-
Notifications
You must be signed in to change notification settings - Fork 0
/
fitRainfallData.R
242 lines (202 loc) · 10.1 KB
/
fitRainfallData.R
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
# script for fitting North American rainfall dataset
# fit North American rainfall data set
# LatticeKrig paper also uses NorthAmericanRainfall dataset
# 1720 stations precip in JJA=June,July,August based on data from 1950-2010 (61 years).
# Also includes elevation.
# dataset in LK package only includes linear trends and intercepts for each station
# 1720 x 1 = 1720 observations (or, with full dataset, 1720 x 61 = 104,920 observations)
# int.strategy: integration strategy of INLA.
# doCovs: whether or not elevation is included as a covariate
testRainfallData = function(normalize=TRUE, NC=5, nLayer=3, nBuffer=5, seed=1, maxit=25,
int.strategy="ccd", strategy="gaussian", fastNormalize=TRUE) {
# load it
data(NorthAmericanRainfall)
x<- cbind(NorthAmericanRainfall$longitude, NorthAmericanRainfall$latitude)
y<- log(NorthAmericanRainfall$precip/10) # to mm units (take log first?)
x = mercator(x)/1000 # m to km units
X = matrix(NorthAmericanRainfall$elevation, ncol=1) # include elevation as covariate if desired
# plot it
png("Figures/Rainfall/rainfallObservations.png", width=500, height=500)
par(mfrow=c(1,1))
quilt.plot( x,y, main="Mean JJA Precipitation, 1950-2010 (log mm)", xlab="Longitude", ylab="Latitude")
world( add=TRUE)
dev.off()
# set up prediction locations for comparison with LatticeKrig
latLim = c(31.75, 47.25)
lonLim = c(-115, -101)
lims = mercator(cbind(lonLim, latLim))/1000
eastLim = lims[,1]
northLim = lims[,2]
# predLon = seq(lonLim[1], lonLim[2], length = 50)
# predLat = seq(latLim[1], latLim[2], length = 50)
predEast = seq(eastLim[1], eastLim[2], length = 50)
predNorth = seq(northLim[1], northLim[2], length = 50)
predCoords = make.surface.grid(list(east = predEast, north = predNorth))
predCoordsLonLat = mercator(predCoords*1000, inverse=TRUE)
Xpred = matrix(getElevation(predCoordsLonLat[,1], predCoordsLonLat[,2]), ncol=1)
# fit the models
LKITime = system.time(LKIout <- fitLKINLAStandard2(x, y, predCoords, nu=NULL, seed, nLayer, NC, nBuffer, priorPar=getPCPrior(2500, .1, 700/2, nLayer=nLayer),
cbind(1, x, X), cbind(1, predCoords, Xpred), normalize=normalize, intStrategy=int.strategy,
fastNormalize=fastNormalize))
LKTime = system.time(LKout <- fitLKStandard(x, y, predCoords, X, Xpred, NC, nLayer, normalize, nBuffer, nu=NULL, verbose=TRUE,
normalize=normalize, maxit=maxit))
# print out computation times
print(paste0("LatticeKrig computation time: ", LKTime))
print(paste0("LatticeKrig-INLA computation time: ", LKITime))
# transform log scale predictions and standard deviations to standard scale
LKMeans = exp(LKout$preds + LKout$SEs^2/2)
LKVars = (exp(LKout$SEs^2)-1) * LKMeans^2
LKIMeans = exp(LKIout$preds + LKIout$sigmas^2/2)
LKIVars = (exp(LKIout$sigmas^2)-1) * LKIMeans^2
browser()
# show predictions just for LatticeKrig
zlimPreds = range(LKMeans)
zlimSEs = range(sqrt(LKVars))
pdf(file="Figures/Rainfall/rainfallPredsLK.pdf", width=7, height=7)
par(mfrow=c(1,2))
quilt.plot(predCoords, LKMeans, main="LatticeKrig predictions (in mm)", zlim=zlimPreds,
col=viridis(64))
points(x, pch=19, cex=.4)
quilt.plot(predCoords, sqrt(LKVars), main="LatticeKrig SEs", zlim=zlimSEs)
points(x, pch=19, cex=.4)
US(add=TRUE)
dev.off()
# show it all
zlimPreds = range(LKMeans, LKIMeans)
zlimSEs = range(sqrt(LKVars), sqrt(LKIVars))
pdf(file="Figures/Rainfall/rainfallPreds.pdf", width=7, height=7)
par(mfrow=c(2,2))
quilt.plot(predCoords, LKMeans, main="LatticeKrig predictions", zlim=zlimPreds)
quilt.plot(predCoords, sqrt(LKVars), main="LatticeKrig SEs", zlim=zlimSEs)
quilt.plot(predCoords, LKIMeans, main="LatticeKrig-INLA predictions", zlim=zlimPreds)
quilt.plot(predCoords, sqrt(LKIVars), main="LatticeKrig-INLA SDs", zlim=zlimSEs)
US(add=TRUE)
dev.off()
pdf(file="Figures/Rainfall/rainfallPredsVs.pdf", width=10, height=5)
par(mfrow=c(1,2))
plot(LKMeans, LKIMeans, pch=".", main="LK-INLA vs LatticeKrig predictions",
xlab="LatticeKrig", ylab="LK-INLA")
abline(0,1, col="green")
plot(sqrt(LKVars), sqrt(LKIVars), pch=".", log="xy", xlab="LatticeKrig SEs", ylab="LK-INLA SDs",
main="LK-INLA vs LatticeKrig predictive uncertainty")
abline(0,1, col="green")
dev.off()
kappaMarg = inla.tmarginal(function(x) {sqrt(8)/exp(x) * latticeWidth}, LKIout$mod$marginals.hyperpar$`Theta1 for field`)
pdf(file=paste0("Figures/Rainfall/posteriorKappa.pdf"), width=5, height=5)
plot(kappaMarg, type="l", xlab=TeX("$\\kappa$"), main=TeX("Marginal for $\\kappa$"))
abline(v=inla.qmarginal(c(.025, .975), kappaMarg), col="purple", lty=2)
abline(v=mean(sqrt(LKout$a.wghtVals - 4)), col="green")
legend("topright", c("95% CI", "LK Est"), lty=c(2, 1), col=c("purple", "green"))
dev.off()
rhoMarg = inla.tmarginal(function(x) {exp(x)}, LKIout$mod$marginals.hyperpar$`Theta2 for field`)
pdf(file="Figures/posteriorRho.pdf", width=5, height=5)
plot(rhoMarg, type="l", xlab=TeX("$\\rho$"), main=TeX("Marginal for $\\rho$"))
abline(v=inla.qmarginal(probs=c(.025, .975), rhoMarg), col="purple")
abline(v=mean(LKout$rhoVals), col="green")
legend("topright", c("95% CI", "LK Est"), lty=c(2, 1), col=c("purple", "green"))
dev.off()
## Now generate marginals for the alpha parameters if they exist. In order to do this, we must generate draws from
## the posterior, and transform them back to the probability scale
out = inla.hyperpar.sample(20000, LKIout$mod, improve.marginals=TRUE)
if(nLayer >= 2) {
if(!separateRanges) {
zSamples = out[,3:(2+nLayer-1)]
xSamples = apply(zSamples, 1, multivariateExpit)
xSamples = rbind(xSamples, 1-colSums(xSamples))
} else {
zSamples = matrix(out[,(nLayer+1+1):(nLayer + 1 + 1 + nLayer-2)], ncol=nLayer-1)
xSamples = matrix(apply(zSamples, 1, multivariateExpit), nrow=nLayer-1)
xSamples = rbind(xSamples, 1-colSums(xSamples))
}
for(l in 1:nLayer) {
theseQuantiles = quantile(probs=c(.025, .975), xSamples[l,])
thisQuantileRange = abs(diff(theseQuantiles))
# if(thisQuantileRange <= 0.2) {
# plotRange = range(xSamples[l,])
# } else {
plotRange = c(0, 1)
# }
if(theseQuantiles[1]-0 <= 1-theseQuantiles[2])
legendLocation = "topright"
else
legendLocation = "topleft"
pdf(file=paste0("Figures/Rainfall/posteriorAlpha", l, ".pdf"), width=5, height=5)
hist(xSamples[l,], xlab=TeX(paste0("$\\alpha_", l, "$")), main=TeX(paste0("Marginal for $\\alpha_", l, "$, LK estimate (green)")), breaks=100, freq=F, xlim=plotRange)
abline(v=mean(xSamples[l,]), col="purple", lty=1)
abline(v=theseQuantiles, col="purple", lty=2)
abline(v=rowMeans(LKout$alphaVals)[l], col="green")
legend(legendLocation, c("95% CI", "LK Est"), lty=c(2, 1), col=c("purple", "green"))
dev.off()
}
}
browser()
# produce figures like in the LatticeKrig paper of central predictions and standard errors?
list(LKout=LKout, LKIout=LKIout, LKTime=LKTime, LKITime=LKITime)
# how good are the INLA results? Compare with MCMC?
}
# get elevation at the given set of lat/lon coordinates
# uses GMTED elevation data available from https://www.usgs.gov/land-resources/eros/coastal-changes-and-impacts/gmted2010?qt-science_support_page_related_con=0#qt-science_support_page_related_con
getElevation = function(lon, lat) {
# require(rgdal)
# require(raster)
# require(sp)
# # ogrListLayers("gtopo30/gtopo30.shp")
# shape = readOGR("gtopo30/")
# shape <- shapefile("gtopo30/gtopo30.shp")
# test = extract(shape, SpatialPoints(cbind(lon, lat)),method="bilinear")
# datapol <- data.frame(shape)
# pointtoplot <- data.frame(x=-20, y=40)
# coordinates(pointtoplot) <- ~ x + y
# proj4string(pointtoplot) <- CRS("+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0")
# test <- data.frame(xx=over(shape, pointtoplot))
# combine <- cbind(test, datapol)
# combine <- na.omit(combine)
temp = raster("elevation.nc")
extract(temp, SpatialPoints(cbind(lon, lat)),method="bilinear")
}
# uses GMTED elevation data available from https://www.usgs.gov/land-resources/eros/coastal-changes-and-impacts/gmted2010?qt-science_support_page_related_con=0#qt-science_support_page_related_con
# creates a single-layer netcdf file readable using the raster command
convertNC2raster = function() {
# require(gdalUtils)
# gdalinfo("GMTED2010_15n015_00625deg.hdf")
# hdf_dataset <- system.file("GMTED2010_15n015_00625deg.hdf")
# gdal_translate("GMTED2010_15n015_00625deg.hdf", sds=T, of="GTiff", dst_dataset = "test.tif")
# sds
#
# test <- raster("GMTED2010_15n015_00625deg.hdf")
library(ncdf4)
library(raster)
library(rasterVis)
library(maptools)
library(maps)
# tmpin <- raster("GMTED2010_15n015_00625deg.nc", values= TRUE)
# open netcdf file
ncObject = nc_open("GMTED2010_15n015_00625deg.nc")
# get desired variables and their attributes
latVar = ncvar_get(ncObject, "latitude")
lonVar = ncvar_get(ncObject, "longitude")
lat = ncatt_get(ncObject, "latitude")
lon = ncatt_get(ncObject, "longitude")
elevation = ncatt_get(ncObject, "elevation")
elevationVar = ncvar_get(ncObject, "elevation")
# reformat the variables
londim <- ncdim_def("lon", "degrees_east", as.double(lonVar))
latdim <- ncdim_def("lat", "degrees_north", as.double(latVar))
tmp.def <- ncvar_def("elevation", "m", list(londim, latdim), -1e20,
prec = "double")
# create new netcdf file
ncfname <- "elevation.nc"
ncout <- nc_create(ncfname, list(tmp.def), force_v4 = TRUE)
# put the array
tmat = elevationVar
ncvar_put(ncout, tmp.def, tmat)
# put additional attributes into dimension and data variables
ncatt_put(ncout, "lon", "axis", "X")
ncatt_put(ncout, "lat", "axis", "Y")
# add global attributes
title <- "Elevation netCDF file"
ncatt_put(ncout, 0, "title", title)
# close the file, writing data to disk
nc_close(ncout)
invisible(NULL)
}