Opening Page

Pre-assessment
Find out what you already know about Ocean Modeling.

Before you begin, please complete a short pre-assessment by
clicking the link below. When you have completed the module, be sure
to take the quiz to see how much you've learned.

Taking the pre-assessment will help you see where you need to focus
your learning as you work through the module. And taking the module
quiz at the end will help you gauge how much you've learned once
you're done. This information will also help us see how well the module
teaches the key terminology and concepts of numerical ocean models.

If you have already completed the pre-assessment, click the Begin
Module link below.

Complete Preassessment (link to Pre-assessment)

Begin Module (link to section 1)

National Weather Service users:
If you have accessed this module through the E-learning@DOC system, please click Begin Module to proceed.


0. Pre-Assessment

Q1. [Obj-1, 2 pts]
How does the specific heat of air compare to that of water?

1/4 of water
1/2 of water
roughly equal
2 times
4 times

Q2. [Obj-1, 1 pt]
Which is more stratified, the atmosphere or the ocean?

Atmosphere
Ocean

Q3. [Obj-2, 3 pts]
The Equation of State accounts for which of the following?
(Choose the best answer)

Angular momentum
Conservation of mass and energy
Geostrophic balance
Salinity, density, and temperature

Q4. [Obj-2, 5 pts]
Which of the following are types of dynamic forcing are accounted for in operational ocean models?
(Choose all that apply)

Bathymetry
Lunar gravity
Sediment transport
Solar radiation
Wind stress

Q5. [Obj-3, 4 pts]
Which of the following processes are parameterized by ocean models?
(Choose all that apply)

Bottom friction
Brine exclusion
Geostrophic balance
Subgrid-scale mixing

Q6. [Obj-3, 3 pts]
When an ocean model has a cold start, what is the source of the initial conditions for the ocean temperature and salinity?

Cold-season average
Forecast from previous model run
Long-term average (climatology)
Recent observations

Q7. [Obj-3, 3 pts]
When an ocean model has a warm start, what is the source of the initial conditions for the ocean currents?

Forecast from previous model run
Long-term average
Ocean at rest
Warm-season average

Q8. [Obj-3, 1 pt]
[T/F] A model hindcast is generated between the time of a warm start and the time of the model analysis.

True
False

Q9. [Obj-4, 3 pts]
What is the smallest size feature that can be resolved by a model with a 20 km horizontal grid spacing?

4 km
5 km
20 km
80 km
100 km

Q10. [Obj-5, 3 pts]
What vertical coordinate system is shown in this cross-section?
quiz graphic

Hybrid
Isopycnal
Sigma
Z

Q11. [Obj-5, 2 pts]
Select the terms that characterize the model grid shown in this image.
(Choose all that apply)
quiz graphic>

Regular
Irregular
--
Finite element
Plaid

Q12. [Obj-5, 6 pts]
Which of the following do ocean models predict?
(Choose all that apply)

Bathymetry
Currents
Density
Sea surface height
Temperature
Wind

Q13. [Obj-6, 6 pts]
Which of the following properties are measured by satellites and assimilated into ocean models?

Freshwater runoff from land
Mixed-layer depth
Salinity
Sea surface height
Sea surface temperature
Surface winds

Q14. [Obj-6, 1 pt]
[T/F] Most moored data buoys record vertical profiles of temperature and salinity.

True
False

1.1 Introduction

[globe_grid.swf]
Animation of rotating earth. Globe shows topography and blue ocean. Oceans are overlain by a lat/lon grid.
Click to open animation in a new window.

Oceans cover over 70% of the surface of the earth, yet many details of their workings are not fully understood. Ocean observations are sparse, widely spaced, and only rarely penetrate beyond the first few meters. To better understand and forecast the state of the ocean, we rely on numerical models. Like their better-known cousins, numerical weather prediction (NWP) models, ocean models combine observations and physics to predict the ocean state at any time and any place across the ocean basins.

This training module provides an introduction to ocean modeling. Because many users of this module are primarily weather forecasters, there are frequent references to NWP models. We will note the similarities and differences between ocean and atmosphere and their respective models. If you are unfamiliar with NWP models, it may help to view two brief COMET modules before you start: Model Fundamentals (http://meted/nwp/pcu1/ic1) and How Mesoscale Models Work (http://meted.ucar.edu/mesoprim/models).


1.2 Objectives

After completing this module, you should be able to do the following things:

  1. Explain the similarities and differences between ocean and atmospheric modeling.
  2. Explain the physical laws and processes that must be considered in developing an ocean model.
  3. Explain how the physical properties of the ocean differ from those of the atmosphere.
  4. Explain the processes that are built into a numerical ocean model.
  5. Explain how resolution and scale are important to global, regional, and local ocean models.
  6. Describe a numerical model and how it can be used as a prediction tool.
  7. Explain how real-time observations and climatology contribute to ocean models.

2. What is a model?

Producing an accurate forecast of ocean processes involves careful consideration of many data sources, including ocean models. This flowchart shows how the components of an ocean model fit into the forecast process. Starting at the BOTTOM and working your way up, click each component for a brief discussion of its role in ocean modeling and the forecast process.

[om_flow.gif]
Ocean forecast process flow chart

  • Data: Observations are collected to describe the initial state of the ocean. Data sources include satellites, coastal stations, fixed and drifting buoys, ships, and gliders. These data include ocean temperature, ocean salinity, surface elevations, currents, wave height and direction, ocean color, etc.
  • Quality Control and Analysis: A series of checks and tests are used to ensure the viability of the information input into the forecast model.
  • Computer Resources: The capacity and speed of the computing resources available to run an ocean model govern the complexity and resolution of the model components. Thus, computer resources can be a significant limitation to ocean models.
  • Numerics: Similar to atmospheric models, ocean models use a particular mathematical formulation to solve a set of physical equations in making a forecast. Model numerics include how data are represented, model resolution, computational domains, the chosen coordinate systems, and solution techniques.
  • Assimilation: An assimilation system is a complex procedure in which observations are statistically compared and blended with analyses or short-range forecasts from an earlier model run to develop the initial conditions for the next model run.
  • Dynamics: In ocean modeling, dynamic processes involve the motion of water or currents. These processes are described by a set of horizontal and vertical momentum, mass conservation, and thermodynamic equations within the model, generally known as the primitive equations.
  • Physics: In ocean modeling, physical processes refer to:
    1. Processes that involve the exchange of energy, mass, and momentum between the ocean and external sources (for example, radiation, evaporation, precipitation, river runoff, kinetic energy that creates waves or currents, etc.)
    2. Ocean movement or dynamics including horizontal advection, vertical convection, and 3-dimensional mixing processes at scales from molecular to ocean basin.
    3. Some processes that operate on scales smaller than the model resolution, but exert a cumulative effect felt at resolvable scales. We deal with their effects by parameterization, discussed later.
  • Postprocessing: Here, the "native" model output is transformed into formats and products that can be used by forecasters. Model variables may be reinterpolated horizontally and vertically to match output grids or contour plots at standard levels.
  • Observations: Observations of all types are needed (1) for assimilation to provide accurate initial conditions and (2) to evaluate the skill of a model's analysis or forecast.
  • Understanding Oceanographic Principles: A thorough understanding of basic physical oceanography is necessary to intelligently use model guidance so one can, for example, identify when model output is not oceanographically sound or consistent with expectations.
  • Forecast Process: In the forecast process, model output and real-time observations are combined with the forecaster's understanding of physical oceanography to develop a forecast for the area of responsibility.
  • Forecast: This represents the final product for which ocean models were developed. The format, oceanographic variables, forecast period, and frequency are driven by customer needs.
  • Verification: Forecasters use model verification data to identify model skill and uncertainty. This helps identify deficiencies and leads to improved forecast model components.

3. Ocean versus Atmosphere


3.1 Introduction

[lenticular_ani.swf]
Time-lapse animation of a lenticular cloud
Click to open animation in a new window.

Both water and air are fluids. In nature, they are subject to the same physical forces and processes. As a result, they frequently behave in similar ways. This time-lapse animation of a lenticular cloud reveals how a standing wave can form in the atmosphere, similar to a standing wave that may form in a river.

river wave
Click to open animation in a new window.

So why should oceanic and atmospheric models be different? Many of the differences arise from the properties of seawater and air. Others are due to the horizontal and vertical structures of the ocean and atmosphere. This section examines some of the differences that lead to variations between atmospheric and oceanic models.


3.2 Liquid versus Gas

[airsea_pv.swf]
Conceptual animation showing that air is a compressible gas, while water is an incompressible liquid
Click to open animation in a new window.

The most fundamental difference between air and seawater is that air is a compressible gas while seawater is a nearly incompressible liquid. As this animation shows, if we double the pressure experienced by a parcel of air, its volume shrinks by a half while its density doubles. However, if we double the pressure on a parcel of sea water, the volume and density remain almost unchanged. This relationship requires a fundamentally different equation of state to describe seawater behavior. The familiar ideal gas law cannot be applied. Instead, density changes in the ocean result from complex, nonlinear relationships between temperature, salinity, and pressure.

For some applications, we assume the ocean is incompressible, but this is not always possible. For example, sound speed, important for antisubmarine warfare, increases with ocean depth and pressure.

In Depth: Density units.
The density of pure water is 1 gram per cubic centimeter or 1000 kilograms per cubic meter (kg/m3). Due to its salinity (see below), saltwater is a little denser at an average of 1028 kg/m3). Because local ocean density changes are usually very small, on the order of tenths to hundredths of kg/m3, oceanographers express density in terms of sigma units, where sigma = (density - 1000) kg/m3. Thus saltwater with a density of 1028 kg/m3 has a sigma of 28.


3.3 Salinity versus Humidity

[airsea_density.jpg]
Side by side graphs showing that adding humidity to air lowers the density, while adding salt to water increases the density

Just as air has the "impurity" of water vapor or humidity, seawater contains dissolved chemicals known collectively as salinity (measured in practical salinity units, or psu's).

While air density decreases as humidity increases, sea water density increases as the salinity increases. This means ocean models must account for the effects of salinity on density, just as atmospheric models must account for humidity. Salinity, however, plays no role in heat transfer processes like humidity does through atmospheric processes such as convection, evaporation, and condensation.

In Depth: Practical Salinity Units (psu)
If we were to boil away all the water in a container of saltwater, the dissolved residuals would account for about 3.5%, or 35 parts per thousand, of the total mass. While most of this salt is the familiar sodium chloride, almost every element is present. Boiling water to determine salinity or finding salt content by chemical analysis are impractical, so oceanographers have developed methods to determine the chlorine ion content using its electrical conductivity. While this provides a measure of the equivalent salt content, it is not quite the same as parts per thousand, so they refer to salinity in terms of practical salinity units (psu).


3.4 Vertical Structure

[graphic: temp_profile.jpg]
Temperature profile from seafloor to stratosphere.

The vertical structures of the ocean and atmosphere share both similarities and differences. Both "fluids" are characterized by a well-mixed layer near the surface, where most of the heating and cooling occurs. However, mixing occurs to some degree throughout the atmosphere, even above the highly mixed boundary layer, while the ocean is much more stratified below its thin mixed layer.

At the surface, the ocean mixed layer is heated by the sun. It is quite shallow, on the order of 100 m (330 ft) deep. Below depths of about the 1000 m (3300 ft) lies a thick, nearly isothermal deep region. Between the mixed layer and deep water lies a thermocline where temperatures rapidly decrease with depth. There is little vertical motion in the highly stratified thermocline except in zones where upwelling and downwelling overcome the stratification.

Because the ocean is so stratified, ocean models can make assumptions about the dominance of horizontal processes over those in the vertical. Modelers can then use vertical coordinate systems to take advantage of the fact that most action occurs in the near-surface mixed layer.

In Depth: Upwelling and Downwelling

Schematic showing the relationship between surface wind, surface water movement, and upwelling

When winds blow with persistence over an ocean surface, the Coriolis force acts to move surface water at an angle to the wind direction: to the right in the northern hemisphere and to the left in the southern hemisphere. Along the coast, when winds push water offshore, cold water rises from beneath to replace it. This upwelling substantially reduces sea surface temperatures.

[upwell_eq.jpg]
Conceptual image of equatorial upwelling

Equatorial upwelling occurs in response to easterly winds along the equator. Surface water north of the equator moves northward, while surface water south of the equator moves southward. This divergence results in upwelling of colder deep water to replace water at the surface.

[brine_exclusion.swf]
Animation showing brine exclusion during sea ice formation
Click to open animation in a new window.

An example of downwelling occurs at high latitudes. As sea ice forms, it excludes a saltier brine, which makes the sub-ice seawater denser than the surroundings. The brine sinks, resulting in downwelling.


3.5 Horizontal Structure

[global_ir.swf]
Loop of global composite IR images: 1800 UTC 28 Oct 2006 to 1500 UTC 1 Nov 2006
Click to open animation in a new window.

The horizontal structure of the ocean differs significantly from that of the atmosphere. The atmosphere blankets the earth in a laterally continuous layer, with some interference from relatively small mountain ranges. For example, this animation shows how atmospheric disturbances drift across land and water alike. Conversely, the ocean is broken into a series of basins by landmasses fringed with relatively narrow continental shelves. The bathymetry of these basins shapes ocean currents. In addition, freshwater continually runs off of continents into the ocean, altering density and currents along the coast. Having to resolve both horizontal and vertical processes along ocean margins places extra constraints on ocean models, and plays a critical role in how we choose horizontal and vertical coordinate systems.


3.6 Similarities between Ocean and Atmosphere

[space_sunset.jpg]
Photo of Earth's horizon as the sunsets over the Pacific Ocean taken from the International Space Station (ISS). Anvil tops of thunderclouds are also visible.

Despite their differences, the oceans and atmosphere share many similarities: Both are thin fluid layers on a rotating sphere. Major features in both can be thousands of kilometers across. Consequently, the physics that drive their circulation are similar. In both cases, solar heating is the major energy source, with the sun's heat redistributed by winds and currents.


3.7 Questions

1. [T/F] If we double the pressure experienced by parcels of both air and water, their volumes and densities remain almost unchanged.
Answer: False. If we double the pressure experienced by a parcel of air, its volume shrinks by a half while its density doubles. However, if we double the pressure on a parcel of sea water, the volume and density remain almost unchanged. The ideal gas law cannot be applied, and instead density changes in the ocean result from complex, nonlinear relationships between temperature, salinity, and pressure.

2. [T/F] While air becomes more dense with increasing humidity, sea water density decreases as the salinity rises.
Answer: False. Increasing humidity decreases air density, while increasing salinity increases seawater density.

3. [T/F] In the ocean vertical mixing occurs through the depth of the thermocline.
Answer: False. There is little vertical motion in the highly stratified thermocline except in zones where upwelling and downwelling occur. Because the ocean is so stratified, ocean models can make assumptions about the dominance of horizontal processes over vertical processes.

4. [T/F] Numerical models can treat both ocean and atmosphere as laterally continuous, thin, fluid layers.
Answer: False. While the atmosphere blankets the earth in a laterally continuous layer, the ocean is broken into a series of basins by landmasses surrounded by relatively narrow continental shelves. Having to resolve both horizontal and vertical processes on the marginal edges places extra constraints on ocean models compared to atmospheric models.


4. What do we model?

[arabian_ncom.swf]
Navy Coastal Ocean Model (NCOM) Analyses of Sea Surface Height for the Arabian Sea, 00 UTC 1 Mar 2006.
Navy Coastal Ocean Model (NCOM) Analyses of Sea Surface Temperature for the Arabian Sea, 00 UTC 1 Mar 2006.
Navy Coastal Ocean Model (NCOM) Analyses of Sea Surface Salinity for the Arabian Sea, 00 UTC 1 Mar 2006.
Navy Coastal Ocean Model (NCOM) Analyses of Sea Surface Currents for the Arabian Sea, 00 UTC 1 Mar 2006.
Click to open animation in a new window.

Ocean models are used to simulate the state of the ocean and predict how it will change. The basic properties predicted are temperature, salinity, and pressure from the surface to the seafloor. In order to do this, models must also predict currents and changes in surface elevation. Similarly, ocean models can also predict waves and surf, which are also driven by winds. This animation shows a series of model fields for the Arabian Sea produced by the Global Navy Coastal Ocean Model (NCOM).

Once we know the state of the ocean, we can use this information to initialize specialized models that determine properties such as sound speed and object drift.


5.Model Physics


5.1 Forces

[ocean_forces.jpg]
Schematic block diagram showing forces acting on a parcel of sea water: pressure gradient force, coriolis effect, gravity, and friction

Ocean models determine the state of the ocean using 3 basic physical relationships. We refer to these relationships as primitive equations.

The first primitive equation is derived from Newton’s Second Law:

ΣF = ma

where
ΣF = the sum of the various forces applied to the ocean,
m = the mass, and
a = the acceleration.

The forces experienced by a parcel of seawater include

  • Gravity
  • Pressure gradient force due to horizontal height and density differences,
  • Coriolis force due to the rotating earth, and
  • Friction: between wind and sea surface, between current and sea floor, and between water masses having different velocities.

Thus we can rewrite Newton’s Second Law as

ΣF = gravity + pressure gradient force + Coriolis force + friction

This is called the Navier-Stokes equation, after the two scientists who discovered the relationship.


5.2 Conservation

[hydro_cycle.swf]
Conceptual animation of the hydrologic cycle
Click to open animation in a new window.

The second physical relationship governing ocean models is the conservation of properties. This is really an elaborate accounting scheme to ensure that what goes in eventually comes out, so that either (a) there is no net gain or loss in the system, or (b) changes can be determined due to imbalances. For example, the fresh water that enters the model ocean through runoff from land and precipitation is balanced by water that leaves the model ocean through evaporation or the ocean salinity changes. Similarly, the solar energy that enters the ocean is either released or the ocean warms up. Conservation applies to several ocean properties including water mass, salt content, and heat. The principle of conservation is expressed by a set of continuity equations.


5.3 Equation of State

[temp_salinity_density.jpg]
Temperature-salinity graph showing lines of constant density (isopycnals)

The pressure gradient force mentioned earlier could result from either a sloping ocean surface or horizontal density differences. In the atmosphere, density is a function of temperature, pressure, and humidity. Determining the density of air is relatively easy using the Ideal Gas Law (pV=nRT). In the ocean, density is a function of temperature, pressure, and salinity, but this relationship is quite complex and requires the solution of a series of nonlinear equations collectively referred to as the equation of state.

Text Note: Ideal Gas Law: pV=nRT

5.4 Questions
[correct = bold text]

1. The Navier-Stokes equation accounts for which of the following experienced by a parcel of seawater?
(Choose all that apply, then click Done.)
a. Gravity
b. Pressure gradient force
c. Coriolis force
d. Friction
Feedback: The correct answers are a), b), c), and d). Remember that the Navier-Stokes equation can be written as follows:
The sum of the forces = gravity + pressure gradient force + Coriolis force + friction.

2. The principle of conservation applies to which of the following ocean properties?
(Choose all that apply, then click Done.)
a. Water mass
b. Salt content
c. Heat
Feedback: The correct answers are b), c), and d). Over the short times that we run operational ocean models, bathymetry does not change. The other properties are in a constant state of flux and thus are a subject to the principle of conservation.

3. What is the equation of state?
a. A series of non-linear equations that describe seawater density.
b. An elaborate accounting scheme to ensure that there is either no net gain or loss in the system or that changes can be determined due to imbalances.
c. The sum of the various forces applied to a parcel of seawater in the ocean.
Feedback: The correct answer is a) a series of non-linear equations that describe seawater density. The set of continuity equations constitute (b) an elaborate accounting scheme to ensure that there is either no net gain or loss in the system or that changes can be determined due to imbalances. The Navier-Stokes equation accounts for (c) the various forces applied to a parcel of seawater in the ocean.


6. Grids


6.1 Introduction

[3d_grid.jpg]
Block diagram showing 3-D grid on the coastal ocean

To apply the primitive equations to a model ocean we need to convert them to a series of algorithms that can be numerically applied to a digitized or gridded ocean. Because our computers basically have to deal with 0s and 1s, the ocean continuum must be broken into a 3D set of points, with a method to move data from point to point. This figure shows a simple three-dimensional grid applied to a coastal ocean. Different models use different grids. For example, as of this time, the Global NCOM uses a 1/8° horizontal grid and 40 vertical levels. When we select a coordinate system, we seek one that is computationally efficient and that allows the greatest resolution or detail where we need it: near the surface and the coast.

Text Note: NCOM = Navy Coastal Ocean Model


6.2 Horizontal Coordinates — Regular Grids

[eas16_grid.gif]
Model domain of the EAS16 ocean model showing every 10th grid point.

Horizontal grids fall into two types: referred to as regular and irregular. Regular grids consist of a series of equally spaced lines. For this reason, they are sometimes referred to as plaid grids. Because the surface of the earth is a sphere, we cannot apply a truly uniform spacing across the grid and keep the lines straight. Thus, the lines tend to be curvilinear and their internal spacing tends to vary. Plaid grids allow us to keep the spacing fairly uniform from one grid cell to the next, while keeping the grid cell boundaries fairly square. Most atmospheric models use regular grids. The Navy's NLOM and NCOM both use regular grids.

Regular grids have the advantage of being computationally efficient, with fairly straightforward algorithms. Their chief disadvantage in ocean models is that in order to increase resolution near the edge of the ocean basin, you need to increase it everywhere, even out in the middle of the ocean where a close grid spacing is much less important. Thus, any increase in regular resolution comes at great computational expense.

Text Note: NLOM = Navy Layered Ocean Model

In Depth: What to do at the North Pole?

[tripolar_grid.gif]
Tripolar Grid

Regular latitude-longitude grids have a problem when they approach the poles: grid lines tend to converge, resulting in shrinking grid cells. And at some point, grid lines converge on a single point, which is difficult for models to handle computationally. One way ocean models deal with this problem is to lay a circular grid over the arctic polar region, thus eliminating a north pole. While this circular arctic grid has two points of grid convergence rather than one, they can be positioned over land. We refer to the resulting model grid as a tripolar grid, with poles located over Canada, Russia, and Antarctica. The Global NCOM uses a tripolar grid.


6.3 Horizontal Coordinates — Irregular Grids

[finelement_grid.jpg]
Finite Element Grid for ADCIRC Model Domain, Long Island Sound

A common irregular gridding scheme is composed of a series of triangles, which we refer to as finite elements. We can easily add triangles and the triangles can vary in size. This allows us to increase the resolution near the coast where small-scale processes are important, while keeping the resolution in the middle of the ocean relatively coarse. This image shows a finite element grid centered on Long Island, New York.


6.4 Vertical Coordinates — z Coordinates

[z_coords.gif]
Example of z vertical coordinate system

We have several choices for a vertical coordinate system. All of the choices allow us to increase detail near the surface where most of the action occurs. Here we discuss 4 common vertical coordinate systems based on absolute depth (z), normalized depth (σ), density (ρ), and hybrid systems that combine more than one of these.

The simplest system is based on a series of depth surfaces and is referred to as a z-coordinate system. This system is simple to set up and is computationally efficient. We can add resolution near the surface by decreasing the spacing between levels. Unfortunately, when we encounter a lateral boundary, such as a continental slope, and need to increase vertical resolution, there is no way to easily add grid cells without adding them throughout the entire ocean basin. Several models developed at NOAA use z-coordinates, including the Modular Ocean Model (MOM).


6.5 Vertical Coordinates — Sigma (σ) Coordinates

[sigma_coords.gif]
Example of sigma vertical coordinate system

Sigma (σ) coordinates provide a way to handle lateral boundaries and complex bathymetry. They are based on the fractional depth, scaled from 0 to 1. Thus, the 0.01σ level is 1% of the depth of the ocean, near the surface, the 0.5σ level is exactly half the depth of the ocean, and the 0.99σ level is at 99% of the depth of the ocean, very near the seafloor. On the continental shelf where the depth is 100 m, the 0.99σ level would be 1 m above the bottom, while in the deep ocean at 5000 m it would be 50 m above the bottom. Sigma coordinates are fairly horizontal near the ocean surface and mimic bathymetry near the seafloor. The fact that sigma coordinates mimic bathymetry allows us to add resolution near the seafloor, regardless of the water depth or proximity to land.

Models that employ sigma coordinates include the Princeton Ocean Model (POM), widely used in academics and the basis of the Navy's Shallow Water and Analysis Forecast System (SWAFS) and Navy Coastal Ocean Model (NCOM).


6.6 Vertical Coordinates — Density (Isopycnal) Coordinates

[layer_coords.gif]
Example of density-layer vertical coordinate system

Because the ocean is stratified below the mixed layer, and because ocean currents generally flow along surfaces of equal density, several ocean models employ a vertical coordinate system based on density. We refer to these models as layered or isopycnal models (an isopycnal is a surface of constant density). The chief advantage of this kind of model is that we can largely neglect mixing across layers, simplifying some computations. The chief disadvantage is that these models perform poorly in shallow water where the ocean is less stratified. The Navy Layered Ocean Model employs an isopycnal coordinate system. Note that the NLOM model domain is confined to areas where the depth is greater than 200 meters, which eliminates its application on continental shelves.

Text Note: NLOM = Navy Layered Ocean Model


6.7 Vertical Coordinates — Hybrid Coordinates

[sigma-z.gif]
Example of sigma-z hybrid vertical coordinate system

Hybrid coordinate systems seek to optimize model performance by combining the best coordinate systems in different regions based on the dominant processes at work. For example, this graphic shows a hybrid sigma-z coordinate system. Sigma vertical coordinates are used above a set depth, usually set near the edge of the continental shelf. Below this depth, z coordinates are used. The Global NCOM uses sigma-z coordinates.

The experimental Hybrid Coordinate Ocean Model (HYCOM) uses a vertical coordinate system with z or sigma coordinates from the surface through the mixed layer, then switches to density (isopycnal) coordinates in the stratified ocean that lies below. The HYCOM system allows the vertical coordinates to evolve through both time and space as the depth of the mixed layer changes. Thus, the vertical coordinate system varies from place to place and from one time step to the next. This approach promises to provide improved results, but with a high computational cost.

Text Note: NCOM = Navy Coastal Ocean Model


6.8 Model Resolution

[wave_res14.gif]
Diagram showing sin wave defined by 5 points, each 14 km apart

The general principles of resolution are the same for both atmospheric and ocean models. In both cases, it takes five grid points to accurately define a feature without aliasing. Thus a model like the 1/8° global NCOM with an average grid cell of 14 km can accurately depict only features larger than 56 km or 30 nm. Recall that finite element ocean models, with their irregular horizontal grids, have variable grid spacing, so the resolution is not uniform. Because operational models need to finish their run quickly in order to provide a useful forecast, the main barrier to improved resolution in these models is computational speed. As we shrink the horizontal grid spacing, we need to add vertical layers and decrease the time step. As a general rule-of-thumb, every halving of the grid spacing requires roughly ten times as many computations.


6.9 Questions

1. Which vertical coordinate system most easily allows you to increase vertical resolution near both the surface and the sea floor?
a. z
b. sigma
c. density layer

2. Which horizontal coordinate system allows you to preferentially increase horizontal resolution near the coast?
a. regular / plaid
b. irregular / finite element

3. The Navy Global Coastal Ocean Model (NCOM) uses a [plaid / finite element] horizontal coordinate system and a [z / sigma / density-layer / hybrid sigma-z] vertical coordinate system.

4. The Navy Layered Ocean Model (NLOM) uses a [plaid / finite element] horizontal coordinate system and a [z / sigma / density-layer / hybrid sigma-z] vertical coordinate system.


7. Parameterization


7.1 Why Parameterize?

[miss_mud_mix.jpg]
True-color MODIS image (March 5, 2001 at 10:55 AM local time), shows the murky brown water of the Mississippi mixing with the dark blue water of the Gulf two days after a rainstorm.

Just like atmospheric models, ocean models cannot simulate features and/or processes that are within the confines of a single grid box. Thus, even high-resolution models cannot properly forecast local currents, eddies, or flow around sub-grid scale obstacles. This satellite image shows elaborate plumes of silty water from the Mississippi River mixing with saltwater in the Gulf of Mexico. We cannot realistically expect ocean models to resolve features at this scale, no matter how high the resolution, but the cumulative effects may still change the local ocean. As a result, a model must account for the total effect on the flow with a single number that represents friction within the grid box. The method of accounting for such effects, without directly calculating them, is called parameterization. Another way to think of parameterization is to numerically estimate the effects of a process (emulation) rather than model the process itself (simulation).


7.2 What Processes are Parameterized?

[param_procs.swf]
Conceptual cross section showing parameterized processes
Click to open animation in a new window.

This image depicts some of the many physical processes that are typically parameterized. Pass your cursor over the image to see descriptions of the different processes. The effects of these processes must be parameterized in a model for two main reasons:

  1. Computers are not yet powerful enough to directly treat them because the phenomena are either too small (sub-grid scale) or too complex to be mathematically simulated, and
  2. Some processes are often not understood well enough to be represented by an equation.

7.3 Microscale Processes

[brine_exclusion.swf]
Animation showing brine exclusion during sea ice formation
Click to open animation in a new window.

Even in the very high-resolution innermost nests of ocean models, there are still significant phenomena that can dramatically impact model forecasts and so they must be parameterized. This example shows brine exclusion during sea ice formation. Brine exclusion leads to very cold, salty water that eventually sinks and forms oceanic bottom water. This process occurs on a microscopic scale as ice forms so it must be parameterized.

Problems associated with using parameterizations can result from the increasing complexity of the model as well as nonlinear interactions between parameterization schemes. Unfortunately, forecast errors created by the interaction of parameterization schemes are more difficult to trace than errors resulting from an individual scheme.


8. Initialization and Boundary Conditions


8.1 Initialization — Cold Start

Every model run, whether oceanic or atmospheric, starts with a set of initial conditions. We refer to this as model initialization. For ocean models, those conditions include temperature, salinity, density, circulation, and weather at the surface. There are two fundamentally different ways to initialize an ocean model: referred to as a cold start (using climatology) or a warm start (using a prior forecast). Let's examine each case.

Conceptual depiction of a model cold start initiation
Click to open animation in a new window.

In a cold start, we begin from scratch with an ocean at rest, meaning there is no circulation. Our initial conditions for temperature and salinity come from climatology, that is, from some set of the average temperature and salinity conditions for that day of the year. These may be interpolated from the 3-D temperature and salinity structure between monthly averages. Then we add weather forcing (winds and heat transfers) from either climatology or weather model analyses and allow circulation to develop. We refer to this process as spin-up. Spin-up requires a substantial period of model time, on the order of weeks to months depending on model complexity. In other words, if we want a forecast for tomorrow, we would initialize the model for a day several weeks prior, assuming that it will have reached a steady state by the analysis time (the 0-hour forecast).


8.2 Initialization — Warm Start

[warm_start.jpg]
Example of dynamic circulation model using a warm start

With a warm start, we initialize the model with the analysis (0-hr forecast) from the previous model run. Thus, the ocean is in motion, circulation is already developed. Now we add a weather forecast by NWP models and the model ocean adjusts in response to the new conditions. This graphic shows two model runs. The analysis from the first one provides the initial conditions for the second one. Note that the wind observations assimilated into the second model run differ from the forecast winds used in the first model run for the same time. This apparently leads to higher water elevations at the analysis in the second model run, in agreement with the observed water level.

A warm start has the advantage that it requires no spin-up. It has the disadvantage that biases and errors in the previous forecast may be carried over into the next model forecast. Finding and reducing these cumulative problems is part of the modeling process.

Pop-up Definition:
Hindcast: The results of the model run from initialization to analysis.


8.3 Assimilating Observations

[corcycle_ocean.gif]
Conceptual diagram depicting effect of data assimilation on model analyses

Regardless of whether we start our model run warm or cold, we can improve our analysis by assimilating observations of the ocean state. Data assimilation in ocean models is similar to that in NWP models: in both cases we nudge the model toward the observed state, rather than forcing the model to mimic the observed state. We do this because forcing a running model to adopt the observed state can potentially throw the dynamic forces out of balance, which can cause unrealistic or even impossible results.


8.4 Assimilation and Hindcasts

[cbofs_timeseries_om.jpg]
Timeseries graph of Forecast and observed winds and tides at Chesapeake Bay Bridge, 29 Apr - 1 May 2006

We can assimilate observations into either warm or cold starts. In a cold start, we start assimilating prior observations when we add weather and set the model in motion. With a warm start, we initialize the run with a model analysis 3 or more days earlier and re-run the model with assimilated observations and analyzed winds up to the current model analysis. We refer to this period from the prior model analysis to the current model analysis as a hindcast. Many model results, particularly time series for tide prediction, show the hindcast.

In Depth: Data Assimilation in Navy Ocean Models

Among operational Navy models:

  • SWAFS assimilates surface temperature and height data, tidal information, and observed vertical profiles.
  • The Global NCOM assimilates surface temperature and height data, but nothing subsurface (until 2008).
  • The Relocatable NCOM assimilates all observations using a system called the Navy Coupled Ocean Data Assimilation (NCODA) System.
  • The Navy version of global HYCOM will also assimilate data using NCODA.
  • The NCEP version of HYCOM in the Atlantic and Pacific basins will also use NCODA.

SWAFS = Shallow Water Assimilation Forecast System (www7320.nrlssc.navy.mil/SWAFS/)
HYCOM = Hybrid Coordinate Ocean Model
(www7320.nrlssc.navy.mil/hycom1-12/skill.html)
NCOM = Navy Coastal Ocean Model (www7320.nrlssc.navy.mil/global_ncom/)
NCEP = National Centers for Environmental Prediction (www.ncep.noaa.gov)


8.5 Initial Conditions in Nested Model Domains

[ncom_nested_grids.gif]
Nested NCOM grid Maritime Rapid Environmental Assessment 2004 (MREA04). Outer grid (red) has horizontal 4-km resolution inner grid (blue) has 1-km resolution.

Some high-resolution regional ocean models start with initial conditions derived from a global model. In the graphic shown here, the outer 4-km grid, shown in red, receives its initial conditions from the global NCOM. Then, the nested 1-km grid, shown in blue, derives its initial conditions from the outer 4-km grid.

This cascade from larger-scale to smaller-scale models is similar to the way that mesoscale NWP models get their initial conditions.


8.6 Questions

For each of the following types of model start, what is the source of the initial conditions?
(Choose the best answer from the drop-down list)
1. Cold start [b]
2. Warm start [c]
3. Nested model domain [d]

Drop-down List:
a. Uniform temperature/salinity
b. Climatology
c. Previous forecast
d. Outer model nest
e. Inner model nest

Feedback 1: In a cold start, we start from scratch with an ocean at rest, meaning there is no circulation. Our initial conditions come from climatology, that is, from the average conditions for that day of the year.

Feedback 2: With a warm start, we initialize the model with the forecast from the previous model run. Thus, the ocean is in motion, circulation is already developed.

Feedback 3: In the case of nested grids, the outer nest provides initial conditions for the inner nest.


9. Running the Model


9.1 Dynamic Forcing

[dyn_forcing.jpg]
Conceptual cross section showing dynamic forcing processes

When we start an ocean model, what happens?

All dynamic forcing in an ocean model happens at the surface. This includes the following processes:

  • Momentum from wind stress that starts, changes, or maintains surface currents and waves
  • Incoming short-wave radiation from the sun
  • Longwave or infrared heat exchanges with the atmosphere. Fluxes are downward or upward, depending whether the ocean is colder or warmer than the air.
  • Latent heat fluxes due to evaporation (cools the ocean) or precipitation
  • Mass exchanges of fresh water in and out of the system through evaporation, precipitation, and river runoff
  • Exchange of salt, primarily from saline marginal seas, such as the Mediterranean or Red Seas (if they are not a part of the model domain). Local salinity changes are generally minimal and usually due to either evaporation or ice formation.
  • Tidal forcing through gravitational interactions between the Earth, Moon, and Sun.

These are the processes that drive our model through the primitive equations. Note that except for a few locations, heat and salt exchanges through the seafloor are negligible.


9.2 Coupled Models

[coastaljets/ekman2.gif]
coastal upwelling

In most cases, weather data from NWP models provide the dynamic forcing for ocean models. However, grids and time steps from the ocean and weather models may not necessarily match. If not, then we must re-interpolate the weather data in both time and space to match the ocean model. Problems arise if the re-interpolation results in land-based weather being used to force ocean processes. This can cause some major mismatches in heat fluxes.

The exchange between atmosphere and ocean is a two-way street. In many areas, the ocean and atmosphere profoundly affect each other. For example, coastal upwelling of cold water can cool and stabilize the lower atmosphere. This in turn supports the formation of a low-level coastal jet, which then enhances further upwelling.

This interaction between the ocean and atmosphere leads model developers to create coupled ocean-atmosphere models that work in concert. Here, surface fluxes of heat, moisture, and momentum pass across the air-sea interface at routine time steps. The processes that rely upon these exchanges are more accurately simulated, resulting in improved forecasts of both weather and ocean state. Of course, the air and sea are just two parts of the earth's environment or ecosystem, and a fully coupled system might include wave, ice, geochemical, and biological processes.

At the present time, the U.S. Navy is developing a system that couples the atmospheric model component of COAMPS with NCOM.

Text Note:
COAMPS = Coupled Ocean Atmosphere Mesoscale Prediction System
NCOM = Navy Coastal Ocean Model


9.3 Bathymetry and Friction

[ca_bath.jpg]
Shaded relief bathymetry of the central California coast

So now we have set up the initial and boundary conditions, along with the dynamic forcing. We need to consider one more factor before the primitive equations can drive the state of the ocean. That is the seafloor: its bathymetry and surface roughness. Unlike the atmosphere which is free to flow over the surface of the earth, the bathymetry, or basin shape, constrains currents. From ocean basins down to estuaries, bathymetry is a principle control on ocean currents.


9.4 Seafloor Roughness

[seafloor.swf] (seafloor 1-4)
Underwater photo of kelp forest

Underwater photo of sea grass

Underwater photo of coral reef

Underwater photo of sandy bottom

The surface roughness of the seafloor is used to determine the force of friction, one of the components in the primitive equations. All models require friction or currents would continually speed up. Friction removes tidal and circulation energy by heat and modulates currents and mixing near both the coast and seafloor.

For global ocean models, we can use one value of surface roughness everywhere. However, for nearshore regions, we need to be more careful about the spatial differences in surface roughness. Unfortunately, we usually know little about bottom characteristics. Consequently, we often parameterize bottom roughness, with poor results.


9.5 Questions

1. Where does dynamic forcing in the model occur?
(Choose all that apply)
a. At the sea surface
b. At the seafloor
c. At the bottom of the mixed layer
d. At the coast

Feedback: The correct answers are a and d. All dynamic forcing in the model happens at the surface, including momentum from wind stress, solar radiation, exchange of water and salinity, and tidal forcing.

2. Why do we couple ocean and atmosphere models?
(Choose all that apply.)
a. Because they otherwise tend to have different grids and time steps
b. Because heat and moisture fluxes between the ocean and atmosphere may flow either way
c. Because atmospheric forcing may result in changes to the ocean that affect the atmosphere.
d. To fully account for non-atmospheric effects in ocean models, such as tides.

Feedback: The correct answers are b) and c). Fluxes of heat and moisture may flow in or out of the ocean from the atmosphere. These fluxes are determined, in part, by the state of the ocean (for example, the sea surface temperature), which is largely controlled by the atmosphere. As a result of this feedback, coupling ocean and atmosphere models improves forecasts of both the weather and ocean state.


10. Role of Observations


10.1 What Observations?

[ocean_obs.swf]
Photo of argo drifting buoy

Photo of accoustic doppler current profiler

Photo of moored weather buoy

Compared to the atmosphere, we make very few observations of the ocean. Twice a day, weather balloons are launched all over the world, collecting a vertical profile of the atmosphere. On the ground, nearly every airport systematically collects weather data. The WMO (World Meteorological Organization) collects and disseminates all of this information in near real-time. Except for some coastal buoy systems such as the U.S. National Data Buoy Center (NDBC), routine sampling of the subsurface ocean just doesn't happen.

Despite these limitations, there are regular observations of the state of the ocean, they just aren't as plentiful as atmospheric observations. We can broadly classify the sources of ocean observations into two groups: in situ measurements and satellite measurements.

In situ measurements come from several sources: coastal stations, fixed current meters, fixed buoys, drifting buoys, ships, and gliders. Most of these sources provide just surface measurements, but gliders and some drifting buoys sink and then rise to the surface, recording vertical profiles of temperature and salinity.

ARGO is a recent international effort to sample the upper 1000 meters (3300 ft) of the ocean. The plan is to have 3000 ARGO profiling floats measuring temperature and salinity globally at 10-day intervals.


10.2 Satellite Measurements

[jason2.jpg]
Artist's rendition of Jason-2 satellite orbiting earth

Satellite measurements used in ocean modeling include sea surface height (SSH) from radar altimetry, temperature (SST) from infra-red radiation and, more recently, winds and wave heights from microwave measurements.

To learn more about ocean remote sensing, see these COMET modules:
Microwave Remote Sensing: Overview (http://meted/npoess/microwave_topics/overview/)
Microwave Remote Sensing: Clouds, Precipitation, and Water Vapor (http://meted/npoess/microwave_topics/clouds_precip_water_vapor/)
Advances in Microwave Remote Sensing: Ocean Wind Speed and Direction (http://meted/npoess/ocean_winds/)


10.3 Assimilation

[nlom_assim_comp.jpg]
SeaWiFS Ocean Color, Arabian Sea, 2-6 Oct 2002

1/32-degree Navy Layered Ocean Model (NLOM) forecast of sea surface height and current with assimilation, Arabian Sea, 2-6 Oct 2002

1/32-degree Navy Layered Ocean Model (NLOM) forecast of sea surface height and current without assimilation, Arabian Sea, 2-6 Oct 2002

What do we do with the data we gather? As we mentioned when discussing model initialization, sometimes we assimilate data into the model analysis. While this process usually brings the analysis closer to reality, it can also introduce problems.

For example, take the case of an ocean front along the north side of the Gulf Stream where a strong gradient separates warm and cold water. If an observation of warm temperature falls on the cold side of the front, the assimilation routine will try to warm the cool water rather than shift the front. In this way, the assimilation of observations in regions of strong gradients tends to smear out the gradient, thereby weakening the dynamic forcing of the feature.

Other errors from assimilating observations may show up as strange features in model products such as bull's-eyes. As a result, an ocean forecaster should always attempt to verify the existence of apparently anomalous features using independent observations.


10.4 Assessment

[nlom_xbt_comp.jpg]
NLOM (model) and XBT (observed) Temperature Profiles across the Kuroshio Current

Observations are also used to verify a model run or, more generally, to assess the skill of a model. By comparing forecasts to observations, we can assess the bias and uncertainty of any given prediction. For example, we may determine that in a particular location, observations indicate that the model under-predicts current strength. Or we may find that the current strength is accurate within 2 knots, but not reliably better than that.

This graphic shows 3 cross sections of temperature across the Kuroshio Current near Japan. The top cross section shows observed temperatures, the middle cross section shows model temperatures, and the bottom cross section shows the difference between the two. Note that the largest errors occur near fronts between water masses.

The assessment of model accuracy is one of the skills that separates novice from expert users of model products. This is true for both weather and ocean forecasts.


10.5 Questions

1. Which of the following platforms provide vertical profiles of temperature and salinity?
(Choose all that apply.)
a) satellites
b) fixed buoys
c) drifting buoys
d) gliders
Feedback: The correct answers are c) and d). Gliders and some drifting buoys sink and then rise to the surface, recording vertical profiles of temperature and salinity.

2. [T / F] Assimilation of ocean observations always improves the model result.
a. True
b. False
Feedback: The correct answer is False. While assimilation usually brings the analysis closer to reality, it can also introduce problems. For example, the assimilation of observations in regions of strong gradients tends to smear out the gradient, thereby weakening the dynamic forcing of the feature.

3. [T / F] There are many more observations of the oceans than the atmosphere.
a) True
b) False
Feedback: The correct answer is False. Twice a day, weather balloons are launched all over the world, collecting a vertical profile of the atmosphere. Meanwhile, routine sampling of the subsurface ocean just doesn't happen, except for some coastal buoy systems such as the U.S. National Data Buoy Center (NDBC).


11. Sources of Errors


11.1 Truncation and Rounding Errors

[error_math.jpg]
Graph showing the hypothetical accumulation of truncations in an ocean model forecast

While ocean models can typically provide our best estimate of ocean conditions, they remain an estimate. The errors in ocean models arise from several sources. Mathematical errors arise from the truncation and rounding of numbers from one time step to the next. While it might seem that these errors would be insignificant, there are several hundred thousand time steps in a typical model run. After that much iteration, errors are bound to accumulate. In addition, model equations are simplified to speed computations, resulting in inexact solutions that lead to model errors. Model developers are obviously aware of these problems and develop schemes to limit their effects.


11.2 Errors from Weather Predictions

[error_wx.jpg]
Graph showing the hypothetical underforecast of mixed layer depth due to underforecast of wind speed

Because the ocean is forced by atmospheric winds and heat transfers, errors in weather forecast models will cause errors in the associated ocean models. For example, under-forecast winds will not produce large enough waves or adequate mixing in the upper ocean. An incorrect wind direction will mean locally generated waves will propagate wave energy as swell in the wrong direction. Over-forecast precipitation will result in a surface layer that is too fresh and thus not dense enough to allow sufficient vertical mixing.


11.3 Parameterization Errors

[param_procs.swf]
Conceptual cross section showing parameterized processes
Click to open animation in a new window.

As we mentioned previously, other computational errors arise from approximations required by parameterization schemes, sometimes compounded by the interaction between different undefined processes. For various reasons, these schemes do not represent the real ocean and introduce errors.


11.4 Assimilation of Observations

[error_assim.jpg]
Graph showing possible errors in assimilating observations in ocean models

One way to reduce model errors is to "correct" the fields by assimilating observations. However, observational errors also play a role in ocean modeling. Some errors arise from the sparseness of data coming from the ocean. Compared with the much denser atmospheric observation network, few resources are dedicated to real-time ocean observations, particularly below the surface. Other errors can be attributed to simple instrument error that will propagate through the modeling process. In addition, temporal errors arise when assimilation schemes assume all observations apply to the analysis time (like 00Z) but they might have been collected at any time since the prior analysis. Similarly, spatial errors may arise when we assimilate observations into the model grids rather than at the actual observation location. Last, as we discussed in a prior section, assimilation schemes tend to nudge the analysis toward the observed state, rather than force it to adopt the observed state. In this diagram, we refer to this discrepancy as the Assimilation Residual.


11.5 Conclusion

In general, ocean forecasters should consider model errors and beware of making a forecast that's too precise or implies too much accuracy. For example, just as weather forecasters would never forecast 12.52 kt winds at 1100 UTC, oceanographers shouldn't forecast tidal currents of 2.4 knots at 1300 UTC. Where a weather forecaster may predict winds of 10-15 kt, an ocean forecaster might predict currents of 2-3 kt. Similarly, the prediction of the exact thickness of the planetary boundary layer is just as difficult as determining the depth of the ocean mixed layer.


12. Summary

To better understand and forecast the state of the ocean, we rely on numerical models to provide guidance. Ocean models resemble atmospheric models in that both simulate a thin fluid layer on a rotating sphere heated by the sun.

Differences between ocean and NWP models arise from the properties of seawater and air:

  • Air is a gas while water is nearly incompressible
  • Water is much denser than air
  • Water has a much greater specific heat than air
  • Sea water has salinity, while air has humidity. Sea water becomes denser with increasing salinity, while air becomes less dense with increasing humidity.

Other differences arise from the horizontal and vertical structure of the ocean compared to that of the atmosphere:

  • Both the oceans and the atmosphere have a well-mixed layer near the surface
  • Oceans are highly stratified below the mixed layer, while the atmosphere is relatively well mixed above the boundary layer.
  • The atmosphere is laterally continuous while the ocean is broken by landmasses into basins.

Despite their differences, the oceans and atmosphere share many similarities:

  • Both are thin fluid layers on a rotating sphere
  • Both have circulation that is driven by solar heating
  • The physics that drives oceanic and atmospheric circulation are similar

Ocean models determine the state of the ocean using 3 basic physical relationships. We refer to these relationships as primitive equations.

  1. Navier-Stokes equation: The forces experienced by a parcel of seawater include
    • Gravity
    • Pressure gradient force
    • Coriolis force
    • Friction
  2. Continuity Equation: Model inputs equal model outputs, so that there is no net gain or loss in the system of water, salt, or heat
  3. Equation of State: Density is a complex function of temperature, pressure, and salinity

To apply the primitive equations to a model ocean we need to convert the equations to a series of algorithms that can be applied to a gridded ocean.

  • Horizontal grids fall into two types: referred to as regular (plaid) and irregular (finite element). Regular grids are easy to set up. Irregular grids allow us to increase the resolution near the coast while keeping the resolution in the middle of the ocean relatively coarse.
  • Vertical coordinate systems may be based on absolute depth (z), normalized depth (σ), density layers, or hybrid systems that combine more than one coordinate system.
  • Model resolution is based on grid spacing: it takes five grid points to accurately resolve a feature. The main barrier to improved resolution in operational ocean models is computational speed: every halving of grid spacing requires roughly ten times as much computation.

Ocean models cannot simulate features and/or processes that occur within the confines of a single grid box. Parameterization is the method of accounting for such effects. Processes must be parameterized in a model for three main reasons:

  1. Computers are not yet powerful enough to directly treat them because the phenomena are either too small or too complex to be simulated.
  2. The processes are often not understood well enough to be represented by an equation
  3. The effects profoundly impact model fields and are crucial to creating realistic forecasts

While ocean models typically provide our best estimate of ocean conditions, they remain an estimate. The errors in ocean models arise from several sources:

  • Mathematical errors (truncation and rounding of numbers)
  • Approximations required by parameterization schemes
  • The interaction between different parameterizations
  • Observational errors

Every model run starts with a set of initial conditions. We refer to this as model initialization. For ocean models, initial conditions include temperature, salinity, density, and circulation.

  • There are two fundamentally different ways to initialize an ocean model: a cold start and a warm start.
    • In a cold start, we begin with an ocean at rest. Initial conditions for temperature and salinity come from climatology.
    • With a warm start, we initialize the model with the forecast from the previous model run, including currents.
  • Regardless of whether we start our model run warm or cold, we can improve our analysis by assimilating observations into our initial conditions.
  • High-resolution, regional ocean models start with initial conditions derived from a global model. In the case of nested grids, the outer nest provides initial conditions for the inner nest.

When we start an ocean model, all dynamic forcing happens at the surface. Weather information from NWP models drives most of the dynamic forcing in ocean models. The remainder comes from tides.

Because of the interaction between ocean and atmosphere, some models are coupled. In coupled models, information is exchanged between the NWP and ocean models at each time step.

Observations of the ocean come from many sources. We can broadly classify these sources into two groups:

  1. In situ measurements:
    • Observations of temperature, salinity, currents, weather
    • Data from coastal stations, buoys, fixed current meters, ships, drifters, gliders
    • Most sources provide surface measurements
    • Gliders and some drifters record vertical profiles
  2. Satellite measurements
    • Sea surface height (SSH)
    • Sea surface temperature (SST)
    • Winds

We use these observations in two ways:

  1. To assimilate into model analyses
  2. To assess the skill of a model run

References Cited

D.-S. Ko, C. Rowley, P. Martin, R. Allard, J. Dykes, and R. Preller, 2005: A Real-Time Coastal Ocean Prediction Experiment. Ocean Science and Technology, 2005 NRL Review,
183-186. [Retrieved 28 January 2007 from http://www.nrl.navy.mil/Review05/images/05Ocean(Ko).pdf]

A. Militello and A. K. Zundel, 2002: Coupling of Regional and Local Circulation Models ADCIRC and M2D. U.S. Army Corps of Engineers Coastal and Hydraulics Engineering Technical Note ERDC/CHL CHETN-IV-42, 13 pp. [Retrieved 28 January 2007 from
http://cirp.wes.army.mil/cirp/cetns/chetn-iv42.pdf]

Murray, R. J., 1996: Explicit Generation of Orthogonal Grids for Ocean Models.
J. Comp. Phys., 126, 251-273.

R. C. Rhodes, H. E. Hurlburt, A. J. Wallcraft, E. J. Metzger, J. F. Shriver O. M. Smedstad,
J. F. Cayula and A. B. Kara, 2003: Validation Test Report for the 1/16° Global NRL Layered Ocean Model Nowcast/Forecast System. NRL Tech Report NRL/FR/7320-03-10,020, 74 pp.[Retrieved 28 January 2007 from http://www7320.nrlssc.navy.mil/pubs/2003/rhodes.pdf]

P. S. Schopf, 2005: Notes on Implementing the Murray Tripole Grid, 9 pp.
[Retrieved 28 January 2007 from http://climate.gmu.edu/poseidon/papers/Tripole.pdf]

Links

Navy Operational Ocean Circulation and Tide Models,
Department of Oceanography, Naval Postgraduate School
http://www.oc.nps.navy.mil/nom/main.html

Naval Research laboratory, Ocean Dynamics and Prediction Branch (Code 7320)
http://www7320.nrlssc.navy.mil/index.php

Naval Oceanographic Office (NAVOCEANO)
https://www.navo.navy.mil/

UNESCO Ocean Teacher Earth System Modeling
http://ioc.unesco.org/oceanteacher/oceanteacher2/06_OcDtaMgtProc/
06_EarthSysMod/EarthSysModl.htm

National Oceanographic Data Center
http://www.nodc.noaa.gov/
Interactive Data Access and Retrieval System (IDARS)
http://www.nodc.noaa.gov/dsdt/