Data Assimilation

So - instead of having a purely mathematically evolving ocean, with external forcing, we are incorporating data into the mathematical simulated ocean. We are using assimilation techniques to make our modeled fields resemble the ocean circulation patterns observed (and measured) at a given time and place.

Gulf Stream from AVHRR - note location of eddies
Gulf of Mexico

What is a hindcast model simulation?

A model simulation that represents the evolution of the ocean for a period of time in the past.

What is a forecast model simulation?

A model simulation that is attempting to represent the ocean's circulation for a time in the future.

Why do we assimilate data?

To make a prediction of future ocean circulation, we want to begin with the state of the ocean (location of eddies, currents) as close to the real ocean as possible.
To understand previous patterns in variability, we want to make the ocean simulation as close to reality as possible.

What sort of features should benefit most from this technique?

How to think about it in practical terms.

T_est(1) = A set of Temperature estimates made by model and evolved by math equations for time = 1

T_obs(1) = A set of Temperature measured in the real ocean at time = 1
This is assumed to be "Truth".

Difference = T_obs(1) - T_est(1)

T_est(2) = T_obs(1) + R*Difference + Math

where R includes

information on errors
how to distribute the observed temperature to nearby points

Note that assimilating temperature data will also cause also will cause U, V, Salinity, SSH to change indirectly.

Variational techniques are useful for dealing with large complex systems such as the ocean where local changes in some variables (eg. temperature) have many consequences for other quantities (eg. currents). In other words, the ocean is a complicated system, and "adjusting" one location's temperature may affect many other quantites. All these other things have to be considered when adjusting one parameter at one location. The goal is to minimize some measure of difference between the model and the data.

How is data assimilated?

In the previous section, we made reference to the analysis - forecast cycle of data assimilation, whereby on a regular schedule, new data are quality-controlled, objectively analyzed in combination with a recent forecast field, the model is initialized, and a new short-term forecast is made. This type of intermittent data assimilation scheme works well for numerical weather prediction, where numerous observations over a large area are available on a preset schedule. This method is also used for some ocean models.

In continuous assimilation schemes, data is inserted whenever it becomes available. This has some advantages for the ocean, where in situ data is sparse and doesn't necessarily arrive on a regular schedule. Often, rather than inserting the data directly, incremental insertion is used, whereby the influence of new data is introduced gradually over time in order to minimize the imbalances that result from mismatches between the model and the data.

Another form of data assimilation used in the ocean is called nudging, whereby the model is gently pushed towards a known state over time.

Where does the data come from to incorporate into an ocean model?

Because the ocean in general evolves more slowly than the atmosphere, the window of time over which data is useful to a model is somewhat longer for the ocean than for the atmosphere. Data available within one to 24 hours might be considered "realtime", and data available within one to 10 days might be considered "semi-realtime". SSH and temperature are the variables most commonly assimilated into ocean models.

NRL (NAVY) semi-realtime

With the recently launched gravity satellite GRACE, SSH anomalies will be combined with the estimate of a mean sea surface to produce a total SSH estimate, rather than just SSH anomalies. http://www.csr.utexas.edu/grace

AVHRR (Advanced Very High Resolution Radiometer) Data
MCSST (Multichannel Sea Surface Temperature)

Since clouds interfere with this measurement, data products may combine measurements made over a number of satellite passes. The radiometers used to measure SST from space have a "footprint" of one to several kilometers, and subsequent data processing may further reduce the spatial resolution. So the SST measured from satellites integrates over an area of several square kilometers.

surface drifters	surface	semi-realtime
Expendable Bathythermograph (XBT)	Temperatures in upper ocean	realtime to semi-realtime
Argo Floats - Global array of profiling floats	Temperatures/Salinities over upper 2000 m	10-day cycle time
PALACE (Profiling Autonomous Lagrangian Circulation Explorer) Floats	upper 1000 m

surface drifters	Surface velocities	At present, not commonly assimilated into models
Buoy measurements (for example TOGA/TAO array Pacific) U/V/T/S	various depths	semi-realtime

What is the quality of the data? (measurement errors)

All data contains some error.
The faster the data arrives at a site, the higher the data error (most data requires some sort of screening).
After a time - an error statistic can be assigned to a given piece of data (measurement +/- some error).
Some type of model of these errors is used in any assimilation technique.

How do we know if the model is close to the truth?

Compare model output to measurements that have NOT been included in the assimilation. For example, compare the model's SSH with measured SSH (altimeter), if only sea surface temperature has been assimilated.
Compare predictions with observations for that predicted field.

Some examples from Navy Products:

example 1 - NRL Stennis
example 2 - FNMOC Monterey
- Click on Monthly Model Summary under Model Performance
- Choose Month
- Choose either 5.0 Model Surface Current Validation or choose TOPS under Verification

Now your model is designed and you've got data to force the model and data to assimilate into the model. But we're not quite done - we've got to find a computer system to run it on. Proceed to the "Implementation" section now.

Ocean Data Assimilation

What does data assimilation mean?

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