Wind Field Models
An important part of wind estimation is wind field modeling. Models
are useful because they take into account the inherent correlation
between neighboring wind vector cells. Various types of models have
been explored for use in ocean wind estimation. The Karhunen - Loeve
(KL) model, often used in image processing is especially effective
because it minimizes the basis restriction error for a given set
of second order statistics.
Creating a KL wind field model
The KL model is generated by taking the eigenvalue decomposition
of the autocorrelation matrix. Specifically, the KL model for wind
fields is formed in the following way:
- A swath is subdivided into NxN regions. No regions are used
that contain missing data points.
- The rectangular (U and V) components for each NxN region
are column scanned to create a 2N2 column vector,
Wn. The first N2 vectors
contain the column scanned U components, and the last N2
vectors contain the column scanned V components.
- The autocorrelation matrix R is estimated:
where M is the number of NxN regions examined.
- The vector F is extracted by taking the singular value
(Note that the singular value decomposition is equivalent to the
eigen value decomposition because
is symmetric.) The columns of F become the basis fields,
or model parameters of the KL model.
- Any arbitrary wind field can be expressed as the linear combination
of the model parameters.
- The basis set F is truncated at a reasonable number
of model parameters in order to suppress high frequency noise
in the model fit of the wind.
The SeaWinds 8x8 KL model
The KL model is used in field-wise estimation and in the point-wise
quality assurance algorithm. The advantage of using a model is that
it acts as a low pass filter to the wind suppressing the effects
of noise in the measurements. The first 6 model parameters for the
8x8 KL model generated using SeaWinds data is shown in the
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