geometry, with three typical surfaces—roof, wall, and road—in order to reproduce the effects produced by buildings. A specific energy balance is computed for each of these three surfaces. This approach is relatively simple, but it still allows most of the physical effects associated with the urban energy balance to be reproduced, including radiative trapping (longwave and shortwave), the momentum flux, the turbulent sensible and latent heat fluxes, heat storage uptake and release, and water and snow interception. The anthropogenic heat fluxes due to traffic and industry are prescribed, and they are implicitly computed for domestic heating by the use of a minimum internal building temperature.

Masson (2000) validated the radiative portions of

<footnote>Corresponding author address: Dr. Valéry Masson, Centre National de Recherches Météorologiques, 42 av Coriolis, 31057 Toulouse Cedex, France.
E-mail: valery.masson@meteo.fr</footnote>
<figure><img src="image_2.png" /><figcaption>FIG. 1. Coupling of TEB within an atmospheric model with relation to measured and modeled variables. Dashed lines are the limits of the atmospheric grid boxes. Dotted lines are the middle of each grid box. For definition of the box see text. Here $\Delta Q_A$ is the advection flux below the measurement height.</figcaption></figure>

TEB; however, only sensitivity experiments were conducted for the complete scheme. Here the objective is to present an independent evaluation of TEB using directly measured surface temperatures and surface energy balance fluxes for two “simple” urban sites. One is a portion of the historic core of Mexico City, Mexico, the other is a light industrial site in Vancouver, British Columbia, Canada. At both sites vegetation cover is less than 5% of the plan area (Grimmond and Oke 2002, their Fig. 5) but the sites are otherwise very different in terms of the structure and building construction. These tests allow direct evaluation of TEB and the appropriateness of the assigned parameter values and their sensitivity/robustness. Evaluation of the combined TEB-ISBA scheme, relevant to vegetated urban areas, is being pursued separately. TEB has been incorporated into MesoNH, the French community mesoscale model (Lafore et al. 1998), but here we consider the offline or stand-alone version.

## 2. The urban energy balance

Fundamental to this paper is the concept of the urban surface energy balance, defined by (Oke 1988)

$$Q^* + Q_F = Q_H + Q_E + \Delta Q_S + \Delta Q_A \quad [\text{W m}^{-2}], \quad (1)$$

with $Q^*$ being the net all-wave radiation, $Q_F$ the an-

thropogenic heat flux, $Q_H$ the turbulent sensible heat flux, $Q_E$ the turbulent latent heat flux, $\Delta Q_S$ the storage heat flux, and $\Delta Q_A$ the net advective heat flux. In numerical models, such as TEB, each of the surface energy balance fluxes in (1) can be addressed independently. In this study, because the sites chosen have very little vegetation cover and there was no precipitation or irrigation, $Q_E$ is set to zero. The TEB-ISBA scheme, when operated in the offline mode, does not explicitly resolve the $\Delta Q_A$ term in (1). The model is forced with a temperature ($T_a$), humidity ($q_a$), and wind speed ($U_a$) measured in the inertial sublayer (Fig. 1). For TEB online, these are at the middle of the first atmospheric level, and for TEB offline they are at the measurement height. The rooftop level is the surface of the atmospheric model, so the TEB computed sensible heat flux ($Q_{HTEB}$) for the urban canopy is assigned at the base of the first atmospheric grid box (Figs. 1 and 2).

The modeled output fluxes ($Q_H$, $Q_E$, outgoing long-wave radiation $L^\uparrow$ and outgoing shortwave radiation $K^\uparrow$, when coupled to a 3D flow model, are assigned as input at the surface of the atmospheric model (the base of level 1 in Fig. 1), while forcing variables correspond to the midpoint of the level 1 grid. Note that the surface of the atmospheric model is located at the top of the mean topography and the building (roughness element) height for the individual grid square. In the 3D case,
the fluxes are then used to calculate the values of $T_a$, $q_a$, and $U_a$ at the next time step. These interact with the surrounding grids, so the $\Delta Q_A$ term can be resolved. The impact on the surface fluxes is returned by the forcing ($T_a$, $q_a$, and $U_a$) driving the next time step of the TEB-ISBA surface scheme. If $\Delta Q_A$ is positive (usually because of energy supplied by the surface), this energy comes from the $Q_H$ term convected from the surfaces, so $Q_H$ at a higher level (typically the middle of level 1) is smaller by an amount $\Delta Q_A$. The converse holds for a negative advection flux ($Q_H$ increasing with height). In this manner the vertical profile of $Q_H$ is affected by this advection flux.

When the energy balance is measured, however, (1) must be modified to read

$$Q^* = Q_H + Q_E + \Delta Q_S \text{ [W m}^{-2}\text{].} \quad (2)$$

The terms in (2) are evaluated here by measurements at the top of a “box,” following the concept of Oke (1987, 1988) illustrated in Fig. 1. The height of the box extends from above the roughness sublayer to a depth in the ground where there is no vertical flux over the period of concern. The height of the box is typically about two times the height of the buildings. The horizontal dimension of the box is sufficient to ensure that microscale inhomogeneity merges into a representative local-scale property. The height and length of the box must be sufficient to ensure that microscale variability of fluxes in the source area (or “footprint”) is eliminated by turbulent mixing in the roughness sublayer, but not so great that the source area extends upwind into anomalous land cover. Thus, $Q_{H OBS}$ is located in the inertial layer, at a height sufficient to avoid microscale effects found in the roughness sublayer, but not so high that anomalous upwind surfaces are sampled.

The $\Delta Q_A$ and $Q_F$ do not appear explicitly in (2). If the land cover in the source area of the sensors is approximately homogeneous at the local scale, $\Delta Q_A$ is minimized and can be neglected. This can also be achieved at less than completely homogeneous sites through filtering the data by wind direction to eliminate sectors with anomalous surface cover. Heat released by combustion of fuels ($Q_F$) is a net source of energy in cities; however, the instruments used to measure $Q^*$, $Q_H$, and $Q_E$ sense such anthropogenic contributions. Hence the total measured fluxes include this term, although the exact partitioning is not known. Adding an additional $Q_F$ term to (2) would therefore double-count this source.

Here three components ($Q^*$, $Q_H$, and $Q_E$) are measured directly and $\Delta Q_S$ is determined as the residual of (2). In effect this means that storage changes in the volume of the box are expressed as an equivalent flux density through the top surface of the box. This has the effect that the net measurement errors incurred in estimating the other terms, including $\Delta Q_A$, accumulate in $\Delta Q_S$. It should be noted that closure of measured energy balances is rarely achieved, either over simple sites

where micrometeorological theory is most likely to hold (e.g., Foken and Oncley 1995) or more complex sites such as forests (e.g., Lee 1998). This contributes to flux uncertainty, especially of $\Delta Q_S$, when resolved as a residual.

Given the differences between the modeled and measured energy balances [i.e., (1) and (2)], exact correspondence between measured and modeled fluxes is not to be expected. In particular, comparisons of the turbulent fluxes are affected by the assumption of zero evaporation by TEB (because ISBA is not run). This means TEB should overestimate $Q_H$ by the value of measured $Q_E$. Here, $Q_H$ calculated by TEB is compared at the measurement height with the sum of measured $Q_H + Q_E$. As discussed above, offline TEB $Q_H$ values at this height include $\Delta Q_A$. Thus from a modeling perspective the grid cell is regarded as homogeneous, but from the measurement perspective the area is homogeneous only if the site has sufficiently extensive fetch to minimize local-scale $\Delta Q_A$ (Fig. 1). Therefore, in the evaluation of the model in the offline version, it is necessary to assume that the turbulent fluxes $Q_H$ and $Q_E$ from top of the urban canopy layer (where TEB fluxes are computed; Fig. 1) to the top of the box (where the measurements are made) remain the same.

### 3. Observations

Here we present a brief overview of the observation methods used to gather data appropriate to the evaluation of TEB; more complete details are available in Grimmond and Oke (1999b), Oke et al. (1999), and Voogt and Grimmond (2000).

#### a. The study sites

Data were collected for Mexico City (referred to here as Me93) for a 7-day period during the dry season in December 1993 (Oke et al. 1999). The study site is located in the historic core of the city (see Fig. 1 of Oke et al. 1999) where the buildings are mainly institutional and commercial. In the vicinity of the measurement location, the mean building height is 18.4 ± 6.6 m. The average complete-to-plan area ratio (or the three-dimensional aspect ratio; Voogt and Oke 1997), $\lambda_c$, is 1.75. Average (3D) surface cover for the dominant source areas for the flux measurements is 25% imperious, 32% roofs, and 42% walls (Oke et al. 1999). Vegetation is negligible (~1%). In the street canyons and alleys adjacent to the tower, the sky view factor varies from about 0.22 to 0.51. Based on an inventory of materials within the radius of 500 m around the Me93 tower site, walls are made of concrete (two thirds) of stone (one third), with roofs of concrete, tar, sheet metal, or tile. Building walls and roofs are usually grey or brown. The roads are paved with concrete or asphalt, or surfaced with tiles, cobblestones, or flagstones.

Data were also collected for 15 days, in August 1992,
at a light industrial site in Vancouver, British Columbia (hereinafter referred to as V192), during an extended period of drought. The area is characterized by flat-roofed buildings one to three stories in height (average height 6.9 ± 2.5 m, $\lambda_c$, is 1.39), used for light industry and as warehouses. The buildings are arranged in city blocks, with east-west and north-south orientation (see Fig. 3 of Voogt and Oke 1997). The axis of the main blocks and alleys run east-west between the main streets. Less than 5% of the plan area is covered by vegetation. Most buildings are made of concrete, and roads and pathways are made of asphalt and concrete.

b. *Measured surface energy balance fluxes and forcing data*

At each site, instruments were mounted high enough above the surface to ensure that the measurement box (Fig. 1) is representative of the integrated local scale (horizontal length scales of ~10²–10⁴ m). In Mexico City and Vancouver, equipment was mounted at 28.4 and 28.5 m above ground, respectively. In both cases the turbulent fluxes were measured using eddy covariance techniques and radiometry was used to determine $Q^*$. At the V192 site, ground heat flux plates were installed at a depth of 80 mm with temperature sensors above to account for flux divergence between the soil surface and the heat flux plates. In addition, standard meteorological data, needed as input for TEB, were collected at both sites.

The primary meteorological variable that forces TEB, incoming solar radiation ($K\downarrow$), was not measured at either site. However, $K\downarrow$ data were collected by the Institute of Geophysics, Universidad Nacional Autónoma de México at the university (~13 km south of the Me93 site), and by the Canadian Atmospheric Environment Service at the Vancouver International Airport (~8 km south of V192 site). Using previous studies on the spatial variation of $K\downarrow$, and patterns of air pollution and flow in the two cities, we assessed the degree to which the measured solar forcing might differ from that at the validation site. We conclude this may amount to a few percent too low (typically less than 5%) in the afternoon at Me93, but it is likely to be negligible (less than 1%) at V192. Incoming longwave radiation ($L\downarrow$) was not measured at either site but was calculated using observed air temperature and humidity following the method of Prata (1996).

In Mexico City, the surface temperatures of a roof and two roads in canyons adjacent to the site were measured by infrared thermometers. In Vancouver, the surface temperatures of four walls (one facing each cardinal direction), the roof, and the inside of the east-facing wall of a building at the site were measured using similar instruments. These observations do not provide a representative sample of all facets found within the local-scale turbulent source area (typically 15–40 × 10³ m² by day, larger at night) at either site. Rather, they rep-

resent fairly typical microscale surfaces to provide some guidance as to the thermal conditions of small areas (sensor field of view about 5–10 m²).

In addition, airborne infrared measurements were conducted at the Vancouver site during one day at three different times: morning, mid-, and late afternoon. These measurements give the surface temperatures of each type of facet (walls, roofs, sunlit and shaded roads) at the local scale, an area more comparable with that of the source area of the turbulent fluxes. Therefore, even though only one day of data is available, it is of great interest to the validation of TEB. Note that the airborne measured wall temperatures compare well with the wall measurements made from a vehicle (Voogt and Oke 1997).

4. Implementation of TEB

Small modifications were made to the scheme originally presented in Masson (2000), notably to the aerodynamic resistance formulations (those indicated with thick lines in Fig. 2).

* The road resistance here follows a roughness length formulation, instead of that of Rowley et al. (1930), although the latter is still used for walls. This modification is included because of analyses of the V192 site, where roads are important and where airborne measured road temperatures allow discrimination between the two formulations (see section 5b). The road roughness length is set to 50 mm. This is much larger than the commonly used roughness for asphalt (<1 mm). However, 50 mm is considered to be a reasonable value when obstacles of the order of 1 m are present, as is the case for roads with cars, pedestrians, signs, lamp posts, bollards, etc. Sample calculations using a morphometric formula (Grimmond and Oke 1999a) show the roughness length can even be larger than the values used here if numerous cars and trucks are present.

* The temperatures of internal roof and wall layers are now linked to the internal temperature of the buildings ($T_{ibld}$) using a standard resistance ($R_i$) equal to 0.123 K m W⁻¹, based on building insulation values (McMullan 1992). In Masson (2000), $T_{ibld}$ was directly applied to the inner surfaces, whereas here $R_i$ mimics both the convection and the radiative interactions in the building. This modification has negligible effect, except for poorly insulated buildings, such as warehouses with metal roofs. In such cases the temperatures of the wall and roof inner layers now have greater diurnal amplitude, leading to larger amplitude for the outside surfaces.

* A new temperature evolution equation is used to represent the annual cycle of the internal temperature inside the buildings (especially for warm temperatures in summer):
<figure><img src="image_3.png" /><figcaption>FIG. 2. Schematic representation of the surfaces (roof, wall, road indicated by subscript *R*, *w*, and *r*, respectively), prognostic temperatures (*T*), and aerodynamic resistances (*R*) used in TEB and the output fluxes. Resistances shown with thick lines have been altered from the original scheme (Masson 2000). Thus, $Q_{HTEB} = f_{roof}Q_{Hroof} + f_{road}Q_{Hrop} + Q_{Findustry}$ and $Q_{ETEB} = f_{roof}Q_{Eroof} + f_{road}Q_{Erop} + Q_{Eindustry}$.</figcaption></figure>

$$T_{i \text{bld}}^{+} = T_{i \text{bld}}^{-} \left( \frac{\tau - \Delta\tau}{\tau} \right) + T^{*} \left( \frac{\Delta t}{\tau} \right),$$

where $T_{i \text{bld}}^{+}$ and are $T_{i \text{bld}}^{-}$ the temperatures at the future and previous time step, respectively, $\Delta t$ is the time step, $\tau$ is equal to 1 day, and $T^{*}$ is the average of the internal (ceiling, wall, and floor) surface temperatures. However, as in the initial version of the scheme, $T_{i \text{bld}}^{+}$ has a minimum value, in order to represent an-thropogenic heating.

The scheme is initialized with the meteorological data. No anthropogenic heat flux is prescribed. The parameters listed in Tables 1 and 2 are used to initialize the scheme in Me93 and V192. In both cases the morphometric parameters are weighted according to the wind direction frequency to be as consistent as possible with the observed fluxes. The roof, wall, and road fractions are calculated from Grimmond and Oke (1999b). The road is estimated to be composed of concrete (40%) and asphalt (60%) pavement (50 mm thick), over stone aggregate (0.2 m) and gravel and sandy clay soil. In general, the thermal parameters and emissivities are esti-

mated from data listed in the American Society of Heating, Refrigerating, and Air-Conditioning Engineers handbook (ASHRAE 1989). The albedo values are based on those listed for roofs, walls, and roads (Oke 1987).

At V192 the building walls are made of uninsulated concrete. The warehouse, where the microscale surface temperatures were observed, had a roof with a steel layer overlaid by a thin gravel layer. However, as most of the other warehouse roofs within this vicinity are made of concrete, topped with a thin insulation layer and gravel, this configuration is used in TEB (Table 2).

## 5. Evaluation of TEB

### a. Mexico City

#### 1) SURFACE TEMPERATURES AT THE MICROSCALE

Since TEB computes only one road surface temperature, independent of direction, the TEB value is compared to the average of two road surface temperature measurements (one in an S–N, one in an E–W street). The general form of the diurnal evolution of roof and
<table><caption>TABLE 1. Input parameters for the TEB scheme for the Vancouver light industrial (VI92) and Mexico City historic core (Me93) sites.</caption><thead><tr><th>Parameters</th><th>Unit</th><th>Mexico City</th><th>Vancouver</th></tr></thead><tbody><tr><td colspan="4"><strong>Geometric parameters<sup>a</sup></strong></td></tr><tr><td>Building fraction<sup>b</sup></td><td>—</td><td>0.55</td><td>0.51</td></tr><tr><td>Building height<sup>b</sup></td><td>m</td><td>18.8</td><td>5.8</td></tr><tr><td>Wall/plane area ratio<sup>b</sup> λ<sub>c</sub></td><td>—</td><td>0.75</td><td>0.39</td></tr><tr><td>Canyon aspect ratio<sup>b</sup> : H/W</td><td>—</td><td>1.18</td><td>0.39</td></tr><tr><td>Roughness length<sup>b</sup></td><td>m</td><td>2.2</td><td>0.35</td></tr><tr><td colspan="4"><strong>Radiative parameters<sup>c</sup></strong></td></tr><tr><td>Roof albedo</td><td>—</td><td>0.20</td><td>0.12</td></tr><tr><td>Wall albedo</td><td>—</td><td>0.25</td><td>0.50</td></tr><tr><td>Road albedo</td><td>—</td><td>0.08</td><td>0.08</td></tr><tr><td>Roof emissivity</td><td>—</td><td>0.90</td><td>0.92</td></tr><tr><td>Wall emissivity</td><td>—</td><td>0.85</td><td>0.90</td></tr><tr><td>Road emissivity</td><td>—</td><td>0.95</td><td>0.95</td></tr><tr><td colspan="4"><strong>Thermal parameters<sup>c</sup> (see Table 2 for values)</strong></td></tr><tr><td>Roof</td><td></td><td>Asphalt roll on concrete, good insulation</td><td>Thin gravel over concrete, poor insulation</td></tr><tr><td>Wall</td><td></td><td>Massive, thick, stone or concrete, insulation, 25% window</td><td>Concrete without insulation</td></tr><tr><td>Road</td><td></td><td>Asphalt 60%, concrete 40% on gravel, sandy clay</td><td>Asphalt 60%, concrete 40% on gravel, sandy clay</td></tr><tr><td>Roof roughness length</td><td>m</td><td>0.15</td><td>0.15</td></tr><tr><td>Road roughness length</td><td>m</td><td>0.05</td><td>0.05</td></tr><tr><td colspan="4"><strong>Temperature initialization</strong></td></tr><tr><td>Inside building temperature</td><td>°C</td><td>20</td><td>23</td></tr><tr><td>Deep soil temperature</td><td>°C</td><td>22</td><td>20</td></tr></tbody></table>

road temperatures are correctly reproduced by TEB (Fig. 3, Table 3). However, TEB roof temperatures show larger diurnal amplitudes than those of the instrumented roof, with faster warming and cooling rates. This may be due to larger storage in the roof by TEB or to incorrect specification of the roof materials (see section

6 for a sensitivity test). A way to correct the daytime overestimation might be to increase the roughness length of the roof and hence the removal of heat via $Q_H$. It must also be appreciated that the observations are only for one roof. The TEB road temperature has both the correct temporal course and diurnal amplitude,

<table><caption>TABLE 2. Thermal parameters for roofs, walls, and roads used in TEB for the Vancouver and Mexico City sites. Layer sequence: 1 is nearest to the surface. Here *d* is thickness of layer (m), *C* is heat capacity of layer (MJ m⁻³ K⁻¹), and *λ* is thermal conductivity (W m⁻¹ K⁻¹).</caption><thead><tr><th></th><th colspan="4">Mexico City</th><th colspan="4">Vancouver</th></tr><tr><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>1</th><th>2</th><th>3</th><th>4</th></tr></thead><tbody><tr><th colspan="9" style="text-align: left;">Roof layer</th></tr><tr><th></th><th>Asphalt roll</th><th>Concrete (stone)</th><th>Insulation</th><th>Gypsum</th><th>Gravel</th><th>Gravel</th><th>Insulation</th><th>Concrete</th></tr><tr><th>d</th><td>0.01</td><td>0.1</td><td>0.05</td><td>0.025</td><td>0.01</td><td>0.02</td><td>0.01</td><td>0.030</td></tr><tr><th>C</th><td>1.7</td><td>1.5</td><td>0.25</td><td>0.87</td><td>1.76</td><td>1.76</td><td>0.04</td><td>2.21</td></tr><tr><th>λ</th><td>0.2</td><td>0.93</td><td>0.03</td><td>0.16</td><td>1.4</td><td>1.4</td><td>0.03</td><td>1.51</td></tr><tr><th colspan="9" style="text-align: left;">Wall layer</th></tr><tr><th></th><th>Stone/window</th><th>Stone/window</th><th>Stone/window</th><th>Insulation/ window</th><th>Dense concrete</th><th>Dense concrete</th><th>Concrete</th><th>Dense concrete</th></tr><tr><th>d</th><td>0.015</td><td>0.12</td><td>0.30</td><td>0.015</td><td>0.010</td><td>0.02</td><td>0.14</td><td>0.03</td></tr><tr><th>C</th><td>1.54</td><td>1.54</td><td>1.54</td><td>0.32</td><td>2.11</td><td>2.11</td><td>1.00</td><td>2.11</td></tr><tr><th>λ</th><td>0.88</td><td>0.88</td><td>0.88</td><td>0.21</td><td>1.51</td><td>1.51</td><td>0.67</td><td>1.51</td></tr><tr><th colspan="9" style="text-align: left;">Road layer</th></tr><tr><th></th><th>Asphalt/ concrete</th><th>Asphalt/ concrete</th><th>Stone aggregate</th><th>Gravel and soil</th><th>Asphalt/ concrete</th><th>Asphalt/ concrete</th><th>Stone aggregate</th><th>Gravel and soil</th></tr><tr><th>d</th><td>0.01</td><td>0.04</td><td>0.20</td><td>1.00</td><td>0.01</td><td>0.04</td><td>0.20</td><td>1.00</td></tr><tr><th>C</th><td>1.74</td><td>1.74</td><td>2.00</td><td>1.40</td><td>1.74</td><td>1.74</td><td>2.00</td><td>1.40</td></tr><tr><th>λ</th><td>0.82</td><td>0.82</td><td>2.1</td><td>0.4</td><td>0.82</td><td>0.82</td><td>2.1</td><td>0.4</td></tr></tbody></table>

<footnote><sup>a</sup> Local-scale parameters.</footnote>

<footnote><sup>b</sup> Source: Grimmond and Oke (1999a).</footnote>

<footnote><sup>c</sup> Microscale parameters of individual facets.</footnote>
<figure><img src="image_4.png" /><figcaption>FIG. 3. Ensemble mean diurnal cycle for 6 days of measured and modeled surface temperatures for the Mexico City site: (top) roof surface temperature, and (bottom) road surface temperature.</figcaption></figure>

but there is a bias of about +4 K. Given the uncertainties in using a calculated $L↓$ (especially at night), the large difference between the observed temperatures in the two canyons (25 K during the day), and the microscale (rather than local scale) representativeness of the measurements, this is considered a good result.

## 2) ENERGY FLUXES AT THE LOCAL SCALE

TEB is evaluated using the measured hourly energy fluxes: net radiation, sensible heat flux, and storage heat flux (Fig. 4 gives the ensemble mean results and Table 4 the summary statistics).

During the night, the observed $Q^*$ mean is -103 W

<table><caption>TABLE 3. Performance statistics for surface temperatures in Mexico City and a Vancouver light industrial site. Bias = TEB - obs.</caption><thead><tr><th></th><th>Bias (K)</th><th>Rmse (K)</th></tr></thead><tbody><tr><td colspan="3">Mexico City</td></tr><tr><td>Average road temperature</td><td>+4</td><td>4.2</td></tr><tr><td>Roof temperature</td><td>+1.9</td><td>4.5</td></tr><tr><td colspan="3">Vancouver</td></tr><tr><td>YD 223-236 (all)</td><td></td><td></td></tr><tr><td>Wall temperature</td><td>+2.3</td><td>3.0</td></tr><tr><td>Roof temperature</td><td>+2.5</td><td>7.4</td></tr><tr><td>YD 225-231 (period 1)</td><td></td><td></td></tr><tr><td>Wall temperature</td><td>+1.9</td><td>2.4</td></tr><tr><td>Roof temperature</td><td>+1.7</td><td>7.5</td></tr><tr><td>YD 232-236 (period 2)</td><td></td><td></td></tr><tr><td>Wall temperature</td><td>+2.7</td><td>3.7</td></tr><tr><td>Roof temperature</td><td>+3.6</td><td>7.2</td></tr></tbody></table>

$m^{-2}$, while TEB is only -82 W $m^{-2}$. The daytime $Q^*$ is well reproduced (Table 4). The observed daytime $\Delta Q_s/Q^*$ ratio is very high (0.58); hence uptake of sensible heat into storage is more efficient than its convection to the boundary layer over this densely built-up district. This can probably be attributed to the thermal properties of the construction materials, the large 3D surface area exposed by this area of dense building and deep canyons, and the relatively light winds during the observation period (the mid- to late afternoon maximum speeds were <3.5 m s$^{-1}$). TEB reproduces this result well; the simulated $\Delta Q_s/Q^*$ ratio is 0.56 (Table 4). The observations show little hysteresis in the diurnal relation between the $\Delta Q_s$ and the $Q^*$, and again TEB reproduces this well (Fig. 5). Similarly, TEB produces $\Delta Q_s$ fluxes of the correct magnitude, especially for the daytime maximum.

The nocturnal measurements show the heat release from the urban fabric to be larger than the $Q^*$ drain (nighttime $\Delta Q_s/Q^* = 1.21$). This imbalance maintains an average upward-directed $Q_H$ of 21 W $m^{-2}$. The model produces a nighttime $\Delta Q_s/Q^*$ ratio of 1.17, but since the calculated $Q^*$ intensity is smaller than observed, the release of stored heat is also underestimated by 30 W $m^{-2}$. Therefore, the modeled $Q_H$ reaches only 12 W $m^{-2}$, on average. However, it is encouraging that TEB is able to create a positive $Q_H$ every night, including the cloudy night, as observed (not shown).

The observed rapid increase of $Q_H$ (reaching between 50 and 100 W $m^{-2}$) in the early morning is not simulated by the model. The observed increase in $Q_H$ might correspond to energy released from traffic ($Q_F$) during the morning commuter activity that is not included in these TEB runs. Ichinose et al. (1999), for example, report a traffic-induced heat flux in downtown Tokyo reaching 60 W $m^{-2}$.

Thus in summary, TEB is able to reproduce correctly most of the behavior of the fluxes typical of the Me93 central city site, including the relatively low $Q^*$ in the
<figure><img src="image_5.png" /><figcaption>FIG. 4. Ensemble mean diurnal cycle of measured and modeled surface energy balance fluxes for 6 days at the Mexico City site: (top) net all-wave radiation, (middle) total turbulent flux, and (bottom) storage sensible heat flux.</figcaption></figure>

<table><caption>TABLE 4. Performance statistics of TEB for heat fluxes (W m⁻²) at the Mexico City site. Average [observed (obs), modeled (TEB)], bias (TEB − obs), and rmse.</caption><thead><tr><th></th><th>Heat flux</th><th>Q*</th><th>Q<sub>H</sub> + Q<sub>E</sub></th><th>ΔQ<sub>S</sub></th></tr></thead><tbody><tr><td rowspan="4">Overall period</td><td>Obs</td><td>45</td><td>57</td><td>-12</td></tr><tr><td>TEB</td><td>55</td><td>54</td><td>1</td></tr><tr><td>Bias</td><td>10</td><td>-3</td><td>13</td></tr><tr><td>Rmse</td><td>32</td><td>25</td><td>39</td></tr><tr><td rowspan="4">Daytime</td><td>Obs</td><td>257</td><td>108</td><td>149</td></tr><tr><td>TEB</td><td>252</td><td>113</td><td>139</td></tr><tr><td>Bias</td><td>-5</td><td>5</td><td>-10</td></tr><tr><td>Rmse</td><td>41</td><td>32</td><td>45</td></tr><tr><td rowspan="4">Nighttime</td><td>Obs</td><td>-103</td><td>21</td><td>-125</td></tr><tr><td>TEB</td><td>-82</td><td>12</td><td>-95</td></tr><tr><td>Bias</td><td>21</td><td>-9</td><td>30</td></tr><tr><td>Rmse</td><td>24</td><td>18</td><td>35</td></tr></tbody></table>

winter, the large daytime heat uptake by the urban fabric, and the positive $Q_H$ at night.

b. Vancouver light industrial site

1) SURFACE TEMPERATURES AT THE MICRO- AND LOCAL SCALES

The surface temperature observations include in situ observations of individual roof, wall, and road facets of a warehouse, that is, at the microscale; and airborne measurements at 1000, 1400, and 1700 LST on one day [yearday (YD) 228] of a large number of buildings and canyons, that is, at the local scale. The latter is most appropriate to use in the evaluation of TEB. For the rest of the observations our discussion focuses on two periods: period 1, six sunny days (YD 225–231) characterized by a sea breeze in the early afternoon; and period 2, five more cloudy days (YD 232–236) when the sea breeze is much weaker and occurs only in the late afternoon.

The observed microscale roof temperatures show a very strong diurnal cycle, with variations of 50 K (Fig.

<figure><img src="image_6.png" /><figcaption>FIG. 5. Ensemble mean (6 days) measured and modeled (TEB) hysteresis loop relating the storage heat flux to the net radiation at the Mexico City site.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 6. Ensemble mean diurnal cycle of observed (microscale) and modeled (TEB) surface temperature for the Vancouver site for (a) YD 225–231 and (b) YD 232–236: (top) roof and (bottom) individual N-, E-, S-, and W-facing walls and average, and simulated wall temperature.</figcaption></figure>

6). TEB simulates a smaller amplitude than is observed (the reverse of the Me93 case). TEB does reproduce the general form of the nocturnal cooling pattern, but observed roof temperatures are low at night and the model overestimates them by 8 K, on average. The roof where

the surface temperature observations were conducted is unrepresentative of the local scale (see section 4), thus the poor comparisons are not unexpected. TEB is in somewhat better agreement with the airborne roof data of the morning and evening flights but underestimates
<figure><img src="image_8.png" /><figcaption>FIG. 7. Time series of observed (micro- and local scale) and modeled (TEB) surface temperatures for YD 228: (left) roof, (middle) averaged microscale and local-scale wall temperature, and (right) local-scale road temperature. Simulated road surface temperature: Masson (2000) scheme [road resistance follows Rowley et al. (1930)] and new roughness length formulation.</figcaption></figure>

the early afternoon value, which is near the daily maximum, by approximately 6 K (Fig. 7).

The TEB *wall* temperature is evaluated against the average of the observed wall temperatures (north, east, south, and west facing). For sunny days in period 1, TEB wall temperatures are similar to this averaged wall temperature (Table 3). The bias and root-mean-square error (rmse) between TEB and the observations are small (1.9 and 2.4 K, respectively). Note that the difference is slightly larger when compared to the airborne measurements; the overestimation probably reaches 5 K in the daytime (Fig. 7), but the maximum wall temperature near 1600 LST is reproduced. However, a discrepancy appears for period 2. On the sunny days of period 1, the individual wall temperatures follow a standard daytime pattern and the mean wall temperature peaks at about 1600 LST (Fig. 6a). In period 2, on the other hand, there is significant cloud cover in the middle of the day. While three of the walls show little change from period 1, the temperature of the south-facing wall was considerably cooler (Fig. 6b). TEB does not capture the magnitude of this reduced warming (except for the cloudiest day, not shown) and model performance is correspondingly poorer. It seems the temporal history of warming of the individual walls over the day, and its disruption by cloud, is responsible. Such temporal specificity is not incorporated in the generic wall approach of TEB. If this is correct, this type of impact can be expected to be greatest in cases of urban geometry with low building height-to-street width ratios, as is the case at the V192 site.

Overall, however, the good agreement between the wall temperature measurement and TEB output, especially when radiative forcing is symmetric through the day, supports one of the main simplifications of the

scheme: the use of only one wall temperature that is independent of orientation.

For *roads*, the airborne-based measurements can be stratified into shaded and sunlit fractions. The sunlit fraction is much larger, because of the small height of the buildings (Voogt and Grimmond 2000). The road temperature, averaged according to sunlit and shaded areas, reaches 38°C in the afternoon of YD 228. TEB simulates only one road temperature, which is comparable to the local-scale observation. TEB simulates it well, with an overestimation of only 3–4 K at midday (Fig. 7). The simplification of TEB to consider only one road temperature is also supported by this comparison.

To illustrate the improvement resulting from the new parameterizations (see section 4), TEB was run with the old formulation of the road aerodynamic resistance (Fig. 7). The main problem with the original TEB predictions is an increase of the temperature during the day, 6 K higher than with the new version. The new roughness length formulation creates a larger conductance, and thus a larger $Q_h$, leading to better agreement between the modeled temperature and the observations. Since the road surface at the V192 site is large, and has an important role for the exchanges from the canyons (walls are low), this validation is particularly pertinent.

## 2) ENERGY FLUXES AT THE LOCAL SCALE

TEB correctly reproduces $Q^*$ during the entire period (Fig. 8). As Table 5 shows this is true for the overall set (bias = -9 W m⁻²) and for both day and night (biases of -17 and +2 W m⁻², respectively).

When comparing modeled and measured data it is important to consider the potential for measurement errors and uncertainties. Here, the observed fluxes and
<figure><img src="image_9.png" /><figcaption>FIG. 8. Ensemble mean diurnal cycle of measured and modeled surface energy balance fluxes for the Vancouver site, for (a) YD 225–231 and (b) YD 232–236: (top) net radiation, (middle) total turbulent heat flux, and (bottom) storage sensible heat flux.</figcaption></figure>
<table><caption>TABLE 5. Performance statistics for TEB for heat fluxes at the Vancouver light industrial site (as in Table 4).</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Days 223–236</th><th colspan="3">Days 225–231</th><th colspan="3">Days 232–236</th></tr><tr><th>Q*</th><th>Q<sub>H</sub> + Q<sub>E</sub></th><th>ΔQ<sub>S</sub></th><th>Q*</th><th>Q<sub>H</sub> + Q<sub>E</sub></th><th>ΔQ<sub>S</sub></th><th>Q*</th><th>Q<sub>H</sub> + Q<sub>E</sub></th><th>ΔQ<sub>S</sub></th></tr></thead><tbody><tr><td rowspan="4">Overall period</td><td>Obs</td><td>150</td><td>95</td><td>55</td><td>161</td><td>87</td><td>74</td><td>136</td><td>103</td><td>32</td></tr><tr><td>TEB</td><td>141</td><td>133</td><td>8</td><td>159</td><td>147</td><td>12</td><td>126</td><td>119</td><td>6</td></tr><tr><td>Bias</td><td>-9</td><td>38</td><td>-47</td><td>-2</td><td>60</td><td>-62</td><td>-10</td><td>16</td><td>-26</td></tr><tr><td>Rmse</td><td>59</td><td>76</td><td>91</td><td>57</td><td>97</td><td>105</td><td>59</td><td>50</td><td>66</td></tr><tr><td rowspan="4">Daytime</td><td>Obs</td><td>323</td><td>168</td><td>156</td><td>318</td><td>143</td><td>175</td><td>323</td><td>196</td><td>126</td></tr><tr><td>TEB</td><td>306</td><td>234</td><td>73</td><td>313</td><td>243</td><td>70</td><td>301</td><td>225</td><td>76</td></tr><tr><td>Bias</td><td>-17</td><td>66</td><td>-83</td><td>-5</td><td>100</td><td>-105</td><td>-21</td><td>29</td><td>-50</td></tr><tr><td>Rmse</td><td>76</td><td>103</td><td>121</td><td>72</td><td>127</td><td>136</td><td>77</td><td>69</td><td>89</td></tr><tr><td rowspan="4">Nighttime</td><td>Obs</td><td>-59</td><td>7</td><td>-66</td><td>-62</td><td>7</td><td>-69</td><td>-56</td><td>8</td><td>-64</td></tr><tr><td>TEB</td><td>-57</td><td>11</td><td>-68</td><td>-59</td><td>11</td><td>-70</td><td>-55</td><td>11</td><td>-66</td></tr><tr><td>Bias</td><td>2</td><td>4</td><td>-2</td><td>3</td><td>4</td><td>-1</td><td>1</td><td>3</td><td>-2</td></tr><tr><td>Rmse</td><td>24</td><td>12</td><td>23</td><td>20</td><td>11</td><td>19</td><td>27</td><td>13</td><td>26</td></tr></tbody></table>

meteorological conditions at the V192 site were compared with concurrent observations made at a residential site (sunset, Vs92; Grimmond and Oke 1999b). In urban areas, Q* is expected to be fairly conservative spatially (Schmid et al. 1991; Oke 1997). Comparison of the data collected concurrently at the two Vancouver sites shows only small differences in Q*; the largest differences <50 W m⁻² occur in the late morning when Q* at V192 is larger. This indicates reason for confidence in the V192 Q* data.

During night, the measurements show relatively large ΔQs, with a peak release just after sunset. This allows a positive QH to be maintained during the first hours of the night. Then ΔQs equilibrates close to the value of Q*, and QH is small for the rest of the night. In terms of the observed storage heat flux, it is important to recall that it is computed here as the residual of the measured energy balance and thus errors in any of the other fluxes accumulate in ΔQs. However, during night, fluxes other than Q* and ΔQs are small (see the measured QH and QE) or negligible (QE or ΔQA). The warehouses in the V192 area have minimal heating or air conditioning, few chimneys, and traffic is light in the day and negligible at night. The ΔQA is negligible, because nocturnal winds are weak except on one night. Therefore,

the observed nocturnal ΔQs is probably reliable. TEB simulates this nocturnal storage pattern well (bias = -2 W m⁻², rmse < 23 W m⁻² throughout the period; see Table 5). The net energy storage of the model during YD 226–231 is 0.4 MJ m⁻², corresponding to a mean storage heat flux of about +0.8 W m⁻², or a 3 K heating of a 0.1-m layer of soil or concrete. This buildup of heat is consistent with results from heat flux plates installed at the site (not shown). Note that hourly values are not necessarily good, but the modeled integrated daily heat uptake is about right.

During the day, observed QH is large and QE is small. In the drought conditions of the measurement period, TEB partitions Q* between ΔQs and QH. For period 2 (Fig. 8b) and YD 224, 225 (not shown), there is reasonable correspondence between the predictions of TEB and the measured sensible heat fluxes (Table 5). The hysteresis behavior of ΔQs (Fig. 9) is slightly overestimated. For period 1, however, TEB significantly overpredicts QH, while measurements show a much larger ΔQs than TEB (Fig. 8a). This discrepancy may be due to an overestimation of observed ΔQs [in (2)], through the neglect of ΔQA. During period 1, the wind direction is predominantly from the west so there may be a sea breeze (Oke and Hay 1994). Under these circumstances it is possible that the lack of ability to evaluate the advection term in both the measurements and the model results prevents a more appropriate comparison of the fluxes. As noted in section 2, the advection flux in the box ΔQA appears in the QH term at the top of the box when modeled offline and in the ΔQs term in the observations. An improved estimate would come from running the model in the 3D mode.

## 6. Sensitivity of the scheme

The ability of the TEB scheme to reproduce most features of surface-atmosphere energy exchanges and the resultant surface temperatures of relatively dry urban districts has been demonstrated. However, many model input properties and some of the forcing data (e.g., radiation) are subject to uncertainties. Therefore, the sen-

<figure><img src="image_10.png" /><figcaption>FIG. 9. Ensemble mean measured and modeled (TEB) hysteresis loop relating the storage heat flux to the net radiation at the Vancouver light industrial site for YD 232–236.</figcaption></figure>
<table><caption>TABLE 6. Sensitivity analysis to varying TEB input parameters relative to the reference case for Mexico City.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Max Q*<br>(W m<sup>-2</sup>)</th><th rowspan="2">Daytime<br>ΔQ<sub>s</sub>/Q*</th><th colspan="2">Nocturnal Nocturnal</th><th rowspan="2">T<sub>roof</sub> bias<br>(K)</th><th rowspan="2">T<sub>wall</sub> bias<br>(K)</th><th rowspan="2">T<sub>road</sub> bias<br>(K)</th></tr><tr><th>Q*<br>(W m<sup>-2</sup>)</th><th>Q<sub>H</sub><br>(W m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>Reference</td><td>439</td><td>0.56</td><td>-82</td><td>+14</td><td></td><td></td><td></td></tr><tr><td>Geometric parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Building fraction + 0.10 (→ H/W = 1.42)</td><td>+1</td><td>-0.01</td><td>+1</td><td></td><td></td><td></td><td>+0.1</td></tr><tr><td>Building fraction - 0.10 (→ H/W = 1.03)</td><td>+1</td><td>+0.01</td><td>-1</td><td></td><td></td><td></td><td>-0.1</td></tr><tr><td>Wall/plane area ratio + 0.20 (→ H/W = 1.40)</td><td>+6</td><td>+0.01</td><td>-2</td><td>+3</td><td></td><td></td><td>+0.1</td></tr><tr><td>Wall/plane area ratio - 0.20 (→ H/W = 0.96)</td><td>-3</td><td>-0.01</td><td>+2</td><td>-3</td><td></td><td>-0.1</td><td>-0.1<br>(σ = 0.7)</td></tr><tr><td>Radiative parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Roof albedo + 0.10</td><td>-32</td><td>+0.03</td><td>+2</td><td>-1</td><td>-1.3<br>(σ = 1)</td><td></td><td></td></tr><tr><td>Wall albedo + 0.10</td><td>-6</td><td></td><td></td><td>-1</td><td></td><td>-0.4</td><td>+0.1</td></tr><tr><td>Road albedo + 0.10</td><td>-6</td><td></td><td></td><td></td><td></td><td></td><td>-0.4</td></tr><tr><td>Roof emissivity - 0.05</td><td>+4</td><td>-0.01</td><td>+1</td><td>+1</td><td>+0.5</td><td></td><td></td></tr><tr><td>Wall emissivity - 0.05</td><td></td><td></td><td></td><td></td><td></td><td>-0.2</td><td></td></tr><tr><td>Road emissivity - 0.05</td><td></td><td></td><td></td><td></td><td></td><td>-0.1</td><td>+0.1</td></tr><tr><td>Thermal parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Roof thickness × 2</td><td>-8</td><td>-0.04</td><td>+4</td><td>-2</td><td>-0.4<br>(σ = 2.2)</td><td></td><td></td></tr><tr><td>Wall thickness ÷ by 2</td><td></td><td></td><td></td><td>-1</td><td></td><td>-0.1</td><td></td></tr><tr><td>Road thickness ÷ by 2</td><td>+2</td><td>+0.01</td><td>-1</td><td>+1</td><td></td><td></td><td>+0.2<br>(σ = 1.2)</td></tr><tr><td>Roughness lengths</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Town z<sub>0</sub> ÷ by 2</td><td>-2</td><td>+0.02</td><td>-1</td><td></td><td></td><td>+0.4</td><td>+0.5</td></tr><tr><td>Town z<sub>0</sub> × 2</td><td>+3</td><td>-0.02</td><td>+1</td><td></td><td></td><td>-0.6</td><td>-0.6</td></tr><tr><td>Road z<sub>0</sub> ÷ by 5</td><td>-1</td><td>+0.01</td><td></td><td>-2</td><td></td><td></td><td>+0.5</td></tr><tr><td>Roof z<sub>0</sub> ÷ by 5</td><td>-11</td><td>+0.05</td><td>-2</td><td>+1</td><td>+1.5<br>(σ = 1.2)</td><td></td><td></td></tr><tr><td>Temperature initialization</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Internal building temperature + 5 K</td><td>-1</td><td>-0.01</td><td>-1</td><td>+1</td><td>+0.2</td><td>+0.1</td><td>+0.1</td></tr><tr><td>Road and deep soil temperature + 5 K</td><td>-1</td><td>-0.01</td><td>-1</td><td>+2</td><td></td><td>+0.2</td><td>+0.6</td></tr><tr><td>Forcing</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Incoming infrared - 20 W m<sup>-2</sup></td><td>-12</td><td>+0.04</td><td>-10</td><td>-5</td><td>-1.9</td><td>-0.7</td><td>-1.1</td></tr><tr><td>Incoming solar - 10%</td><td>-49</td><td>+0.03</td><td>+2</td><td>-3</td><td>-1.1<br>(σ = 0.8)</td><td>-0.6</td><td>-0.7</td></tr><tr><td>Modification of resistance</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Without new road resistance</td><td></td><td></td><td></td><td></td><td></td><td></td><td>+0.1</td></tr></tbody></table>

sitivity of the scheme to input parameters was tested via dedicated runs across a wide range of values for each parameter. Tables 6 and 7 list the modifications and the resulting sensitivity of the calculated fluxes and temperatures. Comparisons are made against a reference run.

Daytime $Q^*$ is relatively insensitive to most parameters except for the albedo of horizontal surfaces, the roof roughness length, and $K^↓$. Geometric parameters modify $Q^*$ to a lesser extent (canyon aspect ratios vary in the range $\pm 0.2$ from the reference). The effect of roofs is always the most important, because there is no trapping effect for this surface. Because of the geometry of the site, the road albedo has a very small impact for Me93. Nighttime $Q^*$ also is not very sensitive, except to the calculated $L^↓$, the roof thickness or its thermal structure (for V192), and the building fraction, if the

road and roof energy balances are very different (as is the case in V192).

The $\Delta Q_s/Q^*$ ratios for these sensitivity analyses, are in the range 0.26–0.31 and 0.52–0.61 for V192 and Me93, respectively. For most parameters, variations in input values result in differences of less than 2% in $\Delta Q_s/Q^*$ between runs. Because only dry sites are involved this also means the scheme is stable with respect to the partitioning between the storage and turbulent sensible heat fluxes. For the V192 simulation, $\Delta Q_s/Q^*$ is sensitive to roof roughness length (because it is a major control on the convective/conductive sensible heat sharing between the air and the roof). A large impact is found for the choice of the road aerodynamic resistance. The road surface temperature measurements at V192 enabled us to discriminate between the two formulations (see section 5b). A too-small roughness length for roads
<table><caption>TABLE 7. Sensitivity analysis to varying TEB input parameters relative to the reference case for Vancouver.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Max Q*<br>(W m<sup>-2</sup>)</th><th rowspan="2">Daytime<br>ΔQ<sub>S</sub>/Q*</th><th colspan="2">Nocturnal Nocturnal</th><th rowspan="2">T<sub>roof</sub> bias<br>(K)</th><th rowspan="2">T<sub>wall</sub> bias<br>(K)</th><th rowspan="2">T<sub>road</sub> bias<br>(K)</th></tr><tr><th>Q*<br>(W m<sup>-2</sup>)</th><th>Q<sub>H</sub><br>(W m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>Reference</td><td>520</td><td>0.28</td><td>-61</td><td>14</td><td></td><td></td><td></td></tr><tr><td>Geometric parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Building fraction + 0.10 (→ H/W = 0.50)</td><td>-5</td><td>-0.02</td><td>+4</td><td>-2</td><td></td><td>-0.1</td><td>-0.3</td></tr><tr><td>Building fraction - 0.10 (→ H/W = 0.33)</td><td>+3</td><td>+0.02</td><td>-4</td><td>+1</td><td></td><td></td><td>+0.1</td></tr><tr><td>Wall/plane area ratio + 0.20 (→ H/W = 0.60)</td><td>+1</td><td>+0.02</td><td>-1</td><td>+2</td><td>+0.1</td><td></td><td>-0.4</td></tr><tr><td>Wall/plane area ratio - 0.20 (→ H/W = 0.19)</td><td>-3</td><td>-0.02</td><td>+2</td><td>-2</td><td>-0.1</td><td></td><td>+0.4</td></tr><tr><td>Radiative parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Roof albedo + 0.10</td><td>-34</td><td>+0.01</td><td></td><td></td><td>-1.0 (σ = 0.9)</td><td></td><td></td></tr><tr><td>Wall albedo + 0.10</td><td>-4</td><td></td><td></td><td>-1</td><td></td><td>-0.6</td><td></td></tr><tr><td>Road albedo + 0.10</td><td>-21</td><td></td><td>+1</td><td>-1</td><td></td><td>-0.2</td><td>-0.8</td></tr><tr><td>Roof emissivity - 0.05</td><td>+4</td><td></td><td></td><td></td><td>+0.3</td><td></td><td></td></tr><tr><td>Wall emissivity - 0.05</td><td></td><td></td><td></td><td></td><td></td><td>+0.1</td><td></td></tr><tr><td>Road emissivity - 0.05</td><td>+2</td><td></td><td>+1</td><td>+1</td><td></td><td></td><td>+0.2</td></tr><tr><td>Thermal parameters</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Roof thickness × 2</td><td>+2</td><td>+0.02</td><td>-6</td><td>+3</td><td>+0.8 (σ = 2.3)</td><td></td><td></td></tr><tr><td>Wall thickness ÷ by 2</td><td></td><td></td><td>+1</td><td>-2</td><td></td><td>-0.3</td><td>-0.1</td></tr><tr><td>Road thickness ÷ by 2</td><td>+2</td><td>+0.01</td><td>-2</td><td>+4</td><td></td><td>+0.1</td><td>+0.2</td></tr><tr><td>Steel roof (see text)</td><td>-2</td><td>-0.02</td><td>+5</td><td>-1</td><td>-0.7 (σ = 2.2)</td><td></td><td></td></tr><tr><td>Roughness lengths</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Town z<sub>0</sub> ÷ by 2</td><td>-3</td><td>+0.01</td><td>-1</td><td>+1</td><td></td><td>+0.6</td><td>+0.6</td></tr><tr><td>Town z<sub>0</sub> × 2</td><td>+3</td><td>-0.01</td><td>+1</td><td>+1</td><td></td><td>-0.6</td><td>-0.6</td></tr><tr><td>Road z<sub>0</sub> ÷ by 5</td><td>-8</td><td>+0.02</td><td>-2</td><td></td><td></td><td></td><td>+1.9 (σ = 1.0)</td></tr><tr><td>Roof z<sub>0</sub> ÷ by 5</td><td>-18</td><td>+0.03</td><td>-1</td><td></td><td>+1.9 (σ = 2.0)</td><td></td><td></td></tr><tr><td>Temperature initialization</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Building internal temperature + 5 K</td><td>-1</td><td>-0.01</td><td>-1</td><td>+1</td><td>+0.1</td><td>+0.1</td><td>+0.1</td></tr><tr><td>Surface and deep soil temperature + 5 K</td><td></td><td></td><td>-1</td><td></td><td></td><td>+0.1</td><td>+0.3</td></tr><tr><td>Forcing</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Incoming infrared - 20 W m<sup>-2</sup></td><td>-15</td><td>+0.02</td><td>-9</td><td>-4</td><td>-1.6 (σ = 0.9)</td><td>-0.9</td><td>-1.0</td></tr><tr><td>Incoming solar - 10%</td><td>-58</td><td>+0.01</td><td>+2</td><td>-2</td><td>-0.8 (σ = 0.7)</td><td>-0.9</td><td>-1.0</td></tr><tr><td>Air temperature - 2 K</td><td>+10</td><td>-0.02</td><td>+4</td><td>+4</td><td>-0.9</td><td>-1.2</td><td>-1.3</td></tr><tr><td>Modification of resistance</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Without building room resistances</td><td>+2</td><td>+0.03</td><td>+3</td><td>-3</td><td>-0.5</td><td>-1.0</td><td>-0.3</td></tr><tr><td>Without new road resistance</td><td>-9</td><td>+0.02</td><td>-2</td><td>+3</td><td></td><td></td><td>+1.8 (σ = 1.4)</td></tr></tbody></table>

leads to an overestimate of the surface temperature during daytime (by 10 K, not shown), which in turn leads to too-large heat storage (Table 7). The impact of modifying the internal building resistance is significant, and it improves the roof temperature, especially at night (not shown). Some warehouses in the V192 study area have roofs made of gravel on steel, instead of gravel on steel and wood. Using such a roof in TEB (20 mm gravel, 0.50 mm steel, 10 mm wood) decreases the storage and gives a ΔQ<sub>S</sub>/Q* ratio of 0.26. This dampens the thermal response of the roof surface (especially at night) compared to microscale measurements on this type of roof (not shown). This signals the need to take care in setting the value of the roof parameters for such cases. For the Me93 site, the roof specification again has a large impact, as does the radiative forcing.

The road and wall temperatures simulated by TEB are not much affected by uncertainties in the radiative and thermal input parameters. In contrast, the roof temperature is sensitive, both on average (bias) and its diurnal evolution (standard deviation), particularly to the

albedo assigned. All temperatures are sensitive to incoming radiation and the roughness length.

Summarizing the results of the sensitivity tests it seems that emissivities, temperature initializations, and wall characteristics have little impact. Similarly, the output is relatively insensitive to the overall roughness length for the city, even when large variations were considered. Road characteristics are not critical, except perhaps for albedo in areas with low buildings and wide roads. Errors in assigning geometric parameters have a moderate impact. Uncertainties in setting incoming radiative fluxes are significant. Thus we recommend that, if possible, measured values be used. Care must be taken not to use roughness values for horizontal surfaces that are too small and to take careful note of roof characteristics. However, it is our view that for the conditions tested, TEB is robust. To put this in perspective, across the range of sensitivity conditions tested here, the ΔQ<sub>S</sub>/Q* ratio is always within 5% of the reference run.
## 7. Concluding comments

Evaluation of TEB using field observations from two relatively dry and sparsely vegetated urban areas, with very different urban structure, suggests that overall the model performs well. The evaluation process resulted in small modifications to the original TEB scheme; these were in the aerodynamic resistance formulations. The agreement between the measurements and TEB gives some support to one of the simplifications of the scheme: the use of only one wall temperature.

The results of this evaluation are informative not only in assessing the ability of the model to calculate fluxes and thermal responses in these urban settings, but also in aiding interpretation of existing field data and to inform the better design of future observational programs. For example, the effect of the timing of clouds in sites with different canyon geometries, and the role of advection both in measurements and modeling need further investigation. Next we intend to extend the evaluation to include vegetated and moist urban districts using the combined TEB-ISBA scheme.

This study is perhaps the first to attempt genuine validation of the output of an urban land surface model that is designed for use within a mesoscale atmospheric model. Several previous studies have provided comparisons with field data from standard climate stations, especially with regard to air temperature, but none has checked output against observed fluxes and temperatures together. Agreement against air temperature can be relatively easily achieved, but when agreement is between fluxes and surface temperatures, it shows that the energetic processes underlying the thermal estimates are also physically realistic.

Significant difficulties remain with obtaining high quality measurements of surface fluxes. Energy balance closure is not achieved even in simple rural sites. In the urban case, uncertainties associated with anthropogenic releases of heat, water, and pollutants including radia-tively active aerosols and gases from concentrated and sometimes organized source distributions, and microd-vection that characterizes exchanges in among elements of the urban canopy layer contribute to uncertainty in fluxes, especially heat storage change, if it is resolved as a residual. Nevertheless, the estimates from several cities show similar features; this gives some confidence that anomalous effects do not dominate in the balance.

Similarly, there are challenges for modeling. Not least is the need to strike a balance between the detail and complexity of the modeled phenomena on the one hand and the simplicity of input properties and computational efficiency on the other. Given certain conceptual and practical difficulties we also note the difficulty of getting model output and observations to apply to a common "surface" or atmospheric plane.

The TEB model and the nature of the observational database used in the present study were not designed together. One of the issues that this research draws at-

tention to is the importance of scale and ensuring that the measurement and modeling communities are both cognizant of this. Better and more comprehensive observational data will emerge and both our understanding of the physics of the urban atmosphere and computational capacity will grow, but in our judgment the present comparison of observed and modeled climatic conditions represents a reasonable convergence of present-day capabilities of measurement and simulation.

*Acknowledgments.* This work has been supported by grants to the authors by the Centre National de Recherches Météorologiques, the Centre National de Recherches Scientifiques de France, the National Science Foundation, the Natural Sciences and Engineering Research Council of Canada, and the Canadian Foundation for Climate and Atmospheric Science. The authors are very grateful to the following colleagues who supplied data or provided assistance with interpretations: Stephanie Meyn of the University of British Columbia; Dr. Rachel Spronken-Smith of the University of Canterbury; Dr. Agustín Muhlia Velázquez, Coordinador del Observatorio de Radiación Solar, Instituto de Geofísica, UNAM; and Dr. James Voogt of the University of Western Ontario.

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