Boemre 2008 Extended Hindcast Calculation of Gulf of Mexico Circulation: Model Development, Comparisons with Observations



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OCS Report

BOEMRE 2010-???


Extended Hindcast Calculation of Gulf of Mexico Circulation: Model Development, Comparisons with Observations
Final Report
fig08abc_topocaustics10_972003word_cleaned

fig09_topocaustics10_972003word_cleaned

OCS Study

BOEMRE 2008-???


Extended Hindcast Calculation of Gulf of Mexico Circulation: Model Development, Comparisons with Observations


Author
Lie-Yauw Oey

Prepared under BOEMRE Contract

M07PC13311

by

Princeton University



Program in Atmospheric and Oceanic Sciences

Sayre Hall

Princeton, NJ 08544

Published by


U.S. Department of the Interior

Bureau of Ocean Energy Management, Regulation and Enforcement, Herndon, VA

Gulf of Mexico OCS Region June 2010

DISCLAIMER
This report was prepared under contract between the Bureau of Ocean Energy Management, Regulation and Enforcement (BEMRE) and Princeton University. This report has been technically reviewed by the BOEMRE and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Service, nor does mention of the trade names or commercial products constitute endorsement of recommendation for use. It is, however, exempt from review and compliance with the BOEMRE editorial standards.
REPORT AVAILABILITY
Extra copies of the report may be obtained from the Public Information Office at the following address:
U.S. Department of the Interior

BOEMRE


Public Information Office (MS 5034)

381 Elden Street

Herndon, VA 20170-4817
CITATION
Suggested citation:
Oey, L.-Y. 2010. Extended Hindcast Calculation of Gulf of Mexico Circulation: Model Development, Comparisons with Observations. OCS Study BOEMRE 2010-???, U.S. Dept. of the Interior, Bureau of Ocean Energy Management, Regulation and Enforcement, Herndon, Virginia. ???pp.


ABOUT THE COVER
Upper 3 panels: simulated sea-surface height (color) and surface currents (black vectors) at 3 indicated times beginning on Oct/22/1999 of the extended hindcast period (1999-2007). Lower panel indicate deep response; shown are 2-20 day power spectral energy (color, plotted as 10×(u2+v2) m/s; red  0.05 m/s) of deep currents below z = 1000 m. Black contours are NT = N|H/H| = 0.1, 0.2 and 0.3 in cycles per day. White lines are SSH = 0.05 and 0.3 m contours indicating the outlines of Eddy Juggernaut on Oct/22/1999. Thick dashed lines are 10 and 20-day Topographic Rossby Wave rays traced backward from the Sigsbee mooring (as indicated). Thin dotted contours are the 3000 m (southern contour) and 2000 m isobaths.
acknowledgments
Sponsor Acknowledgments: The study was sponsored by the Bureau of Ocean Energy Management, Regulation and Enforcement/DOI, under Contract# M07PC13311. The Contract Officer Technical Representative was Dr. Walter Johnson and period of study was from Sep, 2007 through Aug, 2010. We are also grateful to the NOAA/Geophysical Fluid Dynamics Laboratory for the permission to use their supercomputing facilities.
Other Acknowledgments: Special thanks to Dr. Walter Johnson for his encouragements throughout the course of this project.
TABLE OF CONTENTS
Page

List of Figures………………………………………………………………………… ix-xv

List of Tables…………………………………………………………………………… xvii
SUMMARY…………………………………………………………………………….1-2
Section 1: Introduction…………. ………………………….……………………….. 3-7
3.1 Background of Princeton Modeling Efforts …………………………..5-7

3.2 Observational Data………………………………………………………7


Section 2: The Model……………………. ……………………….…………………..8-14
2.1 Wind Forcing…………………………………………………………9-12

2.2 Baroclinic Pressure Gradient Error at Steep Topography...…………… 13


Section 3: Data Assimilation………………….………………………………..…….15-21

3.1 Statistical Optimal Interpolation Scheme…………………………...16-17

3.2 Ensemble Kalman Filter Scheme……………………..……………..17-21
Section 4: Skill Assessments……………….…………………………..…………….22-39
Section 5 : Topocaustics………………………………………………………..…….40-44
Section 6 : Conclusions & Recommendations……………………………………….45-46
REFERENCES………………………………………………………………………..47-51
Appendix 1:….………………………………………………………………………..52-63
LIST OF FIGURES
Page
Figure 1.1 The northwest Atlantic Ocean model (  6~12 km within the Gulf of Mexico) (NWAOM; the whole region shown) and the fine-grid resolution (  3~7 km) Gulf of Mexico and northwest Caribbean Sea region (west of the dashed line). Contours show isobaths in meters, and silhouettes at 55oW show steady transports specified for the Gulf Stream and returned flows.

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Figure 1.2. Daily-averaged analysis sea-surface height (SSH; color) and surface currents shown on the first of each month from Sep/1999 through Aug/2000 in the Gulf of Mexico. Thick dark contour is the zero-value of satellite SSH. [From Lin et al. 2007].

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Figure 2.1. Bi-monthly variance ellipses and mean (vectors originating from ellipses’ centers) for wind stress derived from the Qblend product, computed for 1988-2008. Vector scale (0.2 N m-2) is shown for the mean wind stress, and color background indicates the standard deviation, also in N m-2.

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Figure 2.2. Twelve hourly plots of HRD/NCEP winds showing the path of Hurricane Katrina from (A) August 24 at 12:00 GMT through (K) 29 at 12:00 GMT, 2005. The last panel (L) is for August 29 at 19:00 GMT. Dots indicate daily locations of the storm’s eye.

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Figure 2.3 Stream functions (+ for cyclonic circulation) after 180 days for a the pom2nd method, b the pom4thMcC method, c the pom4thCmp method, d the sm4thCubicH method, e the sm4thpoly method, and f the pom6th method. For clarity, small values for water depths less than 200m are omitted.

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Figure 3.1a Illustrating how observational points are defined within the neighborhood of a model grid.

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Figure 3.1b Illustrating how temperature (or any variable) is assimilated at subsurface.

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Figure 4.1. Top: model region from fig.1.1. The red-dashed rectangle indicates MMS’ 2003-2004 observations [Donohue et al. 2006]. Lower panel: mooring locations superimposed on an averaged (2003-2004) SSH color map (m). The L’s are full-depth moorings consisting of C/T/D, ADCP’s and current-meters. Other stations are deep measurements only: 500m and 100m above the bottom. Not shown are 25 PIES stations nearly evenly spaced covering the main portion 88o-92oW, 25.5o-28oN.

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Figure 4.2. Model (u,v) at z = 0 m superimposed on color maps of SSH for the 12-month period Apr/2003 through Feb/2004 during the MMS Exploratory Observations [Donohue et al. 2006]. The model analysis uses the Mellor-Ezer scheme. Each panel is a daily-averaged field at the indicated date and the time interval between two consecutive panels is one month. The zero-contour from AVISO altimetry SSH product is shown as the thick black line.

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Figure 4.3. Correlations between modeled and observed (AVISO) SSHA fields for the QEnKFssh25 (see Table 1) analysis: (A) spatial correlation (north of 23oN, west of 84oW and in water depths > 500 m) and (B) time correlation (Mar/01/2003 through May/01/2004).

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Figure 4.4a. Observed (upper panel) and modeled (MEssh25 analysis; lower panel) eigenvectors of the upper-layer (z > 400 m) EOF’s at the six L-moorings shown in Fig.4.1. Red is mode 1 and green is mode 2.

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Figure 4.4b. Observed (blue) and modeled (MEssh25 analysis; green) time series of the upper-layer (z > 400 m) EOF mode-1 at the six indicated L-moorings shown in Fig.4.1. The %energy and correlation coefficient between observed and modeled modes are displayed at top of each panel.

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Figure 4.4c. Observed and modeled (MEssh25 analysis) time series of the upper-layer (z > 400 m) EOF mode-2 at the six indicated L-moorings shown in Fig.4.1. The %energy and correlation coefficient between observed and modeled modes are displayed at top of each panel.

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Figure 4.5. Model (u,v) at z = 0 m superimposed on color maps of SSH for the 12-month period Apr/2003 through Feb/2004, in the Loop Current and the eastern Gulf of Mexico. Locations of the L-moorings are marked. The model analysis uses the Mellor-Ezer scheme. Each panel is a daily-averaged field at the indicated date and the time interval between two consecutive panels is one month. The zero-contour from AVISO altimetry SSH product is shown as the thick black line.

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Figure 4.6a. Observed (blue) and modeled (green; MEssh25) vector sticks at mooring L1 (see Fig.4.1 for location) at the indicated depths 96m (top 2 panels), 750m (next two panels, etc), 1000m and 1400m below the surface. The “ang” on the top panel is the clockwise angle of the local isobath from true north; it is also the y-direction of the sticks. The |CC| and  on the model panels are the magnitude and phase angle, respectively, of the complex correlation between modeled and observed sticks.

………………………………………………………………………………..55


Figure 4.6b. Observed (blue) and modeled (green; MEssh25) vector sticks at mooring L1 (see Fig.4.1 for location) at the indicated depths 96m (top 2 panels), 750m (next two panels, etc), 1000m and 1650m below the surface. The “ang” on the top panel is the clockwise angle of the local isobath from true north; it is also the y-direction of the sticks. The |CC| and  on the model panels are the magnitude and phase angle, respectively, of the complex correlation between modeled and observed sticks.

………………………………………………………………………………..56


Figure 4.6c. Observed (blue) and modeled (green; MEssh25) vector sticks at mooring L1 (see Fig.4.1 for location) at the indicated depths 96m (top 2 panels), 750m (next two panels, etc), 1000m and 2900m below the surface. The “ang” on the top panel is the clockwise angle of the local isobath from true north; it is also the y-direction of the sticks. The |CC| and  on the model panels are the magnitude and phase angle, respectively, of the complex correlation between modeled and observed sticks.

………………………………………………………………………………..57


Figure 4.6d. Observed (blue) and modeled (green; MEssh25) vector sticks at mooring L1 (see Fig.4.1 for location) at the indicated depths 96m (top 2 panels), 750m (next two panels, etc), 1000m and 3250m below the surface. The “ang” on the top panel is the clockwise angle of the local isobath from true north; it is also the y-direction of the sticks. The |CC| and  on the model panels are the magnitude and phase angle, respectively, of the complex correlation between modeled and observed sticks.

………………………………………………………………………………..58


Figure 4.7. The magnitude (upper panel) and phase angle (lower panel), respectively, of the complex correlation between modeled (MEssh25) and observed current profiles at the six L-moorings (see Fig.4.1 for locations).

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Figure 5.1. Similarities and differences between (A) internal waves trapped in a thermocline (upper panel; for clarity only one set of rays are sketched) and (B) topographic Rossby waves in a TRW-valley (lower panel).

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Figure 5.2. (A) AVHRR (Advanced Very High Resolution Radiometry; http://fermi.jhuapl.edu/avhrr/gm/averages/) seven-day composite sea-surface temperature in the Gulf of Mexico in Feb/1993 showing the Loop Current and a warm-core ring further west; (B) contours (dark lines and color shading) of maximum allowable TRW frequency NT = N|Ñh| (cycles/day or cpd) in the vicinity of the Sigsbee escarpment (box in panel A). Here the N = 610-4 s-1. Thin brown contours are isobaths, and the dotted line = 2000 m. The escarpment is identified with the band of high NT oriented northeast to southwest, approximately along the 2000 m isobaths in the north and along the 3000 m isobaths in the south. The “*” is one mooring from Hamilton (2007) and the along-isobath velocity component (daily-averaged, 200 m above the bottom) is plotted in (C) which also shows the corresponding vector sticks. The dashed arrowed lines in the time-series plot in (C) indicate periods when bursts of TRW’s were identified by Hamilton (2007). (Data courtesy of Dr. Peter Hamilton).

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Figure 5.3. A comparison of observed and modeled current variance ellipses at six tall (L) moorings in the east-central Gulf of Mexico (left inset) for the period Apr/2003 through Apr/2004, and also at the Sigsbee (I1) mooring for the period Aug/1999 through Aug/2000, i.e. the “*” mooring shown in Fig.1. Vectors at ellipse centers are 1-year mean velocities but these are not representatives of the long-term means because they were dominated by a few strong current events. Note that scales are different above and below z = 700 m (as indicated by the dotted line). The observational data are courtesy of Dr. Peter Hamilton of SAIC.

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Figure 5.4. Observed (A) and modeled (B) first six Intrinsic Mode Functions (IMF’s) of the south-to-north (v) component velocity at the Sigsbee mooring. Units are m/s (ordinate) and days since Sep/02/1999 (abscissa). The velocity is 200 m above the bottom (water depth  2000 m).

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Figure 5.5. Modeled sea-surface height (color; red = +0.6m, blue = 0.6 m) and velocity (vectors) on (A) t = 50 day showing the warm-core ring Eddy Juggernaut over the mooring location at the Sigsbee escarpment (solid dot). Panels (B) and (C) show the corresponding plots 130 and 260 days later, respectively. The time “t” is Julian day from Sep/02/1999, the same as that used in Figure 5.4.

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Fig.A1.1. A comparison of the wind used in the model with the Qnblend wind on Dec/21/06:00GMT, 1999. Locations of three NDBC stations 42019 (27.9 N 95.4 W), 42035 (29.2 N 94.4 W) and 42040 (29.2 N 88.2 W) are also shown.

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Fig.A1.2. Qnblend and CCMP3 wind comparisons at NDBC buoy 42019. The black line in the time-series plots of U and V in the first 2 panels is for CCMP3 wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for CCMP3 while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for CCMP3 and that in the fourth panel is for Qnblend. Time is from Nov/1999 through Feb/2000 (in GMT).

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Fig.A1.3. Qnblend and CCMP3 wind comparisons at NDBC buoy 42040. The black line in the time-series plots of U and V in the first 2 panels is for CCMP3 wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for CCMP3 while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for CCMP3 and that in the fourth panel is for Qnblend. Time is from Nov/1999 through Feb/2000 (in GMT).

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Fig.A1.4. Comparisons of simulated ocean’s surface currents at NDBC buoy 42019 forced by Qnblend and CCMP3 winds. The black line in the time-series plots of U and V in the first 2 panels is for CCMP3 wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for CCMP3 while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for CCMP3 and that in the fourth panel is for Qnblend. Time is from Nov/1999 through Feb/2000 (in GMT).

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Fig.A1.5. Comparisons of simulated ocean’s surface currents at NDBC buoy 42040 forced by Qnblend and CCMP3 winds. The black line in the time-series plots of U and V in the first 2 panels is for CCMP3 wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for CCMP3 while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for CCMP3 and that in the fourth panel is for Qnblend. Time is from Nov/1999 through Feb/2000 (in GMT).

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Fig.A1.6. Qnblend, CCMP3 and buoy wind comparisons at NDBC buoy 42035. The black line in the time-series plots of U and V in the first 2 panels is for CCMP3 wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for CCMP3 while red are for Qnblend. The blue line is buoy wind data while the purple line is buoy wind-gust data assuming the same directions as the wind data. Stick plot (plotted every 2days for clarity) in the third panel is for CCMP3 and that in the fourth panel is for Qnblend. Time is from Nov/1999 through Feb/2000 (in GMT).

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Fig.A1.7. Qnblend and buoy wind comparisons at NDBC buoy 42019. The black line in the time-series plots of U and V in the first 2 panels is for the buoy wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for buoy data while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for buoy wind and that in the fourth panel is for Qnblend. Time is from Sep/1999 through Sep/2001 (in GMT).

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Fig.A1.8. Qnblend and buoy wind comparisons at NDBC buoy 42035. The black line in the time-series plots of U and V in the first 2 panels is for the buoy wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for buoy data while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for buoy wind and that in the fourth panel is for Qnblend. Time is from Sep/1999 through Sep/2001 (in GMT).

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Fig.A1.9. Qnblend and buoy wind comparisons at NDBC buoy 42040. The black line in the time-series plots of U and V in the first 2 panels is for the buoy wind, while the red line is for Qnblend wind. Similarly, black numbers across the top are for buoy data while red are for Qnblend. Stick plot (plotted every 2days for clarity) in the third panel is for buoy wind and that in the fourth panel is for Qnblend. Time is from Sep/1999 through Sep/2001 (in GMT).

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LIST OF TABLES
Page
Table 4.1. Descriptions of various experiments and the time-mean (from Mar/01/2003 through May/01/2004) spatial correlations “MCorr” of their SSHA with AVISO SSHA in the region north of 23oN and west of 84oW and in water depths > 500 m in the Gulf of Mexico; here, MCorr = Mean[<.aviso>/(<2><aviso2>)1/2],  = SSHA, <.> = spatial correlation over the stated region, and Mean[.] = time-mean. For the NoAssim experiment, the two values of MCorr correspond to time-means over the first four months and over the entire 17-month period respectively.

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Table 4.2. Correlation coefficients (CC; significant to 99% confidence value) between observation and model EOF’s modes 1 and 2 at the L-moorings (see fig.4.1 for locations) and the corresponding %energies. The observed %energies are shaded and are displayed under the mooring column. Dashes (“”; CC’s for mooring L4, for the QEnKFssh25 and MEssh25C analyses) indicate insignificant correlations.

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Table A1.1. Comparisons between observed, Qnblend and CCMP3 winds at NDBC buoys 42019, 42035 and 42040 in the northern Gulf of Mexico. The “R” and “” are the vector correlation (with respect to the observed) coefficient and angle respectively.



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SUMMARY
The goal is to provide the Bureau of Ocean Energy Management, Regulation and Enforcement (BOEMRE) with information and analysis that improve our understanding of the physical oceanography of the Gulf of Mexico. Deliverable products include surface and subsurface current (and other ocean) data that BOEMRE can then use for environmental assessments such as in the oil spill trajectory analysis. To meet this goal, Princeton University proposed to conduct a high-resolution model hindcast of the circulation in the Gulf of Mexico from year 2000 to 2007, a period that is an extension of the hindcast period from 1993 to 1999 previously conducted for BOEMRE [Oey, 2004]. Here, “hindcast” means that observational data from satellite (and other data sources such as hydrography and current-meter mooring) are assimilated into the dynamical circulation model. The circulation model is three-dimensional and time-dependent, and includes realistic topography, surface fluxes (wind, heat and salt fluxes), ocean temperature and salinity fields, as well as 34 daily river discharges from the northern Gulf of Mexico. In this project, the model was further improved from Oey [2004] taking advantage of a number of systematic improvements we have made over the past few years from other works conducted for BOEMRE. The extended hindcast model:


  1. is on a fine grid () that is doubled that used previously,  = 3~7 km instead of 6~15km;

  2. is forced by a higher-resolution wind dataset (1/2o×1/2o instead of 1o×1o) that also has satellite data wind blended into it;

  3. is corrected for intense wind field due to tropical storms using high-resolution and accurate analysis;

  4. is assimilated with satellite sea-surface height and temperature data using ensemble optimal interpolation Kalman filter as well as using the original statistical correlation technique;

  5. has improved numerics to reduce potential bias over steep topography; and

  6. has improved mixed layer physics that also includes the effects of (wind) wave-breaking.

In this project, we also examined both surface and deep currents. Therefore, the extended dataset will not only be subjected to rigorous model-data comparison for the surface currents [as in previous work: Oey, 2004], but is also checked and analyzed extensively against deep observations. Since there is much less data in the deep layers of the Gulf of Mexico than surface, this project will also deal with some fundamental questions on the characteristics of deep currents, as well as their connection with topography. It is hoped that these more process-oriented studies will yield knowledge that is useful for the scientific community in general, and for BOEMRE’ ongoing and future research in the Gulf of Mexico in particular.
In addition to surface and subsurface data which were delivered to BOEMRE in Aug/2009 (currents (u, v, w) and other ocean variables such as sea-surface height SSH, depth-integrated transports (U,V), (potential) temperature T, salinity S, and turbulence eddy viscosity (KM)), the project has also resulted in 2 peer-reviewed publications and one manuscript to be submitted. The 2 publications are summarized in the main text of this report, which therefore focuses on topics related to the submitted manuscript:
Skill-assessments of statistical and ensemble Kalman-filter data assimilative analyses using surface and deep observations in the Gulf of Mexico, part 1: model descriptions & basic comparisons with observations.

The report begins with an introduction (section 1) of the circulation physics of the Gulf of Mexico, as well as a summary of the past modeling efforts at Princeton. These are then followed by section 2 on model descriptions and ways for numerical error-reduction; section 3 on data assimilations; section 4 on skill assessments; and section 5 on a brief summary of “topocaustics” - deep current energetics and trapped topographic Rossby waves. Section 6 concludes the report.


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