In order to start a model run, certain variables need to be specified. We have already talked about various model parameters like domains, grids, and bathymetry; and now we will talk about the starting values used for the variables that the model is actually going to predict. These include temperature, salinity, density, sea level, and velocity.
One way to initialize models is by using climatological values of temperature and salinity from databases and assuming the velocity field is zero at the start. The model physics will spin up a velocity field in balance with the density field, even in the absence of forcing. As forcing is applied, the velocity field will respond to it initially with transient flows that may not be realistic for an ocean that undergoes continuous, albeit always changing, forcing. For this reason, the results from the beginning of ocean circulation model runs are usually not used. This model spin-up phase is discussed more below.
"Climatologies consist of data averaged over well-defined spatial grids and over time periods such as month, seasons, or years." "Climatologies provide boundary conditions and first-guess fields for models."(Fox, et al., 2002b).
The Levitus climatology, first published in 1982, and updated frequently over the last 20 years, objectively analyzed all temperature and salinity data available through the National Oceanographic Data Center (NODC) into monthly values on a 1o by 1o global grid (Levitus, 1982). Boyer and Levitus (1997) produced a high-resolution climatology on a 1/4o grid (http://www.nodc.noaa.gov/OC5/pr_woa4.html).
Another widely used climatology is the Generalized Digital Environmental Model, GDEM (Teague, et al., 1990). Like Levitus, it provides global coverage, but with spatial resolution that varies from 1/2o in the open ocean to 1/6o in some coastal areas, and with daily temporal resolution. The source of data for GDEM is MOODS, the Master Oceanographic Observation Data Set maintained by NAVO. In the deep ocean, GDEM is matched to Levitus. http://18.104.22.168/gdemv/
Other climatologies include:
Another common way to initialize a model is with fields from a previous run of that model, or with the results from another model. For instance, to use an atmospheric example, one could imagine interpolating the results from NOGAPS which is run continuously but on a relatively coarse grid, to a finer grid to initialize a COAMPSTM model for an area that needs to be implemented quickly. There have been varying degrees of success with this for ocean models, one of the reasons for which is discussed below under disadvantages.
Results from a data analysis system, such as MODAS, can be used to initialize a model. This is the approach taken with the relocatable MODAS/POM, system, and some of the other models, that will be discussed later. It is very difficult to use observations directly since they are so irregularly spaced and extensive error checking needs to be done.
Spin-up is the time taken for an ocean model to reach a state of statistical equilibrium under the applied forcing.
It is usually difficult for basin-scale and global general circulation models to reach this state, as it can take hundreds of years. The ocean model is initialized with the present ocean state (climatologies just discussed) and is integrated forward until the circulation is consistent with the prescribed water mass structure. In other words, it adjusts geostrophically to its initial state. This initial state is imperfect due to the sparseness of data at depth.
How long does it take for the ocean model to reach equilibrium? (The following discussion relies heavily on Kantha and Clayson, 2000.)
In spin-ups of several decades (duration dictated by available resources) deep watermass properties away from strong currents or deepwater formation sites, will not evolve far from the initial state. To study upper ocean processes, such as El Niño, only the upper ocean (above the main thermocline) needs to be in equilibrium. Effectively, the spinup time scale is the time needed for the first and second mode long Rossby waves (large-scale planetary waves) to cross the basin from east to west, affecting currents, and ultimately the watermass properties. Along the equator, the first mode baroclinic Rossby wave takes about 9 months to cross the Pacific; however the second, and higher, baroclinic modes travel slower. Hence, in the equatorial band, it takes several years for the spinup to reach equilibrium. In the mid-latitudes, the long waves travel more slowly. It takes about 11 years for a Rossby wave to cross the Pacific. For a global ocean model, it will take several decades to achieve equilibrium in the upper ocean. It is important to understand, that an ocean model cannot be studied until this equilibrium is reached.
If only the barotropic modes are considered, or the model is 2D, then the adjustment time will be much quicker, on the order of days, since the barotropic waves travel faster. It is also possible to reduce spin-up time by using data assimilation to nudge the model toward the observed state. Since SSH is the most widespread type of data coverage, this works best with barotropic models.
Also, if one is concerned only with the wind driven flows, including that arising from sea surface slopes resulting from Ekman pumping, a spin-up time on the order of days may be adequate. (Ekman pumping is the convergence or divergence of water in the Ekman layer due to spatial gradients in the Ekman transport.)
When implementing an ocean circulation model for a new domain, allowance must be made for spin-up time. This can be quite long for basin-scale models such as NLOM and POP while regional models, which don't include deep ocean basins, may be spun up more quickly.
The terms "cold start" and "warm start" may mean slightly different things to different people. The term "hot start" is even used occasionally. Therefore, the definitions below are given in fairly general terms. For any particular model implementation, the specifics of how a cold or warm start are carried out, may be different.
A cold start usually occurs when a model is first initialized and needs to be spun up. For example, if a regional model is configured in a new domain, it would need to be started in this manner. A cold start could be from climatology (commonly used to initialize global models), an analysis of data (such as MODAS), a forecast from a different model (like using NOGAPS to initialize (COAMPSTM), or a combination of the above. The model is then run until a statistical equilibrium is achieved.
A warm start is a restart of a model, which is used to eliminate or reduce the model spin up time. The saved fields from a recent forecast of the same model can be used to initialize a new simulation, or continue the previous simulation. The saved fields may be used as a first guess for an analysis including new data, and then that field is used to initialize the new forecast.
If there is a continuous cycle of forecast - data analysis - forecast, this could also be thought of as data assimilation.
Continue now to the next section on data assimilation.