American Meteorological Society 14th Conference on Interactions of the Sea and Atmosphere 30 January – 2 February 2006, Atlanta , Georgia 8.2 USE OF REAL-TIME HIGH FREQUENCY RADAR OBSERVATIONS TO ESTIMATE WINDS THAT CAN BE USED AS PART OF ON-LINE OBJECTIVE ANALYSES IN CALIFORNIA COASTAL REGIONS Jessica Drake and John F. Vesecky Electrical Engineering Dept., University of California at Santa Cruz, 1156 High St., Santa Cruz CA 95064 831-459-4099, fax 831-459-4829, [email protected] Francis L. Ludwig Environmental Fluid Mechanics Laboratory, Stanford University, Stanford, CA 94305-4020 650-725-5948, fax 650-725-9720, [email protected] Douglas Sinton Meteorology Dept., San Jose State University, One Washington Square, San Jose, CA 95192-0104 408-924-5181, fax 408-924-5191, [email protected] Jeffrey D. Paduan Dept. of Oceanography, Naval Postgraduate School, 833 Dyer Rd., Monterey, CA 93943 831-656-3350, fax 831-656-2712, [email protected] I. Introduction the U. S. Geological Survey (USGS) and San Jose Winds in coastal areas are both important and State University (SJSU). These archives also include difficult to measure. In the San Francisco and several sites around Monterey Bay that can be used Monterey Bay areas, several systems offer data via with an objective analysis computer program to real-time web access. These include high frequency estimate winds over both the San Francisco and (HF, decameter wavelength) ground-wave radars at Monterey Bays. The inclusion of wind estimates from multiple frequencies and on shore and offshore (buoy) radar observations adds important information for the anemometers. This paper contains a brief review of analyses (Vesecky et al., 2005). The objective our empirical technique for measuring ocean winds analysis of all these merged data is the final product with surface-wave HF radar, and reports how we that is published in real-time via the WWW. integrate those winds into a system for objective 2. Methods analysis of routine meteorological information and finally produce a wind field map over the San 2.1 Measurement of ocean surface currents and Francisco and Monterey Bay areas – land and sea. winds with high-frequency radar HF radar has established itself as a useful tool for High frequency, ground-wave radar is useful for observing near surface currents in the coastal ocean. observing near surface currents in the coastal ocean Radar observations of ocean currents are not directly (e.g. Barrick et al. 1985). The radars detect currents related to winds, but the shear in surface currents because constructive interference gives returns results from wind stress at the surface. Current shear almost exclusively from a single (Bragg resonant) can be estimated from radar measurements at multiple ocean wavelength equal to half the radar wavelength. frequencies (Meadows, 2002), making it reasonable to Oversimplifying, the radar deduces radial current consider estimating winds from radar data. The M0 components from the difference between the radar and M1 buoys (see Fig, 1) can provide independent return’s Doppler shift and the expected Doppler shift data for building and testing empirical wind estimation due to the theoretical gravity wave speed (in the methods, The buoys are maintained by the Monterey absence of surface current) for the observed ocean Bay Aquarium Research Institute. (MBARI) wavelength. Effective depth of the current measurement depends on the radar wavelength, with Onshore anemometer data obtained from many longer waves feeling the current to greater depths. sources around San Francisco Bay are archived by Theoretical (Stewart and Joy, 1974) and empirical (Teague et al. 2001) relationships have been developed between effective current measurement Corresponding Author Address: Jessica A. Drake, depth and wavelength. Electrical Engineering Dept., University of California at Santa Cruz, 1156 High St., Santa Cruz CA 95064, Multiple radars observing the same area of the [email protected] ocean, with some straightforward trigonometry, provide estimates of the two dimensional current motion. In this method we typically use data from 0.5 0.5 uw a 1.1 (2) multi-frequency coastal radars (MCR’s), measuring = 0.033 currents at depths to a few meters below the surface. ua w 1025 MCR systems are research tools built by a –3 consortium: University of Michigan, Veridian ERIM Seawater density (w=1025 kg m ) is used to get the International, Stanford University and University of constants in Equation 2, but the result is essentially California at Santa Cruz. At present we also use data the same for fresh water. It should be possible to from one MCR and four Codar OS SeaSondes. determine u* w from the MCR current profile, then Frequencies and effective depths are shown in determine u*a from Equation 2. Hasse and Weber Table 1. (1985) show how wind speed and u*a. are related. –3 Radar echoes from waves moving toward the They use a drag coefficient of 1.310 and showed radar differ from those moving away, causing that the wind speed at 10 m, u1028u*a. Substituting in asymmetry in radar reflectivity that can be used to Equation 2, then gives determine wind direction (but not speed). Among u 840u . (3) others, Long and Trizna (1973) and Georges et al. 10 w (1993) developed methods for using the Bragg return The preceding discussion suggests that there is signal strength difference between the positive enough information to estimate wind speed and Doppler (approaching wave) echo and the negative direction directly from MCR observations, but it has Doppler (receding wave) signal (S in dB) to estimate been difficult. One reason for the difficulties may be large number of confounding variables. We sought a wind direction relative to the radar line of sight (, statistical approach that uses MCR information in a degrees). We use the relationship developed by way that might filter out noise and incorporate Georges et al. (1993) : variables whose relationship is not fully understood. The approach adopted below uses the MCR Bragg line = 0° S –24 24 + S (1) ratios and MCR and SeaSonde radial and vector =±180 for –24 < S < 24 48 currents as a training data set for the method of S 24 =180° Partial Least Squares (PLS, StatSoft 2004). Partial Least Squares was developed in the Winds toward (=180°) or away from (=0°) the radar 1960’s by economist Herman Wold for modeling poorly have no ambiguity, but Equation 1 gives two understood relationships with collinear input variables. possibilities for all other directions, e.g. when To illustrate how PLS works we will first look at S=0 dB, wind direction will be at right angles to the comparable methods. (StatSoft, 2004; Tobias, 1995) look direction, either from the right or left. At the center of any linear regression is the equation: TABLE 1: Operating frequency and effective depth of measured ocean currents of radars y = b0 + x1b1 + x2b2 +K+ x pbp + (4) operating in the Monterey Bay, used for this study. where is residual error; x is the input data, y is the prediction and b are coefficients. In matrix form this Radar Location Frequency Effective becomes type (MHz) Depth (m) Y = XB + E (5) Santa Cruz 1 4.80 2.5 where X is the input data having n cases by p MCR Santa Cruz 2 6.80 1.8 variables, Y is the prediction data having n by m responses, B is p by m and E is an error matrix. Santa Cruz 3 13.55 0.9 Various techniques for solving for B include Santa Cruz 4 21.77 0.6 Multiple Linear Regression (MLR), Principal Components Regression (PCR), and Maximum Moss Landing 22.8 0.6 Redundancy Analysis (MRA). MLR uses a least CODAR Naval Post Grad 13.47 0.9 squares approach to solve for B , which requires Pt. Pinos 13.40 0.9 matrix inversion. MLR requires relationships between predicted and input variables to be clearly defined, no Santa Cruz 12.15 0.9 co-linearity in the input variables and the number of input variables must not exceed the number of samples. PCR first breaks down the data into X- Steady-state conditions (admittedly infrequent) scores using a decomposition of X’X, where the prime produce wind profiles and ocean current profiles that denotes the transpose. The X-scores capture the are related to the friction velocity at the surface. maximum variability in the input data and are then According to Meadows (2002), the air friction velocity regressed (using least squares) against the prediction (u*a) is related to the friction velocity in water (u*w) variables to generate B. However, PCR focuses on through the ratio of air/water densities (a/w). The the largest variability of the input data, which may not equation is: be correlated to the prediction variables. MRA uses a decomposition of Y’Y to calculate Y-scores. This data space and has an even distribution of both signal captures the variability of the prediction data in the and noise, is generally the most important. regression, but still ignores the correlations between A computer script has been written to generate of the X and Y data, and tends not to be stable. PLS few training sets and test the many possible calculates scores using a decomposition of the matrix combinations. To rank the models, the algorithm Y’XX’Y. Skipping how, the decomposition calculates calculates the bias and standard error of prediction the p by c matrix W such that T = XW, and T has the (SEP) for four groups, high and low +/- wind vectors. maximum correlation with the prediction data. This Each section is weighted by performance in such a means that W captures the space that best relates to way that if the model has large errors in one section the prediction variables.