dash.localize.gc1d
Computes localization weights along a depth/height/Z dimension using a Gaspari-Cohn 5th order polynomial
Syntax
Description
Calculates covariance localization weights for an assimilation using a specified cutoff distance. The method proceeds by determining the distances between a set of depths/heights/Z-coordinates and then applying a Gaspari-Cohn 5th order polynomial to the distances. This can be used to implement localization along the depth/height/Z coordinate of an ensemble. If the distance between two depths/heights/Z-coordinates is NaN, returns a weight of 1 (i.e. no localization).
Specifies the length scale for the polynomial. By default, uses a length scale of 0.5, which sets the localization distance equal to the cutoff distance.
Input Arguments
stateDepths
numeric vector [nState]
The depth/height/Z coordinate of the state vector elements. Any units are permitted so long as the siteDepths and cutoff distance use the same units.
siteDepths
numeric vector [nSite]
The depth/height/Z coordinate of the proxy sites. Should use the same units as stateDepths.
distance
positive numeric scalar
The localization cutoff distance. Should use the same units as stateDepths
scale
numeric scalar
The length scale to use for the Gaspari-Cohn polynomial. Must be on the interval 0 < scale <= 0.5. By default, uses a length scale of 0.5, which sets the localization distance equal to the cutoff distance
Output Arguments
wloc
numeric matrix [nState x nSite]
The covariance localization weights between the state vector elements and proxyobservation sites.
yloc
numeric matrix [nSite x nSite]
The covariance localization weights between the proxy/observation sites and one another.