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GEMPAK grid programs which plot contours and vectors use algorithms which require data on a rectangular grid. The process of contouring, as well as calculating finite differences uses the gridpoints to perform the desired operation.
Numerical model simulations are perfomed using gridpoints, so that data is already on a regular grid. However, for standard surface and upperair measurements the data must first under go a process known as gridding.
The objective analysis procedure accomplishes another task in the process at arriving at the final grid. All data which undergoes objective analysis is filtered in one way or another. The process of filtering occurs as stations surrounding a nearby grid point receive a relative weight, typically based on the distance they lie from the gridpoint. The process of assigning weights to grid points determines the eventual contribution that point will have in the final value of the gridpoint.
Stations which lie closest to the gridpoint receive the greatest weight, while those that lie farther away contribute less to the overall value. In this way, the gridpoint is not representative of a single station, but is instead a best fit to all the surrounding data. As a result, the final grid value is a compromise between all the stations which are used to determine the value. The effect of considering several stations leads to smoothing of the data. The final grid point value will range somewhere between the maximum and minimum values of the stations used.
The Objective Analysis procedure used for GEMPAK is known as a Barnes scheme. For a detailed technical description, see Koch, desJardins,and Kocin: Journal of Climate Appl. Meteor., 22, 1487-1503.
The Barnes Scheme applies a Gaussian Weighting function, in which the weight a station contributes to the overall value of the grid point falls off rapidly with increasing distance from the point. Since tha tails of a Gaussian function are infinite, in practice a radius of influence is is chosen such that stations outside the circle about the gridpoint are not considered. The GEMPAK implementation requires that at least 3 stations be within the radius for a value to be assigned to a grid point.
The depiction above represents the Barnes Analysis process. For each gridpoint, stations within the radius of influence are assigned a weight value W using the formula:
where d is the distance from the station to the gridpoint and R is the radius of influence.
After the weights are determined the first guess of the gridpoint is determined by:
This is known as the first pass of the scheme. If more than 1 iteration of the scheme is desired (typically 2 passes are preformed), a method known as successive corection is applied. This method interpolates from the new grid values back to the original station. The difference in the interpolated from the original value is then used as a correction to the first pass grid point value. A new parameter called the convergence parameter (GAMMA) is use to control the amount of smoothing. Each correction step can be represented as:
where W' is the correction weight parameter:
The convergence parameter gamma ranges between 0 and 1. A value between .2 and .3 is generally assumed.
Since the grid point values are essentially weighted
averages of surrounding stations, the grid point value will always be less than
the maximum, and greater than the minimum values surrounding the point.
As a result, there is smoothing occuring within he grid. The purpose of the
convergence parameter on successive correction passes is to mittigate
over smoothing of the data.
| 19.0 | GEMPAK Objective Analysis Programs |
| 19.1 | GEMPAK Objective Analysis: Surface Data |
| 19.2 | GEMPAK Objective Analysis: Sounding Data |
| 19.3 | GEMPAK Objective Analysis Exercises |
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