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Validating measurements at De Middelste Molen

Validating measurements at De Middelste Molen by Victor Reijs is licensed under CC BY-NC-SA 4.0

Introduction

• Conclusions
• References
• Acknowledgements

GIS functionality was build using R, Excel and VBA functions (to determine windspeed&direction, z₀, a resolution of a 10deg windrose; based on some 6 speed factor formula to determine windloss).

Meteorological station KNMI-Cabauw info

In general

Looking at Benschop [2005b Chapter 3] the conditions of meteorological stations should be:

• The roughness z₀ should be < 0.5 m in all directions. This condition implies a shelter factor SF [Shelter Factor aka 'my' speedfactor] of < 1.2 (less than 20% reduction of the average wind speed).
• The distance from the wind mast to any obstacles in the vicinity must be at least ten times and preferably twenty times the height of the obstacle (applies to all obstacles).
• The terrain in the immediate vicinity of the wind mast (radius ≥ 100 metres around the measurement site) is flat grassland or a water surface.

KNMI-Cabauw

Location: WGS84 (Latitude 51.97028827, Latitude 4.92618799); Rijksdriehoeksstelsel (X 123320, Y 442530)
DSM data (AHN4: R_38EZ1.tif)
The wind direction and speed are provided at the reference height of 10m.
Windspeed and direction at KNMI Cabauw

Evaluation of z₀

KNMI-Cabauw stands in between open and roughly open environment [Davenport, 2000]. So a likely z₀=0.05m.

Using average wind (>=5m/sec@10m) and gust speeds (hour averaged) and a minimum of 20 measurements in each direction sector [Beljaars, 1987, page 17] at Cabauw [Benschop 2005b Chapter 1 & pers. comm. van der Meulen, 2025] we get an z₀ with an average around 0.20m (during leafed period: May-September):

The z₀ is also determined by using the DSM/GIS data (800*800m) around KNMI-Cabauw (some artefacts [guy cables, measurement platforms, errors, parallax] around the KNMI-mast were removed); we get the following picture:

The high z₀ at 40deg, 100deg and 150deg are caused by high trees rows at 8m@330m, 11m@380m and 6m@360m.
This gaves an average z₀ of around 0.08m (in the graph 3*z₀[m] has been depicted as a percentage).

At this moment the z₀ derived from the gust speeds is used: z₀=0.2m.

De Middelste Molen info

Location: WGS84 (Latitude 51.96589782, Longitude 4.87169194); Rijksdriehoeksstelsel (X 119574, Y 442066)
DSM data (AHN4: R_38BZ2.tif)

The height of the anemometer (wind speed and direction) is around 16m from the field level (sail tip from ground: 0.5m + sail length:13.5m + anemometer on finial [makelaar] related to poll end [askop]: 2m).

A compasite view from behind the finial, towards the open landscape over the ridgeboard [vorstplank]) (right click to see the full picture):

Evaluation of z₀

De Middelste Molen is in a open environment. So a likely z₀=0.03m.

The z₀ is determined by using the DSM/GIS data (800*800m) around De Middelste Molen, we get the following picture:

The larger z₀ at 120deg (0.24m) and 315deg (0.08m) are due to the pumping station&house (8m@100m) and house (5m@25m) near the mill.
When removing these peaks an average z₀ of 0.03m is seen (in the graph 10*z₀[m] has been depicted as a percentage).

Alignment error at De Middelste Molen

Photometric method

Below needs to be measured on site.

Wind speed

As the wind speed is referenced to a height of 10m, we need to determine the speed at the mill's anemometer height (which is 16m) to be able to compare like with like.

It is assumed the average roughness length at meteorological stations is z_0a=0.2m and assuming the average roughness length at the mill's anemometer is z_0m=0.03m. Looking at the panorama's at each location, the mill's will likely have a lower z₀.

The speed at anemometer height (16m) will have an additional increase of [Beljaars, 1979, page 4]:
u_shaft=u₁₀*(ln(60/0.2)/ln(10/0.2))*(ln(16/0.03)/ln(60/0.03)) = u₁₀* 1.08

Wind direction

KNMI: https://daggegevens.knmi.nl/klimatologie/uurgegevens
OpenMetero: https://open-meteo.com/en/docs/historical-weather-api?latitude=51.970242&longitude=4.926193&start_date=2024-05-01&end_date=2024-09-30&hourly=wind_speed_10m,wind_direction_10m

Wind roses

The wind roses for Cabauw and De Middelste Molen have been derived from KNMI-Cabauw (in pirinciple only for location Cabauw) and OpenMeteo (the same for both locations as they are within the OpenMeteo grid resultion of 9km) data:

Sanitising the smartmolen database

• rows with a wind speed below 1.5m/sec (1Bft) and higher than 13.9m/sec (7Bft) are removed
  
• rows that have an MILL_ORIENTATION_CONFIDENCE of lower than 20 are removed
  
• remove rows with an absolute direction angle difference between De Middelste Molen and meteorolocal station/OpenMeteo of larger than 90 degrees.
  

Analysis of the measurements

Comparing with De Middelste Molen

Wind speeds

The wind direction of the meteorological stations can be seen below with the wind direction at De Middelste Molen mill on the x-axis (for 1Bft upto and including 7Bft). The meteorological station's speeds have been compensated for the height of the anemometer.

Speed comparison at the mill cap

Expectations

What is to be expected when looking at the wind speed effects around the anemometer, which is some 2m above the mill cap? The wake will have influence, by increasing or decreasing the windspeed at the anemometer. The following effects could happen (negative angle of attack [AoA] means a backed wind and positive AoA means veered wind):

• If the wind comes from the back (AoA lower -150 or higher than150deg).
  It is expected that the wind speed of the meteorological station will be similar (close to 100%) to the anemometer's if wind is from the NNE to SSW; or the meteorological station's could be higher than the anemometer's if the wind comes over the town (SSW to NNE).
  This situation is not happening in reality a lot. In the below analysis this is could not be checked, as there were not enough measurements for this situation.
  
• If the wind comes from the front (AoA between -30 and 30deg).
  It is expected that the wind speeds of the meteorological station will be higher or smaller than at the anemometer's if wind is from the NNE to SSW. The higher or smaller depends on the effect of the wake due to the mill cap (see also). The meteorological station's speed would likely be higher than the anemometer's if the wind comes over the town (SSW to NNE).
  This situation happens a lot.
  
• If the wind comes from the side (AoA between -45 and -135deg or between 45 and 135deg).
  This will have an in between effect of the earlier two bullets.
  This situation happens a lot between 45 and 105deg or -45 and -105deg. In the below analysis angles outside this range could not be checked, as there were not enough measurements for that range.

Evaluation

1. The utilised z₀ for the mill and the meterological statiosn need to be as close as possible to reality.
• The recommendation for meteorogical stations is in general z₀<0.5m [Benschop, 2005, chapter 3], the z₀ for HERW was determined using this method, and was around 0.26m.
2. The accuracy of the anemometer is around 5%.
3. The anemometer might be in the wake of the mill cap; this would introduce a higher or lower wind speed, depending where the anemometer is in the wake.
   Rijn en Lek's anemometer is at a height of 1.09*H_cap, it is not 100% sure what would happen at this height, will it reduce or increase the wind speed.
   To be verified with a CFD of the mill-body.

Conclusion???

Wind direction

The relative wind direction of the meteorological stations can be seen below (relative to the wind direction at De Middelste Molen mill). The meteorological station's directions have been compensated for the average winds direction in winter. De Middelste Molen wind direction (on x-axis) has been compensated for the alignment error.
The distribution of directions can be seen below:

The standard deviation of relative meteorological stations' direction is some ???deg. Assuming that the standard deviation of the meteorological stations' and anemometer's wind direction are similar, they are both around 15deg.

Matching mill anemometer readings with calculations

De Middelste Molen

The above compensated direction and wind speed data have been used. The speedfactor has been derived by dividing the De Middelste Molen (LOCAL) anemometer's wind vector by the meteorological (Carbauw and OpenMeteo) station's wind vector. From these, the (non-weighted) average speedfactor magnitude per 10deg sector has been derived.

<right click a picture, to see a larger version in another browser window>

De Middelste Molen&KNMI-Cabauw	De Middelste Molen&Open-Meteo

• Looking at the anemometer measurements
  
• Mesurements are for the period 8 November 2025 to 13 March 2026, so winter time (November upto and including March). The trees are leaveless.
• Leaved trees are between May and upto inlcuding September
  
• ???It looks that the anemometer speeds are most of the time higher than at KNMI-Cabauw. That would not have been expected.
• Non weighted sectors were used.
• The speedfactors (anmometer/meteorological) have been decreased with a scaling factor of ~??? to match somewhat the calculations.
  
• ???The wind did not blown a many times from North North West), so the uncertainty (the yellow dots around the white curve) of the Speedfactor is larger.
• ???Open-Meteo data (in Winter time) matches reasonably well with the calculations (of Summer time)
  We have around 80days of measurements, this migth not be enough to reduce uncertainty. Longer period of measuring is needed,. As we need to keep season in minds; so over multiple (2???) years.
  
• Remember there is a scale factor that mapped speedfactor on the calculations.
  
• Looking at the De Middelste Molen calculations (aVR_nag and aVR_belj)
  
• Difference between speedfactor with anemometer and the calculation is smallest for aVR_belj. So aVR_belj is being used in further analysis.
  
• Non weighted sectors were used.
  
• The trees are calculated as leafed, so summertime.
  
• Wind channeling is not covered by the calculations (one would need CFD for that).

Some conclusions

References

Acknowledgements

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