OTC Vertical current structures in the Deep Gulf using EOF analysis S.F. DiMarco, R.O. Reid, and W. D.Nowlin, Jr., Texas A&M University

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1 OTC Vertical current structures in the Deep Gulf using EOF analysis S.F. DiMarco, R.O. Reid, and W. D.Nowlin, Jr., Texas A&M University Copyright 21, Offshore Technology Conference This paper was prepared for presentation at the 21 Offshore Technology Conference held in Houston, Texas, 3 April 3 May 21. This paper was selected for presentation by the OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any postion of the Offshore Technology Conference or its officers. Electronic reproduction, distrbtion, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract Empirical orthogonal function (EOF) analysis was performed on current meter records and model outputs in the deep regions of the Gulf of Mexico. The results of the EOF analysis were similar for model and observation stations located on the continental slope and rise. The vertical structure of modes, generally, shows a surface-intensified mode containing a high percentage of total variance and a bottom-intensified nearbarotropic mode beginning at roughly 8 m and extending to the bottom. Introduction We examined current meter records and model outputs of the University of Colorado Princeton Ocean Model (CUPOM) to construct empirical orthogonal functions (EOFs) which describe the vertical current structure in the deep Gulf of Mexico. EOF analysis, also known as principal component analysis, has become an accepted tool to quantify patterns of variability present in large sets of time-series data 1. To facilitate analysis of the EOF modal time series, all EOFs done in this paper used singular value decomposition (SVD) to provide both the modal amplitudes and principal component time series. Further, both east-west (U) and north-south (V) current velocity EOFs were done simultaneously. Therefore, percentages of variance reported are based on the variance contained in both the U and V time series. Data Current meter observations. Analyzed were datasets that consisted of simultaneous point measurements of current velocity of 5 or more distinct depths and which lasted at least 4 months 2. Initial EOF analysis concentrated on observations in water depths greater than 7 m during the period The analysis was done on raw unfiltered data from the eastern, central, and western Gulf of Mexico. The analysis was performed using those data that were available at all depth levels, i.e., irrespective of any temporal gaps. CUPOM data. Model data were generated from a version of the Princeton Ocean Model adapted for the Gulf of Mexico. The model has 1/12 horizontal resolution and 24 vertical sigma levels. The model hindcast covered the years EOF analysis of model output was performed using data from cross- and along-isobaths as well as from single locations. The across-isobath lines went from 2-3 m total depth across the continental slope at longitudes 88, 9, 92, 94, and 96 W and across the slope meridionally in the eastern and western Gulf at 26 N. Along-isobath lines were in the central Gulf along the 5,, and -m isobaths between 89 W and 94 W. In this paper we concentrate on the along-isobath line at m and the cross-slope line at 9 W (Fig. 1). Results Fig. 2 illustrates the typical modal structure seen from slope locations around the northern Gulf of Mexico. The data used to construct the modes of Fig. 2 were from CUPOM model year 1993 and taken near 27.2 N and 89.9 W and at the edge of the Sigsbee Escarpment. Unfiltered hourly current velocity time series at all 24 sigma levels were used to construct the EOF modes. Mode 1, containing the largest percentage of total variance, has a surface maximum that decreases exponentially with depth. Mode 2, containing the second largest percentage of variance, is bottom-intensified with a zero-crossing at 3 meters and a barotropic span at below m. Mode 3 has two zero-crossings in the upper 5 m. Below m, mode 3 resembles mode 2 with a deep barotropic span. The modal structure based on the observational stations, which had at least 5 depth locations which spanned the entire water column, showed marked similarity in all three Gulf of Mexico regions and all resembled the modal pattern of Fig. 2. These patterns were also consistent with modal patterns found at locations which had four or less instruments and did not span the entire water column. Because the depth levels were not the same at each observational location, a direct comparison of the variance of each mode is not prudent. However, the percentage of variance in the first (surface intensified) mode is substantially greater then that of mode 2. We note that during model year 1993, mode 1 accounted for roughly 89% of the total variance (Fig. 2). Examination of the time series at this location suggests that there were few energetic bottom events during that year. However, examination of subsequent model years indicates significant variation of bottom events suggesting substantial year-to-year variation in the mode 2 variance. The spatial variability of the EOF modes is seen in Fig. 3 which shows vertical profiles of current velocity at the nine along-slope locations shown in Fig. 1. These EOFs were constructed from model data taken at 1 fixed depths at 2 m increments beginning at 2-m depth and spanning the model years The raw hourly current velocity time series

2 2 S.F. DiMARCO, R.O. REID, W.D. NOWLIN, JR. OTC were 4-hr low-pass filtered and then decimated to once per 48 hours prior to performing the EOF analysis. Each panel depicts a different mode, however, the structure of each mode at each location is similar. Notable differences in the structures are: Mode 1, the magnitude of the lower m is larger for stations toward the center of the line; Mode 2, the location of the zero-crossing varies between 4-7 m, while the modal maximum falls between and 17 m; there is little variability among stations for mode 3. The nominal values of percentage of variance accounted for by the first three modes are: 55% (mode 1), 35% (mode 2), 8% (mode 3). Note the dissimilarity of mode 3 in Figs. 2 and 3 is likely the result of the number of layers used and the low-pass filtering of the data used to construct Fig. 3. The sharp decrease in modal amplitude for the deepest point is an artifact of that point being close to the model boundary layer which constrains the bottom level to zero velocity. Fig. 4 shows the zero-lag correlation of the principal component time series for modes 1 through 4 at each alongslope location relative to the central location and displayed versus distance from the central location. Negative values are west of the central location and positive are to the east. The correlation is unity for all modes at distance equals, since this simply represents the zero-lag auto-correlation at the central location. The correlation falls off with distance from the central location, faster to the east than to the west and more sharply for the higher-order modes. This indicates a smaller spatial scale for the higher modes. In Fig. 5, the two-dimensional vertical EOF structures are shown for the first six EOFs for CUPOM model year 1993 taken from the cross-slope section along 9 W. The patterns are complex, but a few general statements can be made regarding their structure. Modes 1-3 are surface intensified and account for roughly 47% of the total variance. Modes 4-6 are bottom-trapped and account for roughly 17% of the total variance. These patterns of representative of other cross-slope sections of the northern Gulf of Mexico Since EOF modes are statistical constructs and do not represent actual physical modes, it is useful to decompose the EOF modes into dynamic modes using the method of Charney and Flierl 3. A preliminary analysis using this method and based on an EOF analysis using CUPOM bi-daily current velocity at 17 depth levels during model years places roughly 23% of the total variance in the pure bottomtrapped mode and roughly 6% in the first baroclinic (purely surface-intensified) mode 1. Conclusions The vertical current structures at slope/rise locations of the northern Gulf of Mexico based on EOF analysis shows two dominant modes: a surface intensified mode and a bottom intensified mode. Our interpretation of the EOF modes is that the surface-intensified mode is primarily related to motions associated with the Loop Current and it's associated Loop Current Eddies. Generally this mode exponentially decreases with depth. The bottom-trapped mode generally is small in the upper m (the region populated by Loop Current Eddies), followed by a sharp increase, and remaining relatively constant with depth to the bottom. These bottom-trapped modes are believed to be related with topographic Rossby waves which are thought to propagate cyclonically around the slope regions of the Gulf of Mexico 4. The vertical patterns of current velocity seen from observations and the CUPOM output are remarkably similar from year-to-year and at different location. We expect the percentage of variance accounted for by each mode, however, to vary significantly by location and by year. Acknowledgments We thank the many ocean specialists with oil and gas operators who have helped us identify and gain access to data in the Gulf of Mexico and Dr. Alexis Lugo-Fernandez of the Minerals Management Service for his encouragement and assistance in obtaining background information. This study was funded by the Minerals Management Service under OCS contract number CT-391. Additional funding was provided by Texas A&M University, Texas Institute of Oceanography, and Texas Engineering Experiment Station. References 1. Emery, W.J. and Thomson, R.E.: Data Analysis Methods in Physical Oceanography, Pergamon, New York (1997) DiMarco, S.F., Howard, M.K., and Jochens, A.E.: "Deepwater Gulf of Mexico Historical Physical Oceanography Program: Data Report", TAMU Oceanography Tech. Rpt. No. 1-1-D. Texas A&M University, College Station, Texas (21). 3. Charney, J.G. and Flierl, G.R.: "Evolution of Physical Oceanography", Eds. B. A. Warren and C. Wunsch, Chapter 18. Oceanic analogues of Atmospheric Motions, MIT Press, Cambridge, Massachusetts (1981) Hamilton, P.: "Deep currents in the Gulf of Mexico," J. Phys. Oceanogr., (199) 2, N 29 N 28 N 27 N 92 W 91 W 9 W 89 W 88 W 2 Fig. 1 Map of north-central Gulf of Mexico showing locations of along-slope (circles) and across-slope (heavy line along 9 W) pseudo-array current velocity stations.

3 3 VERTICAL CURRENT STRUCTURES IN DEEP GULF USING EOF ANALYSIS OTC Mode 1 5 Mode 1 (solid): 88.6% Mode 2 (dashed): 4.6% Mode 3 (dashdot): 3.2% Mode Fig. 2 Vertical structure of current velocity EOF modes 1-3 based on one year of CUPOM model output (1993) at a location near 89.9 W and 27.2 N. Current velocity at 24 depth levels was used. Percentage of variance accounted for by each mode is also shown Mode Fig. 3 Vertical profiles of current velocity EOF mode 1 (top), 2 (middle), and 3 (bottom) at along-slope locations shown in Fig. 1 showing spatial variability of modes based on 6 years of CUPOM data ( ). Current velocity at ten depth levels was used.

4 4 S.F. DiMARCO, R.O. REID, W.D. NOWLIN, JR. OTC Correlation Distance (km) Fig. 4 Zero-lag correlation relative to central along-slope station for each current velocity EOF mode (1-4) versus distance from central location. Negative distances are to the west of the central station and positive distances are to the east.

5 .8-5 VERTICAL CURRENT STRUCTURES IN DEEP GULF USING EOF ANALYSIS OTC Mode Mode Mode % of variance 16.7% of variance 9.6% of variance Mode 4 - Mode Mode % of variance 5.7% of variance 5.1% of variance Fig. 5 Two-dimensional structure of current velocity EOF modes 1-6 for cross-slope stations along 9 W shown in Fig. 1. Percentage of variance accounted for by each mode is shown in each panel.