A practical understanding of dynamic adjustment

When the model run starts with a new analysis, imbalances in the initial conditions cause gravity wave noise early in the forecast and an adjustment of the large-scale fields. This is described on the previous page. It is why most analyses apply some sort of balance constraint and why an initialization procedure may be run following the analysis.

For models with an assimilation cycle (such as the operational Eta but not the "threats" runs), the forecast impact of new data is the model's response to the analysis increments (changes from the first guess). Thus, what matters is whether the analysis increments are primarily in the wind field or the mass field and whether they are large or small in scale compared to our favorite length scale, 2L_R. This means

• In the tropics, the forecast can be most improved with wind observations
  
• In middle latitudes, the large-scale forecast winds will be determined largely by the initial mass field, making temperature observations most important
  
• Moisture observations don't create much dynamic adjustment by themselves but are linked to both mass and wind changes through the model integration during the assimilation period, during which the model evolution is affected by changes in radiation and latent heating in model precipitation
• How the data are put into the model makes a huge difference
  
  • Forcing the analysis to tightly fit observations, especially of pressures/heights/temperatures, in a small region around the observation will not have much lasting impact on the forecast and may produce adjustment toward an incorrect large-scale state, resulting in degradation after some time into the forecast
    
  • Mesoscale data assimilation is a major challenge, and getting consistent forecast benefit beyond a few hours from assimilating mesoscale observations is extremely difficult
    

Correlation length, or forecast error covariances

Statistical analysis systems, including 3D-VAR, assume that there is some relationship between corrections required to the first guess some distance from an observation and the correction required at that observation location. For more background on how 3D-VAR works, refer to the COMET module, Understanding Data Assimilation. This relationship, properly expressed as forecast error covariances but also characterized with a correlation length (distance over which the relationship extends), results in a smoothing of the analysis increments. Both horizontal and vertical relationships are used, so there is effectively some smoothing in both the vertical and horizontal. Generally correlation lengths will tend to be longer in coarser resolution models.

The horizontal correlation length affects the horizontal scale at which data enter the analysis. If this length scale is large, only synoptic-scale features will be changed by observations, and the mass observations will be most critical to the forecast. If the correlation length is short, then wind observations become more important because the analysis increments will involve more small-scale structure.

The vertical correlation length affects the depth through which data affect the analysis, and thus the Rossby radius of features in the analysis increments. If the vertical correlation length is short, then the Rossby radius will be smaller, making mass observations more useful.