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Some remarks on Stephen Temple Mill Biotope spreadsheet

Some remarks on ST workflow by Victor Reijs is licensed under CC BY-NC-SA 4.0

Introduction

Background

ST workflow is bsed on the DHM formula of Werkrgoep Molenbiotoop [1982]. That formula uses the principles presented in Beljaars [1979].
The conditions are:

• As some background of the DHM formula is used, this migth also be of importance for the ST workflow.
  An important part of this is, that it assumes no obstacles within 100m (or in general 10*H, which is the length of the cavity boundary area).
  ST uses as background the DHM formula framework, but he built his own framework; which importantly was verified with real measurements.
• ABL can be logarithmic or lineair
• It determines the Intercept height at the mill of the obstacles based on the WakeDecayRatio (called by ST WakeDecayLength and it is equivalent to DHM's n). The spreadsheet of ST uses maximum 3 obtsacles, but the underlaying functions can support many obstacles.
  At the mill location the Intercept heights of the obstacles are combined, using the hightening of the ABL by these (effective by including porosity) Intercept heights. This provides the SpeedFactor for each sector (see Temple' function ABL).
• So all the influences (Intercept heights) are evaluted together for the location of the mill (no interaction between indivudual obstacles).
• There are overall multiplier for (Cd )Tree and (Cd ) House heights (effective height); to increase the aerodynamic effects of the obstacle; aka a multiplier to the drag coefficient.
  Remember this is not needed with some other methods (like DHM formul or CFD); as the effective heigth is part of the underlaying experiments/theory.
  
• The real height of the object is input parameter. The effective height (Cd) is determined in the spreadsheet.
  
• Porosity of trees has been included through C_px, which is a aerodynamic porosity coefficient ap (between 0 and 1).
  
• Speedfactor calculations (Temple, 2025, section 2.6):
• The Intercept height of each obstacle is determined (Intercept height = effective height of obstacle minus the reduction due to WakeDecayRatio and the obstacles's distance to the mill).
• height of obstacle is increased (with C_x) as the wake region effectively heightens the obstacle.
• Only obstacles that have an Intercept height higher than zero are further evaluated
• for each such obstacle, the ABL is heightened (at the location of the mill) with a 'stacking' of the Intercept heights and aerodynamic porosities (C_px); starting with the smallest Intercept height.
• this determines the speedfactor due to the obstacles.
  
  

• ST workflow additonally has a Blocking factor if the obstacle is not fully covering the wind direction sector, so the obstacle does not have to be long. It also allows for multiple adjacent rows of the 'same' obstacle (Rows).
• Real measured wind speeds at mill and meteorological station were used to verify the ST workflow.
• The calculated Speed Factors (Today) in his spreadsheet is Weighted Averaged over 3 sectors. As the standard deviation (1 sigma) of the anemometer is ~15deg, a weighted average might be better over 5 sectors, aka almost 2 sigma.
• The functionality of ST workflow is:
• evaluate the measured wind speed/direction at the mill with wind speed/direction at meteorological station (to determine actual-windfactor for summer/winter)
• model the environment around the mill with several obstacles (different types/rows) per sector (a sector is 10deg) over a 360deg wind rose
• calculate the calculated-speedfactor with the model
  
• if not calibrated yet: minimise the difference between calculated-windfactor and actual-windfactor: by varying a few parameters: effective height, porosity of trees, z_0m, z_0a, etc.
• use the model with the optimised parameters to calculate the speedfactor, loss and effective energy of the modeled before and after comparison scenarios.

Some typos/errors

• Slide Importance of the Molenbiotope in Planning
• c is slightly depending on H/z_0m. No need to include this weak dependency on H/z_0m in the first place.
• ST workflow uses c ~ (1 - Speed Factor) [aka speed loss], but it should be: c ~ (1 - Speed Factor)*3
  
• Mills data spreadsheet
  
• Slightly higher heights of obstacles have been found in first echo DSM2020 (around 12.5% higher) [Defra Data Service]
• A picture of the included houses and trees can be seen here.
  
• Mill Biotope spreadsheet (only looking at Summer related columns/cells/etc)
  
• He calls porosity Cd, while in most literature this is p (or sometimes OP [Optical porosity] or AP [aerodynamic porosity]).
  
• The conversion of meteorological station wind speeds needs to be done with a conversion formula that refers first to 60m (where we see a common windspeed regradless of z_0a); so one needs to include the z_0a of the meteorological station and the z_0m of the mill's average region. The z_0a could perhaps be determined with the method mentioned in Benschop [2005, section 2.2].
  Remark: Benschop's method seems to work for meteorological stations, but don't know if this method also works for the mill region!
  
• The ST's Excel is using functions (e.g. LET) whch is only support in Excel 365, 2021 and web. Older Excel (e.g. Micorsoft Office Professional Plus 2019) can't compute this.
  
• ST workflow is calibrated with real measurements at two mills. Thls calibration is done by varying z_0a, z_0m, C_d, C_px and n in such a way that the difference between calculated results and measured windspeeds was minimsed for two mills.
  So mainly an emperical methodology.

Optimisation of the ST workflow

Conclusions

References

Acknowledgements

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