• Observed statistical relations between observations
  1. showed plot of correlation between "H" at one radiosonde site and another site, for 50 sites in the U.S. H is the estimated forecast error
  2. while there is much scatter, some properties are:
     • correlation decreases with distance.
     • significant negative values occur (peaking roughly at 1800 km, which approximates the half-wavelength of a typical synoptic patter of high and low pressure.)
     • one can approximate the median pattern with an exponential decay, and possibly ignore stations more than 2000 km from the grid point. (useful information for the objective analysis schemes to follow.)

• The Cressman objective analysis scheme
  1. the first scheme to use a first guess followed by a correction
  2. weights are an exponential function of distance between grid point and observation
  3. advantages:
     1. the scheme is simple
     2. the scheme is quick to calculate
            (for fixed observation locations, the w_k 's can be stored as a table, and not recalculated each time.)
  4. disadvantages:
     1. does not incorporate balances between variables
     2. assumes a relation (for the weights) that is too simple: It is only a function of distance, but more complex relations exist in nature
            e.g. Fresno is farther from Davis than Blue Canyon, but Fresno is likely better correlated. Cressman scheme does not recognize this.
     3. treats all data as independent.
            e.g. Cressman scheme does not recognize that data from 2 stations side by side not as independent (or as useful) as 2 stations on opposite sides of your grid point.
     4. does not discriminate accurate from inaccurate observations

• A note on application of Objective Analysis:
  • See the 5 steps in the "forecast-analysis cycle" figure
  • the Cressman scheme discussion implies that the first guess at each grid point is modified by means of a sum of differences at nearby obs.
  • at some operational centers the difference between first guess and observation is used to define a array of corrections by means of interpolation from the differences at the obs locations.
  • the advantages are:
    1. speed: only calculate a difference between ob and first guess once for each observation.
    2. smoothness: interpolation onto a grid (from the differences at the observation locations) gives a smooth pattern
  • disadvantage: cannot weight observations differently.

• Statistical objective analysis
  • the subject can be highly technical, some simple examples were shown for illustrative purposes
  • procedure is like the Cressman scheme: a first guess is modified by a weighted sum of nearby differences between ob and first guess
  • the difference from the Cressman scheme is in how the weights are defined
  • weights drawn from past associations (i.e. past "statistics")
  • weights depend on the fidelity of the observation
  • weights depend on the location: relative to the grid point but also relative to other observations
  • the closer two observations, the less independent the information in those obs.

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