Spatial Superposition Method via Model Coupling for Urban Heat Island Albedo Mitigation Strategies [Journal of Applied Meteorology and Climatology]
(Journal of Applied Meteorology and Climatology Via Acquire Media NewsEdge) ABSTRACT
A spatial superposition design is presented that couples the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) with the National Center of Excellence (NCE) lumped urban thermal model for application to the city of Phoenix, Arizona. This technique utilizes an approach similar to Reynolds decomposition from turbulence theory. The presented decomposition takes the NCE model prediction from a mitigated strategy as the mean temperature and the difference between the NCE and MM5 predictions without mitigation strategy as the perturbed temperature. The goal of this coupled model is to provide spatial variability when simulating mitigation strategies for the urban heat island effect, as compared with the spatially invariant lumped model. A validation analysis was performed incorporating a maximum 35% change from the baseline albedo value for the urban environment. It is shown that the coupled model differs by up to 0.39°C with comparable average surface temperature predictions from MM5. The coupled model was also used to perform analysis of three different albedo-driven spatial mitigation schemes. This resulted in the identification that having a lesser number of mitigated points on a square urban grid in Phoenix with the same average albedo leads to a greater reduction in average hourly temperature.
(ProQuest: ... denotes formulae omitted.)
There are many developed models that can be used to evaluate the spatial variability of the urban heat island (UHI), such as the Weather Research and Forecasting model (WRF; Michalakes et al. 1998) and the fifthgeneration Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5; Alapaty et al. 1995). Both of these models are continuously developed and validated (Chen and Dudhia 2001; White et al. 1999). However, they are both computationally expensive relative to simpler models such as the National Center of Excellence (NCE) model (Silva et al. 2009). This paper presents an alternative methodology to reduce computational cost by coupling our straightforward lumped urban thermal (NCE) model with a single MM5 run to superpose temperature fields (mesoscale resolution) for the greater Phoenix, Arizona, area (66 km 3 111 km). This computational speed is made possible because the coupling methodology allows a straightforward formulation instead of using extrapolation techniques (Wahab and Essa 1998), Kalman filtering (Komarov et al. 2007), Fourier integrals, or other more costly mathematical techniques to predict the unknown variables. The motivation for our proposed coupling approach is to provide a faster computational effort when compared with more comprehensive models like MM5 or WRF while being able to incorporate some aspects of the spatial distribution of the thermophysical properties (albedo, emissivity, thermal conductivity, etc.) of an urban area.
2. Superposition methodology
a. Lumped urban thermal model recap
We follow the Urban Thermal Model design of Golden et al. (2005) where energy flows for an urban volume are linked with six major components. Keeping intact the surface energy balance while simultaneously simplifying a very complex problem, one can express the following governing equation for the lumped urban temperature (Bhardwaj et al. 2006; Silva et al. 2009):
wheremis mass, c is specific heat, t is time, a is albedo,A is area, qs0ol is the incident time-dependent solar heat flux, qa0nthro is the incoming anthropogenic heat flux, qe0vap is the evapotranspiration heat flux, qc0ond is the conductive heat loss to the deep ground, qc0onv is the outgoing convective heat flux, qr0ad is the outgoing emitted radiative heat flux, and T is the characteristic temperature. Dividing through by A and transforming the formula to a finite-difference scheme ready for numerical implementation yields
where r is density and dx is the distance between the surface and the measured 50.8-cm (20 in.) ground temperature, Dt is the time step, the superscript n represents the present time step, and the superscript n 1 1 represents the future time step.
The characteristic urban temperature T (Silva et al. 2009) can be expressed as
where kgrd is the thermal conductivity of the ground, Tgrd is the ground temperature measured at a depth of 50.8 cm (20 in.) (AZMET 2009), Et0 is the measured evapotranspiration (in meters) for vegetated areas, hfg is the latent heat of vaporization for water, rH20 is the density of water, Tair(Rural) is the measured rural drybulb air temperature, hconv is the convection heat transfer coefficient, hrad is the radiation heat transfer coefficient, and Tsky is the "sky" temperature, that is, the effective temperature of the sky with respect to the emitted radiation (ASHRAE 2004). Note that the variables qn anthro, hn rad,Tn sky, and hn conv have embedded terms. Equation (3) is the model that will be applied to all analyses in this paper. All of the meteorological data needed in Eq. (3) are taken from the Arizona Meteorological Network (AZMET 2009) and the anthropogenic heat data are taken from the Energy Information Administration (EIA 2007) via the formulation from Sailor and Lu (2004). Given the explicit time discretization, numerical stability requires the imposition of the Courant-Friedrichs-Lewy (CFL) criterion on Eq. (3) (Hoffman and Chiang 2004). Collecting all terms that are multiplied by Tn and then setting the appropriate requirement and solving the resulting inequality yields
The time increment Dt of 140 s or less was found to be stable for all calculations. Most notable is that this semiempirical model was shown to correlate well with average MM5 surface temperatures for the city of Phoenix (Silva et al. 2009) and will be used in tandem with MM5 surface temperatures for the subsequent model enhancement when implementing albedo mitigation strategies. Further details about this lumped model can be drawn from Silva et al. (2009).
b. MM5 setup
For the calculations in this article, the MM5 (version 3.6) model had a 111 km 3 66 km grid, with a grid cell resolution of 1 km 3 1 km. Specifically, we extracted data from the 1998 26-category classification from work already developed (Grossman-Clarke et al. 2005). The urban categories were taken as classifications 1 (urban built-up land), 25 (urban mesic residential), and 26 (urban xeric residential) from Stefanov et al. (2001). The Phoenix metropolitan area was divided into elements and each element was given a value of 1-26 for its land cover type; see Silva et al. (2009) for further details about the element breakdown. CFL criteria for theMM5 model and the lumped model are different but equivalent points in time (interpolated linearly on the lumped model where necessary) for each model were compared for this analysis. Specific details about this version of the MM5 model can be drawn from Grossman-Clarke et al. (2005).
c. Reynolds decomposition
The foundation for this superposition approach derives its central methodology from a basic statistical concept of turbulence theory commonly known as Reynolds decomposition. Following Reynolds (1895), we can decompose a variable (temperature in this case) into a mean component and a perturbed (fluctuation from mean) component. The mean component for our coupled model is only a function of time t, while the perturbed component is a function of location x, y, and t. This mean component is computed from the lumped urban thermal model when a mitigation scheme is implemented. We will call this mean component the NCE model [Eq. (3)]. The perturbed component is simply the difference between the NCE value and an MM5-calculated surface temperature for each urban location considered when no mitigation scheme is implemented. We refer to this coupled approach of two different models as the Smodel, which stands for the superposition model. The utility of this Smodel becomes apparent when mitigation schemes are prescribed that modify the original composition of the land-cover type in a spatially nonuniform manner. Pointwise, the spatial model concept of Smodel has the following methodology:
1) First we extract a perturbation value [ ~ T(x, y)] from an MM5 surface calculation and the NCE model calculation using the following formula again when no mitigation strategy is implemented:
where T(x, y, t) is the surface temperature calculated by MM5 for a particular point in space (x, y) for each time step t considered, and T(t) is the mean characteristic value calculated at corresponding time steps t via the NCE model.
2) Now, we have a fixed perturbed temperature field ~ T(x, y) for all future mitigation-scheme-driven calculations. To calculate a new temperature value [T(x, y, t)] for some mitigation scheme at any particular point and time, we use the following formula for that point on the spatial grid being modified:
where T(t) is the newly calculated characteristic temperature via the NCE model at some particular time. Remember, T(t) is calculated using the modified composition for the specific point under consideration.
3) Finally, all T (x, y, t) are found for every unique spatial and temporal point being modified (from some UHI mitigation strategy) via Eq. (6) (effectively utilizing Reynolds decomposition a second time). Finally, these modified aggregate temperature values T (x, y, t) serve as the Smodel temperature values we present in the succeeding analysis.
The efficiency of this Smodel is made possible given that a user only has to run the surface MM5 calculation once before any mitigation scheme is enforced. Mathematically, it can be shown that the perturbed component of the Smodel is fixed in time, which is reviewed in the appendix for readers who are unfamiliar with this consequence from classical turbulence. The next section will attempt to validate this Smodel against MM5 calculations for certain mitigation strategies.
3. Smodel validation
The Smodel methodology was validated against two different datasets: 1) MM5 surface temperature for a given mitigation strategy-an increase in albedo for the built-up urban elements in this case and 2) MM5 change in surface temperature from its original temperature for the same given mitigation strategy. A typical summer day, 14 July 2003, in Phoenix was chosen for evaluation. We used the classic correlation analysis [Kreyszig 1999; Eq. (7)] where A and B are the two sets of data that are being compared and where A and B are the means (averages) of their respective datasets:
For these two dataset comparisons we wanted to choose a strategy that includes a range that is physically reasonable and also worthwhile from an urban planning perspective. The work, as shown in Silva et al. (2010), states that modifying the average albedo of the urban section of Phoenix from its original composition by a 20% increase is physically reasonable. This work also states that this mitigation strategy (increasing albedo) is the most effective when compared to an increase in thermal conductivity, emissivity, or vegetated area to achieve the greatest daily average temperature reduction. Thus, for these two dataset comparisons, we choose an increase in albedo as our mitigation strategy. Keep in mind we will go well beyond what has been shown to be physically reasonable (up to a 35% increase in baseline urban average albedo). The purpose of having the widest range of albedos is to eliminate uncertainty well beyond the physically reasonable range (up to a 20% increase in baseline urban average albedo). The original average urban albedo is aoriginal50:17 and we increase this value by approximately 35% to anew50:23 for both of these comparative analyses. Again, we incorporated the 26-category land-cover classification for Phoenix developed by Stefanov et al. (2001) for this study. The correlation value between the Smodel and the MM5-calculated surface temperature is r50.998 and the slope of the linear fit is 1.011. The associated scatterplot for the first comparison is presented in Fig. 1. The Smodel is meant to be used for UHI mitigation strategies only but we will also perform a comparison between the changes in temperature from the original composition to hopefully give additional credence to the validity of the first dataset being compared. The correlation value between the Smodel change in temperature and the MM5 change in temperature is r 5 0.999 and the slope of the linear fit is 1.006, as presented in Fig. 2. For completion we want to display a snapshot of what these different models predict for anew, as shown in Figs. 3 and 4. These spatial temperature snapshots [1500 Pacific standard time (PST)] taken roughly during the hottest part of the day, which is also the time of the greatest difference in temperature predictions for the two models, exhibit minor discrepancies. The correlation coefficient at this time for the two temperature fields is r 5 0.993. With these results we find that the Smodel is valid for an albedo mitigation strategy within a physically reasonable range increase with high confidence. To demonstrate the typical behavior differences between the two models (MM5 and the proposed Smodel), we plot their average hourly temperature curves in Fig. 5. The maximum difference between the two curves in Fig. 5 is 0.398C and their respective curves closely follow one another, again with maximum differences around the solar peak. These results exemplify that we can predict a relatively accurate average surface temperature with the Smodel, but more importantly we can predict relatively accurate average changes in temperature efficiently with the Smodel. Remember, these results occur when mitigation strategies are implemented. As stated before, the intent of the Smodel is to provide the ability to rapidly calculate the effects of UHI mitigation strategies in an approximate manner, and not to replace the forecasting capabilities of more sophisticated models such as MM5. Conclusively, we can report that the Smodel calculates a change in temperature that is validated by comparison with an MM5 prediction for urban albedo mitigation strategies.
Finally, we want to illustrate how much more time efficient the Smodel is for UHI mitigation strategies when compared to MM5. Mitigation runs are identical to each other from a model run time perspective because all that is changed is the land cover classification (preprocessed data) and requires no additional setup. Therefore, we took the total processor time for a typical summer day (14 July 2003) for both models (12 h for MM5, and 1.6 s for the Smodel) and calculating the difference of the two ('½ day) to serve as the slope of the curve. Figure 6 qualitatively shows the time saved if unique mitigation schemes were imposed. The processor architectures for the MM5 run and Smodel run were similar (;3.2 Ghz, 2 GBytes RAM). Note, however, that MM5 was run in parallel on multiple processors (six in this case) and the Smodel was run on a single processor. Figure 6 reveals that the typical wall-clock time saved by using the Smodel versusMM5 is approximately 12 h for every unique mitigation strategy for the architecture under consideration. Therefore, if we were to implement 1000 unique mitigation strategies over a 24-h period, we could typically save 500 days of total wall-clock time. Note that this is a relationship for only a single day's calculations. Thus, as temporal resolution and/or range are increased, proportionally the typical time saved (slope of the linear relationship) should also increase.
4. Smodel application
a. Spatial mitigation schemes
The next step is to demonstrate the potential utility of the Smodel as a spatial mitigation tool for the UHI effect. Also, we want to develop strategies that are realistic as well as strategies previously uninvestigated in the literature. Moreover, since the Smodel is a spatial UHI mitigation tool that provides average temperature outputs, we want to exclusively treat the urban section (or a segment of it) of the greater Phoenix area as our region of study for this work. To present schemes that are valid for use in the Smodel, we considered a contiguous urban area while maintaining the same mesoscale resolution as theMM5calculation (elements are 1 km2). Furthermore, we examined the largest urban area whose typical land cover classification already has been shown to be capable of alteration. Therefore, an urban area analogous to the urban classification makeup as in Silva et al. (2010) was chosen in which a 20% increase in baseline albedo was considered to be physically reasonable. These criteria yielded a square area (441 km2) that has universal transverse Mercator zone 12 (UTM12) coordinates of (379, 3695) in the southwest corner and (399, 3715) in the northeast corner, which is an area just west of Phoenix Sky Harbor International Airport. Continuing, we present three unique spatial mitigation strategies whose details are specified in Table 1 and Fig. 7. Scheme 1 has elements modified in a checkered distribution, scheme 2 has a block (uniform) distribution across the entire computational domain, and scheme 3 has a reduced block distribution in which the albedo is increased uniformly over a small block of elements at the center of the computational domain. None of the elements being modified in any scheme exceeds the physically reasonable albedo baseline increase. Finally, a 20% increase from baseline (0.17) yields a modified albedo value of a50:204.
Recall that the baseline albedo for all schemes is 0.17. One can easily conclude that scheme 2 will yield a greater reduction in average hourly temperature from the original composition when compared to scheme 3. This is because scheme 2 has almost twice as many elements modified and a larger area distribution. The Smodel corroborates this straightforward result as shown in Fig. 8. Next, we compare scheme 1 with scheme 3. Here, we have an equal number of modified elements and the same average albedo over the respective areas of consideration. The distributions are different for both schemes but the area of modification for scheme 1 is larger and the modified elements have higher albedo values than in scheme 3. Based on these distributions with some uncertainty, one can conclude that scheme 1 will lead to a greater reduction in average hourly temperature using the preceding statement when compared with scheme 3. Here, the Smodel assists in establishing more confidence to this conclusion (see Fig. 8). For the most compelling scenario, we compare scheme 1 with scheme 2. Here, scheme 1 has a higher modified-element albedo and scheme 2 has more modified elements. Both schemes have the same area being modified and the same average albedo over this area. Neither scheme clearly has more advantages than the other so we must consult with the Smodel results. Figure 8 shows that scheme 1 produces a greater average hourly temperature change, by almost 28C at solar peak, when compared to scheme 2. This is an important result because it is demonstrated from this scenario that reducing the number of mitigated points by nearly 50% on a square urban grid in Phoenix with the same average albedo leads to a greater reduction in average hourly temperature. From a thermophysical standpoint, this result is given credibility because scheme 1 has a 10%-higher mitigated-element albedo. Also, this result can be analytically validated via Eq. (5) by generally showing that scheme 1 has a larger temperature change. Finally, we obtain a nondimensional (normalized by scheme 1) comparison of the three schemes. Figure 9 shows that scheme 1 has almost 2 times the effect as scheme 2 and 2.5 times the effect as scheme 3 when comparing the average daily reductions in temperature.
a. General synopsis
A spatial superposition model coupling a lumped urban thermal model and MM5 is applied to the city of Phoenix. The coupled model is based on the Reynolds decomposition concept normally applied for turbulence modeling, and consists of a mean temperature component that is computed by the simple lumped model and a perturbation temperature component that must be computed by a more sophisticated model, such as MM5 in tandem with the simple lumped model. The resulting coupled model, termed the Smodel, is validated here with respect to MM5 predictions for urban albedo mitigation strategies up to a 35% increase in average baseline urban albedo. Finally, we present representative UHI mitigation schemes in which albedo is increased spatially across an urban core. These results suggest that in order to deliver the greatest reduction in average urban temperature, the best strategy is to increase the albedo in a checkered fashion, rather than to increase the albedo uniformly. Thus, the Smodel can be applied as a practical tool in helping policy makers strategize on the most effective spatial UHI mitigation scenarios by giving them quantitative comparisons of proposed schemes.
b. Concluding limitations and advantages of Smodel
The limitations of the Smodel versus more complex models are that the Smodel
1) calculates only surface temperatures,
2) requires a comprehensive atmospheric model (MM5) to be run once to compute perturbation temperatures for the aggregate initial surface temperature calculation,
3) is currently designed for elements with urban classifications implementing albedo UHI mitigation strategies with mesoscale resolution,
4) requires knowledge and validation of two different models for implementation, and
5) is intended for typical (low humidity, low wind speed) Phoenix summer days with preexisting data (it is a semiempirical model).
The advantages of the Smodel versus more complex models are that the Smodel
1) is significantly less computationally expensive (again see Fig. 6),
2) requires no modifications for UHI mitigation strategies with respect to the MM5 portion of the model,
3) is validated well beyond the physical spectrum of possible albedo UHI mitigation strategy modifications for the city of Phoenix,
4) is comparatively as numerically accurate (greater than 99% correlation) for albedo UHI mitigation strategies when compared with MM5, and
5) gives policy makers a quick and valid quantitative (average temperature) analysis for spatially variant albedo mitigation strategies.
Acknowledgments. The authors thank Patrick E. Phelan and Ronald Calhoun of Arizona State University for their edits and guidance regarding this work. Author Silva gratefully acknowledges the partial support of this work by the National Consortium for Graduate Degrees for Minorities in Engineering and Science, Inc., in the form of a GEM doctoral fellowship.
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HUMBERTO SILVA III
School for Engineering of Matter, Transport and Energy, and National Center of Excellence on SMART Innovations,
Arizona State University, Tempe, Arizona
JAY S. GOLDEN
Division of Earth and Ocean Sciences, Nicholas School of the Environment and Pratt School of Engineering,
Duke University, Durham, North Carolina
(Manuscript received 5 March 2011, in final form 29 May 2012)
Corresponding author address: Humberto Silva III, National Center of Excellence on SMART Innovations, Arizona State University, P.O. Box 875402, Tempe, AZ 85287-5402.
(ProQuest: Appendix omitted.)
(c) 2012 American Meteorological Society
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