- Email: [email protected]
Comments on the correct specification of the analytical CTTC model for predicting the urban canopy layer temperature
Energy and Buildings 38 (2006) 1015–1021 www.elsevier.com/locate/enbuild
Comments on the correct specification of the analytical CTTC model for predicting the urban canopy layer temperature E. Erell a,*, T. Williamson b b
a J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, 84990 Midreshet Ben-Gurion, Israel School of Architecture, Landscape Architecture and Urban Planning, The University of Adelaide, Adelaide 5005, Australia
Received 1 August 2005; received in revised form 31 October 2005; accepted 10 November 2005
Abstract The paper responds to a recent article by Shashua-Bar et al. that asserted that the modification proposed by Elnahas and Williamson to the original formulation of the ‘‘cluster thermal time constant’’ (CTTC) model for predicting air temperature in the urban canopy layer causes serious errors in predictions. It reviews the development of both versions of the model, highlighting the differences between them. A methodology is suggested for analysis of the quality of the model predictions and the performance of the Elnahas–Williamson version is evaluated. The analysis shows that both versions of the CTTC model give similar predictions in stable meso-climatic conditions, but the Elnahas–Williamson version is clearly superior in changing weather. The revised CTTC model is proposed as the basis for a tool to account for urban modification to air temperature in the simulation and design of HVAC systems in buildings. # 2005 Elsevier B.V. All rights reserved. Keywords: Urban microclimate; Climate modelling; Model validation
1. Introduction Knowledge of site-specific conditions is essential for the development of an architectural design that responds to the local environment and for accurate design of HVAC systems. Many building simulation software packages come with inbuilt climate data files compiled from ‘representative’ stations such as airports. However, evidence of urban modification to weather indicates that the differences between city-centre locations and the typical reference sites used by meteorological services are often quite substantial. In a recent study, computer simulation of the energy demand of a typical office building in Adelaide, Australia, demonstrated that accounting correctly for urban modifications to the microclimate could lead to estimates of the annual heating consumption that were 25% lower and cooling 15% higher than estimates that do not incorporate these effects [1]. The ability to predict accurately both peak loads on HVAC equipment and total annual energy consumption is essential in the design of HVAC systems and in economic calculations regarding their operation and maintenance. The design of such
* Corresponding author. Tel.: +972 8 6596875; fax: +972 8 6596881. E-mail address: [email protected] (E. Erell). 0378-7788/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2005.11.013
systems is routinely carried out using detailed whole-building energy simulation models. As the Adelaide example illustrates, failing to account for urban modifications to air temperature may lead to errors that are too large to overlook. HVAC plant may be either over-sized or too small, leading to unnecessary expenditure in the first instance or to failure to cope adequately with loads in the latter. Any optimisation of life cycle costs of the equipment can only be done if the capital cost is realistic and if running costs are estimated accurately. Finally, certification of the performance of the building within the framework of a building energy-rating scheme, a procedure that is now required by an increasing number of local authorities in many countries, might be affected if local climate modifications are not accounted for. This has legal and financial implications that should not be ignored. There is therefore a clear need for a robust tool that can predict site-specific modification of weather conditions. The analytical ‘‘cluster thermal time constant’’ (CTTC) model, which predicts air temperature in the urban canopy layer, was initially proposed by Sharlin and Hoffman [2] to address this need and was subsequently developed and expanded by Swaid and Hoffman in a series of papers [3–8]. A recent addition to the model attempts to account for the effect of trees on air temperature in the urban canyon [9–11].
1016
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
The CTTC model in its original form was restricted to fair weather conditions, i.e. clear skies and light-to-moderate winds. It also had no provision for dealing with the contribution of vegetation to the latent heat flux and did not account for anthropogenic heat. Elnahas and Williamson [12] proposed a modified form of the CTTC model to extend its applicability to a wider range of weather conditions and urban landscapes. The revised model included a more detailed analysis of radiant exchange to account for diffuse solar radiation, and simplified methods of describing the effect of vegetation and anthropogenic heat sources. However, the main modification consisted of the use of hourly air temperature data measured at a reference weather station to establish boundary conditions for the calculation, instead of a using a fixed reference temperature representing the regional meso-scale conditions. The revised model was validated using measured meteorological data in the city of Adelaide. A slightly modified version of the model was later validated using additional measured meteorological data from two Adelaide streets, demonstrating its capacity to predict the evolution of air temperature in an urban canyon over an extended period in weather conditions ranging from clear to cloudy with rain [13,14]. A recent paper by Shashua-Bar et al. [15] claimed that the revised model proposed by Elnahas and Williamson inadvertently adds an error to the prediction of air temperature in the urban street canyon, giving unacceptable results. The present paper will refute this claim, demonstrating that the two variants of the model give similar predictions in stable atmospheric conditions, while the revised formulation is clearly better at predicting temperature correctly in changeable weather. 2. Comparison of the CTTC model variants 2.1. The original CTTC model The original formulation of the CTTC model [3] is based on predicting the contribution to air temperature at a specific location of the solar and long wave radiation and adding these to a constant base temperature representing the meso-scale conditions, as follows: Ta ðtÞ ¼ T0 þ DTa;solar ðtÞ DTNLWR ðtÞ
(1)
where T0 is the base temperature and the time dependent contributions to air temperature of solar radiation and the net long wave radiant exchange are given by Eqs. (2) and (3) (following the original nomenclature):
DTa;solar ðtÞ ¼
t X m DIpen ðtÞ l¼0
h
1 exp
tl CTTC
participating ground layer per unit change in the heat flux through it. DTNLWR ðtÞ ¼
ðsTa4 sBrTa4 ÞSVF h
where s is the Stefan–Boltzmann constant, Ta the air temperature at screen height, Br the Brunt number, h the surface convective heat transfer coefficient and SVF is the sky view factor from the centre of the street canyon. Later formulations were expanded to include an anthropogenic heat term. Swaid and Hoffman suggested two methods for estimating the base temperature T0 [5]: (a) T0 at a certain day is the mean daily air temperature measured at a representative rural meteorological station. (b) Solving Eq. (1) for T0 using the (measured) minimum air temperature at the site and the predicted values of the parametric factors DTa,solar and DTNLWR at the time. In either case, the base value T0 is constant for duration of the period being simulated, typically 24 h. 2.2. The modified CTTC model The main motivation for development of the modified CTTC model was to have a technique to adjust hourly climate data files to account for urban conditions that did not require a priori knowledge of climatic variables at the urban site, as is the case in the original formulation. In the modified CTTC model [12], the effect on air temperature at any location of exposure to solar radiation and of net long wave radiant exchange is expressed in essentially the same way as in the original model. Air temperature at an urban site and at a reference meteorological station may thus be expressed as follows: Ta ðtÞurb ¼ Tb ðtÞ þ DTsol ðtÞurb DTlw ðtÞurb
(4a)
Ta ðtÞmet ¼ Tb ðtÞ þ DTsol ðtÞmet DTlw ðtÞmet
(4b)
The actual air temperature at the urban site is found by solving Eq. (4b) for Tb and combining Eqs. (4a) and (4b): Ta ðtÞurb ¼ Ta ðtÞmet þ ðDTsol ðtÞurb DTsol ðtÞmet Þ ðDTlw ðtÞurb DTlw ðtÞmet Þ
(2)
where m is the absorptivity of the surface to solar radiation, DIpen the step-change in the mean magnitude of solar radiation received at ground surface, h the surface convective heat transfer coefficient, l the time and CTTC, the cluster thermal time constant, is defined as the heat energy stored in the
(3)
(5)
The difference between the original CTTC model and the modified version is therefore that Tb, the base temperature, is recalculated at every time step, instead of only once a day. The following section addresses the complex issue of errors in models, and will demonstrate that the analysis in ShashuaBar et al. [15] is flawed, because having assumed that the base
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
temperature is constant over a daily cycle, it fails to address all of the possible sources of error resulting from this assumption. 2.3. Sources of error in model predictions Differences between observed values and values predicted by a model (henceforth ‘errors’) might be the result of any of the following factors, singly or in combination: (a) Measured inputs may be inaccurate, due to deficiencies of the instruments or the data acquisition system. (b) Modelled parameters may be inaccurate, due to deficiencies of the analytical model. (c) The model may be incomplete, lacking a methodology for dealing with one or more factors affecting the process being described. The contribution of each of these categories of errors to the overall error of the prediction is independent of the others. Analysis of the errors inherent to the original CTTC model compared to the modified version yields some interesting observations. For the sake of comparison, it will be assumed that both versions consider that the surface is dry and that latent heat flux is very small (although the modified version incorporates a simplified method for describing the effects of vegetation), and that anthropogenic heat may also be ignored (although both the modified version and later formulations of the original model do in fact describe manmade sources of heat). Neither version of the model incorporates a means of describing the net effects of advection, which is in any case assumed to be negligible. In the framework of these restrictions, if the effects of radiant exchange and energy storage are modelled in a similar fashion then differences between the models in predicted air temperature would be due solely to the definition of the base (or reference) air temperature. It is useful in this context to consider two possibilities: first, a hypothetical scenario in which meso-scale weather conditions are constant, and second, a scenario incorporating a rapid change in conditions in the region, such as the passage of a cold front. In the first scenario, evolution of air temperature at any given point is determined solely by the local heat balance at the surface. If the modified CTTC model is used to ‘predict’ air temperature at a reference site on the basis of air temperature measured at that site itself (as Shashua-Bar et al. [15] have apparently done), then by definition the time-varying temperature Tb will yield a perfectly accurate output, since the effect of each factor on air temperature is exactly balanced by subtracting its contribution in the reverse calculation. (Such a test is, however, meaningless, since the same result is obtained irrespective of the value of Tb.) On the other hand, calculating the reference temperature (T0) on the basis of the original CTTC model incorporates all possible errors in the prediction, and in particular errors resulting from environmental factors not accounted for in the simulation. The conceptual difference between the two approaches may be
1017
illustrated by the following example: if the sky is cloudy and no correction factor is applied to the parameterisation of sky radiation, then the base temperature calculation in both versions of the model will be inaccurate. However, in the original version, this error is allowed to affect the entire simulation, whereas in the revised version it is cancelled out (Eq. (5)). In the second scenario, differences between the two methods of estimating Tb become even more pronounced. The effect of changes in the weather on a regional scale may theoretically be modelled by adding to Eq. (1) a term accounting for the effects of advection on air temperature—a feature neither model currently incorporates. However, while neither version is capable of dealing directly with the complexity of modelling meso-scale winds and the accompanying advective heat transfer, the modified CTTC model has a built-in correction mechanism: since the base temperature is recalculated at every time step, any changes in regional weather, such as the passage of a cold front, are automatically incorporated in the calculation. The original version of the model lacks this flexibility: neither of the two methods proposed by Swaid and Hoffman [5] for calculating the reference temperature is capable of reflecting dynamic regional-scale weather conditions. The case for a constant base temperature is also flawed from a conceptual point of view, since determination of this temperature according to either of the two methods suggested by Swaid and Hoffman requires a priori knowledge of conditions occurring after the period being simulated. The implications of this requirement are potentially very serious: consider two hypothetical periods of 24 h, in which conditions are identical until noon but which diverge sharply afterwards, resulting in substantially different base temperatures according to the original CTTC model. As a result, the temperature predicted for any given time during the morning of the respective hypothetical days would be different, too—although the environmental conditions at that time and at all preceding periods were in fact identical. The assumption underlying the original CTTC model that the base temperature is constant over a 24-h period is thus simply not tenable. 3. Evaluating the performance of a model Empirical validation is necessary to provide confidence that model predictions are likely to correspond to real situations. A variety of statistical techniques may be used to evaluate the goodness-of-fit between measured and predicted data. Among the most commonly used is Pearson’s product–moment coefficient of correlation (r), or the coefficient of determination (r2), usually accompanied by a test of significance. However, Willmott suggested in a series of papers [16–18] that significance testing is often inappropriate, and use of the correlation coefficient (r) or its square (r2) alone may be insufficient. He recommended using the observed and predicted ¯ P) ¯ and standard deviations (so, variates’ respective means (O; sp); the intercept and slope of a least squares linear regression between the variates; the errors described by the root mean
1018
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
squared error (RMSE), and its systematic and unsystematic components. He also proposed an index of agreement ‘d’ that varies between 0 and 1, 1 indicating perfect agreement: PN ðPi Oi Þ2 d ¼ 1 PNi¼1 0 0 2 i¼1 ½jPi j þ jOi j ¯ and O0 ¼ Oi O. ¯ In the expression above, where P0i ¼ Pi O i the denominator of the main term represents the potential error of the sample while the numerator represents the portion of this error left unexplained by the simulated variate. All of the above statistical tests may still be inadequate if there is a high degree of auto-correlation in the variables. For example, in numerous situations, the value ‘v’ of an input variable (or combination of several variables) can provide a fairly close approximation to the measured parameter ‘m’. A model may be considered useful only if the estimated value of the parameter in question ‘e’ is closer to the observed value than this trivial approximation of the input variable. Williamson [19] proposed a confirmation factor Cs, such that Cs ¼ Uðm; vÞ Uðe; mÞ where Uðm; vÞ is Theil’s inequality coefficient between the measured value and the trivial variable estimate, and U(e, m) is Theil’s inequality coefficient between the estimated value and the measured value of the parameter in question. The maximum value of the confirmation factor is thus Uðm; vÞ, when U(e, m) is equal to zero, indicating perfect correlation between the measured and estimated values. The value of Cs represents a single measure combining the difficulty of the validation test and how well the model performs, given the input parameters. Dividing the confirmation factor Cs by Uðm; vÞ normalises all possible values of this factor, giving a degree of confirmation D: D¼
Uðm; vÞ Uðe; mÞ Uðm; vÞ
The Williamson degree of confirmation has a maximum value of unity, indicating perfect agreement between predicted and measured values, and may have negative values if model predictions are poorer than the trivial approximation of the input variable. In spite of the difficulty of demonstrating goodness-of-fit in a satisfactory manner, researchers frequently rely for validation only on visual inspection of graphs comparing measured data with model predictions. For example, Shashua-Bar et al. [15] present only figures showing air temperature predicted using the original CTTC model compared with observed values at a rural location during two 24-h periods, in winter and summer. These figures, which are intended to be an indication of the quality of the model, are then followed by figures (drawn to a different scale) showing the difference between the base temperatures calculated by the two versions of the model— which are then claimed to be an indication of the error resulting from the use of the modified CTTC model. The authors do not give a table showing the actual results of the simulation, nor do they provide any statistical analysis of the predictions. However, if the size of the error in prediction is measured
Fig. 1. Comparison of the error in prediction of air temperature using the Swaid–Hoffman version of the CTTC model and the error claimed to result from using a varying reference temperature, for July data (a) and January data (b). All data obtained graphically from Shashua-Bar et al. [15] (Figs. 1 and 2).
directly from the graph – admittedly a very crude method – it appears to be almost identical to the difference between the base temperatures, also obtained graphically. The correlation between the two parameters is shown in Fig. 1a and b. It therefore appears that the methodology suggested in the paper by Shashua-Bar et al. [15] to evaluate the difference between the models inadvertently shows that the error in prediction of the original CTTC model is due almost entirely to an invalid assumption of a constant base temperature. 4. Validating the revised CTTC model of Elnahas and Williamson The performance of the revised CTTC model (and a later variant, URBANm) was evaluated using experimental data from
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
1019
Fig. 2. Aerial photograph of central Adelaide showing location of monitoring sites.
two separate monitoring studies carried out in Adelaide in 1993 and 2000 [12–14]. Details of the second of these studies are given in brief in the following paragraphs, followed by a graphic representation of the results of this experiment and performance statistics for the model. In the study carried out during the year 2000, welldocumented and comprehensive meteorological measurements were made at two urban street canyons within the City of Adelaide for a period of nearly a year. These data were compared with data recorded concurrently at a reference site at the Adelaide City Council Nursery, north of the Torrens River, and with records provided by the Bureau of Meteorology from the Kent Town station, which is located about 1.5 km east of the urban sites. The reference site is located in a green belt surrounding the central business district of Adelaide, approximately 2.1 km northeast of the city centre. The urban sites are two relatively narrow streets about 0.5 km from the centre of the business district, and about 1.5 km southwest of the reference site, one with a north–south axis and the other with an east–west one. Fig. 2 shows an aerial photograph of central Adelaide, highlighting the test sites. The area as a whole comprises the core of the Adelaide metropolitan area, which extends about 20 km east–west from the Gulf of St. Vincent to the Adelaide Hills, and about 25 km from north to south. Data recorded directly, representing the whole of the study area, included global solar radiation, diffuse solar radiation and net all-wave radiation. At the reference station dry bulb temperature, relative humidity, wind speed and direction and soil temperature were monitored. At the urban sites air temperature was recorded at several points in each street (Fig. 3), as well as relative humidity, wind speed and direction and mean surface temperature of the road surface (by IR sensing). Evaluation of the performance of the model was carried out by comparing the predicted air temperature at the urban street canyon with measured air temperature, using data from the
Fig. 3. Urban street canyon monitoring site (location of five temperature sensors highlighted by circles).
reference site as inputs to the revised CTTC model. Fig. 4 shows results for a period of 1 week during May 2000. The period displayed includes several days of generally fine weather, conducive to the formation of a substantial nocturnal urban heat island, followed by cool, windy and overcast conditions. Visual inspection of the graph shows what appears to be fairly good agreement between predicted and observed air temperatures over the entire period. Confidence in the performance of the model is given further support when basic descriptive statistics are assembled that compare the predicted and observed air temperature over the course of an entire month (Table 1). All of the measures indicate
Fig. 4. Performance of the modified CTTC model: observed dry bulb temperature of the air at the reference site, and the observed and predicted temperatures at the urban site. Data from Adelaide experiment, May 22–27, 2000.
1020
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
Table 1 Descriptive statistics for 1 month of hourly data, showing air temperature measured in a reference meteorological station and in an urban street canyon in Adelaide, Australia, during May 2000, and air temperature in the street predicted using the revised CTTC formulation
Mean monthly Standard deviation Mean daily maxima Mean daily minima Absolute monthly maxima Absolute monthly minima
Reference (observed)
Urban Observed
Predicted
12.5 3.8 17.3 8.1 22.4 4.2
14.9 2.6 18.0 12.4 22.6 8.0
15.3 2.9 18.9 12.3 23.7 8.1
Table 2 Goodness-of-fit statistics for 1 month of hourly data, comparing air temperature in an urban street canyon predicted using the revised CTTC formulation with temperature observed in Adelaide, Australia, during May 2000 Statistic
Value
Total number of hours Mean error Standard deviation MSE Systematic MSE Unsystematic MSE Willmott index Theil’s inequality coefficient Degree of confirmation
742 0.42 1.36 2.02 0.18 1.84 0.93 0.05 0.60
that air temperature predicted using the revised CTTC model is a much closer approximation of actual air temperature in the street canyon than are measurements carried out at the reference station. (These were, in turn, very similar to data recorded at the weather station operated by the Australian Bureau of Meteorology.) Not only is the mean monthly temperature predicted accurately – 14.9 8C compared with 15.3 8C measured at the urban canyon and 12.5 8C at the reference site – but mean daily minima and maxima for the 31-day period are predicted with an accuracy of better than 1 8C, too. Finally, statistical goodness-of-fit tests also support the claim that the revised CTTC model is in fact capable of producing a useful approximation of air temperature in an urban street canyon, subject to the restrictions on its application noted in the original papers. As Table 2 shows, in addition to displaying a small error of prediction, the predicted and observed values of air temperature have a high Willmott index of agreement (0.93) and a fairly high Williamson degree of confirmation (0.60). The impression given by visual inspection of the graph (Fig. 4) and by the descriptive statistics is therefore also supported by rigorous statistical goodness-of-fit tests.
exposition that is based on a constant base value. This conclusion is supported by the results of the monitoring experiment carried out in Adelaide, described in Section 4. The promising results obtained with the revised CTTC model suggest that the basic methodology adopted, namely calculation of micro-scale climate modifications to a representative mesoscale base, may provide a practical means of predicting sitespecific air temperature data from measured data at a regional meteorological station. The model is predicated on the proposition that the properties of the mixed layer above the urban canopy layer are, on the average, uniform over an area in which both the reference station and the urban canyon are located. It is not applicable in its present form where this condition cannot be met, for example, where there are substantial differences in the meso-scale properties of the sites such as topography, elevation, distance from a large body of water, etc. The revised CTTC model, in common with many models of the urban microclimate, is also restricted by the assumption that net advective heat transfer within the urban area is negligible. It is clearly applicable where building density, typology and ground cover in the source area for energy fluxes are approximately homogeneous. However, measurements made in the urban sites as part of this research suggest that the presence of urban parks or large variations in building height and street sections in the source area of the airflow advected to them may have only a minor effect on canyon air temperature. There is need for further field research to establish the magnitude of the effect on canyon air temperature of such meso-scale features, taking into account their distance from the street in question, the direction of the wind and the intensity of the fluxes. Subsequent work by the authors to develop a robust urban climate model, while maintaining the same basic overall approach, has in fact abandoned the CTTC methodology of describing the heat flux and storage characteristics of the canyon surfaces in favour of well-documented parameterisations presented in the climatological literature that include both sensible and latent heat exchanges. Performance evaluation of a model incorporating these parameterisations [20] gives further support to a modelling approach based on a dynamic base temperature that is constantly updated to reflect changes in meso-scale weather. Many building codes and professional design handbooks currently in use already account for urban effects on the microclimate, typically the wind field. None of them currently suggest a methodology that can give a quantitative estimate of the magnitude of the modification of air temperature, in spite of widespread evidence of this phenomenon, typically in the form of an urban heat island. The revised CTTC model provides a basis for the development of such a methodology. References
5. Discussion and conclusion The theoretical analysis in Section 2 suggests that the description of the CTTC model in terms of a base temperature that is updated at regular intervals to reflect changing weather conditions may have substantial advantages compared with an
[1] E. Erell, Predicting air temperature in city streets on the basis of measured reference data, Ph.D. Thesis, School of Architecture, Landscape Architecture and Urban Design, The University of Adelaide, Adelaide, 2005, p. 161. [2] N. Sharlin, M.E. Hoffman, The urban complex as a factor in the airtemperature pattern in a Mediterranean coastal region, Energy and Buildings 7 (1984) 149–158.
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021 [3] H. Swaid, M.E. Hoffman, Prediction of urban air temperature variations using the analytical CTTC model, Energy and Buildings 14 (1990) 313–324. [4] H. Swaid, Nocturnal variations of air-surface temperature gradients for typical urban and rural surfaces, Atmospheric Environment 25B (3) (1991) 331–341. [5] H. Swaid, M.E. Hoffman, Climatic impacts of urban design features for high and mid-latitude cities, Energy and Buildings 14 (1990) 325–336. [6] H. Swaid, The role of radiative-convective interaction in creating the microclimate of urban street canyons, Boundary-Layer Meteorology 64 (1993) 231–259. [7] H. Swaid, Urban climate effects of artificial heat sources and ground shadowing by buildings, International Journal of Climatology 13 (1993) 797–812. [8] H. Swaid, Numerical investigation into the influence of geometry and construction materials on urban street climate, Physical Geography 14 (4) (1993) 342–358. [9] L. Shashua-Bar, M. Hoffman, Vegetation as a climatic component in the design of an urban street: an empirical model for predicting the cooling effect of urban green areas with trees, Energy and Buildings (2000) 221–235. [10] L. Shashua-Bar, M. Hoffman, The Green CTTC model for predicting the air temperature in small urban wooded sites, Building and Environment 37 (2002) 1279–1288. [11] L. Shashua-Bar, M. Hoffman, Geometry and orientation aspects in passive cooling of canyon streets with trees, Energy and Buildings 35 (2003) 61–68. [12] M.M. Elnahas, T.J. Williamson, An improvement of the CTTC model for predicting urban air temperatures, Energy and Buildings 25 (1997) 41–49.
1021
[13] T.J. Williamson, E. Erell, Thermal performance simulation and the urban micro-climate: measurements and prediction, in: Proceedings 7th International IBPSA Conference, Rio de Janeiro, Brazil, (2001), pp. 159–165. [14] E. Erell, T. Williamson, Predicting air temperatures in the urban canopy layer from measured reference data, in: Proceedings 19th PLEA International Conference—Design with the Environment, Toulouse, France, (2002), pp. 145–152. [15] L. Shashua-Bar, H. Swaid, M. Hoffman, On the correct specification of the analytical CTTC model for predicting the urban canopy layer temperature, Energy and Buildings 36 (2004) 975–978. [16] C.J. Willmott, On the validation of models, Physical Geography 2 (2) (1981) 184–194. [17] C. Willmott, Some comments on the evaluation of model performance, Bulletin American Meteorological Society 63 (11) (1982) 1309–1313. [18] C. Willmott, S. Ackleson, R. Davis, J. Feddema, K. Klink, D. Legates, J. O’Donnell, C. Rowe, Statistics for the evaluation and comparison of models, Journal of Geophysical Research 90 (5) (1985) 8995–9005. [19] T.J. Williamson, A confirmation technique for thermal performance simulation models, in: Proceedings Building Simulation’95, Madison, WI, USA, (1995), pp. 268–275. [20] E. Erell, T. Williamson, The CAT model: predicting air temperature in city streets on the basis of measured reference data, in: Proceedings ‘‘Contexts of Architecture’’, the 38th Annual Conference of the Architectural Science Association, ANZAScA and the International Building Performance Association, Australasia, Launceston, Tasmania, Australia, (2004), pp. 210–215.
Comments on the correct specification of the analytical CTTC model for predicting the urban canopy layer temperature E. Erell a,*, T. Williamson b b
a J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, 84990 Midreshet Ben-Gurion, Israel School of Architecture, Landscape Architecture and Urban Planning, The University of Adelaide, Adelaide 5005, Australia
Received 1 August 2005; received in revised form 31 October 2005; accepted 10 November 2005
Abstract The paper responds to a recent article by Shashua-Bar et al. that asserted that the modification proposed by Elnahas and Williamson to the original formulation of the ‘‘cluster thermal time constant’’ (CTTC) model for predicting air temperature in the urban canopy layer causes serious errors in predictions. It reviews the development of both versions of the model, highlighting the differences between them. A methodology is suggested for analysis of the quality of the model predictions and the performance of the Elnahas–Williamson version is evaluated. The analysis shows that both versions of the CTTC model give similar predictions in stable meso-climatic conditions, but the Elnahas–Williamson version is clearly superior in changing weather. The revised CTTC model is proposed as the basis for a tool to account for urban modification to air temperature in the simulation and design of HVAC systems in buildings. # 2005 Elsevier B.V. All rights reserved. Keywords: Urban microclimate; Climate modelling; Model validation
1. Introduction Knowledge of site-specific conditions is essential for the development of an architectural design that responds to the local environment and for accurate design of HVAC systems. Many building simulation software packages come with inbuilt climate data files compiled from ‘representative’ stations such as airports. However, evidence of urban modification to weather indicates that the differences between city-centre locations and the typical reference sites used by meteorological services are often quite substantial. In a recent study, computer simulation of the energy demand of a typical office building in Adelaide, Australia, demonstrated that accounting correctly for urban modifications to the microclimate could lead to estimates of the annual heating consumption that were 25% lower and cooling 15% higher than estimates that do not incorporate these effects [1]. The ability to predict accurately both peak loads on HVAC equipment and total annual energy consumption is essential in the design of HVAC systems and in economic calculations regarding their operation and maintenance. The design of such
* Corresponding author. Tel.: +972 8 6596875; fax: +972 8 6596881. E-mail address: [email protected] (E. Erell). 0378-7788/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2005.11.013
systems is routinely carried out using detailed whole-building energy simulation models. As the Adelaide example illustrates, failing to account for urban modifications to air temperature may lead to errors that are too large to overlook. HVAC plant may be either over-sized or too small, leading to unnecessary expenditure in the first instance or to failure to cope adequately with loads in the latter. Any optimisation of life cycle costs of the equipment can only be done if the capital cost is realistic and if running costs are estimated accurately. Finally, certification of the performance of the building within the framework of a building energy-rating scheme, a procedure that is now required by an increasing number of local authorities in many countries, might be affected if local climate modifications are not accounted for. This has legal and financial implications that should not be ignored. There is therefore a clear need for a robust tool that can predict site-specific modification of weather conditions. The analytical ‘‘cluster thermal time constant’’ (CTTC) model, which predicts air temperature in the urban canopy layer, was initially proposed by Sharlin and Hoffman [2] to address this need and was subsequently developed and expanded by Swaid and Hoffman in a series of papers [3–8]. A recent addition to the model attempts to account for the effect of trees on air temperature in the urban canyon [9–11].
1016
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
The CTTC model in its original form was restricted to fair weather conditions, i.e. clear skies and light-to-moderate winds. It also had no provision for dealing with the contribution of vegetation to the latent heat flux and did not account for anthropogenic heat. Elnahas and Williamson [12] proposed a modified form of the CTTC model to extend its applicability to a wider range of weather conditions and urban landscapes. The revised model included a more detailed analysis of radiant exchange to account for diffuse solar radiation, and simplified methods of describing the effect of vegetation and anthropogenic heat sources. However, the main modification consisted of the use of hourly air temperature data measured at a reference weather station to establish boundary conditions for the calculation, instead of a using a fixed reference temperature representing the regional meso-scale conditions. The revised model was validated using measured meteorological data in the city of Adelaide. A slightly modified version of the model was later validated using additional measured meteorological data from two Adelaide streets, demonstrating its capacity to predict the evolution of air temperature in an urban canyon over an extended period in weather conditions ranging from clear to cloudy with rain [13,14]. A recent paper by Shashua-Bar et al. [15] claimed that the revised model proposed by Elnahas and Williamson inadvertently adds an error to the prediction of air temperature in the urban street canyon, giving unacceptable results. The present paper will refute this claim, demonstrating that the two variants of the model give similar predictions in stable atmospheric conditions, while the revised formulation is clearly better at predicting temperature correctly in changeable weather. 2. Comparison of the CTTC model variants 2.1. The original CTTC model The original formulation of the CTTC model [3] is based on predicting the contribution to air temperature at a specific location of the solar and long wave radiation and adding these to a constant base temperature representing the meso-scale conditions, as follows: Ta ðtÞ ¼ T0 þ DTa;solar ðtÞ DTNLWR ðtÞ
(1)
where T0 is the base temperature and the time dependent contributions to air temperature of solar radiation and the net long wave radiant exchange are given by Eqs. (2) and (3) (following the original nomenclature):
DTa;solar ðtÞ ¼
t X m DIpen ðtÞ l¼0
h
1 exp
tl CTTC
participating ground layer per unit change in the heat flux through it. DTNLWR ðtÞ ¼
ðsTa4 sBrTa4 ÞSVF h
where s is the Stefan–Boltzmann constant, Ta the air temperature at screen height, Br the Brunt number, h the surface convective heat transfer coefficient and SVF is the sky view factor from the centre of the street canyon. Later formulations were expanded to include an anthropogenic heat term. Swaid and Hoffman suggested two methods for estimating the base temperature T0 [5]: (a) T0 at a certain day is the mean daily air temperature measured at a representative rural meteorological station. (b) Solving Eq. (1) for T0 using the (measured) minimum air temperature at the site and the predicted values of the parametric factors DTa,solar and DTNLWR at the time. In either case, the base value T0 is constant for duration of the period being simulated, typically 24 h. 2.2. The modified CTTC model The main motivation for development of the modified CTTC model was to have a technique to adjust hourly climate data files to account for urban conditions that did not require a priori knowledge of climatic variables at the urban site, as is the case in the original formulation. In the modified CTTC model [12], the effect on air temperature at any location of exposure to solar radiation and of net long wave radiant exchange is expressed in essentially the same way as in the original model. Air temperature at an urban site and at a reference meteorological station may thus be expressed as follows: Ta ðtÞurb ¼ Tb ðtÞ þ DTsol ðtÞurb DTlw ðtÞurb
(4a)
Ta ðtÞmet ¼ Tb ðtÞ þ DTsol ðtÞmet DTlw ðtÞmet
(4b)
The actual air temperature at the urban site is found by solving Eq. (4b) for Tb and combining Eqs. (4a) and (4b): Ta ðtÞurb ¼ Ta ðtÞmet þ ðDTsol ðtÞurb DTsol ðtÞmet Þ ðDTlw ðtÞurb DTlw ðtÞmet Þ
(2)
where m is the absorptivity of the surface to solar radiation, DIpen the step-change in the mean magnitude of solar radiation received at ground surface, h the surface convective heat transfer coefficient, l the time and CTTC, the cluster thermal time constant, is defined as the heat energy stored in the
(3)
(5)
The difference between the original CTTC model and the modified version is therefore that Tb, the base temperature, is recalculated at every time step, instead of only once a day. The following section addresses the complex issue of errors in models, and will demonstrate that the analysis in ShashuaBar et al. [15] is flawed, because having assumed that the base
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
temperature is constant over a daily cycle, it fails to address all of the possible sources of error resulting from this assumption. 2.3. Sources of error in model predictions Differences between observed values and values predicted by a model (henceforth ‘errors’) might be the result of any of the following factors, singly or in combination: (a) Measured inputs may be inaccurate, due to deficiencies of the instruments or the data acquisition system. (b) Modelled parameters may be inaccurate, due to deficiencies of the analytical model. (c) The model may be incomplete, lacking a methodology for dealing with one or more factors affecting the process being described. The contribution of each of these categories of errors to the overall error of the prediction is independent of the others. Analysis of the errors inherent to the original CTTC model compared to the modified version yields some interesting observations. For the sake of comparison, it will be assumed that both versions consider that the surface is dry and that latent heat flux is very small (although the modified version incorporates a simplified method for describing the effects of vegetation), and that anthropogenic heat may also be ignored (although both the modified version and later formulations of the original model do in fact describe manmade sources of heat). Neither version of the model incorporates a means of describing the net effects of advection, which is in any case assumed to be negligible. In the framework of these restrictions, if the effects of radiant exchange and energy storage are modelled in a similar fashion then differences between the models in predicted air temperature would be due solely to the definition of the base (or reference) air temperature. It is useful in this context to consider two possibilities: first, a hypothetical scenario in which meso-scale weather conditions are constant, and second, a scenario incorporating a rapid change in conditions in the region, such as the passage of a cold front. In the first scenario, evolution of air temperature at any given point is determined solely by the local heat balance at the surface. If the modified CTTC model is used to ‘predict’ air temperature at a reference site on the basis of air temperature measured at that site itself (as Shashua-Bar et al. [15] have apparently done), then by definition the time-varying temperature Tb will yield a perfectly accurate output, since the effect of each factor on air temperature is exactly balanced by subtracting its contribution in the reverse calculation. (Such a test is, however, meaningless, since the same result is obtained irrespective of the value of Tb.) On the other hand, calculating the reference temperature (T0) on the basis of the original CTTC model incorporates all possible errors in the prediction, and in particular errors resulting from environmental factors not accounted for in the simulation. The conceptual difference between the two approaches may be
1017
illustrated by the following example: if the sky is cloudy and no correction factor is applied to the parameterisation of sky radiation, then the base temperature calculation in both versions of the model will be inaccurate. However, in the original version, this error is allowed to affect the entire simulation, whereas in the revised version it is cancelled out (Eq. (5)). In the second scenario, differences between the two methods of estimating Tb become even more pronounced. The effect of changes in the weather on a regional scale may theoretically be modelled by adding to Eq. (1) a term accounting for the effects of advection on air temperature—a feature neither model currently incorporates. However, while neither version is capable of dealing directly with the complexity of modelling meso-scale winds and the accompanying advective heat transfer, the modified CTTC model has a built-in correction mechanism: since the base temperature is recalculated at every time step, any changes in regional weather, such as the passage of a cold front, are automatically incorporated in the calculation. The original version of the model lacks this flexibility: neither of the two methods proposed by Swaid and Hoffman [5] for calculating the reference temperature is capable of reflecting dynamic regional-scale weather conditions. The case for a constant base temperature is also flawed from a conceptual point of view, since determination of this temperature according to either of the two methods suggested by Swaid and Hoffman requires a priori knowledge of conditions occurring after the period being simulated. The implications of this requirement are potentially very serious: consider two hypothetical periods of 24 h, in which conditions are identical until noon but which diverge sharply afterwards, resulting in substantially different base temperatures according to the original CTTC model. As a result, the temperature predicted for any given time during the morning of the respective hypothetical days would be different, too—although the environmental conditions at that time and at all preceding periods were in fact identical. The assumption underlying the original CTTC model that the base temperature is constant over a 24-h period is thus simply not tenable. 3. Evaluating the performance of a model Empirical validation is necessary to provide confidence that model predictions are likely to correspond to real situations. A variety of statistical techniques may be used to evaluate the goodness-of-fit between measured and predicted data. Among the most commonly used is Pearson’s product–moment coefficient of correlation (r), or the coefficient of determination (r2), usually accompanied by a test of significance. However, Willmott suggested in a series of papers [16–18] that significance testing is often inappropriate, and use of the correlation coefficient (r) or its square (r2) alone may be insufficient. He recommended using the observed and predicted ¯ P) ¯ and standard deviations (so, variates’ respective means (O; sp); the intercept and slope of a least squares linear regression between the variates; the errors described by the root mean
1018
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
squared error (RMSE), and its systematic and unsystematic components. He also proposed an index of agreement ‘d’ that varies between 0 and 1, 1 indicating perfect agreement: PN ðPi Oi Þ2 d ¼ 1 PNi¼1 0 0 2 i¼1 ½jPi j þ jOi j ¯ and O0 ¼ Oi O. ¯ In the expression above, where P0i ¼ Pi O i the denominator of the main term represents the potential error of the sample while the numerator represents the portion of this error left unexplained by the simulated variate. All of the above statistical tests may still be inadequate if there is a high degree of auto-correlation in the variables. For example, in numerous situations, the value ‘v’ of an input variable (or combination of several variables) can provide a fairly close approximation to the measured parameter ‘m’. A model may be considered useful only if the estimated value of the parameter in question ‘e’ is closer to the observed value than this trivial approximation of the input variable. Williamson [19] proposed a confirmation factor Cs, such that Cs ¼ Uðm; vÞ Uðe; mÞ where Uðm; vÞ is Theil’s inequality coefficient between the measured value and the trivial variable estimate, and U(e, m) is Theil’s inequality coefficient between the estimated value and the measured value of the parameter in question. The maximum value of the confirmation factor is thus Uðm; vÞ, when U(e, m) is equal to zero, indicating perfect correlation between the measured and estimated values. The value of Cs represents a single measure combining the difficulty of the validation test and how well the model performs, given the input parameters. Dividing the confirmation factor Cs by Uðm; vÞ normalises all possible values of this factor, giving a degree of confirmation D: D¼
Uðm; vÞ Uðe; mÞ Uðm; vÞ
The Williamson degree of confirmation has a maximum value of unity, indicating perfect agreement between predicted and measured values, and may have negative values if model predictions are poorer than the trivial approximation of the input variable. In spite of the difficulty of demonstrating goodness-of-fit in a satisfactory manner, researchers frequently rely for validation only on visual inspection of graphs comparing measured data with model predictions. For example, Shashua-Bar et al. [15] present only figures showing air temperature predicted using the original CTTC model compared with observed values at a rural location during two 24-h periods, in winter and summer. These figures, which are intended to be an indication of the quality of the model, are then followed by figures (drawn to a different scale) showing the difference between the base temperatures calculated by the two versions of the model— which are then claimed to be an indication of the error resulting from the use of the modified CTTC model. The authors do not give a table showing the actual results of the simulation, nor do they provide any statistical analysis of the predictions. However, if the size of the error in prediction is measured
Fig. 1. Comparison of the error in prediction of air temperature using the Swaid–Hoffman version of the CTTC model and the error claimed to result from using a varying reference temperature, for July data (a) and January data (b). All data obtained graphically from Shashua-Bar et al. [15] (Figs. 1 and 2).
directly from the graph – admittedly a very crude method – it appears to be almost identical to the difference between the base temperatures, also obtained graphically. The correlation between the two parameters is shown in Fig. 1a and b. It therefore appears that the methodology suggested in the paper by Shashua-Bar et al. [15] to evaluate the difference between the models inadvertently shows that the error in prediction of the original CTTC model is due almost entirely to an invalid assumption of a constant base temperature. 4. Validating the revised CTTC model of Elnahas and Williamson The performance of the revised CTTC model (and a later variant, URBANm) was evaluated using experimental data from
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
1019
Fig. 2. Aerial photograph of central Adelaide showing location of monitoring sites.
two separate monitoring studies carried out in Adelaide in 1993 and 2000 [12–14]. Details of the second of these studies are given in brief in the following paragraphs, followed by a graphic representation of the results of this experiment and performance statistics for the model. In the study carried out during the year 2000, welldocumented and comprehensive meteorological measurements were made at two urban street canyons within the City of Adelaide for a period of nearly a year. These data were compared with data recorded concurrently at a reference site at the Adelaide City Council Nursery, north of the Torrens River, and with records provided by the Bureau of Meteorology from the Kent Town station, which is located about 1.5 km east of the urban sites. The reference site is located in a green belt surrounding the central business district of Adelaide, approximately 2.1 km northeast of the city centre. The urban sites are two relatively narrow streets about 0.5 km from the centre of the business district, and about 1.5 km southwest of the reference site, one with a north–south axis and the other with an east–west one. Fig. 2 shows an aerial photograph of central Adelaide, highlighting the test sites. The area as a whole comprises the core of the Adelaide metropolitan area, which extends about 20 km east–west from the Gulf of St. Vincent to the Adelaide Hills, and about 25 km from north to south. Data recorded directly, representing the whole of the study area, included global solar radiation, diffuse solar radiation and net all-wave radiation. At the reference station dry bulb temperature, relative humidity, wind speed and direction and soil temperature were monitored. At the urban sites air temperature was recorded at several points in each street (Fig. 3), as well as relative humidity, wind speed and direction and mean surface temperature of the road surface (by IR sensing). Evaluation of the performance of the model was carried out by comparing the predicted air temperature at the urban street canyon with measured air temperature, using data from the
Fig. 3. Urban street canyon monitoring site (location of five temperature sensors highlighted by circles).
reference site as inputs to the revised CTTC model. Fig. 4 shows results for a period of 1 week during May 2000. The period displayed includes several days of generally fine weather, conducive to the formation of a substantial nocturnal urban heat island, followed by cool, windy and overcast conditions. Visual inspection of the graph shows what appears to be fairly good agreement between predicted and observed air temperatures over the entire period. Confidence in the performance of the model is given further support when basic descriptive statistics are assembled that compare the predicted and observed air temperature over the course of an entire month (Table 1). All of the measures indicate
Fig. 4. Performance of the modified CTTC model: observed dry bulb temperature of the air at the reference site, and the observed and predicted temperatures at the urban site. Data from Adelaide experiment, May 22–27, 2000.
1020
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021
Table 1 Descriptive statistics for 1 month of hourly data, showing air temperature measured in a reference meteorological station and in an urban street canyon in Adelaide, Australia, during May 2000, and air temperature in the street predicted using the revised CTTC formulation
Mean monthly Standard deviation Mean daily maxima Mean daily minima Absolute monthly maxima Absolute monthly minima
Reference (observed)
Urban Observed
Predicted
12.5 3.8 17.3 8.1 22.4 4.2
14.9 2.6 18.0 12.4 22.6 8.0
15.3 2.9 18.9 12.3 23.7 8.1
Table 2 Goodness-of-fit statistics for 1 month of hourly data, comparing air temperature in an urban street canyon predicted using the revised CTTC formulation with temperature observed in Adelaide, Australia, during May 2000 Statistic
Value
Total number of hours Mean error Standard deviation MSE Systematic MSE Unsystematic MSE Willmott index Theil’s inequality coefficient Degree of confirmation
742 0.42 1.36 2.02 0.18 1.84 0.93 0.05 0.60
that air temperature predicted using the revised CTTC model is a much closer approximation of actual air temperature in the street canyon than are measurements carried out at the reference station. (These were, in turn, very similar to data recorded at the weather station operated by the Australian Bureau of Meteorology.) Not only is the mean monthly temperature predicted accurately – 14.9 8C compared with 15.3 8C measured at the urban canyon and 12.5 8C at the reference site – but mean daily minima and maxima for the 31-day period are predicted with an accuracy of better than 1 8C, too. Finally, statistical goodness-of-fit tests also support the claim that the revised CTTC model is in fact capable of producing a useful approximation of air temperature in an urban street canyon, subject to the restrictions on its application noted in the original papers. As Table 2 shows, in addition to displaying a small error of prediction, the predicted and observed values of air temperature have a high Willmott index of agreement (0.93) and a fairly high Williamson degree of confirmation (0.60). The impression given by visual inspection of the graph (Fig. 4) and by the descriptive statistics is therefore also supported by rigorous statistical goodness-of-fit tests.
exposition that is based on a constant base value. This conclusion is supported by the results of the monitoring experiment carried out in Adelaide, described in Section 4. The promising results obtained with the revised CTTC model suggest that the basic methodology adopted, namely calculation of micro-scale climate modifications to a representative mesoscale base, may provide a practical means of predicting sitespecific air temperature data from measured data at a regional meteorological station. The model is predicated on the proposition that the properties of the mixed layer above the urban canopy layer are, on the average, uniform over an area in which both the reference station and the urban canyon are located. It is not applicable in its present form where this condition cannot be met, for example, where there are substantial differences in the meso-scale properties of the sites such as topography, elevation, distance from a large body of water, etc. The revised CTTC model, in common with many models of the urban microclimate, is also restricted by the assumption that net advective heat transfer within the urban area is negligible. It is clearly applicable where building density, typology and ground cover in the source area for energy fluxes are approximately homogeneous. However, measurements made in the urban sites as part of this research suggest that the presence of urban parks or large variations in building height and street sections in the source area of the airflow advected to them may have only a minor effect on canyon air temperature. There is need for further field research to establish the magnitude of the effect on canyon air temperature of such meso-scale features, taking into account their distance from the street in question, the direction of the wind and the intensity of the fluxes. Subsequent work by the authors to develop a robust urban climate model, while maintaining the same basic overall approach, has in fact abandoned the CTTC methodology of describing the heat flux and storage characteristics of the canyon surfaces in favour of well-documented parameterisations presented in the climatological literature that include both sensible and latent heat exchanges. Performance evaluation of a model incorporating these parameterisations [20] gives further support to a modelling approach based on a dynamic base temperature that is constantly updated to reflect changes in meso-scale weather. Many building codes and professional design handbooks currently in use already account for urban effects on the microclimate, typically the wind field. None of them currently suggest a methodology that can give a quantitative estimate of the magnitude of the modification of air temperature, in spite of widespread evidence of this phenomenon, typically in the form of an urban heat island. The revised CTTC model provides a basis for the development of such a methodology. References
5. Discussion and conclusion The theoretical analysis in Section 2 suggests that the description of the CTTC model in terms of a base temperature that is updated at regular intervals to reflect changing weather conditions may have substantial advantages compared with an
[1] E. Erell, Predicting air temperature in city streets on the basis of measured reference data, Ph.D. Thesis, School of Architecture, Landscape Architecture and Urban Design, The University of Adelaide, Adelaide, 2005, p. 161. [2] N. Sharlin, M.E. Hoffman, The urban complex as a factor in the airtemperature pattern in a Mediterranean coastal region, Energy and Buildings 7 (1984) 149–158.
E. Erell, T. Williamson / Energy and Buildings 38 (2006) 1015–1021 [3] H. Swaid, M.E. Hoffman, Prediction of urban air temperature variations using the analytical CTTC model, Energy and Buildings 14 (1990) 313–324. [4] H. Swaid, Nocturnal variations of air-surface temperature gradients for typical urban and rural surfaces, Atmospheric Environment 25B (3) (1991) 331–341. [5] H. Swaid, M.E. Hoffman, Climatic impacts of urban design features for high and mid-latitude cities, Energy and Buildings 14 (1990) 325–336. [6] H. Swaid, The role of radiative-convective interaction in creating the microclimate of urban street canyons, Boundary-Layer Meteorology 64 (1993) 231–259. [7] H. Swaid, Urban climate effects of artificial heat sources and ground shadowing by buildings, International Journal of Climatology 13 (1993) 797–812. [8] H. Swaid, Numerical investigation into the influence of geometry and construction materials on urban street climate, Physical Geography 14 (4) (1993) 342–358. [9] L. Shashua-Bar, M. Hoffman, Vegetation as a climatic component in the design of an urban street: an empirical model for predicting the cooling effect of urban green areas with trees, Energy and Buildings (2000) 221–235. [10] L. Shashua-Bar, M. Hoffman, The Green CTTC model for predicting the air temperature in small urban wooded sites, Building and Environment 37 (2002) 1279–1288. [11] L. Shashua-Bar, M. Hoffman, Geometry and orientation aspects in passive cooling of canyon streets with trees, Energy and Buildings 35 (2003) 61–68. [12] M.M. Elnahas, T.J. Williamson, An improvement of the CTTC model for predicting urban air temperatures, Energy and Buildings 25 (1997) 41–49.
1021
[13] T.J. Williamson, E. Erell, Thermal performance simulation and the urban micro-climate: measurements and prediction, in: Proceedings 7th International IBPSA Conference, Rio de Janeiro, Brazil, (2001), pp. 159–165. [14] E. Erell, T. Williamson, Predicting air temperatures in the urban canopy layer from measured reference data, in: Proceedings 19th PLEA International Conference—Design with the Environment, Toulouse, France, (2002), pp. 145–152. [15] L. Shashua-Bar, H. Swaid, M. Hoffman, On the correct specification of the analytical CTTC model for predicting the urban canopy layer temperature, Energy and Buildings 36 (2004) 975–978. [16] C.J. Willmott, On the validation of models, Physical Geography 2 (2) (1981) 184–194. [17] C. Willmott, Some comments on the evaluation of model performance, Bulletin American Meteorological Society 63 (11) (1982) 1309–1313. [18] C. Willmott, S. Ackleson, R. Davis, J. Feddema, K. Klink, D. Legates, J. O’Donnell, C. Rowe, Statistics for the evaluation and comparison of models, Journal of Geophysical Research 90 (5) (1985) 8995–9005. [19] T.J. Williamson, A confirmation technique for thermal performance simulation models, in: Proceedings Building Simulation’95, Madison, WI, USA, (1995), pp. 268–275. [20] E. Erell, T. Williamson, The CAT model: predicting air temperature in city streets on the basis of measured reference data, in: Proceedings ‘‘Contexts of Architecture’’, the 38th Annual Conference of the Architectural Science Association, ANZAScA and the International Building Performance Association, Australasia, Launceston, Tasmania, Australia, (2004), pp. 210–215.