P1.3 ANALYSIS OF WIND STRESS ALGORITHMS AND COMPUTATION OF THE WIND STRESS CURL IN BODEGA BAY, CALIFORNIA Adam Kochanski* and Darko Koracin Desert Research Institute, Reno, Nevada Clive E. Dorman Scripps Institution of Oceanography and San Diego State University, San Diego, California. 1. INTRODUCTION 2.2 Hellerman and Rosenstein (1983) Difficulties in obtaining direct wind stress data cause, in The next level of complexity in calculating the drag many cases, the wind stress to be computed from bulk coefficient, and subsequently the wind stress, is to formulas that estimate turbulent fluxes on the basis of include the air-sea temperature difference in addition to standard meteorological data. Since this approach to the the wind velocity. This approach gives a relatively wind stress evaluation is used in climate and ocean simple formula for drag coefficient calculation, which modeling, the goal of the presented work was to also takes into account a simplified treatment of stability compare various wind stress formulas, and to estimate conditions. As a consequence, the Hellerman and to what extent the choice of method alters the computed Rosenstein formula has been widely used in many wind stress and wind stress curl. oceanic models such as: the Geophysical Fluid Dynamics Laboratory-Modular Ocean Model ‘GDFL- Three commonly used algorithms of various MON’ (Roussenov et. al. 1995), the Oceanic complexities have been examined. As an example of the Component Model of Flexible Global Climate ‘FGCM0’ traditional scheme, we chose the Large and Pond (Jin et al. 1999), and the Naval Research Laboratory’s (1981) formula (LP), that relates the drag coefficient Layered Ocean Model ‘NLOM’ (Metzger 2003). (and consequently also the wind stress) only to the wind According to the Hellerman and Rosenstein formula the speed. The second scheme analyzed was the drag coefficient is calculated as: 2 Hellerman and Rosenstein (1983) formula (HR), which CT=αα+V(+α −T)++−αVα(TT)22+αV(T−T) (2) for estimation of drag coefficient takes into account not DH,1R 23a s 4 5a s 6a s only the wind speed, but also stability represented as where V is the absolute value of the wind velocity, Ta the difference between the sea and air temperature. The and Ts are the temperatures of the air and sea most advanced of the analyzed schemes was the TOGA -3 respectively, and [α1,...,α6] are constants [0.934×10 , Coare algorithm (TC), taking into account the complexity 0.788×10-4, 0.868×10-4, -0.616×10-6, -0.120×10-5, and of surface processes and computing the wind stress on -0.214×10-5]. the basis of surface fluxes analysis (Fairall et al. 1996 a,b). 2.3 TOGA Coare algorithm 2. ANALYZED WIND STRESS ALGORITHMS Fairall et al. (1996a,b) developed a comprehensive algorithm for the wind stress computation, which takes 2.1 Large and Pond (1981) into account dynamical and thermodynamical processes. The drag coefficient appears to be a Large and Pond (1981) developed a simple algorithm complex function of the wind velocity, air temperature, consisting of a bulk formula for calculating the drag SST, humidity, atmospheric pressure, shortwave and coefficient using only the wind velocity: longwave radiation fluxes, and the height of the atmospheric boundary layer. The algorithm computes Cf=⋅1.2 10−31, or4≤V<11ms− DL, P (1) transfer coefficients for the momentum, heat and humidity on the basis of an iterative estimation of the CV=+0.49 0.065 ⋅10−31, for11≤V≤25ms− DL, P () scaling parameters and stability functions, according to the similarity theory. where is the absolute value of the wind velocity, and V CD,LP is the drag coefficient. This algorithm has been 3. METHODOLOGY used in many studies such as Dorman et al. (2000), Samelson et al. (2002), and Koracin et al. (2004). 3.1 Field program As a part of the NSF-sponsored Coastal Ocean *Corresponding author address: Processes (CoOP) program, the Wind Events and Shelf Adam Kochanski, DRI, Division of Atmospheric Sciences, Transport (WEST) study was conducted in northern 2215 Raggio Parkway, Reno, NV 89512 California. A comprehensive field program including e-mail: [email protected] meteorological, and marine biology measurements was 3.3 Analysis of the wind stress curl carried out over the shelf of Bodega Bay during 2001 and 2002. A special set of 5 buoys (see Fig.1), provided For the wind stress curl computation, the triangle detailed measurements of wind speed and direction, air formation of buoys D090, E090 and 46013 was used and sea surface temperature, humidity, and the (see Fig. 1). This setup allowed to estimate directly the longwave and shortwave radiation fluxes. On the basis wind stress curl, using the spatial variation of the wind of these, as well as additional National Data Buoy stress computed from the buoy data. The buoy Center (NDBC) buoy data, an analysis of the computed measurements included wind speed components, air wind stress and wind stress curl has been performed. and sea surface temperatures, radiation fluxes, and humidity. On the basis of this data, for each of the analyzed buoys, the west-east and south-north wind stress components τx and τ y were computed. The wind stress curl for a given wind stress scheme was computed from the following equation: ∆τ y ∆τ Curl =−x (4) ∆x ∆y where: ∆τy = τ south-north,D090 - τ south-north,E090 ∆τ = τ - τ x west-east,D090 west-east,46013 ∆x – west-east distance between buoys D090 and E90 ∆y – south-north distance between buoys D090 and 46013 4. RESULTS 4.1 Differences between the drag coefficient and the Fig. 1. Position of measurement buoys in Bodega Bay CA. wind stress, computed using various schemes 3.2 Wind stress analysis Data for the period form 28 June to 4 August 2001 was used for computations of the drag coefficient and the A comparison of the wind stress computed from the wind stress. The drag coefficients computed from the three selected schemes has been performed using data three analyzed schemes using data from buoy D090 are from the central buoy D090 for the period from 28 June shown in Fig.2a,b. to 4 August 2001 (see Fig. 1). In order to investigate the effect of the broader range of the wind speed on the a) CDN Coare 2.5E-03 CDN LP mean drag coefficient, calculations were performed also CDN H&R for three NDBC buoys - 46023, 46054 and 46062 - 2.0E-03 exposed to higher wind speeds during the same period. These buoys provided wind speed components, 1.5E-03 CD humidity and air and sea-surface temperatures. The 1.0E-03 longwave and shortwave radiation fluxes (required by the TC algorithm), were computed using the Bignami 5.0E-04 (1995) and Rosati and Miyakoda (1999) formulas. 0.0E+00 0 5 10 15 b) In order to separate the influence of the wind speed Wind speed [m s-1] from the influence of the temperature, humidity and CD Coare 2.5E-03 CD LP other parameters, at the first step, all drag coefficients CD H&R were computed under the neutral stability assumption 2.0E-03 (the same temperature of the air and the sea-surface). In this case, the Hellerman and Rosenstein formula 1.5E-03 (Eq. 2) reduces to the following: CD 1.0E-03 _ _ 2 C DN ,HR = α1 + α 2 V + α 4 V (3) 5.0E-04 In order to obtain the neutral drag coefficient from the 0.0E+00 0 5 10 15 TOGA Coare algorithm, the friction velocity and the -1 Wind speed [m s ] roughness length were calculated with the stability correction function equal to zero. Fig. 2. a) Neutral drag coefficient, b) Non-neutral drag coefficient computed from TC, LP and HR formulas. Table 1. Neutral and non neutral drag coefficients computed from TC, LP and HR formulas for buoys D090, 46023, 46054 and 46062 Measurement buoy Wind speed Drag coefficient Neutral drag Drag coefficient Drag Neutral drag [m.s-1] from TC coefficient from form LP coefficient coefficient form algorithm TC algorithm formula from HR HR formula formula AVERAGE 5.89 1.140E-03 1.128E-03 1.211E-03 1.318E-03 1.355E-03 D090 STD. DEV 3.92 2.966E-04 1.611E-04 3.820E-05 3.272E-04 2.685E-04 MEDIAN 5.18 1.175E-03 1.058E-03 1.200E-03 1.303E-03 1.315E-03 AVERAGE 6.23 1.102E-03 1.121E-03 1.201E-03 1.344E-03 1.396E-03 46023 STD. DEV 2.76 2.460E-04 1.167E-04 6.700E-06 2.067E-04 1.968E-04 MEDIAN 6.3 1.146E-03 1.102E-03 1.200E-03 1.352E-03 1.406E-03 AVERAGE 8.09 1.146E-03 1.214E-03 1.217E-03 1.514E-03 1.524E-03 46054 STD.DEV 3.36 2.975E-04 1.520E-04 3.940E-05 2.417E-04 2.346E-04 MEDIAN 8.6 1.215E-03 1.226E-03 1.200E-03 1.553E-03 1.566E-03 AVERAGE 5.9 3.288E-03 1.115E-03 1.203E-03 1.321E-03 1.372E-03 46062 STD. DEV 3.03 4.688E-04 1.292E-04 1.750E-05 2.303E-04 2.152E-04 MEDIAN 5.69 1.139E-03 1.078E-03 1.200E-03 1.309E-03 1.362E-03 α ⋅ U2 ν c * (6) As can be seen in Fig. 2a, even the neutral drag zo = + 0.11 coefficient exhibits significant difference among the g U* analyzed schemes.