Wind calculation model (Heat Stress Overlay)

Frontal surface and average obstacle heights are both parameters for the wind translation to 1.2 meters above ground.

The wind speed on street level (1.2 meter) is calculated using a translation of the 10 meter wind speed measured at a weather station. A single reduction field per wind direction can be calculated, which in turn can be multiplied with the 10 meter wind speed to obtain the wind speed at street level. The calculation model is based on the McDonald (2000) method for wind in cities. It uses the vertical surfaces of buildings perpendicular to the wind direction to determine in what way the wind speed is slowed down. The DPRA Heat stress report has extended this method with perpendicular vertical tree surfaces as well.

Implementation

The calculation implemented in the Tygron Platform differs from the implementation described by the DPRA Heat stress report. Specifically, rather than performing the described cubic interpolation from coarse grids to more detailed grids, all operations are done on a detailed grid.

Averaging window

Main article: Average calculation model (Heat Stress Overlay)

Average wind speed is calculated across a larger area. The window for averaging is established based on wind speed and direction. For slow wind speeds (below 1.5m/s), a window of 175x175m is used. For high wind speeds, a window of 280x140m is used.

Per grid cell

Per grid cell in the averaging window:

1. Determine the average obstacle height for buildings and trees higher than 2 meters, using a minimum value of 4 meters.
2. Determine the average vertical building surface perpendicular to the wind direction, divided by the number of cells in the strip.
3. Determine the frontal surface compactness factor $\lambda$, separately for buildings and trees. Combine these to obtain ${\lambda }_{cor}$.
4. Determine the average height of trees, with 4 meters as minimum value.
5. Using these values, select the correct formula parameters from the McDonald 2000 table for $d$, $z_w$, $z_0$, $A$ and $B$
6. Using the obtained parameters, calculate the wind translation factor.
7. Obtain the wind speed at $u_{1.2}$ by multiplying the wind translation factor with the $u_{10}$ measured at the weather station. Since the wind speed can still be too low, apply a correction formula to $u_{1.2}$ to obtain the end result.

Determine average object height

For each cell in the wind direction window the average obstacle height of the buildings and foliage are calculated. Only foliage and buildings with a minimum height of 4.0 meters are taken into account. If no obstacles were present, the average height will still be at the minimum of 4 meters.

$H_{obstacles}=\frac{\sum _{c=0}^n\sum _{r=0}^m(H_{r,c}>2.0)\cdot \max (H_{r,c},4.0)}{\sum _{c=0}^n\sum _{r=0}^m(H_{r,c}>2.0)}$

Determine average vertical surface perpendicular to wind direction

Evaluated horizontal slices from top to bottom, for a wind window of a wind coming from the west

For each strip in the direction of the wind:

Check if the height of buildings is higher than the previous cell:

  if $H_{curr}>H_{prev}$ and $H>2.0$
     $S_{frontal}=S_{frontal}+(H_{curr}-H_{prev})\cdot w_{cell}$
  $H_{prev}=H_{curr}$

where: $w_{cell}$ is the width of a cell. So we only calculate additional heights.

Next, divide $S_{frontal}$ by n, the amount of cells visited to obtain $\lambda$.

${\lambda }_{buildings}=S_{frontal}/n_{cells}$

For ${\lambda }_{foliage}$ the same process is repeated, but then with foliage heights instead of Building heights.

Determine the combined frontal surface compactness factor

First, calculate ${\lambda }_{buildings}$ and ${\lambda }_{foliage}$ in a similar way, described in step 2.

Next, calculate the ${\lambda }_{cor}$ using the ${\lambda }_{buildings}$ and ${\lambda }_{foliage}$.

${\lambda }_{cor}=0.6\cdot {\lambda }_{buildings}+0.3\cdot {\lambda }_{foliage}+0.015$.

Determine average tree height

Calculate the average obstacle height $H$, where a minimum height threshold of 4 is used. This means it is always at least 4 meters high.

Select applicable formula parameters from McDonald 2000 table

Select the function parameters $d$, $z_w$, $z_0$, $A$ and $B$ from the table using $H$ and ${\lambda }_{cor}$:

${\lambda }_{cor}$	$\frac{d}{H}$	$\frac{z_w}{H}$	$\frac{z_0}{H}$	$\frac{A}{H}$	$B$
0.05 (<0.08)	0.066	2	0.048	-0.35	0.56
0.11 (<0.135)	0.26	2.5	0.071	-0.35	0.50
0.16 (<0.18)	0.32	2.7	0.084	-0.34	0.48
0.20 (<0.265)	0.47	1.5	0.08	-0.56	0.66
0.33 (>=0.265)	0.57	1.2	0.077	-0.85	0.92

Calculate wind translation factor

Calculate the translated intermediate wind speeds:

$u_{zw}=u_{60}\cdot \frac{\ln (\frac{z_w-d}{z_0})}{\ln (\frac{60-d}{z_0})}$

$u^{*}=0.4\cdot \frac{u_{60}}{\ln (\frac{60-d}{z_0})}$

$u_H=\frac{-u^{*}}{B}\ln \frac{A+B\cdot z_w}{A+B\cdot H}+u_{zw}$

$u_{1.2}=u_H\exp (9.8\cdot {\lambda }_{cor}\cdot (\frac{1.2}{H}-1))$

where:

$z_w$ is the roughness sub layer height.

$z_0$ is the reference roughness height.

$d$ is the displacement height.

$u_{zw}$ is the calculated wind speed at the top of the roughness layer.

$u_{60}$ is the measured wind speed at 60m.

$u^{*}$ is the friction velocity.

$A$ is the wind interpolation parameter A from the table above.

$B$ is the wind interpolation parameter B from the table above.

$u_H$ is the calculated wind speed at building roof height.

${\lambda }_{cor}$ is the corrected frontal area density.

$u_{1.2}$ is the calculated average wind-profile at stress level.

Obtain final corrected wind speed

The obtained wind speed $u_{1.2}$ can be too low. Therefore it is corrected with the following formula:

$u_{1.2corr}=u_{10}\cdot ((u_{1.2}-0.0796)\cdot 0.9175+0.1254)$

This corrected value is used in the formula for PET.

Improved wind model

The roughness of the frontal surface influences wind speed, which in turn affects Heat. In the original DPRA Heat stress report, the frontal surface is estimated using simplified tree shapes that are aggregated into large woodland/forest polygons.

• 
  Trees combined in single forest polygon
• 
  Same trees as individual spaced polygons

However, the model was not designed for, and cannot always be applied to, situations that use very detailed foliage data. For example when using AI-detected polygons for individual trees the estimated frontal surface can become excessively large (when there is a small single cell gap between tree foliage). Although the original model acknowledges this issue and compensates with a 0.3 surface density λ (see page 95 of the report), this can still lead to unrealistic outcomes: wind speed is reduced too much and Heat increases around wooded areas, due to the impact of frontal surface area in the formula: $S_{frontal}=(H_{curr}-H_{prev})\cdot w_{cell}$

To address this issue, a WIND_DECLINE_ANGLE of e.g. 45 degrees can be applied to smooth the wind flow, leading to a more accurate representation of the frontal surface and producing more realistic values in wooded areas or parks with individual tree polygons.

DPRA: Wind has full impact ($S_{frontal}$) on next tree even when distance between them is a single cell.

DPRA Improved: Wind impact ($S_{frontal}$) on next tree is reduced producing more realistic results.

Note that this value has a minimal impact on large woodland/forest polygons or connecting tree foliage because all trees then become a single entity without space between them. This has been verified by comparison in the Benchmark project showing average of only 0.05 °C difference.

Notes

• The model currently only calculates the adjusted wind speeds in the 4 cardinal directions: north, east, south, west.

See also

• Wind speed result type

API Endpoints

• Api session event editor overlay set attribute

References

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Heat Stress Module

Heat Stress Module

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Foliage height • Sky view factor • Shade • Average vegetation and sky view factor

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Calculation models and formulas • Feature attributes • Model attributes • Result types