FLUXES ESTIMATION AND THE DERIVATION OF THE ATMOSPHERIC STABILITY AT THE OFFSHORE MAST FINO1.

29 November 1 December 211, Amsterdam, The Netherlands FLUXES ESTIMATION AND THE DERIVATION OF THE ATMOSPHERIC STABILITY AT THE OFFSHORE MAST FINO1. Beatriz Cañadillas 1, Domingo Muñoz-Esparza 2, Thomas Neumann 3 1,3 DEWI GmbH - Deutsches Windenergie-Institut, Wilhelmshaven, Germany e-mail 1 :b.canadillas@dewi.de Phone: +49 () 4421 488-813 Fax: +49 () 4421 488-843 2 von Karman Institute for Fluid Dynamics, Environmental and Applied Fluid Dynamics Department, 1. Introduction Belgium Knowledge of vertical momentum/heat exchange processes over the sea is relevant for a better understanding of the Marine Boundary Layer (MBL) and essential not only to improve the parameterizations used in atmospheric numerical models but also in other applications such as wind energy, due to its direct relation to wind conditions. Moreover, atmospheric stability is a key parameter in wind resource assessment as it is in direct relation to wind and turbulence profiles. In addition, atmospheric stability plays a crucial role in wind turbine wakes. Wind power loss, as a consequence of wind turbine wakes, is largest in stable conditions and least in unstable conditions. Therefore a correct estimation of the stability is required. In the present study, an analysis of the local momentum/heat fluxes based on measurements from the offshore mast FINO1 is presented for a period of one year (January-December 21). Spectral analysis is applied in order to determine an appropriate averaging-flux time taking into account stability effects. After, the Obukhov length, L, is obtained in order to derive the atmospheric stability. These results are compared with L obtained from a bulk formulation. Finally, the influence of atmospheric stability on local wind shear is studied. 2. Measurements 2.1. Measurement Site The German research platform FINO1 used in this study is located 45 km off the Borkum Island (lat. 54.87 N, lon. 6 35.24 E) in the North Sea and is in operation since 23. The mean water deep of the platform is about 3 m. The platform is equipped with a tall meteorological mast up to about 1 m performing continuous multilevel measurements of the lower part of the atmospheric boundary layer as well as oceanographic measurements. FINO1 was built mainly for wind energy applications, providing high quality data to cover investigations with a very broad scope. The mast is a bottom-mounted jacket construction providing a very stable platform which avoids data contamination by the motion of sensors. (a) (b) Figure 1 (a) Research platform FINO1 in the North Sea [1] and (b) sonic instrument at FINO1.

29 November 1 December 211, Amsterdam, The Netherlands 2.2. Dataset In the present work, a one year period (Jan. 21 - Dec. 21) is investigated. Measurements from the sonic anemometers at 41.5 m, 61.5 m and 81.5 m were used as the primary source of data while slow profile response sensors (wind direction, relative humidity, air pressure and temperature) are used when necessary (for instance for data corrections or comparison). The measured parameters, sensor type and heights are summarized in Table 1. Table 1 Parameter Sonic anemometer Cup anemometer Sea Temperature Air Temperature Air pressure Air Humidity Wind direction Sensor type (Accuracy) SOLENT 121R3-5 (< 1 % rms) Vector A1LK-WR-PC3 (±.1 ms -1 ) Wavec datawell buoy (± 3%) Pt-1 (±.1K at C) Barometer, Viasala (±.3 hpa) Hydrometer, Thies (± 3% RH) Thies Wind Vane Classic (±1 ) Measurements involved in this study. Height [m] LAT 41.5, 61.5, 81.5 41,5 SST 41.5, 52, 72, 11 22.5 34.5 91.5 Slow-response profile instrumentation (e.g. temperature, pressure, etc.) is sampled once per second (1 Hz) and stored as 1 min averages. Fast-response instrumentation is sampled with a frequency of 1 Hz (e.g. sonic anemometers). 3. Methodology The so-called Eddy-Covariance method (EC-technique) [2] is used to determine turbulent fluxes of momentum (<w u >, <w v >) and heat (<w T >) from direct calibrated sonic data, where u, v and w are the orthogonal wind components, T is the potential temperature and the prime denotes turbulence fluctuations. A two-fold rotation was applied after which the x-axis is aligned with the mean wind vector and the mean vertical component is removed. This correction is important even at small tilt angles, since the horizontal wind speeds are an order of magnitude higher than the vertical wind speeds. The instantaneous measurements were compared to allowable upper and lower limiting values based on instrument manufacturing specifications and the prevalent weather over the North Sea. Values exceeding those thresholds were discarded as instrumental errors. Temperature measurements exceeding 3 C and lower than -15 C, were rejected. A maximum horizontal wind speed of 35 ms 1 was allowed; the vertical wind speed had to be between -15 ms 1 to 15 ms 1. Furthermore, unreasonable peaks (unrealistically large or small values) associated with non-meteorological events in the data were removed. The criterion was settled to remove signals that are not more than ±5 time the standard deviation with a window of 3 minutes averaging period in a similar way to that described in [3]. As pointed out by [4], flow distortion produced when the wind comes from the mast (mast shadow) can be an important source of error in data post-processing. Mean values (1 min) were corrected from mast shadowing by using uniform ambient flow mast correction scheme, UAM [5], whereas turbulence values (1 Hz) were corrected from lateral acceleration by using a trigonometric approach as a first approximation. In this study, the wind from the sector (24-36 ] related to open sea conditions (Figure 2) and which is undisturbed for either direct mast shadow or wind farm (alpha ventus) is used.

29 November 1 December 211, Amsterdam, The Netherlands NORTH 6% 8% WEST 2% SOUTH 4% EAST v=[ms 1 ] >2 16 2 12 16 8 12 4 8 4 Figure 2 Wind direction distribution at 91.5 m and selected wind sector between dashed green lines. After data pre-processing and selected wind sector, the data availability ranged from 29% to 32% at different heights for the all the sensor used. 3.1. Choose of the averaging period: It has been shown by several investigations (e.g. [6] [7] [8] ), that the choice of the averaging time influences the magnitude of the averaged turbulent flux. In addition, it has been shown to depend on the wind speed, measurement height and atmospheric stability. An optimum value of the averaging time should be used in order to include the low frequency contribution to the fluxes and to fulfill the steady state condition (requirement of the eddy-covariance method). The previous targets can be not reached if shorter or longer time periods are considered, respectively. Due to the nature of the turbulent flux of two magnitudes, for instance, x and w, the crossspectrum has a close link with it. Indeed, it can be demonstrated that the sum over frequency of all the cospectral amplitudes, Co x,w (real part of cross-spectrum) is equal to the covariance in between x and w, and consequently, equal to the averaged turbulent flux [9]. [1] applied the Ogive function to verify if all the low frequency content was included in the turbulent flux measured with the eddy-covariance method. The Ogive is the cumulative integral of the cospectrum from the highest to the lowest frequencies:,, (1) where f N is the Nyquist frequency and the maximum value of the integral upper limit is the lowest computed frequency. To illustrate the influence of the atmospheric stability, the Ogive function for <u w > and 3min averaging time is shown in Figure 3 (a) for stable and convective conditions. Moreover in Figure 3 (b), a sensitivity test by varying the integration time: 5min, 1min, 2min, 3min and 6min is presented.

29 November 1 December 211, Amsterdam, The Netherlands Normalized Ogive [ ] 1.9.8.7.6.5.4.3 Stable stability Convective stability Ogive max [m 2 s 2 ].1.2.3.4 5min 1min 2min 3min 6min.2.1 (a) 1 4 1 3 1 2 1 1 1 1 1 Frequency [Hz].5 (b).5.4.3.2.1 Ogive [m 2 s 2 ] Figure 3 (a) Normalized Ogive function. Dashed lines indicate 3 min, 1 min and 5 min, from lower to higher frequencies. (b) Sensivility test: Ogive values for different averaging times vs maximum Ogive. In Figure 4 the error distribution (estimated flux - maximum of the Ogive) due to the choice of time averaging is presented. From these results a 3 min averaging time is found to be appropriate to compute the fluxes at FINO1. 1 9 Cumulative frequency [%] 8 7 6 5 4 3 5min 2 1min 2min 1 3min 6min 8 7 6 5 4 3 2 1 Flux Error [%] Figure 4 Error distribution as a function of time averaging. 4. Results and Discussion 4.1. Momentum fluxes: In Figure 5, the mean covariances of <w u > and <w v > are plotted as a function of wind speed at 41.5m LAT. After the alignment with the mean wind, <w v > values remain around zero whereas <w u > shows the expected dependency with wind speed. Here the total stress is composed only of the turbulent shear stress since wave-induced stress and viscosity stress are assume to be negligible at this height. Therefore, only downward momentum transfer (from the air to the sea, negative <w u >) is expected.

29 November 1 December 211, Amsterdam, The Netherlands <w u > [m 2 s 2 ].4.2.2.4.6.8 1 (a) 1.2 2 4 6 8 1 12 14 16 18 2 22 U [ms 1 ] <w v > [m 2 s 2 ].4.2.2.4.6 (b).8 2 4 6 8 1 12 14 16 18 2 22 U [ms 1 ] Figure 5 Mean momentum covariances: (a) along wind direction, (b) crosswind wind direction. The solid lines show the bin-averaged values and bars denote one standard deviation. Figure 5 also highlights the range of horizontal wind speeds over which the measurements are made. 4.2. Heat fluxes: Sonic anemometers do not really measure temperature but the speed of sound, which depends not only on air temperature but also to a minor extent on humidity. Therefore, in order to obtain the fluctuations of the actual temperature instead of the fluctuation of the sonic temperature, the humidity effect was corrected based on [11] :.51 (2) where <w θ > is the kinematic heat flux, <w θ > s includes the humidity component and <w q > are the humidity vertical fluctuations. In absence of fast humidity response sensors at FINO1, a bulk formulation was used as first approximation to determine the second term on the right side in Eq.(2). If the humidity flux is included, the pdf distribution of heat flux is shifted towards unstable conditions. Note that correction for cross-wind contamination, caused by signal deflection of the sound path in the instruments due to the vertical wind component, was not included in Eq.(2) since it is internally implemented on the sonic anemometers used in this study. The probability distribution of the corrected surface heat flux <w θ > is shown in Figure 6. The distribution exhibits an asymmetric shape skewed towards positive values, indicating warm air transported upward from the sea surface to the air, which is associated to unstable conditions. The estimated accuracy of <w θ > is about ± 5%. Frequency [%] 2 18 16 14 12 1 8 6 4 2.5.4.3.2.1.1.2.3.4.5 <w θ > [Kms 1 ] Figure 6 Probability distribution function of corrected <w θ > over the study period.

29 November 1 December 211, Amsterdam, The Netherlands 4.3. Atmospheric stability: Once turbulence fluxes of heat and momentum are calculated, the atmospheric stability as described by the Monin-Obukhov similarity theory (MOST) was computed based on Eq.(3). (3) where κ =.4 is the von Kàrman constant, g is the acceleration due to gravity (g = 9.81 ms 2 ), z is the height above the surface, u * (=(<w u > 2 + <w v > 2 ) 1/4 ) is the friction velocity, θ z is the potential temperature and <w θ > represents the corrected sensible heat flux. In Figure 7 the zl -1 histogram at the three sonic heights is depicted, showing a good agreement among them. 2 15 81.5m 61.5m 41.5m Frequency (%) 1 5 1.8.6.4.2.2.4.6.8 1 zl 1 Probability distribution of flux- at all the sonic heights. Figure 7 based zl 1 4.3.1. Comparison of stability methods: sonic versus bulk method Since sonic anemometry is not routinely used in wind energy. Here, an alternative way to estimate the atmospheric stability based on local gradient of mean meteorological measurements (Bulk Richardson number, Ri b ) is computed and compared to the flux-based zl -1 parameter (Eq. 3). The meteorological parameters involve in the computation of the bulk Richardson number (Eq. 4) are mean virtual potential difference between air (T air ) at the reference height (z) and sea (SST) temperature, mean wind speed at z. =.51 1 Conversion, into zl -1 [12] 1 1 4.5.2 (4) θ and q denote the potential temperature and specific humidity differences between air (41.5 m) and sea surface (SST). For 21, θ v ±2.9 K and q ±41-3 kgkg -1. The Ri b is converted into zl -1 following [12].The stability classification used in this study is given in Table 2. Table 2 Stability classification based on the Obukhov length, L.

29 November 1 December 211, Amsterdam, The Netherlands Figure 8 shows, (a) the comparison between zl -1 based on direct flux estimations and zl -1 _Rb based on bulk parameters and (b) both parameters classified using intervals given in Table 2. 1.8.6 3 25 Flux Gradient zl 1.4.2.2.4 Frequency [%] 2 15 1.6.8 (a) 1 1.5.5 1 zl 1-1 _Ri b 5 vs s n un vun (b) Figure 8 (a) Scatter plot of flux-based (zl -1 ) versus gradient-based (zl -1 _Ri b ) stability parameter at 41.5 m LAT. (b) Histogram by stability classes. The relatively large scatter could be associated to the complex interplay of different parameter involved in the calculations and to the different uncertainties of the different methods and sensors. The gradient-based method tends to produce more stable conditions than the sonic one. One of the causes for this discrepancy could be related to the air sea differences. As pointed out by [13], given that sea surface temperature varies slowly (see Figure 9), the use of SST- T air may result in a large number of extreme (i.e., very unstable and very stable) stratification conditions. Nevertheless, the overall agreement between both sets of data is acceptable. Figure 9 Time series of air temperature at 42 m and sea surface temperature. 4.4. Wind shear dependence on atmospheric stability In this section, the effect of atmospheric stability on the wind shear is assessed using the local wind dimensionless gradient (φ m ): where k, as before, is von Karman s constant. φ (5) The M-O theory [14] predicts that the dimensionless wind shear defined in Eq. (5) is only a function of the stability parameter (zl 1 ) within the surface layer. For zl 1 1 (neutrally-stratified PBL), it is expected that φ m =1. and thus, no stability correction term to the logarithmic profile is added.

29 November 1 December 211, Amsterdam, The Netherlands For the calculation of φ m, the partial derivative of the wind speed is obtained from the fitting to a logarithmic second order polynomial (Eq. (6)) using the three sonic anemometer measurements (41.5, 61.5 and 81.5 m LAT). The corresponding equation is the following: with ln ln z (6) 2 (7) where a, a 1 and a 2 were determined using least-squares method. Almost the 9% of the values (profiles) had a correlation coefficient (R 2 ) higher than.9, values with R 2 <.9 are not considered in the following. Using the values of u *, and k=.4, the wind dimensionless gradient is calculated. In Figure 1, the wind dimensionless gradient, φ m, is plotted against zl 1 together with the empirical curve suggested by [15] to provide a reference. In order to better compare the experimental results with the empirical curve (blue solid line), measured data were bin-median averaged (black solid circles) together with the best fit (black solid line). The scatter in the data is considerable for zl 1 > (stable stratification), which is probably related to the fact that, in stable cases, the measured level does not well represent surface conditions and therefore the results are not expected to be explained by the surface layer M-O theory. However, the same pattern of increasing non-dimensional shear with stability was found. For unstable conditions (zl 1 <), there is a good agreement with [15]. In addition, it can be noticed that the data has the expected trend and that the scatter is considerably reduced. 8 7 6 Data Hogstrom (1988) FINO1 fit Bin averages 5 φ m [ ] 4 3 2 1 Figure 1 1 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5 zl 1 [ ] Local non-dimensional gradient of the wind as a function of stability, zl 1. Binmedian values and correlation fit. Blue solid line represents the empirical stability function given in [15]. 5. Conclusions In this study, a detailed data analysis focused on the turbulent fluxes calculation under offshore conditions was presented. A time average of 3-min interval was found, by means of an Ogive analysis, to be adequate to estimate the turbulent fluxes at FINO1 for all the stability classes observed, ranging from very unstable to very stable conditions. Calculation of the stability parameter zl -1 based on turbulent fluxes reveals that unstable and neutral conditions are predominant at FINO1, considering open sea conditions (24º-36º] during 21. In addition, zl-1 was also computed using a gradient based method (Bulk Richardson number). Despite of the relatively large scatter in the comparison, an overall good agreement was found. Further investigations are needed to confirm these results however the

29 November 1 December 211, Amsterdam, The Netherlands discrepancy could be attributed to differences in frequency and amplitude of air and temperature variations. Non-dimensional shear dependency with the stability parameter, zl 1, was checked. FINO1 data agrees well with previous studies (e.g.[15] ) under unstable and neutral stratification. However, higher shear is found for stable conditions. In FINO1 the closest fast response instrument (sonic) to the surface has a height of 41.5m LAT and therefore cannot be a good representative of the near surface conditions, especially for stable stability. In the future, it is planned to install a sonic at about 15-2 m height as a temporal campaign which will give us the opportunity to analyze and compare with results presented in this study. Moreover, atmospheric stability is very sensible to humidity changes, which is especially important under offshore conditions. In this work a bulk approximation was used to estimate humidity fluxes, however a deeper study of humidity effects on the stability is foreseen in the new TUFFO project [16]. It is also worthy to mention that FINO1 mast provides high-quality data which can be used to check modeling results and obtain a more detailed picture of the physical processes in the MBL (e.g. [17] ). 6. Acknowledgements: The FINO1 platform is one of three offshore platforms of the FINO Project [1] funded by the Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU). Domingo Muñoz-Esparza has been supported by the European Commission through the Marie-Curie FP7 actions under the WAUDIT project, contract number # 238576. 7. References [1] FINO: Forschungsplattformen in Nord- und Ostsee, www.fino-offshore.de. [2] T. Foken, Micrometeorology, Springer-Verlag, Berlin Heidelberg, 28. [3] D. Vickers and L. Mahrt. Quality control and flux sampling problems for tower and aircraft data. J.Atmosph. and Oceanic Technol. 1997; 14:512 526. [4] U. Högström. Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Boundary-Layer Meteorology 1987; 42:55 78. [5] A. Westerhellweg, V. Riedel, T. Neumann: Comparison of Lidar- and UAM-based offshore mast effect corrections, EWEA 211, Brussels. [6] T. Foken, F. Wimmer, M. Mauder, C. Thomas, C. Liebethal, Some aspects of the energy balance closure problem, Atmospheric Chemistry and Physics Discussions 26; (6) 3381 342. [7] X. M. Sun, Z. L. Zhu, X. F. Wen, G. F. Yuan, G. R. Yu, The impact of averaging period on eddy fluxes observed at ChinaFLUX sites, Agricultural and Forest Meteorology 26; (137) 188 193. [8] Xiao X., Zuo, Yang Q. D., Wang S. J., Wang L. J., Chen J. W., Chen B. L., Zhang B. D. On the factors influencing surface-layer energy balance closure and their seasonal variability over semiarid loess plateau of Northwest China, Hydrology and Earth System Sciences discussions 8 211; 555 584. [9] R. B. Stull, An introduction to boundary layer meteorology, Kluwer Academic Publishers, Dordrecht, 1988. [1] S. P. Oncley, J. A. Businger, C. A. Friehe, J. C. LaRue, E. C. Itsweire, S. S. Chang, Surface layer profiles and turbulence measurements over uniform land under nearneutral conditions, in: 9th Symposium on Boundary Layer and Turbulence, pp. 237 24. [11] Schotanus P., Nieuwstadt F. T. M., De Bruin H. A. R.. Temperature measurement with a

29 November 1 December 211, Amsterdam, The Netherlands sonic anemometer and its application to heat and moisture fluxes. Boundary-Layer Meteorology 24; 26(1): 81 93. [12] Grachev, A. and C. Fairall. Dependence of the Monin-Obukhov stability parameter on the bulk Richardson number over the ocean. J. Appl. Meteorol. 1996; 36, 46 414. [13] Motta M, Barthelmie R. J. The Influence of Non-logarithmic Wind Speed Profiles on Potential Power Output at Danish Offshore Sites. Wind Energ. 25; 8:219 236. [14] Monin A. S. and Obukhov A. M.. Basic laws of turbulent mixing in the ground layer of the atmosphere. Akad. Nauk. SSSR Geofiz. Inst. Tr., 151:163 187, 1959. [15] U. Hogstrom, Review of some basic characteristics of the atmospheric surface layer, Boundary-Layer Meteorology 78 (1996) 215 246. [16] TUFFO Project. Erfassung und Bewertung des Einflusses turbulenter Feuchteflüsse auf die Turbulenzintensität in Offshore Windparks. Part of RAVE project (www.raveoffshore.de). [17] Muñoz-Esparza D., Cañadillas B., Neumann T., van Beeck J. WRF mesoscale modelling and LiDAR measurements of tall wind profiles at FINO1. PO.394. EWEA OFFSHORE 211, Amsterdam, the Netherlands.