OC4331-Mesoscale Oceanography
Final Project Summary

Topic Area

Project Team Member(s)

LCDR Eric Gedult von Jungenfeld, USN

LCDR (sel) Mike Kuypers,USN

Major Findings

Objective analysis is the process by which a randomly distributed and temporally dispersed set of observations are interpolated to a uniform grid of parameter values from which the model can be run. A description of the Multiquadric Interpolation scheme was presented as a valid method of Objective Analysis. The most common method of objective analysis in current operational numerical forecast centers is the Optimal Interpolation method. This method uses predefined covariance functions derived from climatological data in order to relate the covariance between the field at the grid point and the observation point. In addition, a length scale "L" must be defined. This scale drives the correlation between data points at a given distance. (e.g. higher length scales tend to keep data points more correlated but field becomes smoother). Since both of these variables must be predetermined, the use of this data assimilation method is certainly less than "objective." The advantage of the OI scheme is that since the wind and mass fields are statistically derived from actual climatology, the fields are dynamically consistent. While this is certainly advantageous on the synoptic scale, mesoscale structures are often removed due to the smoothing effect of the scheme. Multiquadric Interpolation uses hyperboloid radial basis functions in a distance weighting scheme to interpolate the data to the model grid. It is a 3 - D single variable analysis procedure and thus can not be applied independently to various vertical levels and/or mass and wind fields. It also has some predefined variables with its smoothing parameter and the multiquadric parameter (c). Its advantages are that it allows the model to draws closer to the actual data and since the length scale is determined by the data distribution, it tends to maintain mesoscale structure better.

A comparison of an Optimal OA scheme vs a multiquadric scheme was done for an SST data set of the coast of California. Findings showed that there were significant differences in the representation of the field when various length scales and covariance functions were used. Both schemes seemed to be able to pick out the major features of the actual data.

Conclusions

• Multiquadric interpolation of meteorological observations is a valid technique.
• For fewer obs, the multiquadric interpolation method was much better than Optimal OA.
• Any interpolation scheme is subject to symmetrical biases that are not the norm in local (mesoscale) data.
• A choice must be made - assume the statistics are known and model them better, or assume nothing and possibly miss things.

 

Figure 1. A comparison of the Optimal OA scheme with L=250km (left) and Multiquadric Scheme at 27 observations (right). Bottom slides show the percent difference of the analysis from the true data.

References

Cressman, G.P., An Operational Objective Analysis System, Monthly Weather Review, January, 1960.

Carter, E., Notes on Optimal Objective Analysis, NPS OC 4331 class notes package.

Nuss and Titley, Use of Multiquadric Interpolation for Meteorological Objective Analysis, Monthly Weather Review, Vol. 122, July, 1994.

Barnes, S.L., Comments on "Use of Multiquadric Interpolation for Meteorological Objective Analysis", Monthly Weather Review, July, 1995.

Nuss W.A., Reply, Monthly Weather Review, Vol. 123, July, 1995.

Von Storch, H. and Zwiers, F.W. Statistical Analysis in Climate Research, Cambridge University Press, 1999, 484 pp.

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