Daytime Thermal Anisotropy of Urban Neighbourhoods: Morphological Causation
"> Figure 1
<p>Conceptual diagram elaborating the indirect and direct factors that drive and modulate effective thermal anisotropy, and their relatedness. * The only “indirect” factor that affects facet-sky (or sensor-facet) view factors; ** Effective thermal anisotropy is observed by limited fields of view (FOV) sensors, in which case the facet-sky view factor distribution underlies the variation of sensor-facet view factor with sensor view angle.</p> "> Figure 2
<p>A schematic of a sensor at height <span class="html-italic">Z<sub>S</sub></span> viewing a limited domain composed of regular “urban units”. θ<span class="html-italic"><sub>max</sub></span> = maximum off-nadir viewing angle; FOV = sensor field of view.</p> "> Figure 3
<p>Directional sensor apparent (brightness) temperature of the Vancouver Light Industrial neighbourhood at ≈1300 LST 15 August 1992, for four view directions at an off-nadir view angle of 45°. Observed (obs) temperature median and interquartile range of all images during the flight are shown, as well as “Temperatures of Urban Facets in 3-D” (TUF3D)-Surface–sensor–sun Urban Model (SUM) temperature with and without small scale structure (6% and 12% refer to the plan area coverage of small scale structures).</p> "> Figure 4
<p>Example TUF3D domains for two λ<span class="html-italic"><sub>p</sub></span> and <span class="html-italic">H/L</span> ratios, showing (approximately) the range of geometries considered.</p> "> Figure 5
<p>Example polar plots of TUF3D-SUM simulated effective anisotropy, for two neighbourhood geometries (top row: λ<span class="html-italic"><sub>P</sub></span> = 0.32, <span class="html-italic">H/L</span> = 0.4, <span class="html-italic">H/W</span> = 0.6; bottom row: λ<span class="html-italic"><sub>P</sub></span> = 0.31, <span class="html-italic">H/L</span> = 1.6, <span class="html-italic">H/W</span> = 2.0) and three street directions, at 1200 LST 21 June at a latitude of 60° (solar zenith angle = 36.5°). Concentric circles are, from center, off-nadir angles of 5°, 15°, 25°, 35°, and 45°. Labelled radial lines refer to azimuthal angle. The vertex of the black, bold “<b><</b>” indicates the position of the sun.</p> "> Figure 6
<p>Maximum anisotropy (<b>left</b>) and maximum difference from nadir (<b>right</b>) as a function of geometric ratios <span class="html-italic">H/L</span> and λ<span class="html-italic"><sub>P</sub></span>, for 1200 LST 21 June at latitudes 30° (<b>a</b>,<b>b</b>) and 60° (<b>c</b>,<b>d</b>). Values are averaged over all street orientations. Dashed, numbered lines are building height to street width ratios (<span class="html-italic">H/W</span>).</p> "> Figure 7
<p>Maximum anisotropy as a function of building height to street width ratio <span class="html-italic">H/W</span> for all latitudes and hours 1200–2000 LST (inclusive) on 21 June. Values are averaged over all street orientations.</p> "> Figure 8
<p>Maximum anisotropy (<b>a</b>) and maximum difference from nadir (<b>b</b>), both divided by forcing shortwave radiation (<span class="html-italic">K↓</span>) and canopy area (1 − λ<span class="html-italic"><sub>P</sub></span>), as a function of canyon height-to-width ratio. Median values with interquartile range (error bars) are plotted for each <span class="html-italic">H/W</span>. Slopes of best fit lines for <span class="html-italic">H/W</span> ≤ 1.25 (in red) are 0.011 and 0.008, respectively, with <span class="html-italic">R</span><sup>2</sup> values of 0.93 and 0.94, respectively. Constant values (dashed horizontal red lines) for 1.25 < <span class="html-italic">H/W</span> < 4.0 are 0.014 and 0.010, respectively.</p> "> Figure 9
<p>Total view factor from SUM sensor to roads and walls for <span class="html-italic">T<sub>B</sub></span><sub>,<span class="html-italic">max</span></sub> and <span class="html-italic">T<sub>B</sub></span><sub>,<span class="html-italic">min</span></sub> view angles as a function of <span class="html-italic">H/W</span> for six solar zenith angle ranges (data from all latitudes and all hours between 1200 LST and 2000 LST, inclusive). Median (symbols) and interquartile range (error bars) for each value of <span class="html-italic">H/W</span> are plotted for clarity.</p> "> Figure 10
<p>Mean temperature difference from nadir view as a function of <span class="html-italic">H/W</span> for three off-nadir angles (ONA), over four solar zenith angle ranges. Model output is for 1200 LST and 1800 LST for all latitudes.</p> "> Figure 11
<p>Diurnal evolution of TUF3D-SUM predicted maximum anisotropy (Λ) for four Local Climate Zones on 21 June. Solid lines indicate default material properties for each zone and the average of the anisotropy for each street orientation (<span class="html-italic">i.e.</span>, full regularity of street orientation). (<b>a</b>) Latitude = 30°, anisotropy derived from a neighbourhood with equal coverage of all street orientations, <span class="html-italic">i.e.</span>, no regularity of street orientation (dotted lines); (<b>b</b>) latitude = 30°, anisotropy derived from neighbourhoods with identical material properties (dash-dot lines); (<b>c</b>) latitude = 60°, anisotropy derived from a neighbourhood with equal coverage of all street orientations, <span class="html-italic">i.e.</span>, no regularity of street orientation (dotted lines); (<b>d</b>) latitude = 60°, anisotropy derived from neighbourhoods with identical material properties (dash-dot lines).</p> ">
Abstract
:1. Introduction
1.1. Neighbourhood-Scale Thermal Anisotropy
1.2. Observations of Urban Effective Thermal Anisotropy
1.3. Modelling Urban Effective Thermal Anisotropy
1.4. Objectives and Degrees of Freedom
2. Defining Effective Thermal Anisotropy
3. Model Linkage and Evaluation
3.1. Coupling TUF3D and SUM Models
3.2. Sampling the TB Distribution
3.3. Model Evaluation: Vancouver Light Industrial Site
4. Effects of Urban Geometry on Anisotropy: Simulation Design
Arrays of Buildings with Square Footprints
5. Effects of Urban Geometry on Anisotropy: Results and Discussion
5.1. Variation of Anisotropy With Neighbourhood Geometric Structure
5.2. Geometric Causation of Anisotropy
5.2.1. Anisotropy as a Function of Canopy Height-to-Width Ratio
5.2.2. Normalization of Anisotropy Magnitude
5.2.3. Facets Contributing to Anisotropy
5.3. Sampling Anisotropic Distributions: Maximum Off-Nadir Angle
6. Anisotropy of Common Neighbourhoods: Local Climate Zones
6.1. Effects of Neighbourhood Regularity: Street Orientation
6.2. Effects of Material Property Variability
7. Conclusions
- Urban effective anisotropy depends strongly on solar elevation and irradiance. It is increased for smaller solar zenith angle and greater irradiance. When normalized by solar irradiance (or roof surface temperature), anisotropy magnitude is independent of solar zenith angle.
- Urban effective anisotropy depends strongly on urban morphology, in particular, the ratio of building height to street width (H/W). It is maximized for H/W ≈ 1.5–3.0, and within this range it is greater for tall, moderately-spaced buildings than for shorter, closely-spaced buildings. Normalizing anisotropy magnitude by canyon (non-building) plan area (1 – λP) removes this dependence on building shape and spacing, strengthening the relation between anisotropy and H/W.
- Modelled effective thermal anisotropy increases linearly as a function of H/W for H/W < 1.25 (approx.), with a slope that depends on maximum sensor off-nadir angle. For a maximum off-nadir angle of 45°, modeled anisotropy magnitude (in K) is Λ = 0.011 K↓ (1 – λP) H/W over this range of H/W, where K↓ is solar irradiance on a flat surface in W·m−2. This is considered a minimum estimate of anisotropy magnitude for real urban neighbourhoods because small scale structure, tree crowns and other neighbourhood features are neglected.
- Variation of minimum brightness temperature with H/W controls the dependence of anisotropy on H/W more than the corresponding variation of maximum brightness temperature. Cool shaded walls are critical to production of anisotropy for H/W < 3.0.
- Compact and high-rise zones generate greater anisotropy than an “open low-rise” (e.g., suburban) zone. With lower solar elevation angles (i.e., higher latitude), the difference is reduced: the “open low-rise” zone changes little, while the compact and highrise zones’ anisotropy is reduced.
- Regularity of street orientation increases anisotropy. For this limited sample of solar angles and urban geometries, it represents 3%–31% of anisotropy magnitude depending on morphology and time of day (solar elevation).
- Building shape and density, i.e., urban morphology, more strongly modulate anisotropy than material radiative and thermal properties.
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
FOV | Field of view |
TUF3D | Temperature of Urban Facets in 3-D |
SUM | Surface–sensor–sun Urban Model |
AVHRR | Advanced Very High Resolution Radiometer |
MODIS | Moderate-resolution Imaging Spectroradiometer |
LST | Local solar time |
LCZ | Local climate zone |
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Krayenhoff, E.S.; Voogt, J.A. Daytime Thermal Anisotropy of Urban Neighbourhoods: Morphological Causation. Remote Sens. 2016, 8, 108. https://doi.org/10.3390/rs8020108
Krayenhoff ES, Voogt JA. Daytime Thermal Anisotropy of Urban Neighbourhoods: Morphological Causation. Remote Sensing. 2016; 8(2):108. https://doi.org/10.3390/rs8020108
Chicago/Turabian StyleKrayenhoff, E. Scott, and James A. Voogt. 2016. "Daytime Thermal Anisotropy of Urban Neighbourhoods: Morphological Causation" Remote Sensing 8, no. 2: 108. https://doi.org/10.3390/rs8020108