ForWindCenter for Wind Energy Research

Optimization of the MYNN PBL scheme for windresource assessment based on comparisons to

mast and UAV measurementsHauke Wurps, Gerald Steinfeld

ForWind - Center for Wind Energy Research, Carl von Ossietzky Universität Oldenburg

MotivationAn accurate and reliable estimation ofturbulence, shear and veer is necessaryfor the prediction of wind energy produc-tion and loads on wind turbines.The upper tip height of offshore windturbines is in the order of 150 m andthus exceeds the height of currently ex-isting measurement masts (e.g. FINO1:103 m).Mesoscale model simulations can be aconvenient tool to gain information onthe wind conditions at these heights.

Mesoscale SimulationWe use the meso-scale model WRF [1]for the simulation of the lower atmosphereabove the North Sea. Fifteen simulationsof one year using the combination of threedifferent reanalyses (CFSR, ERA-Interim,MERRA) and five PBL-schemes (ACM2,MYJ, MYNN, QNSE, YSU) were carriedout. Comparisons to the offshore metmastFINO1 showed best results for the combi-nation of ERA-Interim data and the MYNNPBL-scheme:

Table 1: Bias (left) and RMSE (right) of the windspeed compared to a sonic anemometer at 80 m.

Foreman and Emeis [2] showed that bythe adaption of closure constants the cal-culation of TKE can be improved.

Figure 1 : Mean wind and TI profiles for stable con-ditions at FINO1 in 2007

However the improvement was limited tosituations with stable stratification.Governing Equations in MYNNThe parameterization of turbulent fluxesin the Mellor-Yamada model uses severalconstants.Velocity:

D

DTU +

∂

∂z⟨⟩ = −

1

ρ

∂P

∂+ ƒV

Turbulent kinetic energy (TKE):

D

DT

q2

2

!

−∂

∂z

LqSq∂

∂z

q2

2

!

=

−⟨⟩∂U

∂z− ⟨⟩

∂V

∂z−

q3

B1L

Contact: hauke.wurps@forwind.de

Covariance u and w:

⟨⟩ = 3A1L

q

�

−(⟨2⟩ − C1q2)∂U

∂z

+(1 − C2)βg⟨θ⟩�

Turbulent quantities are parameterizedusing constant factors and a stabilitydependent length scale L:

1

L=1

LS+1

LT+1

LB

LS =

κz/3.7, ζ ≥ 1κz/(1 + 2.7ζ), 0 ≤ ζ < 1κz(1 − 100ζ)0.2, ζ < 0

LT = α1

∫ ∞

0qzdz/

∫ ∞

0qdz

LB =

α2q/N,∂Θ∂z > 0, ζ ≥ 0

[α2q+α3q(qc/LTN)1/2]N , ∂Θ∂z > 0, ζ < 0

∞, ∂Θ∂z ≤ 0

LES SimulationFor the validation of constants a set oflarge-eddy simulations with different at-mospheric situations were used. Thesimulations were performed with the LESmodel PALM [3].

The dissipation term in the equation forthe TKE can be used to get the lengthscale from the LES:

ε =q3

B1L⇒ B1 =

q3

εL

Figure 2 : Closure constant B1 computed with L

However if B1 is determined using L com-puted according to the MYNN scheme, itturns out that B1 is not a constant but re-mains a function of ζ (= z/LM, LM: Monin-Obukhov Length).

A change of the constants that are usedfor the computation of L can lead to aconsiderably more constant behaviour ofB1:

Figure 3 : Closure constant B1 computed with anadapted L

OutlookWithin the project OWEA-Loads the work-ing group Environmental Physics of Uni-versität Tübingen performed measure-ments with an unmanned aerial vehicle(UAV) at the island Helgoland.

Figure 4 : Comparison of a WRF simulation to UAVmeasurements at Helgoland

These measurements provide valuabledata for the verification of the simulationsalso above 100 m.

ConclusionThe choice of constants can considerablyimprove the calculation of turbulence inmesoscale models.Further results indicate that a choiceof generic constants is difficult. Thusmore dependencies on stability and alsoroughness length in the formulation ofthe PBL-scheme might be necessary.

Literature1. W. C. Skamarock, J. B. Klemp, "A time-split nonhydrostatic atmospheric model for

weather research and forecasting applications." Journal of Computational Physics227.7 (2008): 3465-3485.

2. Foreman, Richard J., and Stefan Emeis. "A Method for increasing the turbulent kineticenergy in the Mellor–Yamada–Janjic boundary-layer parametrization." Boundary-layermeteorology 145.2 (2012): 329-349.

3. Maronga, B., Gryschka, M., Heinze, R., Hoffmann, F., Kanani-Sühring, F., Keck, M.,Ketelsen, K., Letzel, M. O., Sühring, M., and Raasch, S.: "The Parallelized Large-EddySimulation Model (PALM) version 4.0 for atmospheric and oceanic flows: model for-mulation, recent developments, and future perspectives", Geosci. Model Dev., 8,2515-2551, doi:10.5194/gmd-8-2515-2015, 2015.

AcknowledgementThe project OWEA-Loads is funded by the FederalMinistry for Economic Affairs and Energy (FKZ0325577B). Computing resources have beenprovided by the HPC Cluster FLOW (Facility forLarge- Scale COmputations in Wind EnergyResearch).