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@@ -13,27 +13,29 @@ values will be treated as NULL cells in both the input and the output map.
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<p>
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Spline step values <b><i>se</i></b> for the east-west direction and
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<b><i>sn</i></b> for the north-south direction should not be smaller than
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-the east-west and north-south resolutions of the input map. For very large
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-areas with missing values (NULL cells), larger spline step values may be
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-required, but most of the time the defaults (1.5 x resolution) should be fine.
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+the east-west and north-south resolutions of the input map. For a raster
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+map without NULL cells, 1 * resolution can be used, but check for
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+undershoots and overshoots. For very large areas with missing values
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+(NULL cells), larger spline step values may be required, but most of the
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+time the defaults (1.5 x resolution) should be fine.
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<p>
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The Tykhonov regularization parameter ("<b><i>lambda</i></b>") acts to
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smooth the interpolation. With a small <b><i>lambda</i></b>, the
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interpolated surface closely follows observation points; a larger value
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will produce a smoother interpolation. Reasonable values are 0.0001,
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-0.001, 0.005, 0.01, 0.02, 0.05, 0.1. For seamless NULL cell interpolation,
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-a small value is required and default is set to 0.001.
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+0.001, 0.005, 0.01, 0.02, 0.05, 0.1 (needs more testing). For seamless
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+NULL cell interpolation, a small value is required and default is set to 0.005.
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<p>
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From a theoretical perspective, the interpolating procedure takes place in two
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-parts: the first is an estimate of the linear coefficients of a spline function
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-is derived from the observation points using a least squares regression; the
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+parts: the first is an estimate of the linear coefficients of a spline function;
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+these are derived from the observation points using a least squares regression; the
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second is the computation of the interpolated surface (or interpolated vector
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points). As used here, the splines are 2D piece-wise non-zero polynomial
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-functions calculated within a limited, 2D area. The length of each spline step
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+functions calculated within a limited 2D area. The length of each spline step
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is defined by <b><i>se</i></b> for the east-west direction and
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-<b><i>sn</i></b> for the north-south direction. For optimum performance, the
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+<b><i>sn</i></b> for the north-south direction. For optimal performance, the
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spline step values should be no less than the east-west and north-south
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-resolutions of the input map. Each non NULL cell observation is modeled as a
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+resolutions of the input map. Each non-NULL cell observation is modeled as a
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linear function of the non-zero splines in the area around the observation.
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The least squares regression predicts the the coefficients of these linear functions.
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Regularization avoids the need to have one one observation and one coefficient
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