GIS Section 4.2 Flashcards
What is spatial interpolation?
process of predicting/estimating calues for unsampled or un-visited locations using measured values
Why is spatial interpolation so common?
because it is impossible to measure all of the infinite measurements and locations in an area
What types of features can be interpolated?
- point, line, small areas
What is the output of spatial interpolation?
raster
What are the two main types of spatial interpolation?
- Deterministic
- Probabilistic
What types of fitting methods can be used for interpolation (depending on scale)?
- Global fitting methods
- Local estimation (neighbourhood)
What is a Global Fitting Method for interpolation?
Trend Surface Analysis - polynomial regression on coordinate pairs
- probabilistic
What are the 4 types of local fitting methods for interpolation?
- Inverse Distance Functions (IDW)
- Plate Surface (bi-cubic splines)
- Nearest Neighbour interpolation
- moving averages with arbitrary weights
What is the geostatistical spatial interpolation method?
Kriging!!!
How does Global polynomial interpolation (trend surface analysis) work?
- fits a smooth surface defined by a polynomial to the sample points
- fits over the full extent of the data (‘global’)
- multiple regression of coordinate pairs
What is the result of global polynomial interpolation?
- smooth surface representing gradual changes
What can be said of complex polynomials produced through Global polynomial interpolation?
the more complex, the harder it is to ascribe physical meaning to it
What is the Thiessen Polygon Method of interpolation?
- split an area into zones
- each zone represents areas that are closer to the central point than any other point
- all parts of a Thiessen polygon have the same value
How does Inverse Distance Weighting (IDW) interpolation work?
- uses measured values close the a location to give the location a value
- assumes every nearby point has a local influence that decreases with distance
- known points are given weights that diminish as a function of distance
What is an assumption of IDW interpolation?
things that are close together are more alike
What two factors are important in IDW interpolation?
SIZE and SHAPE of neighbourhood
- neighbourhood generally circular, but could make adjustments depending on site specifics
How is IDW an ‘exact interpolator’?
known input points define the maximum and minimum values that will appear in the interpolation
How does a spline work?
- two-dimensional minimum curvature spline
- cubic polynomials are fitted as ‘panels’ that are smoothed together
What are the two kinds of spline?
- regularized
- tension
What is the optimal interpolation method?
Kriging
How does kriging work?
- uses calculated semi-variance to find how distance affects change in a given area
What two tasks are necessary for kriging?
- uncover dependancy rules (by semi-variogram)
- make the predictions
What are the two steps in kriging?
- Estimate the semi-variogram
- Fit a mathematical model to those values
(then it can use the model to make a prediction)
What are the structural components of variability in kriging?
- C = maximum ‘sill’ variance
- Co = ‘nugget’ variance (chance)
- C-Co = variability due to spatial dependence
b = range of influence
points = experimental semi-variance values
What is the semi-variogram?
graph depicting the spatial autocorrelation of measured sample points
What competing models might fit to a semi-variogram?
- Gaussian
- Spherical
- exponential
What is the recommended procedure for kriging?
- plot the experimental semi-variogram
- choose candidate models
- Check Residual Sum of Squares (RSS) and RMS in predicitions (ie do the kriging a bunch and check errors)
- Select midel that minimizes RMS
- Inspect visually
- select model and parameters that minimize RMS
Essentially, what is kriging?
a weighted local moving average of variable Z which has been measured at points within a neighbourhood
What is ‘cross-validation’ of a semi-variogram model fit?
trying models iteratively and comparing the RMS values
- the best indicator for finding the best model!
What is a major shorrtcoming of kriging?
takes a long time to fit semi-variogram models
What can Empirical Bayesian Kriging do?
- compare dozens of models at once using empirical simulation (checking a family/’ensemble’ of similar models at once
- select the average/best of a family of models
What’s so great about Empirical Bayesian Kriging?
saves a lot of time!
- uses the mean model of the ‘ensemble’ of models
