# Presentation: 803630

## NUMERICAL MODELING OF COASTAL CIRCULATION: 

- FRONTS, CROSS-SHELF TURBULENT FLUXES AND COASTAL CLIMATOLOGY
- NADYA VINOGRADOVA

- PRESENTATION TO NATIONAL CENTERS FOR ENVIRONMENTAL PREDICTION
- CAMP SPRING, MD

- USM/DMS/SSC
- OCTOBER 26, 2004

**Notes:**
Hello and thank you everyone for coming. I appreciate your interest in my work and I will do my best to keep it simple and appealing through the rest of my talk. The topic of my dissertation is ‘title’.  

## OUTLINE

- INSTABILITY OF SHELF-BREAK FRONTS AND CROSS-SHELF EXCHANGE:
- INTRODUCTION AND STUDY AREA
- GOALS AND OBJECTIVES
- METHODS
- NUMERICAL EXPERIMENTS
- SUMMARY AND CONCLUSIONS
- COASTAL CLIMATOLOGY USING VARIATIONAL INTERPOLATION

## 1. INTRODUCTION AND STUDY AREA 

**Notes:**
  The Gulf of Mexico is a marginal sea. It is connected to the Caribbean Sea by the Yucatan Strait and the only connection with the Atlantic Ocean is through the Straits of Florida. Here’s a highly idealized illustration, describing general circulation in the Gulf. Caribbean Current passes through the Yucatan Strait and enters the Gulf. The current loops anticyclonically around the warm Caribbean waters and heads toward the Straits of Florida. On the continental shelf, which surrounds the margins of the Gulf of Mexico basin, a mean circulation is cyclonic. Generally, the surface temperature in the region of the Loop Current regime ranges from 24 to 27C, whereas along the coast is cooler and ranges between 18 and 21C.  
  The area I’m interested in is the Mississippi Bight region. So, we are zooming in on the northeastern part of the Gulf of Mexico offshore of the Louisiana-Mississippi-Alabama coast. This satellite image shows you a typical example of wintertime temperature front. It is located at the shelfbreak and separates cool shelf water from warmer slope waters. The front in the Mississippi Bight is a dynamical feature, which exhibits a meandering motion, instabilities, warm water intrusion and other signs of variability. A high level of frontal variability, in turn, has an important impact of redistribution of water properties across the shelf, such as heat, momentum, oxygen, speed of sound and others. Therefore, the goal of this study is to characterize and understand variability of the frontal flow and to quantify cross-frontal exchange. 

## 1. GOALS AND OBJECTIVES 

- TO EXAMINE THE ROLE OF LOCAL FRONTAL INSTABILITY ON THE CROSS-FRONTAL EXCHANGE IN THE ABSENCE OF EXTERNAL FORCES
- TO STUDY SENSITIVITY OF FRONTAL STABILITY AND CROSS-FRONTAL EXCHANGE TO EXTERNAL FACTORS:
- BOTTOM TOPOGRAPHY
- WIND STRESS
- RIVER INFLOWS
- LOOP CURRENT EDDY INTRUSION

**Notes:**
Specifically, I address the following objectives:

## 1. METHODS 

- FRONTAL DYNAMICS AND CROSS-FRONTAL EXCHANGE ARE EXAMINED USING TWO NUMERICAL MODELS:
-   NRL MODEL (REALISTIC EXPERIMENT):
-  REAL-TIME INTRA-AMERICAS SEA OCEAN NOWCAST/FORECAST SYSTEM
-  DEVELOPED AT NRL (*MARTIN, 2000*). RESULTS ARE PROVIDED BY: DR. KO AND DR. PRELLER
-  DAILY FORECAST OF  	 	ARE USED AS BACKGROUND DATA FOR COMPARISON

- MONTHLY MEAN SURFACE TEMPERATURE

**Notes:**
	Frontal dynamics is examined using two numerical models. One of which is complex and as faithful as possible. And another is a simplified model to explain the essential physics. There is an extensive modeling database covering Northern Gulf of Mexico. Among them is a real-time Intra-Americas Seas Ocean Nowcast/Forecast System. The system is developed at the Naval Research Laboratory at the Stennis Space Center by Dr. Ko and Dr. Preller. During my talk I’ll refer to the system as NRL model. 
	The system is operational, daily nowcasting and forecasting sea surface elevation, and 3D fields of temperature, salinity and currents. Here is a monthly mean surface temperature during wintertime, computed based on results of realistic simulation of the NRL model. As seen in this Figure, temperature front is located near the shelfbreak at a depth of 50 – 70 m, with a mean temperature value of 18.2C (yellow color). 
	I use the results of this model to reveal dynamics of the front, shelfbreak current, associated with the front, cross-frontal fluxes and other background information. The results of the realistic modeling experiments reveal dynamics of the front, shelfbreak current, associated with the front, cross-frontal fluxes and other background information. However, neither observations nor a realistic model experiments allows one to differentiate the importance of different factors controlling frontal dynamics. Because, in the realistic experiment many factors affect the front simultaneously. 

## 1. METHODS 

- 2. ECOM MODEL (IDEALIZED EXPERIMENTS):
- TO ISOLATE DOMINANT PROCESSES AND TO STUDY OCEAN RESPONSE TO INDIVIDUAL FACTORS
- TO USE SIMPLIFIED NUMERICAL MODEL AS A CONTROLLED
- ENVIRONMENT TO UNDERSTAND PHYSICS OF THE PROMINENT
- PHENOMENA
- RESULTS OF THE IDEALIZED MODEL ARE COMPARED WITH
- THE NRL (REALISTIC) MODEL RESULTS TO IDENTIFY SIMILAR PHYSICS AND PROCESSES
- ESTUARINE AND COASTAL OCEAN MODEL (ECOM), DESIGNED BY HYDROQUAL, INC. (2002) IS USED AS IDEALIZED MODEL

**Notes:**
	On the other side, simplified numerical models allow one to isolate any particular process and to examine the response of the ocean to it. In particular, through a series of idealized numerical experiments, we can study physical mechanism and contribution of different external forces on frontal stability and cross-frontal exchange. Simplified numerical model is therefore, a controlled environment, in which we can isolate a process of interest and understand physics of the prominent phenomena. Results, predicted by idealistic model, are then compared with realistic experiment in order to identify similar physics controlling frontal dynamics. 
	To explain the physics of shelfbreak fronts, it is necessary to have a model that is able to simulate coastal processes. For that purpose, I use the Estuarine and Coastal Ocean Model (ECOM).

## 1. METHODS 

- 2. IDEALIZED EXPERIMENTS (CONT.):
- ECOM:
-  3D, TIME-DEPENDENT, SIGMA-COORDINATE, FREE SURFACE
-  SEEKS A SOLUTION ON A INITIAL-BOUNDARY VALUE PROBLEM IN A DOMAIN
-  GOVERNING EQUATIONS: CONSERVATION OF MOMENTUM, HEAT, SALT AND MASS (HYDROSTATIC AND BOUSSINESQ APPROX.); EQUATION OF STATE
-  MIXING IS PARAMETERIZED USING TURBULENCE CLOSURE: VERTICAL – MELLOR-YAMADA 2.5 (*MELLOR-YAMADA, 1982*), HORIZONTAL – SMAGORINSKY (*SMAGORINSKY, 1963*)
-  MODE SPLITTING TECHNIQUE: 2D (EXTERNAL) AND 3D (INTERNAL)
-  ECOM WAS TESTED IN COASTAL ENVIRONMENT (HYDROQUAL, MS BIGHT)

**Notes:**
	The ECOM is a three-dimensional, time dependent, sigma coordinate, free surface model. The model seeks a solution of an initial-boundary value problem in a specified domain. Governing equations are in the Eulearian frame of reference and consists of equations fro momentum, heat, salt and mass. The two simplifications in the model are the hydrostatic and Boussinesq approximations.  The small sub-grid processes, such as horizontal and vertical and horizontal mixing are parameterized using the turbulence closure. The vertical mixing coefficients are computed using the Mellor-Yamada 2.5 turbulence closure scheme. The horizontal diffusivities are computed are computed using Smagorinsky scheme.
	The ECOM incorporates a mode splitting technique, solving the two-dimensional fro the fast (external) and the three-dimensional equation for the slower (internal) processes. The ECOM equations are solved explicitly for the horizontal derivatives and implicitly for the vertical. 
	Previous studies demonstrate that the ECOM hydrodynamics has a history of successful application to oceanic and coastal waters. In particular, the ECOM has been implemented to the Mississippi Bight by HydroQual, Inc two years ago. We compared the results of the ECOM simulations with measurements, which showed a good model/data agreement. Serge and I presented the results of this comparison on Departmental seminar earlier, thanks to Charlotte who kindly invited us to give a talk. 
	So, my previous experience with the ECOM was a good motivation to run idealized experiments using the ECOM hydrodynamics. 

## 1. METHODS 

- ECOM EXPERIMENTS:
- FIVE TYPES OF THE ECOM EXPERIMENTS
-  REFERENCE EXPERIMENT
- TOPOGRAPHIC EXPERIMENTS
- WIND EXPERIMENTS
- RIVER DISCHARGE EXPERIMENTS
- OCEANIC EDDY INTRUSION EXPERIMENT

**Notes:**
Therefore, response of the shelfbreak front to different types of forcing is studied through a series of the ECOM experiments. Specifically, to address my objectives, five types of numerical experiments are designed. The first is a reference experiment, my standard run. The second is a series of topographic experiments, followed by the experiment examining the effect of wind, river discharges and oceanic intrusion event.

## OBJECTIVES: 

- OBJECTIVES:
- TO EXAMINE THE ROLE OF LOCAL FRONTAL INSTABILITY ON THE CROSS-FRONTAL EXCHANGE
- EXPERIMENT DESIGN:
***1. ECOM DOMAIN:***
- 300 KM x 200 KM x 1KM
- Y – NORTHWARD,
- X – EASTWARD,
-      ALIGNED WITH ISOBATHS

**Notes:**
	The first type of simulations is the reference experiment, where I set up the ECOM to represent an idealized coastal ocean and run it without anu external forces. This type of experiment reveal the role of local frontal instability on the cross-frontal exchange. 
	For this experiment, the ECOM is set to represent an ocean domain of 1-km deep, 200-km wide and 300-km long. The y-coordinate increases northward, and the x-coordinate increases eastward. Direction of the x-coordinate is aligned with isobath in order to simplify model bathymetry. 

## 2. ECOM BOTTOM TOPOGRAPHY: 

- 1. REFERENCE EXPERIMENTS - DESIGN

***2. ECOM BOTTOM TOPOGRAPHY:***
- DETERMINED FROM THE FIT TO AN ALONG-SHORE AVERAGE BOTTOM SLOPE
- HYPERBOLIC FUNCTION FIT:

**Notes:**
	The model bottom slope for the reference case is determined as an approximation for an average slope in the study area.  Here’s a two-minute bathymetry in the Mississippi Bight. The steepness of the bottom topography varies from gentle at the western side of the domain to a steep one at the eastern side of the Bight. The reference bathymetry is determined from the fit of a hyperbolic tangent function to the average slope in the Mississippi Bight. The fit is given by the following formula. Where Hs is the shelf depth (20m), Hd is maximum depth in the domain (1 km), ym is the location of maximum slope (118 km), and alpha is a lateral extent of slope (20 km). The steepness of the slope is regulating by this parameter alpha. The averages slope and the hyperbolic fit is shown on this Figure. 
	Based on a computed bottom slope, idealized model bathymetry is determined as uniform in the x-direction (alongshore direction) and deepens gradually from the shallow shelf to a steep slope in y-direction. 

## 3. ECOM RESOLUTION: 

***3. ECOM RESOLUTION:***
- HORIZONTAL GRID SPACING = 5 KM < ROSSBY RADIUS (HORIZONTAL SCALE OF RESPONSE, 20 – 30 KM IN MS BIGHT)
- VERTICAL: 16 SIGMA LAYERS;
- VERTICAL INCREMENT VARIES :
- HIGHER RESOLUTION
- NEAR SURFACE AND BOTTOM

- ECOM VERTICAL RESOLUTION

**Notes:**
	It is essential to ensure that the model’s horizontal resolution in a cross-front direction (y-direction) is adequate to resolve the Rossby radius of deformation. Baroclinic Rossby radium in the Mississippi Bight is about 20 – 30 km and it characterizes the horizontal scale of response in a rotating fluid. 
	There are 16 levels in the vertical. As previously mentioned, the ECOM uses bottom-following sigma coordinates in the vertical. Previous studies suggest that use of such coordinate system better resolves coastal processes than the ordinary Cartesian coordinate system. The vertical increment varies in thickness to accommodate more resolution near the surface and the bottom.  

## 4. ECOM INITIAL CONDITIONS: 

- THE GOAL IS TO EXAMINE EVOLUTION OF THE FRONT TYPICAL FOR THE MS BIGHT  THE ECOM IS INITIALIZED WITH THE OBSERVED FRONT

- 1. REFERENCE EXPERIMENTS - DESIGN

- DATA WERE COLLECTED DURING NORTHEASTERN GULF MEXICO PHYSICAL OCEANOGRAPHY PROGRAM (NEGOM)

- CTD TRANSECTS  WERE **** TO ISOBATHS; COVER THE AREA
-  DATA IS AVERAGED ALONG-SHORE AND BI-LINEARLY INTERPOLATED IN SPACE  I.C. FOR THE ECOM
- THERMOCLINE IS OBSERVED AT  50 – 70 M

- ECOM INITIAL TEMPERATURE

**Notes:**
	Each oceanic front has a unique character, based on water masses involved, geographical location and other factors. The goal of my study is to examine evolution of the front, that is typical for the Mississippi Bight. Therefore, the ECOM is initialized with the frontal flow, that was actually observed in the area. 
	To determine frontal characteristics, I used the data collected during winter in support of the NEGOM program. The position of the CTD stations followed the line orthogonal to isobaths as shown on this Figure. They pretty much cover the area, represented by the model. 
	The NEGOM data are averaged in the along-shore direction and bilineary interpolated in space. The resultant 3D field is used as initial conditions for the ECOM experiments. Here’s the initial condition for temperature. Cool shelf waters are separated from warmer, stratified slope waters by a transition region at the shelfbreak. The depth of thermocline is approximately 50  - 70 m. 

## 1. GEOSTROPHIC ADJUSTMENT: 

***1. GEOSTROPHIC ADJUSTMENT:***
- IN EACH EXPERIMENT, ECOM IS RUN DIAGNOSTICALLY FROM THE STATE OF REST FOR 15 DAYS TO REACH THE EQUILIBRIUM

- SSH ADJUSTS TO PRESCRIBED TEMPERATURE AND SALINITY
- COLDER SHELF  LOWER SSH
- MAX GRADIENT AT SHELFBREAK (100 KM OFFSHORE)

- AFTER 2 WEEKS: STEADY GEOSTROPHIC JET
- JET LOCATION: SHELFBREAK, ALIGNED WITH THE FRONT
- JET VELOCITY ~ 25 CM/S, SIMILAR TO OBSERVED 25 – 20 CM/S IN THE NEGOM DATA

- SSH

- SSH AND CURRENTS

**Notes:**
	Each experiment begins from rest. In order for the system to reach equilibrium, the ECOM is run diagnostically for 15 days. During this period, the initial zero surface elevation gradually adjusts toward the prescribed density distribution. The cold and dense shelf waters have lower surface elevation compared to the warmer and lighter slope water. The distance of 100 km offshore corresponds to the location of the ECOM shelfbreak. 
	After 2 weeks of diagnostic integration a steady geostrophic current is formed. The jet is located at the shelfbreak, aligned with the front and flows eastward. Current velocity is about 25 cm/s, similar to those observed in the NEGOM data

## 2. FRONTAL INSTABILITY: 

- 1. REFERENCE EXPERIMENTS - RESULTS

- ZONAL STRUCTURE IS MODIFIED
- FRONT BECOMES NARROWER
- DISTURBANCES PROPAGATE EASTWARD
- END: ANTICYCLONIC WARM EDDIES ARE DEVELOPED

- SHELF IS GRADUALLY COOLING  TOPOGRAPHIC UPWELLING
- UPWARD VERTICAL VELOCITY AT THE SHELFBREAK

***2. FRONTAL INSTABILITY:***
- AFTER ADJUSTMENT, THE ECOM IS RUN FOR 30 DAYS

- 		SSH			     TEMPERATURE AT THE THERMOCLINE DEPTH (50 M)

**Notes:**
	After the adjustment, the ECOM is integrated for a 30-day period. Here’s an example of meander development in the ECOM during 30 days of numerical integration. After 10 days initially zonal structure of the front is perturbed and a wavelike form develops. Front get narrower. Once established, meander continue to grow toward the end of integration. By the end of integration: dominant feature is a strong anticyclonic circulation with associated warm eddies on the deep side of the front. 
	Here’s the evolution of temperature front located at the depth of thermocline. As integration continues, shelf is gradually cooling, indicating topographic upwelling of the cold water onto the shelf. Topographic upwelling is also supported by upward vertical velocities at the shelfbreak (not shown)

## 2. FRONTAL INSTABILITY: 

- 1. REFERENCE EXPERIMENTS - RESULTS

***2. FRONTAL INSTABILITY:***
- ANALYSIS OF ENERGETICS REVEALS NATURE OF DISTURBANCES
- FIELDS ARE DECOMPOSED INTO ALONG-CHANNEL AVERAGE (MEAN, OVEBAR) AND DEVIATION (EDDY COMPONENT, PRIME): 		  , WHERE
- AVERAGING IS APPLIED TO ALL ECOM EQUATIONS
- SUBSTITUTION INTO ORIGINAL GIVES A NEW SYSTEM FOR EDDY QUANTITIES
- MANIPULATIONS  EQUATION FOR EDDY KINETIC ENERGY

- CONVERSION OF MEAN TO EDDY KINETIC ENERGY BY REYNOLDS STRESSES
- CONVERSION OF POTENTIAL ENERGY TO EDDY KINETIC ENERGY
- LOSS OF ENERGY BY DISSIPATION

**Notes:**
	To understand the nature of the disturbances, I look at the energetics of the system. The fields are decomposed into an along-channel average and deviation from this field. They are referred to as mean and eddy fields, respectively.  A mean quantity is denoted by an overbar and defined as follows: where L is the channel length. A deviation (eddy) component is denoted by a prime and defined as follows.
	I applied the same averaging procedure to all ECOM equations. Then I substituted them into the original system of equations, which resulted 
in a new system for eddy quantities. After adding, multiplying and manipulating new equations in a certain way, I obtained the equation for eddy kinetic energy, defined as follows:
	The interpretation is that the time rate of change of eddy kinetic energy is the sum of (1) conversion of mean to eddy kinetic energy by Reynolds stresses, (2) conversion of potential to eddy kinetic energy and (3) loss of energy by dissipation. 

## 2. FRONTAL INSTABILITY: 

***2. FRONTAL INSTABILITY:***

- MEAN KE AND EDDY KE:
-  MEAN KE  ;
-  EDDY KE  AS MEANDERS GROW

- TOTAL PE AND TOTAL KE:
-  LIGHTER SLOPE WATER , HEAVIER SHELF WATER  TO TAKE ITS PLACE  PE DROP;
-  TKE , HOWEVER AMPLITUDE OF KE IS LESS THAN AMPLITUDE OF PE

- BAROCLINIC AND BAROTROPIC TERMS:
-  BAROCLINIC: PE IS CONVERTED TO EKE
-  BAROTROPIC: SOURCE OF INSTABILITY IS KE OF MEAN FLOW
-  1 WEEK: BAROCLINIC INSTABILITY
-  2-3 WEEKS: BAROTROPIC TERM < 0  EDDIES INTENSIFY MEAN FLOW THROUGH REYNOLDS STRESSES

**Notes:**
	Symbolically evolution equation for eddy kinetic energy can be written as  follows. As you can see from the equation, energy is partitioned into 3 components: potential energy, mean kinetic energy and eddy kinetic energy. To analyze the nature of disturbances, interchanges among these three forms are computed at every time step. 
	Middle panel: The following Figures shows a time series of the total PE and Total KE. As we saw from previous animation, lighter slope water has been raised and heavier shelf water has been lowered to take its place. This correspond to the PE drop. Total KE grows for the period of integration. However, supply of KE is smaller compare to the supply of PE to the system.
	Upper panel: Mean and eddy KE, computed at every time step. KE of the mean flow decreases w/time, whereas KE of perturbation steadily increases. This is consistent with growing meanders seen on previous animation. 
	Bottom panel: shows  interchanges among energetics. Baroclinic conversion term (blue): waves extract PE from the system and convert into eddy KE. Barotropic conversion term (red): when source of instability is kinetic energy of the mean flow. Analysis of energetics shows a hybrid baroclinic-barotropic instability of the flow. During the first week of the ECOM integration, fluctuations are clearly baroclinic: they extract PE and convert into EKE. Baroclinic conversion term is large. After 10-15 days, when meanders are established, the barotropic conversion term comes into play. Negative barotropic term represents transfer of energy from eddy to mean flow by Reynolds stresses. In other words, eddies feed and intensify a mean flow. 

## 3. CROSS-FRONTAL EXCHANGE: 

***3. CROSS-FRONTAL EXCHANGE:***
- ASSUME: 		   , CROSS-FRONTAL TURBULENT HEAT EXCHANGE IS COMPUTED AS VELOCITY-TEMPERATURE COVARIANCE:
- POSITIVE CROSS-FRONTAL DIRECTION IS OFFSHORE, I.E. DIRECTION OF

- ECOM HEAT FLUX

- NRL MODEL HEAT FLUX

-  COMPUTED AT THERMOCLINE DEPTH
-  X – DISTANCE FROM THE FRONT. ZERO – FRONTAL POSITION
-  COLD SHELF: < 0 - TRANSPORT OF COLD WATER OFFSHORE; > 0 – OFFSHORE TRANSPORT OF HEAT
-  FRONT ENHANCES TRANSPORT

-  COMPARISON WITH NRL MODEL FLUX TO DETERMINE CONTRIBUTION OF LOCAL FRONTAL INSTABILITY
-  FLUX IS COMPUTED ALONG CHARACTERISTIC SLICE AT THERMOCLINE DEPTH
-  SIMILAR BEHAVIOR WITH ECOM FLUX
-  AMPLITUDE DIFFERENCE IS DUE TO EXTERNAL FORCES  CONTRIBUTION OF LOCAL INSTABILITY ~ 35%

- NRL MODEL SST

**Notes:**
	Assuming the product of seawater density, ro0 and specific heat Cp  are relatively constant, velocity-temperature covariance reflects eddy heat flux. Here Vn prime is eddy velocity in the cross-frontal direction, T prime is deviation of temperature.  Positive cross-frontal direction is chosen to be offshore and coincides with the direction of temperature gradient.
	Figure on the left shows the ECOM monthly mean cross-frontal heat exchange, computed at the depth of seasonable thermocline, which is 50 m. Position of zero on x-axis corresponds to the position of the front. Values of the flux are negative to the left of the front and positive to the right of it, indicating the exchange between the shelf and slope waters. Furthermore, since the shelf is colder, negative values of the flux imply transport of cold water offshore. Positive values of the flux indicate offshore transport of heat. In addition, maximum exchange occurs at the position of the front (zero). Therefore, the shelfbreak front enhances turbulent heat transport across the shelf. 
	To examine contribution of local frontal instability to the cross-frontal exchange, the ECOM flux is compared with the results of the realistic experiment of the NRL model. The NRL model flux is computed along the characteristic slice, which goes across the shelf. Figure to the right shows a monthly mean turbulent heat flux, computed at the thermocline depth. Zero position on x-axis represent the position on the slice, where it intersects the front. Similar to the ECOM flux, nonzero values at the frontal point indicate transport across the front. Again, the front does not act as a barrier for the exchange between the shelf and slope. In order to make sure that disturbances in both models are of the same kind, I performed analysis of mean quantities. This analysis revealed similar background currents that undergo instabilities. Based on that we can conclude that amplitude difference between the two fluxes are due to external forces, which are present in the NRL model. Therefore, contribution of frontal instability into the cross-frontal exchange is about 35% of the total eddy flux, which is an approximate amplitude difference between the two fluxes. 

## OBJECTIVES: 

- OBJECTIVES:
- TO INVESTIGATE THE IMPACT OF TOPOGRAPHY ON THE FRONTAL STABILITY AND EXCHANGE ACROSS THE SHELF
- EXPERIMENT DESIGN:
-  4 EXPERIMENTS WITH VARYING SLOPE ARE CONDUCTED
-  SLOPE MAGNITUDE INCREASES: GENTLE, MEDIUM, REFERENCE, LARGE AND STEEP SLOPES
-  ECOM SLOPES REPRESENT WESTERN (GENTLE) AND EASTERN (STEEP) REGIONS OF MS BIGHT

**Notes:**
	Sensitivity to the bottom topography is analyzed through a series of five experiments with varying steepness of the ECOM bottom slope. Magnitude of the slope progressively increases. The slopes refer as gentle, medium, reference, large and steep. The magnitude of the slop are chosen to be representative for the western (gentle) and eastern (steep) sides of the Mississippi Bight bathymetry.
	All other ECOM parameters are similar to the reference experiment.

## 1. GEOSTROPHIC ADJUSTMENT: 

***1. GEOSTROPHIC ADJUSTMENT:***
- DIAGNOSTIC RUN FOR TWO WEEKS TO REACH EQUILIBRIUM
- SSH AMPLITUDE DECREASES WITH STEEPNESS
- A SIMPLE ANALYTICAL MODEL, DERIVED FOR THE ECOM DIAGNOSTIC COMPUTATIONS, CONFIRMS THE RESULT FOR THE SPECIFIED DENSITY DISTRIBUTION

**Notes:**
	Similar to the reference run, each topographic experiment begins from rest and run diagnostically for two weeks in order for the system to reach equilibrium. This Figure shows adjusted surface circulation for the 4 topographic experiments. In all cases, a strong geostrophic current is developed, flowing eastward, similar to the reference case. The noticeable difference is a varying amplitude of surface elevation, which decreases as the steepness of the bottom increases.  
	The theory behind it lies in the joint effect of the topography and density gradient of the flow. To explain negative correlation between bottom steepness and surface elevation, I considered approximate equations for the baroclinic flow over topography in the ECOM diagnostic computations. A simple analytical model, derived for the ECOM equations, demonstrated that for the specified density distribution, increase of the bottom steepness leads to decrease in the initial surface elevation gradient. 

## 1. FRONTAL INSTABILITY: 

- 1. TOPOGRAPHIC EXPERIMENTS - RESULTS

- INSTABILITIES GENERATE A WAVE , WHICH PROPAGATES EASTWARD
- SLOPE STEEPNESS DETERMINES EDDY ACTIVITY
- GENTLE SLOPE: WEAK ACTIVITY
- STEEP SLOPE: MEANDERS PINCH OFF AS EDDIES

- STEEPNESS LEADS TO LARGER AMPLITUDES OF INSTABILITIES
- CROSS-FRONTAL GRADIENT RISES
- THERMAL FRONT IS DISTORTED
- STRONG UPWELLING

- 		SSH			     TEMPERATURE AT THE THERMOCLINE DEPTH (50 M)

**Notes:**
	After several days of numerical integration, the perturbations in the frontal structure start to appear. Then the disturbances set up a wave on the front, which propagates along the front with an eastward flowing current. For the experiment with the steep slope, by the end of integration, the meanders on the front become so distorted that the loops are closed, and pinch off as an eddy.
	Cross-frontal temperature gradient rises. As slope gets steeper, instabilities develop faster and of larger amplitudes. Thermocline is distorted. Strong upwelling is persistent feature of the frontal circulation at the thermocline depth. The cold shelf waters upwelled from the deep. 

## 1. FRONTAL INSTABILITY: 

***1. FRONTAL INSTABILITY:***

- JET MEANDERS TO CONSERVE PV:
- CURRENT MOVES DOWN-SLOPE  DEPTH INCREASES  POSITIVE VORTICITY, CCW MOTION
- CCW MOTION BRINGS WATER UP-SLOPE  DEPTH DECREASES  ADD NEGATIVE VORTICITY, CW MOTION
- CW MOTION BRINGS WATER DOWN-SLOPE
- .... MEANDERING CURRENT

-    STEEPER SLOPE  LARGE PV GRADIENT  INDUCES MEANDER DEVELOPMENT

**Notes:**
	The reason why the initial shelfbreak jet starts a meandering motion is to conserve potential vorticity. When the current moves down-slope, the changes in relative vorticity are positive. The tendency of the current is to move counterclockwise. The counterclockwise motion brings the water up-slope, which squeezes the water column. This generates additional negative relative vorticity, which tends to move the flow clockwise. A clockwise motion brings the water down-slope again. Therefore, a meandering current is produced. 
	The steeper the slope, the larger gradient of PV. That explains why the slope enhances development of meanders.

## 2. CROSS-FRONTAL EXCHANGE: 

***2. CROSS-FRONTAL EXCHANGE:***

- ABSOLUTE VALUES OF MEAN CROSS-FRONTAL FLUX
- INCREASES WITH STEEPNESS
- COLD SHELF INTRODUCE GRAVITATIONAL ACCELERATION COMPONENT
- EFFECT IS STRONGER FOR STEEPER TOPOGRAPHY

- LINEAR RELATION BETWEEN GS, MS, RS
- LINEARITY COEFFICIENT = 1 (BLUE LINE)

- LS, SS: NO SUCH RELATION
- STEEPER SLOPE DIVERGES MORE  CRITICAL VALUE OF THE SLOPE INCREASE

- CROSS-FRONTAL FLUX VALUES

- FLUX CHANGE VS. BOTTOM SLOPE CHANGE

**Notes:**
	Absolute values of the monthly mean cross-frontal heat exchange. Cross-frontal heat flux increases with increase of bottom steepness. Along with previously mentioned PV gradient, for the cold shelf water, the presence of sloping topography provides a gravitational acceleration component. The effect is stronger as topography becomes steeper. 
	In addition, there is a linear relation between gentle, medium and reference slopes. Moreover, coefficient of linearity is equal to one (points lie on a blue line). It mean if the bottom is reduced on 50%, the frontal flux is also reduced on 50%. However, there is no such relation for larger magnitudes of the slopes (LS and SS). The steeper the slope, the more flux diverges from the blue line. It means, that after a certain critical value of the slope, the flux increases with acceleration, which means, that even a small change in the bottom steepness might lead to a rapid increase of the cross-frontal transport. 

## 2. CROSS-FRONTAL EXCHANGE: 

***2. CROSS-FRONTAL EXCHANGE:***
- COMPARE WITH NRL MODEL
- CROSS-FRONTAL FLUX ALONG TWO TRANSECTS: GENTLE AND STEEP

-   POSITIVE CORRELATION BETWEEN BOTTOM STEEPNESS AND FLUX MAGNITUDE
-   STEEPER SLOPE RESULTS IN LARGER FRONTAL FLUX

- NRL MODEL: CROSS-FRONTAL FLUX

- NRL MODEL BATHYMETRY AND TRANSECT POSITIONS

**Notes:**
	The pattern observed in the ECOM idealized experiments with varying bottom topography is compared with the NRL realistic model results.  Cross-frontal turbulent heat flux is computed along two cross sections shown on Figure. The left (red) line in Figure intersects the shelfbreak front, which is located over the gentle slope. The right (blue) line in Figure intersects the front on the eastern, steeper side of the domain.
	 Positive correlation between the magnitude of the NRL heat flux and bottom steepness agrees with the ECOM results.

## OBJECTIVES: 

- OBJECTIVES:
- TO INVESTIGATE THE IMPACT OF WIND ON THE FRONTAL STABILITY AND EXCHANGE ACROSS THE SHELF
- EXPERIMENT DESIGN:

-  MS BIGHT WINTERTIME WINDS ARE VARIABLE
-  WIND SPEED AND DIRECTION AT NDBC BUOY (EAST OF MS DELTA)
-  WINDS ROTATE CW; CHANGE DIRECTION EVERY 7-10 DAYS
-  MONTHLY MEAN WIND: 6.6 M/S, NORTHEASTERLY COMPONENT
-  4 TYPES OF WIND EXPERIMENTS:
-  SW: SEWARD (0O FROM NORTH)
-  LW: LANDWARD (180O FROM NORTH)
-  DN: DOWNWELLING-FAVORABLE (90O)
-  UP: UPWELLING-FAVORABLE (270O)

**Notes:**
	In the MS Bight, wintertime winds are variable. The following Figure shows variation in wind speed and direction at the NDBC buoy, located east of the MS Delta. Winds rotate CW, changing their direction every 7-10 days. Monthly mean wind speed is 6.6. m/s and has northeasterly component. 
	Wind from any direction is capable to change frontal dynamics. Consequently, to examine the impact of wind forcing on cross-frontal exchange, experiments with 4 types of wind are considered: Seaward, blowing 0 deg from north; Landward, blowing 180 deg from north; upwelling-favorable, blowing 270 deg from north; and Downwelling-favorable, blowing 90 from north. 

## 1. FRONTAL INSTABILITY: 

- WIND-DRIVEN MOTION ALTERS INITIAL FLOW
- UP: FASTEST GROWTH RATES (ADD DOWNWIND COMPONENT)
- BOTH ANTICYCLONIC/CYCLONIC EDDIES ARE DEVELOPED

- WIND CAUSES ADDITIONAL FLUCTUATIONS
- UP: OFFSHORE MOVEMENT OF HEAVIER WATER ATOP OF LIGHTER WATER  ADDITIONAL SOURCE OF INSTABILITIES
- STRONG VERTICAL MOTION
- UP, SW: INITIAL TOPOGRAPHIC UPWELLING IS INTENSIFIED; DN, LW: ADDITIONAL DOWNWARD MOTION

***1. FRONTAL INSTABILITY:***

- 		SSH			     TEMPERATURE AT THE THERMOCLINE DEPTH (50 M)

**Notes:**
	After two weeks of adjustment, in all wind experiments, an eastward shelfbreak jet is developed.  Upwelling wind slightly intensifies the initial geostrophic jet, due to additional downwind component. Downwelling wind blows in the opposite direction to the geostrophic current (westward). Consequently, it slightly slows down the initial jet.
	As integration continues, wind-driven motion alters initial density-driven current. Frontal instabilities grows to large-amplitude waves. The fastest growth rate during upwelling wind. 
	Due to Ekman theory, upwelling induces offshore movement of water. This offshore water transport carries heavier shelf water atop the lighter slope water. Since the center of gravity is raised, potential energy is released into system. The available potential energy feeds the kinetic energy of disturbances, leading to instability, which eventually destroys the shelfbreak jet. 
	The initial topographic upwelling is intensified during the upwelling and seaward winds. During the downwelling and landward wind, an additional downward motion is generated.

## 2. CROSS-FRONTAL EXCHANGE: 

- EDDIES MAJOR SOURCES FOR CROSS-FRONTAL TURBULENT EXCHANGE  EDDY ACTIVITY AND HEAT FLUX ARE POSITIVELY CORRELATED
- WIND FROM EITHER DIRECTION ENHANCES EXCHANGE RELATIVE TO THE REFERENCE EXPERIMENT
- DN: MIN; UP: MAX, ALMOST DOUBLE

- BEGINNING : SIGNIFICANT HEAT EXCHANGE IS DUE TO ADJUSTMENT OF DENSITY CURRENT
- AFTER ADJUSTMENT: FLUX INCREASES DUE TO MEANDER DEVELOPMENT
- GENERAL TREND: FLUX AMPLITUDE DECREASES

***2. CROSS-FRONTAL EXCHANGE:***

- CROSS-FRONTAL FLUX VALUES

- CROSS-FRONTAL FLUX TIME SERIES

**Notes:**
	Eddies and meanders are major sources for turbulent heat exchange. Consequently, eddy activity and heat flux are positively correlated. Maximum cross-frontal exchange occurs during upwelling-favorable wind, followed by exchange during seaward wind, landward and downwelling wind. Wind from either direction enhances the cross-frontal exchange relative to the reference experiment. 
	Here’s time series of heat fluxes across the front during a month of integration. In the beginning of integration, there is a significant heat exchange due to the adjustment of density currents. After the adjustment, due to the frontal instabilities, meanders start to develop causing the increase of the heat flux. The maximum heat flux occurs when the meanders are detaching from the front. Upwelling wind is the most efficient in driving cross-frontal exchange. Upwelling winds can almost double the heat flux across the shelf compare to the downwelling winds 

## 2. CROSS-FRONTAL EXCHANGE (COMPARISON WITH NRL MODEL): 

- 1. WIND EXPERIMENTS - RESULTS

- STRONG UPWARD MOTION ALONG THE JET
- SIMILAR RESULTS IN THE ECOM: MAX VELOCITY AT SHELFBREAK; SIMILAR MAGNITUDES (10-4)
- TWO NRL MODEL SOLUTIONS ARE CONSIDERED: DOWNWELLING AND UPWELLING EVENTS (t1, t2)
- HEAT EXCHANGE DURING UPWELLING ALMOST DOUBLED VS. DOWNWELLING

- ECOM VERTICAL VELOCITY FOR UPWELLING AND DOWNWELLING WINDS

- NRL MODEL: MONTHLY MEAN VERTICAL VELOCITY AT 50 M

- NRL MODEL HEAT FLUX DURING UPWELLING AND DOWNWELLING WINDS

**Notes:**
	To support the relationship between the upwelling/ downwelling events and the increasing/decreasing of the heat flux, the results of the ECOM idealistic experiment are compared with the realistic NRL model results. The vertical shears of the NRL model vertical velocity, is obtained from the divergence of the horizontal velocity using the continuity equation.
	Here’s monthly mean vertical velocity of the NRL model, computed for 50-m depth. Strong upward motion (w>0) occurs in the area of a strong shelfbreak current, which is aligned with the thermal front. Similar results are demonstrated for the ECOM vertical velocities (Figures). The maximum vertical velocity of the ECOM is produced at the location of the shelfbreak front. Furthermore, velocity magnitude is of the order of 10-4 in both models.
	To examine the relationship between the water vertical motion and the cross-frontal heat exchange, predicted by the ECOM, two events in the NRL model solution are considered. One is a strong downwelling event, which occurs in the vicinity of the front . Another is a strong upwelling event in the frontal area. The NRL model vertical velocities for both events are analyzed along the characteristic slice, chosen as shown on Figure. 	As illustrated on Figure, the heat exchange during the upwelling event is almost twice larger compared to the heat transport during the downwelling event. This is consistent with the ECOM results, which show the same difference by a factor of two. 

## AFTER MIXING, MODIFIED WATER DISCHARGES ON SHELF;  

- RIVER/OCEAN INTERACTION BEGINS IN ESTUARY, WHERE MIXING OCCURS;
- AFTER MIXING, MODIFIED WATER DISCHARGES ON SHELF;

- OBJECTIVES:
- TO EXAMINE THE EFFECTS OF TRANSFORMED WATER ON FRONTAL CIRCULATION
- EXPERIMENT DESIGN:
-  4 EXPERIMENTS WITH VARYING CROSS-FRONTAL ANOMALIES (WEAK TO STRONG)
-  FRESHWATER DISCHARGE DURING WINTER IS MODERATE  INITIAL ANOMALIES AS REFERENCE
-  SEASONAL VARIATIONS:
- INITIAL ANOMALIES REDUCED 20%, 40% -  FALL (LOWEST DISCHARGE IN MS BIGHT)
-  INITIAL ANOMALIES AMPLIFIED 20%, 40% - SPRING (MAXIMUM DISCHARGE)

**Notes:**
	An interaction between the river and ocean waters begins in the estuary or river mouth, where intense mixing occurs. After mixing, the modified water discharges onto the shelf. In the following experiments, the goal is to examine the effects of the transformed river water on frontal circulation.
	 River discharge to the continental shelf of the Mississippi Bight varies seasonably. To examine the effect of the river discharge on frontal dynamics, four types of the cross-frontal density gradients and stratification are considered, gradually varying from weak to strong. Freshwater discharge during winter months in the Mississippi Bight is moderate. Therefore, it is reasonable to considerer the initial frontal anomalies as reference ones.  
	To introduce seasonal variations of river discharge, initial anomalies are reduced on 20% and 40%, which corresponds to the fall months, when the river discharge is the lowest in the Mississippi Bight. Amplified anomalies (20% and 40%) represent the spring season, when freshwater inflows reaches its maximum.

## 1. FRONTAL INSTABILITY: 

***1. FRONTAL INSTABILITY:***

- ADJUSTMENT:
- JET INTENSIFICATION FOR HIGHER ANOMALIES, WHICH IS  CONSISTENT WITH GEOSTROPHIC ASSUMPTION
- WEAK ANOMALIES (LOW DISCHARGE) HAVE SLIGHT EFFECT ON MEANDER DEVELOPMENT
- STRONG GRADIENTS INDUCE LARGE-AMPLITUDE INSTABILITIES

- AMPLIFIED GRADIENT CAUSES STRONGER VERTICAL MOTION AND UPWELLING AT THE SHELFBREAK

- 		SSH			     TEMPERATURE AT THE THERMOCLINE DEPTH (50 M)

**Notes:**
	After adjustment, the shelfbreak jet is developed and sea surface gradients are of significant magnitudes. Increase of anomalies (high discharge) intensifies the shelfbreak jet and leads to higher amplitudes of surface elevation. The result is consistent with geostrophic assumptions: larger horizontal gradients give rise to pressure gradients and result in larger velocities.
	The effect of weak anomalies (low discharge) on meander development is slight. Front is wide and meanders develop slow. Stronger gradients induce instabilities, which grow faster. Meander amplitudes increase with increase of anomalies. Strong stratification allows anticyclonic vortices to develop better.
	Amplified gradients causes stronger vertical motion. There is a positive correlation between an increase of anomalies and vertical motion, which result in a strong upwelling at the shelfbreak. 

## 2. CROSS-FRONTAL EXCHANGE: 

***2. CROSS-FRONTAL EXCHANGE:***

- LOW DISCHARGE INHIBITS EXCHANGE, DUE TO LOW EDDY ACTIVITY AND LOW CROSS-FRONTAL GRADIENTS
-  LINEAR RELATION BETWEEN ANOMALIES AND FLUXES IS PREDICTED, I.E. INCREASE OF CROSS-FRONTAL ANOMALIES BY 40% CAUSES INCREASE OF FLUX VALUE BY 80%
- NEGATIVE OFFSET IMPLIES THAT RELATION BETWEEN SMALL (< 20%) CROSS-FRONTAL ANOMALIES AND FLUX CHANGES IS NON-LINEAR

- CROSS-FRONTAL FLUX VALUES

- FLUX CHANGE VS. DISCHARGE CHANGE

**Notes:**
	It is clear that low discharge inhibits cross-shelf turbulent heat exchange. The values of the monthly mean heat flux grow, as gradients increase, due to increase of eddy activity. 
	In the river discharge experiments, anomalies changes linearly, decreasing and increasing by 20 % and 40%. The corresponding values of the frontal heat flux change linearly as well. The red line is a linear fit of flux change with respect to gradient change. The slope of this line is about 2, implying that frontal flux changes with rate almost twice larger than gradient rate of change. Example, 40% reduced anomalies result in 80% smaller value of frontal flux relative to the reference flux.
	However, this linear fit has a negative offset, ~ 8%, implying that zero changes in anomalies do not converge to the reference flux. A possible reason is that fro small changes of anomalies, (< 20%), the effect is not necessary linear. And since the offset is negative, it is likely that small changes in anomalies are less effective in changing flux rates. 

## OBJECTIVES: 

- OBJECTIVES:
- TO EXAMINE THE EFFECTS OF INTRUSION OF OCEANIC EDDY ON FRONTAL CIRCULATION
- EDDY:
- SPAWNED FROM LC THROUGH INSTABILITY AND REACHED SHELFBREAK
- EXPERIMENT DESIGN:
-  3 EXPERIMENTS WITH GAUSSIAN-STRUCTURE EDDY PLACED AT SHELFBREAK:
-  EDDY CORE WATER ANOMALIES SIMULATE COLLISION OF SE, ME, AND LE  WITH THE FRONT

**Notes:**
	The last external forcing considered here is the intrusion of the oceanic eddy into the domain. The focus of the study is the intrusion of the small-scale eddy, which spawned from the Loop Current or Loop Current Eddy though instability and reached the shelfbreak. To examine the effect of the oceanic eddy on the front and its development, three types of experiment are performed. In each experiment, a Gaussian-structure eddy is placed at the shelfbreak.
	Tref: initial ambient temperature and salinity of the reference case
	Xeddy: is the position of the shelfbreak;
	L: is the horizontal e-folding width scale of the eddy. L= 40 km is taken as the internal Rossby radius of deformation.
	A: amplitudes of temperature anomaly of the eddy (max at the surface and decrease with depth).
Three eddy intrusion experiments with varying amplitudes of the Loop Current eddy are considered. 
The values of the eddy core water anomalies are chosen to simulate the collision of the small-amplitude eddy (SE), medium-amplitude eddy (ME), and large-amplitude eddy (LE) .Initial temperature and salinity for the eddy intrusion experiments are shown on Figure

## 1. FRONTAL INSTABILITY: 

***1. FRONTAL INSTABILITY:***

- IN ALL EXPERIMENTS: EDDY IS ADVECTED EASTWARD BY THE JET
- SE: ASSIMILATED BY AMBIENT WATERS
- ME, LE: NORTHERN SIDE OF EDDY INTERACTS LONGER  GREAT DISTORTION OF THE JET

- EDDY SPLITTING:
-  PAIR OF ANTICYCLONIC/CYCLONIC EDDIES IS FORMED
-  PAIR MIGRATES EASTWARD AND INDUCES INSTABILITIES  MEANDERS DETACHMENT  JET DISTORTION

-  EDDY MAINTAIN ITS IDENTITY TO DAY 5-7, AFTER THAT, IT IS ERODED AND MOVED AWAY, CAUSING ADDITIONAL INSTABILITIES

- 		SSH			     TEMPERATURE AT THE THERMOCLINE DEPTH (50 M)

**Notes:**
	In all experiments, the eddy is initially advected eastward by the shelfbreak current. If the amplitude of the eddy is small enough, it is assimilated by ambient waters. For a larger-amplitude eddies, the northern side of the eddy interacts with the jet longer. This interaction produces a great distortion to the jet. Eddies themselves maintain their identities only to a certain time, after which eddies are eroded and move away from the front.
	Eddy erosion is attributed to a Rossby dispersive decay. For anticyclones: velocities on the eastern (left) side of the eddy are more intense, which result in southward (offshore) eddy advection. 
	Eddy splitting: and a pair of anticyclonic/cyclonic eddy is formed. Pair migrates eastward and induces instabilities. End: shelfbreak is distorted, eddy detachment; skewed shape of eddies indicate their eastward migration.   

## 2. CROSS-FRONTAL EXCHANGE: 

***2. CROSS-FRONTAL EXCHANGE:***

- HEAT FLUX GROWS DUE TO INSTABILITY AND RAPID MEANDER FORMATION AS EDDY AMPLITUDE INCREASES
- NO LINEAR RELATION BETWEEN EDDY AMPLITUDE AND HEAT FLUX IS FOUND

- CROSS-FRONTAL FLUX VALUES

-  FLUX IN THE FRONTAL VICINITY ARE  ARE NON-SYMMETRICAL , INDICATING DIFFERENT TRANSPORT INTENSITIES  ON BOTH SIDES OF THE FRONT

- FLUX CHANGE VS. EDDY AMPLITUDE CHANGE

**Notes:**
	As amplitude of the eddy increases, values of the heat flux grow, due to increase of instability, more rapid eddy formation. However, unlike in the previous experiments, no linear relation is found between heat flux increase and eddy intensification. 
	Flux in the vicinity of the front: (1) Curves are not symmetrical, implying different intensity of heat transport on both sides of the front. (2) Eddy amplitude also affects intensity of the heat flux, carrying water onshore and offshore. Flux can be positive and negative. If it’s negative, it implies that onshore flux is more intense, than the flux, carrying water offshore. When the flux changes sign, it implies that frontal intensification occur through both fluxes – one, which carries heat offshore (>0). SE: both fluxes are intense, since front meanders in both direction. LE: both fluxes are intense,since a pair of eddies with opposite signs is formed. ME: flux, carrying heat onshore is more intense, since eddy pair formation is still in progress, so offshore transport of cold dominates until eddy detached as in LE experiment.

## 1. SUMMARY AND CONCLUSIONS

- IN THE MS BIGHT, WINTERTIME SHELFBREAK FRONT IS UNSTABLE AND UNDERGOES 3 PHASES OF DEVELOPMENT: (1) ADJUSTMENT, (2) MEANDER GROWTH , AND (3) EDDY DETACHMENT
- A HYBRID BAROCLINIC-BAROTROPIC LOCAL INSTABILITY OF FRONTAL FLOW SIGNIFICANTLY CONTRIBUTES TO CROSS-FRONTAL EXCHANGE
- FRONT ENHANCES CROSS-SHELF TRANSPORT AND DOES NOT ACT A BARRIER FOR TURBULENT CROSS-FRONTAL EXCHANGE OF PROPERTIES IN IDEALIZED EXPERIMENTS
- ONSHORE HEAT FLUX EXHIBITS MAXIMUM VALUE AT THE POSITION OF THE FRONT

## 1. SUMMARY AND CONCLUSIONS

- FRONTAL CIRCULATION AND EDDY HEAT EXCHANGE IS VERY SENSITIVE TO
- BOTTOM TOPOGRAPHY:
- SLOPE STEEPNESS ENCHAINS EXCHANGE DUE TO PV CONSTRAINTS AND ADDITIONAL GRAVITATIONAL COMPONENT
- LOCAL WINDS:
- JET IS MODIFIED IN A MANNER CONSISTENT WITH EKMAN DYNAMICS
- UPWELLING WIND IS THE MOST EFFICIENT IN DRIVING CROSS-FRONTAL EXCHANGE, WHICH COULD ALMOST DOUBLE THE TRANSPORT COMPARED TO DOWNWELLING WINDS
- FRESHWATER DISCHARGE:
- POSITIVE CORRELATION BETWEEN RIVER DISCHARGE AND FLUX INTENSITY
- CHANGES IN DENSITY ANOMALIES MORE THAN 20% COULD DOUBLE CORRESPONDING CHANGES OF THE CROSS-FRONTAL HEAT FLUX
- INTERACTION WITH OCEANIC EDDIES:
- SMALL-AMPLITUDE EDDIES ARE ASSIMILATED BY AMBIENT WATER
- LARGER-AMPLITUDES EDDIES CAUSE FRONT DISTORTION, GET ERODED AND MOVE AWAY, INDUCING INSTABILITY AND CROSS-FRONTAL EXCHANGE

- TURBULENT PROCESSES PLAY AN IMPORTANT ROLE IN MS BIGHT CIRCULATION. IT IMPLIES THAT TEMPORAL AND SPATIAL SCALES OF THE FLOW ARE SMALL. THEREFORE, HIGH RESOLUTION SAMPLING AND MODELING ARE NECESSARY TO RESOLVE EDDY CONTRIBUTION TO THE CROSS-SHELF EXCHANGE.

**Notes:**
	The primary conclusion is that turbulent processes play an important role in MS Bight circulation. It implies, that the scales of the flow are small. Therefore, a high resolution sampling and modeling are necessary to resolve eddy contribution to the cross-shelf exchange. 
	Furthermore, we saw that the flux changes dramatically over short timescales as various eddies cross the front. Therefore, conclusions, that are based on a single hydrographic transect might be misleading. To resolve temporal variability, simultaneous or at least replicate direct measurements are necessary.

##   NORTHERN GULF OF MEXICO LITTORAL INITIATIVE (NGLI) IS A MULTI-AGENCY PROGRAM TO FORECAST CIRCULATION, SEDIMENT TRANSPORT AND WAVES IN MS BIGHT

-   NORTHERN GULF OF MEXICO LITTORAL INITIATIVE (NGLI) IS A MULTI-AGENCY PROGRAM TO FORECAST CIRCULATION, SEDIMENT TRANSPORT AND WAVES IN MS BIGHT
-   IN-SITU OBSERVATIONS (USM, NAVO): SHIP SURVEY DURING FEB’ 99 – SEPT’ 00
-   1339 CTD STATIONS; 21 TIME-SERIES STATIONS
-   ECOM WAS APPLIED TO MS BIGHT TO HINDCAST TEMPERATURE AND SALINITY DURING ONE OF THE NGLI SURVEY (AUGUST/SEPTEMBER 2000)

- OBJECTIVES:
- TO VALIDATE THE ECOM ON DIFFERENT TEMPORAL SCALES
- TO COMPARE OBSERVED AND SIMULATED CLIMATOLOGIES

## J(X) = 	(1) (IX-D)TWD(IX-D) + ...

- J(X) = 	(1) (IX-D)TWD(IX-D) + ...
- 	(2) (X-XREF)TWREF(X-XREF) + (2X)TWSM(2X) + ...
- 	(3) (H X)TWBOT(H X)

-  INTERPOLATION FROM IRREGULAR COARSE DATA GRID TO REGULAR FINE GRID
-  TAKING INTO ACCOUNT OBSERVED VARIABILITY TO RECREATE A MEAN STATE OF THE OCEAN – LARGE-SCALE CLIMATOLOGY
-  MINIMIZATION OF THE COST FUNCTION:

*Attracts the field to the observations.  I - interpolating operator, D - observations, W**D **-  data error covariance matrix*

*Takes into account the correlation in the observed field: X**REF** - expected value W**REF** – diagonal matrix of variances,W**SM **– non-diagonal matrix describing correlation between different nodes of X.*

*Describes correlation between bottom topography H and observed field X. *

- (1)

- J(X)  min

- August/September  2000 NGLI CTD Data

- 2. COASTAL CLIMATOLOGY USING VARIATIONAL INTERPOLATION

- (2)

- (3)

## ECOM CLIMATOLOGY: TEMPORAL AVERAGE OVER TWO WEEKS

- 2. COASTAL CLIMATOLOGY USING VARIATIONAL INTERPOLATION

- A good model/data agreement within the error of estimators.

- ECOM VS. OBSERVED  CLIMATOLOGY

- SURFACE SALINITY: (DATA-MODEL) / ERRORVAR.INT.

- SURFACE TEMPERATURE: (DATA-MODEL) / ERRORVAR.INT.

- ECOM SALINITY

- ECOM TEMPERATURE

## THANK YOU !

- EMAIL: Nadya.Vinogradova@usm.edu
- WEB: http://ocean.otr.usm.edu/~nvinogra

**Notes:**
	For my last slide,  I wanted to show a picture of the Mississippi Bight waters at the sunset. I took this picture when Megan and I were on a research cruise with Dr. Bill Teague as a chief scientist. It made me realize that we can use computer models to understand the ocean, but no model could ever create something as beautiful as the real thing. 
	Thank you and I am ready for your questions.