• Creating a KL wind field model
• The SeaWinds 8x8 KL model

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:

1. A swath is subdivided into NxN regions. No regions are used that contain missing data points.
2. The rectangular (U and V) components for each NxN region are column scanned to create a 2N² column vector, W_n. The first N² vectors contain the column scanned U components, and the last N² vectors contain the column scanned V components.
3. The autocorrelation matrix R is estimated: where M is the number of NxN regions examined.
4. The vector F is extracted by taking the singular value decomposition of where (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.
5. Any arbitrary wind field can be expressed as the linear combination of the model parameters.
6. 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 following figure.