NCSU GIS/MEA582:
Geospatial Modeling and Analysis

Spatial interpolation and approximation II

Resources: ESRI Academy

Launch ArcGIS Pro and login with ArcGIS Online credentials if required. Select New> Map> Create New Project. Create a new project in your preferred workspace, in the instructions below we are using the default C:\Users\myname\Documents\ArcGIS\Projects\ folder.

Use your judgement to decide which maps to include in your report.

Interpolation using splines

Interpolate elevation surfaces from spot point heights using the Spline tool in the Spatial Analyst toolbox.
Use three different weights (0.1, 1, 1000) to control the tension, and thus, the resulting surface character.
For the first interpolation, you'll leave the Weight field blank, accepting the default 0.1 value.
In subsequent interpolations, you'll enter the explicit weights. 
On the Map tab, in the Layer group, click 'Add Data'
Browse to C:\Users\myname\Documents\ArcGIS\582data\ncshape.gdb
select elev_lid792_randpts
'OK'

In the Geoprocessing pane, search for and select the 'Spline' tool
Set 'Input Point Features' to 'elev_lid792_randpts'
Set 'Z value field' to 'value_'
Set 'Output Raster' to 'elev_tps'
Set 'Output cell size' to '2'
Set to Spline Type to 'TENSION'
Leave the other inputs as defaults 
Click 'Run'

Evaluate impact of interpolation function parameters on the resulting surface using hillshade. 

Top ribbon->Analysis->Geoprocessing Group->Raster Analysis->cell size
enter '2' for cell size
Click 'OK'
In the Geoprocessing pane, search for and select the 'Hillshade' tool
Set 'Input raster' to 'elev_tps'
Set 'Output Raster' to 'Hillsh_tps'
Leave the other inputs as defaults
Click 'Run'

Repeat the spline interpolations above, using weights of 1 and then 1000,
and generate the associated hill shade surfaces.
Compare the three hill shade surfaces, and discuss your findings in your report.
(Tip, use the 'history' tab to reload and change values for previously run geoprocessing tools)

Interpolate surface using Radial Basis Functions

Use the Geostatistical Analyst tool's Radial Basis Functions to generate at least two different elevation surfaces by selecting different Kernel functions.
In the first surface you'll use the RBF multi-quadric method.
In the second, you'll choose Regularized Spline. 
In the Geoprocessing pane, search for and select the 'Radial Basis Functions' tool
Set the 'input features' to 'elev_lid792_randpts'
Set the 'Z value' to 'value_'
Set the 'output raster' to 'elev_lid792_multi'
Set the Radial basis function to 'Multiquadric'
Click 'Run'

Rerun the interpolation in the Radial Basis Functions tool using
Set the Radial basis function to 'Completely Regularized Spline' and compare your results.

Optional: compute empirical and model variogram for 'elev_lid792_randpts' and interpolate the surface using kriging with a model variogram that fits the best the empirical variogram.