Interpolation
In
the mathematical field of numerical analysis, interpolation is a method of
constructing new data points within the range of a discrete set of known data
points.
Interpolation
is a Geo statistical term. It means to fill up missing values estimate missing
or example values by using knowing or sampled values with statistical and
mathematical models, linear.
On
the map the digitize is called spatial interpolation. Between two missing
values to fill them is called interpolation.
Types
of Interpolation:
There
are six major types of interpolation
Ø Exact Interpolation:
The
exact interpolation is one in which the surface line passes through the sampled
points.
Ø Inexact Interpolation:
Inexact
interpolation is one in which the surface line passes near to the sampled.
Ø Deterministic:
Deterministic
interpolation creates surface from measured points based on either extent
of similarity or degree of
smoothing. Errors cannot be measured in deterministic interpolation.
Ø Stochastic Interpolation:
Stochastic
interpolation is a statistical based interpolation. It creates surface measured
points and can measure errors.
Ø Global Interpolation:
In
global interpolation we may take all points in given area. To construct
interpolation
Ø Local Interpolation:
In
global interpolation only specific points in assign location are used to create
interpolation surface.
Method
of Interpolation:
There
are many methods of interpolation we will describe four major methods of
interpolation.
Ø
IDW:
The IDW (Inverse Distance Weighted)
tool uses a method of interpolation that estimates cell values by averaging the
values of sample data points in the neighborhood of each processing cell. The
closer a point is to the center of the cell being estimated, the more
influence, or weight, it has in the averaging process.
Ø
Kriging:
Kriging is an advanced geostatistical
procedure that generates an estimated surface from a scattered set of points
with z-values. More so than other interpolation methods, a thorough
investigation of the spatial behavior of the phenomenon represented by the
z-values should be done before you select the best estimation method for
generating the output surface.
Ø
Natural Neighbor:
Natural Neighbor interpolation finds
the closest subset of input samples to a query point and applies weights to
them based on proportionate areas to interpolate a value (Sibson, 1981). It is
also known as Sibson or "area-stealing" interpolation.
Ø
Spline:
The Spline tool uses an interpolation
method that estimates values using a mathematical function that minimizes
overall surface curvature, resulting in a smooth surface that passes exactly
through the input points.
Ø
Spline with Barriers:
The Spline with Barriers tool uses a
method similar to the technique used in the Spline tool, with the major
difference being that this tool honors discontinuities encoded in both the
input barriers and the input point data.
Ø
Topo to Raster:
The Topo to Raster and Topo to Raster
by File tools use an interpolation technique specifically designed to create a
surface that more closely represents a natural drainage surface and better
preserves both ridgelines and stream networks from input contour data.
The algorithm used is based on that of
ANUDEM, developed by Hutchinson et al at the Australian National University.
Ø
Trend:
Trend is a global polynomial
interpolation that fits a smooth surface defined by a mathematical function (a
polynomial) to the input sample points. The trend surface changes gradually and
captures coarse-scale patterns in the data.
Ø Linear Interpolation Method:
Linear
interpolation is the simplest method of getting values at position in between
the data points. The points are simply joined by straight line segments. Each
segment (bounded by two data points) can be interpolated independently.
The
parameter mu defines where to estimate the value on the interpolated line, it
is 0 at the first point and 1 and the second point.
Digital
Elevation Model:
Digital
elevation model is a raster data set provides 3D dimensional information of
earth surface. Different function can be applied digital elevation model
through spatial analyst toolbar, contour, slope, aspect Hill/ shade.
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