1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
|
%#
%# fields is a package for analysis of spatial data written for
%# the R software environment.
%# Copyright (C) 2024 Colorado School of Mines
%# 1500 Illinois St., Golden, CO 80401
%# Contact: Douglas Nychka, douglasnychka@gmail.edu,
%#
%# This program is free software; you can redistribute it and/or modify
%# it under the terms of the GNU General Public License as published by
%# the Free Software Foundation; either version 2 of the License, or
%# (at your option) any later version.
%# This program is distributed in the hope that it will be useful,
%# but WITHOUT ANY WARRANTY; without even the implied warranty of
%# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%# GNU General Public License for more details.
%#
%# You should have received a copy of the GNU General Public License
%# along with the R software environment if not, write to the Free Software
%# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
%# or see http://www.r-project.org/Licenses/GPL-2
%##END HEADER
%##END HEADER
\name{fields}
\alias{fields-package}
\alias{fields}
\title{
fields - tools for spatial data
}
\description{
\code{fields} is a collection of functions for curve and function
fitting with an emphasis on spatial data and spatial statistics. It was developed over 20+ years to provide easy to use but sophisticated tools for analyzing
spatial data, particularly that encountered in the environmental sciences. For the impatient users, jump to the examples below to see how easy this is use.
Please send bugs and questions to Doug Nychka, nychka@mines.edu. Positive
comments are also welcome!
The
major methods implemented include cubic and thin plate splines,
universal
Kriging and Kriging for large data sets. A more modern framework for Kriging is
spatial process estimation with covariance parameters determined by maximum likelihood and the uncertainty derived from assumptions of a Gaussian process.
Throughout we try to include reasonable defaults in functions that reflect
our experience with analyzing spatial data. For example, the Matern covariance function is the default choice for the main spatial method.
A key feature of this package is any
covariance function implemented in R code can be used for spatial prediction through the spatial functions.
Another important feature is that fields will take advantage of compactly
supported covariance functions in a seamless way through
the spam package.
See \code{library( help=fields)} for a listing of all the
fields contents. We also recommend the thoughtful vignette created by Ashton Weins, Mitchell Krock, and Emma Lilly (\code{fieldsVignette.pdf}) in the
\href{https://github.com/dnychka/fieldsRPackage}{fields github repository}.
\code{fields} strives to have readable and tutorial code. Take a look at the
source code for \code{mKrig} to see how things work
"under the hood". E.g. how a linear algebra computation is
overloaded to handle sparse matrices and how an output object is built up sequentially throughout a computation.
The \code{fields} source code is liberally commented. Unfortunately on loading
this package, R will
strip comments from the source for efficiency. You can go to
\href{https://cran.r-project.org/package=fields}{CRAN fields page} to download
the latest "tarball" ( aka Package Source) and unzip to get code with comments.
We also keep the most recent version of this package at the
\href{https://github.com/dnychka/fieldsRPackage}{fields github repository}.
and for commented source go to the
the subdirectory \code{fields/R}. This may be a more recent version, however, than what is posted to CRAN.
}
\details{
\strong{Major methods}
\itemize{
\item \code{\link{spatialProcess}} An easy to use method that fits a spatial process model
( e.g. Kriging) but also estimates the key spatial parameters: nugget variance, sill variance and range parameter by maximum likelihood. The default covariance model is a Matern covariance. This function and related functions called by this are the core methods in fields and have much flexibility.
\code{\link{spatialProcess}} allows one to supply a covariance
function that is
written in native R code. See (\code{\link{stationary.cov}}) that
includes
several families of covariances including the
Matern and several distance metrics including great circle distance
.
\code{\link{sim.spatialProcess}} and \code{\link{simLocal.spatialProcess}} provide "one liners" for conditional simulation of the fitted surface.
\item \code{\link{Tps}} Thin Plate spline
regression including GCV and REML estimates for the smoothing parameter. For moderate size data sets as a first look we use \code{Tps} all the time. See also \code{\link{fastTps}} for an
approximate method to handle very large numbers of spatial locations.
Also see the help file for \code{spatialProcess} to see how to fit a thin plate plate using the more extensive set of spatial stats functions.
\item \code{\link{sreg}} , \code{\link{splint}} Fast 1-D cubic smoothing
splines and interpolating splines, a workhorse algorithm for more EDA and more complicated methods.
\item \code{\link{mKrig}} (micro Krig)
Efficient Universal Kriging and Gaussian process function,
that can take advantage of sparse covariance
functions and is the core algorithm called by optimization
functions and for spatial predictio.
\item \code{\link{QTps}} A easy to use extension of thin plate splines for quantile and robust surface fitting.
\item \code{\link{mKrigMLEGrid}} and \code{\link{mKrigMLEJoint}} for maximum likelihood estimates of covariance parameters. These functions also
handle replicate fields, assumed to be independent realizations, at the same locations and can also take any covariate function function written in R following the \code{fields} format
}
% end itemize
\strong{Other noteworthy functions}
\itemize{
\item \code{\link{vgram}} and \code{\link{vgram.matrix}} find variograms for spatial data (and
with temporal replications.
\item \code{\link{cover.design}} Generates space-filling designs where the distance
function is expresed in R code.
\item There are many
convenient functions for working with image data and rationally (well,
maybe reasonably) creating and placing a color scale on plots. This suite of tools are for the users who want to extend the "base R grahics" and retain control over details. See the last amusing example in help(imagePlot) for an example.
\code{\link{as.image}}, \code{\link{imagePlot}}, \code{bubblePlot}, \code{
\link{drape.plot}}, \code{\link{quilt.plot}}
\code{\link{add.image}}, \code{\link{crop.image}}, \code{\link{half.image}},
\code{\link{average.image}},
\code{\link{designer.colors}}, \code{\link{color.scale}},
\code{\link{in.poly}}
See also \code{\link{grid.list}} for how fields works with grids and
\code{\link{US}}
and \code{\link{world}} for adding a map quickly.
}
\strong{ Generic functions that support the methods}
\code{plot} - diagnostic plots of fit \cr
\code{summary}- statistical summary of fit \cr
\code{print}- shorter version of summary \cr
\code{\link{surface}}- graphical display of fitted surface \cr
\code{predict}- evaluation fit at arbitrary points \cr
\code{\link{predictSE}}- prediction standard errors at arbitrary points. \cr
\code{\link{sim.rf}}- Simulate a random fields on a 2-d grid.
} % end details
\section{Getting Started}{
Try some of the examples from help files for
\code{\link{spatialProcess}} or \code{\link{Tps}}.
}
\section{\strong{Some fields datasets}}{
\itemize{
\item \code{\link{CO2}} Global satelite CO2 concentrations (simulated field)
\item \code{\link{COmonthlyMet}} Monthly mean temperatures and precip for Colorado
\item \code{\link{glacier}} An elevation dataset of a glacier also used by the applied math community to test interpolation methods.
\item \code{\link{lennon}} Image of John Lennon
\item \code{\link{NorthAmericanRainfall}} 50+ year average and trend for summer rainfall at
1700+ stations.
\item \code{\link{ozone2}} Daily max 8 hour ozone concentrations for the US midwest
for summer 1987.
\item \code{\link{PRISMelevation}} Digital elevations for the
continental US at approximately 4km resolution
\item \code{\link{rat.diet}} Small paired study on rat food
intake over time.
\item \code{\link{RCMexample}} Regional climate model output
\item \code{\link{RMelevation}} Digital elevations for the Rocky
Mountain Empire
\item \code{\link{WorldBankCO2}} Demographic and carbon emission data
for 75 countries and for 1999.
}
}
\section{\strong{DISCLAIMER:}}{
The
authors can not guarantee the correctness of any function or program in
this package.
}
\examples{
# some air quality data, daily surface ozone measurements for
# the Midwest:
data(ozone2)
s<-ozone2$lon.lat
y<- ozone2$y[16,] # June 18, 1987
# quick plot of spatial data with map
bubblePlot( s,y)
US( add=TRUE) # add US map
# fitting a thin plate spline surface (always a good place to
# start). Here the default smoothing (aka lambda) found by cross-validation
fit0<- Tps(s,y)
# fits a GCV thin plate smoothing spline surface to ozone measurements.
# Hey, it does not get any easier than this!
summary(fit0) #diagnostic summary of the fit
set.panel(2,2)
plot(fit0) # four diagnostic plots of fit and residuals.
# quick plot of predicted surface
set.panel()
surface(fit0) # contour/image plot of the fitted surface
# see also predictSurface for more control over the evaluation grid
#
US( add=TRUE, col="magenta", lwd=2) # US map overlaid
title("Daily max 8 hour ozone in PPB, June 18th, 1987")
####
fit2<- spatialProcess( s,y)
# a "Kriging" model. The covariance defaults to a Matern
# with smoothness 1.0.
# the nugget, sill and range parameters are found by maximum likelihood
# summary, plot, and surface also work for \code{fit2} !
surface(fit2) # contour/image plot of the fitted surface
US( add=TRUE, col="magenta", lwd=2) # US map overlaid
title("Daily max 8 hour ozone in PPB, June 18th, 1987")
\dontrun{
# And 20 approximate conditional draws of the spatial field on a grid
# with uncertainty in the 120PPB contour
look<- simLocal.spatialProcess(fit2, M=20)
for( k in 1:20){
contour( look$x, look$y, look$z[,,k], add=TRUE, level=c(120),
col="white", drawlabels=FALSE)
}
}
}
\keyword{datasets}
|
