Wind profiles measured at the research platform FINO1 are used to retrieve surface boundary-layer parameters, namely, the friction velocity, heat flux, and Obukhov length. The latter is used to assess atmospheric stability. Two different retrieval algorithms, the 2D parametric solver [1] and the Hybrid-Wind method [2], are compared with reference to sonic-anemometers retrievals. Regarding atmospheric stability classification, the 2D algorithm provided better performance than the Hybrid-Wind method. When comparing the 2D-estimated (HW-estimated) friction velocity to the anemometers’ reference, a determination coefficient of ρ 2 = 0.70 (ρ 2 = 0.00) were obtained.This research is part of the project PID2021-126436OB-C21 funded by Ministerio de Ciencia e Investigacion (MCIN)/ Agencia Estatal de Investigacion (AEI)/ 10.13039/501100011033 y FEDER “Una manera de hacer Europa”. The work of M.P Araujo da Silva was supported under Grant PRE2018-086054 funded by MCIN/AEI/10.13039/501100011033 and FSE “El FSE invierte en tu futuro”. The work of  A. Salcedo Bosch was supported under grant 2020 FISDU 00455 funded by Generalitat de Catalunya—AGAUR. The European Commission collaborated under projects H2020 ATMO-ACCESS (GA-101008004) and H2020 ACTRISIMP (GA-871115). Data was made available by the FINO (Forschungsplattformen in Nord- und Ostsee) initiative, which was funded by the German Federal Ministry of Economic Affairs and Climate Action (BMWK) on the basis of a decision by the German Bundestag, organised by the Projekttraeger Juelich (PTJ) and coordinated by the German Federal Maritime and Hydrographic Agency (BSH).Peer ReviewedPostprint (author's final draft

Peña Diaz, Alfredo

Rocadenbosch Burillo, Francisco

Salcedo Bosch, Andreu

Silva, Marcos Paulo Aráujo da

English

UPCommons. Portal del coneixement obert de la UPC

ON THE USE OF WIND PROFILES TO ASSESS SURFACE BOUNDARY-LAYERPARAMETERSAraújo da Silva, M. P. 1, Student Member, IEEE, Rocadenbosch, F. 1,2, Senior Member, IEEE,Salcedo-Bosch, A. 1, and Peña, A. 31CommSensLab-UPC, Department of Signal Theory and Communications (TSC),Universitat Politècnica de Catalunya (UPC), E-08034, Barcelona, Spain;2Institut d’Estudis Espacials de Catalunya (Institute of Space Studies of Catalonia, IEEC),E-08034, Barcelona, Spain;3 DTU Wind and Energy Systems, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark.Correspondence: marcos.silva@upc.edu (M.P.A.S.); roca@tsc.upc.edu (F.R.)ABSTRACTWind profiles measured at the research platform FINO1 areused to retrieve surface boundary-layer parameters, namely,the friction velocity, heat flux, and Obukhov length. Thelatter is used to assess atmospheric stability. Two differ-ent retrieval algorithms, the 2D parametric solver [1] andthe Hybrid-Wind method [2], are compared with referenceto sonic-anemometers retrievals. Regarding atmosphericstability classification, the 2D algorithm provided betterperformance than the Hybrid-Wind method. When com-paring the 2D-estimated (HW-estimated) friction velocity tothe anemometers’ reference, a determination coefficient ofρ2 = 0.70 (ρ2 = 0.00) were obtained.Index Terms— Friction velocity, Obukhov length, stabil-ity, heat flux, wind energy.1. INTRODUCTIONOver the last years, the offshore environment has become thehome of large wind farms because of its abundant wind re-source. However, due to the high cost of wind farms implanta-tion in offshore, it is fundamental to obtain accurate informa-tion about the vertical structure of the wind profile at potentialThis research is part of the project PID2021-126436OB-C21 fundedby Ministerio de Ciencia e Investigación (MCIN)/ Agencia Estatal de In-vestigación (AEI)/ 10.13039/501100011033 y FEDER “Una manera dehacer Europa”. The work of M.P Araújo da Silva was supported un-der Grant PRE2018-086054 funded by MCIN/AEI/10.13039/501100011033and FSE “El FSE invierte en tu futuro”. The work of A. Salcedo-Bosch was supported under grant 2020 FISDU 00455 funded by General-itat de Catalunya—AGAUR. The European Commission collaborated un-der projects H2020 ATMO-ACCESS (GA-101008004) and H2020 ACTRIS-IMP (GA-871115). Data was made available by the FINO (Forschungsplat-tformen in Nord- und Ostsee) initiative, which was funded by the GermanFederal Ministry of Economic Affairs and Climate Action (BMWK) on thebasis of a decision by the German Bundestag, organised by the ProjekttraegerJuelich (PTJ) and coordinated by the German Federal Maritime and Hydro-graphic Agency (BSH).sites [3]. Accurate wind-profile and atmospheric-conditionsassessment corroborate to foresee the energy production, thewind shear, the loads over turbines, the turbines design andthe wind farm layout [3, 4].The surface layer is the lowest part of the boundary layerwhere turbulent fluxes and stress vary by less than 10% oftheir magnitude [5]. Within the surface layer the friction ve-locity, surface roughness, and the Obukhov length are themain parameters which lead the wind profile [6]. These pa-rameters are usually derived from sonic-anemometer mea-surements, which provide heat fluxes and momentum, alongwith air-pressure and air-humidity observations [5], thereforerequiring the expensive meteorological-mast (hereafter, mast)structure.Recently, Araújo da Silva et al. [1] introduced the 2Dparametric-solver algorithm, which is an alternative methodto estimate the Obukhov length and friction velocity basedsolely on the measured wind profiles. In comparison to al-ternative methods in the state of the art [7, 2], the 2D algo-rithm does not require temperature measurements and can beextended to any number of measurement heights. The 2Dalgorithm was validated by means of reference retrievals ob-tained from the IJmuiden mast. However, due to the lack ofsonic heat-flux measurements, the validation was carried outby using a proxy of the Obukhov length, which was indirectlyestimated via the bulk Richardson number [1, 4]. Moreover,the sonic-derived friction velocity used in [1] was retrieved at83 m, which may be above the surface layer.Differently from IJmuiden, the FINO1 mast provides bothsonic-anemometer observations of momentum and heat fluxesrelatively closer to the sea surface (42.1 m), which enables di-rect computation of the friction velocity and Obukhov length(see Eqs. 4 and 5, in Sect. 2.2.1). Thus, this paper aims to val-idate the 2D-algorithm using FINO1 data as well as compareits performance with the Hybrid Wind algorithm by Basu [2].© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. DOI 10.1109/IGARSS52108.2023.102817642. MATERIALS AND METHODS2.1. MaterialsThis work uses observational data gathered in June 2006 at theFINO1 platform, which is located in the North Sea, locatedabout 45 km north of Borkum, Germany (N 54° 00’ 53,5” E6° 35’ 15,5”), where the water depth is of approximately 30m. The platform hosts a meteorological mast equipped withthree R3-50 ultra-sonic anemometers at 42.1, 62.1, and 82.1m above the lowest astronomical tide (LAT), which measurethe three-dimensional wind components and temperature witha time resolution of 10 Hz. Additionally, the mast is equippedwith two Vaisala PTB100 air-pressure sensors at 21 m and 93m, and five Thies Hygro-Thermo transmitters at 34.9, 42.4,52.4, 72.4, and 101.2 m above LAT, which provide air tem-perature and relative humidity, respectively. More informa-tion about the FINO1 platform can be found in [3].2.2. Methods2.2.1. Monin-Obukhov Similarity TheoryAccording to Monin-Obukhov Similarity Theory (MOST),the surface-layer wind speed gradient can be expressed as∂U∂z= ϕmu∗κz, (1)where z is the height [m], u∗ is the friction velocity [m/s],κ ≃ 0.4 is the von Kármán constant, and ϕm is the dimen-sionless stability. Based on the Businger-Dyer relationships[8], ϕm takes different functional forms depending on the at-mospheric stability condition [5]ϕm =1 + βζ for ζ > 0 (stable)1 for ζ = 0 (neutral)(1− γζ)−14 for ζ < 0 (unstable), (2)where ζ = zL is the dimensionless stability, L is the Obukhovlength [m], and β = 6.0 and γ = 19.3 are empirical coef-ficients proposed by Högström [8]. The MOST wind speedprofile model is obtained by the integration of Eq. 1 with re-spect to the height [5], thereforeUMOST (z) =u∗κ[ln(zz0)−Ψm( zL)], (3)where Ψm(zL)is the stability-correction function, which cor-respond to Eq. 2 integrated with height, and z0 is the rough-ness length, z0 = αu2∗/g, where α = 0.012 is the Charnock’sparameter and g = 9.81 [m/s2].2.2.2. Reference retrievals from sonic anemometersHigh-resolution (HR) sonic-anemometer measurements wereused to retrieve the reference wind profiles, friction veloc-ity, and Obukhov length. First, the HR measurements weredivided into blocks of 10 minutes, which we screened as fol-lows: (i) the HR-measured wind direction had an instrumentaloffset issue that was corrected by adding 306°, 83°, and 331°to the observations taken at 41.2, 61.2 and 81.2 m, respec-tively; (ii) in order to avoid the mast shadow effect, 10-minblocks with mean wind direction between 60° and 200° wererejected [3]. (iii) Blocks with a mean wind speed below 1 m/swere removed [2]. After that, a total of 2,900 10-min blockswere obtained.The reference observational wind profiles were computedas the 10-min averaged horizontal-wind-speed (HWS) mea-surements from the three sonic anemometers. Reference fric-tion velocity and Obukhov length were computed from thesonic anemometer at 42.1 m, because it is most likely withinthe surface layer.The friction velocity was computed as [5]u∗sonic =(u′w′2+ v′w′2)1/4, (4)where u, v, and w denote the longitudinal, lateral and verti-cal wind components, respectively. The over-bar stands for“mean over time” (10 min), and the “prime” in u′, v′, andw′ denotes the turbulent part of these components, i.e., thedeviations from their respective mean velocity components.The reference Obukhov length was estimated as ([1, 5])L =−θvu3∗κg(w′θ′v)s, (5)where θv is the mean virtual potential temperature [K], g =9.81 is the gravitational acceleration [m/s2], and (w′θ′v)s isthe virtual kinematic heat flux at the surface [K · m/s]. Inpractice, θv was computed using temperature, humidity andpressure data (refer to Eqs. 3.12-13, p. 61; Eqs. 4.1a, 4.4 and4.14a, pp. 88, 91-92, [5]).2.2.3. The 2D parametric solver algorithmThe 2D algorithm assesses the friction velocity, u∗, andObukhov length, L, relying on MOST and wind-profile mea-surements only [1]. The algorithm estimates the model pa-rameters (L,u∗) by minimising the norm of residuals betweenthe model vector, U⃗MOST (L, u∗) (Eq. 3), and the observedwind-profile vector, U⃗obs., via constrained least-squares opti-misation. Two optimisation branches, one for Ψm(zL)> 0and another for Ψm(zL)< 0, are considered for enhancingthe sensitivity of the algorithm and avoiding the asymptoticdiscontinuity, |Ψm(zL)| → 0. The branch which yields thesmallest residual norm is chosen as the solution. Once L andu∗ are obtained, the heat flux can be estimated from Eq. 5 aswθ = − θ0u3∗kgL , where θ0 = 300 K is the reference potentialtemperature [2].2.2.4. The Hybrid-Wind retrieval methodThe Hybrid-Wind method (hereafter, HW) is a MOST-basedalgorithm that retrieves Obukhov length, friction velocity, andheat flux from three height levels of a HWS profile [2]. TheHW assumes a monotonic behaviour of the wind profile sothat higher heights are associated to higher horizontal windspeeds. Thus, the HW reduces the number model parame-ters from three (L, u∗, z0) to one (L) by resorting to the ra-tio of the vertical wind-speed differences R(L) = ∆U31∆U21 =U(z3)−U(z1)U(z2)−U(z1) (see Eq. 4, p. 938, [2]), where U(zi) is the HWSat the height zi. R(L) is only function of the Obukhov length,L, which is retrieved via a non-linear least squares that fitsthe observed to the modelled vertical wind-speed ratio. Then,the estimated L is used to retrieve the friction velocity, u∗,from the formulation of HWS differences ∆U31(u∗, L) and∆U21(u∗, L) (refer to Eqs. 3a and 3b, pp. 937-938, [2]), viaordinary linear least squares. Then, the heat flux can be esti-mated in the same manner as for the 2D algorithm.3. DISCUSSION RESULTSThe first part of our study addressed the goodness of thesonic-anemometer-derived retrievals. This was evaluatedthrough the relationship between the dimensionless windshear, Φm, and dimensionless stability, z/L, Fig. 1. We em-ployed the wind-gradient model by Högström [8] to retrieveΦm along with the following histogrammed data screeningprocedure for outlier rejection (Fig. 1):-2 -1 0 1 2-5051015 = 6  = 19.3 = 8  = 20Lsonic = 50 mLsonic = - 50 mFig. 1. Dimensionless wind shear, Φm, as function of dimen-sionless stability, z/L. (Black and grey dots) stand for “valid”and “outlier” samples, respectively (see text). (Red line) istheoretical model function Eq. 2.First, the dimensionless stability range (−4 < 42.1/Lsonic <4) was divided into 0.02-width bins and, in each bin, Φm val-ues outside of the µ ± 1σ (with µ being the mean and σbeing the standard deviation of the distribution in the bin)were rejected as outliers. Second, profiles in the interval−50 < L < 50 were rejected in order to avoid Eq. 2 singu-larity when L → 0 [6]. Eventually, because the HW methodimplicitly assumes that the HWS monotonically increaseswith height [2], profiles that did not fulfil this requirementwere also excluded. After application of these outlier rejec-tion criteria, the statistical sample reduced to 1,038 10-minrecords.Since Businger-Dyer model coefficients β and γ in(Fig. 1) are empirical, they are not suitable to fit all sortsof observed wind profiles. To check their representativeness,they were re-computed to best fit our measurement datasetyielding β = 8 and γ = 20. The latter values are in roughagreement to the ”standard” model coefficients, β = 6.0 andγ = 19.3 given in Eq. 2.The second part of the study addressed the 2D- and HW-retrieved Obukhov-length and heat-flux frequency distribu-tions and related stability classes with reference to the re-trieved ones from the anemometers.-0.05 -0.03 -0.01 0.01 0.03 0.051/L [1/m]0200400600800CountsSonicHW2D-0.02 -0.01 0 0.01 0.020200400600800CountsSonicHW2D(b)(a)Fig. 2. Statistical distributions. (a) Frequency distributionof the inverse Obukhov length, 1/L, obtained from the 2Dand HW methods with reference to the sonic anemometer re-trievals. (b) Same as in (a) but for the heat flux.Overall, the 2D- and HW-derived estimates reproducedwell the reference distributions of the anemomenters’ refer-ence, the 2D-derived Obukhov length being closer to the ref-erence (Fig. 2a). Although these successful results, Fig. 2histograms hide a population inversion between wind profilescategorised as “stable” (L > 0) and “unstable” (L < 0).Fig. 3 provides a one-to-one comparison with reference tothe classification provided by the anemometers through con-fusion matrices. Due to the limited number of records avail-able in comparison with other studies (1,038 records here vs.84,890 in [2]), we only considered unstable (u) and stable (s)categories. The 2D produced higher hit rates than the HW forboth the stable and unstable types. The MOST shows low sen-sitivity to the Obukhov length in neutral and unstable regimes[1]. Therefore, the poorer performance of the HW in com-parison to the 2D is attributable to the optimization of only Lparameter by the HW. In contrast, simultaneous optimisationof both L and u∗ by the 2D permits to find local minima thatbetter adjust to the observations.Finally, Fig. 4 compares the 2D- and HW-estimated fric-s usu 1534319065219.0% 18.5%81.0% 81.5%s usu 2721379653366.2%33.8%41.2%58.8%(a) (b)Fig. 3. Confusion matrix between the Obukhov length re-trieved by the HW and the 2D algorithms against the oneretrieved by the anemometers. In both panels the summarymatrix at the bottom totals the hit rates (bluish) and miss rates(reddish) for each class. s and u stand for stable and unstableclasses, respectively.tion velocities, u∗2D and u∗HW , respectively, against refer-ence u∗sonic . It emerges that the HW method was not ableto correctly estimate the friction velocity as evidenced by es-timates essentially uncorrelated with the reference (ρ2HW =0.002, scattered grey dots in Fig. 4). In contrast, the 2Dmethod yielded good estimates as indicated by a regression-line slope equal to 0.90 and ρ2 = 0.70.0 0.25 0.5 0.75 100.250.50.7510.905x +0.076-0.02-0.0100.010.021/L 2D [-]2 =0.700RMSE =0.080Fig. 4. 2D- and HW-estimated friction-velocities versus thesonic-anemometer reference (coloured and grey dots, respec-tively). Statistical indicators refer to the 2D method. (Redline) Regression line. (Dashed line) 1:1 line. (RMSE) Root-Mean-Squared Error. (Circles) 2D-algorithm estimates in the−0.02 < 1/L2D < 0.02 interval.4. CONCLUSIONSTwo MOST methods for assessing surface boundary-layer pa-rameters, namely, the 2D [1] and the Hybrid-Wind (HW) al-gorithms [2], were revisited. The 2D directly fits the modelwind profile (Eq. 3) to the observed profile in order to assessthe friction velocity and Obukhov length whereas the HW re-lies on the ratio of the vertical wind-speed differences to re-trieve the Obukhov length, subsequently used to derive thefriction velocity. The 2D method outperformed the (HW) re-garding atmospheric stability typing (overall hit rate of 82 %(60%), Fig. 3) and retrieval of the friction velocity ( ρ22D =0.70 versus ρ2HW = 0.002, Fig. 4).The inferior performance of the HW is attributable to thelow sensitivity of MOST with respect to the Obukhov length,particularly, in unstable regimes. Thus, the optimisation ofonly L by the HW led to biased estimations of the atmo-spheric stability and friction velocity.5. REFERENCES[1] M. P. Araújo da Silva, F. Rocadenbosch, J. Farré-Guarné,A. Salcedo-Bosch, D. González-Marco, and A. Peña,“Assessing obukhov length and friction velocity fromfloating lidar observations: A data screening and sensi-tivity computation approach,” Remote Sensing, vol. 14,no. 6, 2022.[2] S. Basu, “A simple recipe for estimating atmospheric sta-bility solely based on surface-layer wind speed profile,”Wind Energy, vol. 21, no. 10, pp. 937–941, 2018.[3] S. Porchetta, O. Temel, D. Muñoz-Esparza, J. Reuder,J. Monbaliu, J. Van Beeck, and N. van Lipzig, “Anew roughness length parameterization accounting forwind–wave (mis) alignment,” Atmospheric Chemistryand Physics, vol. 19, no. 10, pp. 6681–6700, 2019.[4] M. C. Holtslag, W. A. A. M. Bierbooms, and G. J. W.Van Bussel, “Validation of surface layer similarity theoryto describe far offshore marine conditions in the dutchnorth sea in scope of wind energy research,” Journal ofWind Engineering and Industrial Aerodynamics, vol. 136,pp. 180–191, 2015.[5] R. B. Stull, Practical meteorology: an algebra-basedsurvey of atmospheric science. University of BritishColumbia, 2015.[6] S.-E. Gryning, E. Batchvarova, B. Brümmer,H. Jørgensen, and S. Larsen, “On the extension ofthe wind profile over homogeneous terrain beyond thesurface boundary layer,” Boundary-layer meteorology,vol. 124, no. 2, pp. 251–268, 2007.[7] A. C. M. Beljaars, A. Holtslag, and R. Van Westrhenen,Description of a software library for the calculation ofsurface fluxes. KNMI De Bilt, Netherlands, 1989.[8] U. Högström, “Non-dimensional wind and tempera-ture profiles in the atmospheric surface layer: A re-evaluation,” in Topics in Micrometeorology. A Festschriftfor Arch Dyer. Springer, 1988, pp. 55–78.

On the use of wind profiles to assess surface boundary-layer parameters

https://upcommons.upc.edu/bitstream/2117/398441/1/IGARSS2023_stability_FINO1.pdf

On the use of wind profiles to assess surface boundary-layer parameters

Abstract

Similar works

Full text

Available Versions

UPCommons. Portal del coneixement obert de la UPC