Global Spatial Interpolation: Trend Surface and Regression Method (Especially for GATE-Geospatial 2022)

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Global use all available data to provide predictions for the whole area of interest, while local interpolations operate within a small zone around the point being interpolated to ensure the point being interpolated to ensure that estimates are made only with data from locations in the immediate neighborhood. There are two types of global interpolation methods:

  • Trend surface method
  • Regression methods
Diagram Shows Two Types of Global Interpolation

1. Trend Surface Method

An inexact interpolation method, trend surface analysis approximates points with known values with a polynomial equation. The equation or the interpolation can then be used to estimate values at other points. A linear or first-order trend surface uses the equation:

where the attribute value is a function of and coordinates. The b coefficients are estimated from the known points.

At third-order trend surface requires estimation of 10 coefficients, compared to three coefficients for a first-order surface. A higher-order trend surface model therefore requires more computation than a lower-order model does. A GIS package may offer up to 12th -order trend surface models.

Map Shows an Isohyet Map in Inches from a Third-Order

In figure shows an isoline (isohyet) map derived from a third-order trend surface of annual precipitation in Idaho created from 175 data points with a cell size of 2000 meters. An isoline map is like a contour map, useful for visualization as well as measurement.

2. Regression Method

A regression model relates a dependent variable to several independent variables in a linear equation, which can then be used for prediction or estimation. Many regression models use nonspatial attributes and are not considered methods for spatial interpolation. But exceptions can be made for regression models that use spatial variables such as distance to a river or location-specific elevation.

A watershed-level regression model for snow accumulation developed by Chang and Li uses snow water equivalent (SWE) as the dependent variable and location and topographic variables as the independent variables. One of their watershed models takes the form of:

Where EASTING and SOUTHING correspond to the column number and the row number in an elevation raster, ELEV is the elevation value, and PLAN1000 is a surface curvature measure. After the b coefficients in equation are estimated using known values at snow courses, the model can be used to estimate SWE for all cells in the watershed and to produce a continuous SWE surface.

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