Introduction Representation in WAsP

The choice of roughness length and displacement height for forestry:A retrospective empirical studyJean-François CorbettVindKraftNet Forest Day, 15 October 2010IntroductionForest is commonly represented in WAsP as:z 0 roughness lengthd displacement heights rate at which displacement height decays with distance from forest edgewindmastzhforestahdd = ah - sxxs = ah / x 0x 0Representation in WAsPshorter mastz-dzforest z 0ground z 0

Site selectionSite 4Site 6MethodFor each siteFor each (z 0,d) schemeAdjust WAsP roughness mapFor each mast pair on siteFor each displacement height decay rate sFor initiation mast and target mast• Calculate distance to trees and resulting displacement height in 360directions.• Take 30°-average displacement height in each of 12 sectors• d = average of sector displacement heights, weighted by sector frequency.• Mast height is reduced from z to z -dNext mastWAsP calculation from initiation mast to target mast (each with displaced height)Mean wind speed difference: WAsP-calculated – MeasuredFor displacement height decay rate sNext mast pairNext (z 0,d) schemeNext site

Results: ”bad” mast pairs includedRMS errors are much largerDisplacement height decay rate has a dramatic effect: The slower the decay, the betterNo clear winner, a couple of clear losersWhat determines who wins and who loses?Comparison of canopy models ("bad" mast pairs included)RMS error on mean wind speed9.0%8.0%7.0%all mast pairs6.0%5.0%4.0%3.0%2.0%1.0%good mast pairs only0.0%0 10 20 30 40 50 60WAsP manual z0=0.4mWAsP manual z0=0.8mCurrent GHJarvis et al.GarratKaimal&FinniganESDU1/s Displacement height inverse decay rateDisplacement height and roughness length8.0%8.0%7.0%7.0%Kaimal &FinniganRMS error on mean wind speed6.0%5.0%4.0%3.0%2.0%1.0%R 2 = 0.55R 2 = 0.61R 2 = 0.32all pairs,s=1:15all pairs,s=1:50goodpairs,s=1:15RMS error on mean wind speed6.0%5.0%4.0%3.0%2.0%1.0%R 2 = 0.11R 2 = 0.13R 2 = 0.69all pairs,s=1:15all pairs,s=1:50goodpairs,s=1:150.0%0.6 0.8 1 1.2d/h0.0%0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8z0 (m) for tree height = 12.5 m

Displacement height and roughness length8.0%8.0%7.0%7.0%RMS error on mean wind speed6.0%5.0%4.0%3.0%2.0%1.0%R 2 = 0.70R 2 = 0.86R 2 = 0.53all pairs,s=1:15all pairs,s=1:50goodpairs,s=1:15RMS error on mean wind speed6.0%5.0%4.0%3.0%2.0%1.0%R 2 = 0.002R 2 = 0.05z 0independent of hR 2 = 0.30all pairs,s=1:15all pairs,s=1:50goodpairs,s=1:150.0%0.6 0.8 1 1.2d/h0.0%0.2 0.4 0.6 0.8 1 1.2z0 (m) for tree height = 12.5 mConclusionsParameterDisplacementheightdDisplacementheight decay ratesRoughness lengthz 0Best canopymodel in thisstudyOptimal for ”good” sitesmast not too low relative to treesgood info on distance to forestHigh, 0.9 to 1.0 hWeak trendSweet spot around1:15Low, 0.4 to 0.5 m or 0.03 to 0.04 hWeak trendSlight advantage when z 0proportional to h ?ESDU with s=1:15d = h – 4.3 z 0(1-λ) ≈ 0.93 hz 0= 0.033 h = 0.41 m (12.5 m trees)RMS error on MWS: 1.5%Optimal for”bad”/mixed/unknown sitesHigh, 0.9 to 1.0 hStrong trendThe slower the better1:50No trend to speak ofCurrent GH with s=1:50d = 1.00 hz 0= 0.50 mRMS error on MWS: 3.2%

ConclusionsHigh displacement and slow decay may allow for a ”hedging of bets”:Mast displacement height is less sensitive to errors on the distance from the trees.”Differential error” between initiation and target mast is reduced on average.This analysis benefits from prior knowledge of the wind regime at the target site.Without such prior knowledge, it is not quite as easy to discriminate between ”good”and ”bad” masts, and thus to determine when we should buy the costly ”high-d,low-s insurance”Can the conclusions from this study be appliedto other sites?to other ways of calculating the displacement height?Future workFinish calculations using Raupach and Choudhury canopy modelsPopulate with a few more sites – good and bad!Further explore (d/h, z 0 , s) parameter spaces = 1:100, 1:200…. 1:∞ as a tactical insurance device?Extreme hedging of bets for bad mastsCalculate a separate displacement height for each sector, apply sector-wiseWhen calculating d, include trees located immediately downwindwind

Thanks for you attention!