IbkTemperature: Temperature observations and numerical weather predictions...
In lmSubsets: Exact Variable-Subset Selection in Linear Regression

Description Usage Format Source References Examples

00UTC temperature observations and corresponding 24-hour reforecast ensemble means from the Global Ensemble Forecast System (GEFS, Hamill et al. 2013) for SYNOP station Innsbruck Airport (11120; 47.260, 11.357) from 2011-01-01 to 2015-12-31.

1	data(IbkTemperature)

A data frame containing 1824 daily observations/forecasts for 42 variables. The first column (temp) contains temperature observations at 00UTC (coordinated universal time), columns 2–37 are 24-hour lead time GEFS reforecast ensemble means for different variables (see below). Columns 38–42 are deterministic time trend/season patterns.

temp: observed temperature at Innsbruck Airport (deg C)
tp: total accumulated precipitation (kg m^-2)
t2m: temperature at 2 meters (K)
u10m: U-component of wind at 10 meters (m s^-1)
v10m: V-component of wind at 10 meters (m s^-1)
u80m: U-component of wind at 80 meters (m s^-1)
v80m: U-component of wind at 80 meters (m s^-1)
cape: convective available potential energy (J kg^-1)
ci: convective inhibition (J kg^-1)
sdlwrf: surface downward long-wave radiation flux (W m^-2)
sdswrf: surface downward short-wave radiation flux (W m^-2)
sulwrf: surface upward long-wave radiation flux (W m^-2)
suswrf: surface upward short-wave radiation flux (W m^-2)
ghf: ground heat flux (W m^-2)
slhnf: surface latent heat net flux (W m^-2)
sshnf: surface sensible heat net flux (W m^-2)
mslp: mean sea level pressure (Pa)
psfc: surface pressure (Pa)
pw: precipitable water (kg m^-2)
vsmc: volumetric soil moisture content (fraction)
sh2m: specific humidity at 2 meters (kg kg^-1)
tcc: total cloud cover (percent)
tcic: total column-integrated condensate (kg m^-2)
tsfc: skin temperature (K)
tmax2m: maximum temperature (K)
tmin2m: minimum temperature (K)
st: soil temperature (0–10 cm below surface) (K)
ulwrf: upward long-wave radiation flux (W m^-2)
wr: water runoff (kg m^-2)
we: water equivalent of accumulated snow depth (kg m^-2)
wp: wind mixing energy (J)
w850: vertical velocity at 850 hPa surface (Pa s^-1)
t2pvu: temperature on 2 PVU surface (K)
p2pvu: pressure on 2 PVU surface (Pa)
u2pvu: U-component of wind on 2 PVU surface (m s^-1)
v2pvu: U-component of wind on 2 PVU surface (m s^-1)
pv: Potential vorticity on 320 K isentrope (K m^2 kg^-1 s^-1)
time: time in years
sin, cos: sine and cosine component of annual harmonic pattern
sin2, cos2: sine and cosine component of bi-annual harmonic pattern

Observations: https://www.ogimet.com/synops.phtml.en. Reforecasts: https://psl.noaa.gov/forecasts/reforecast2/.

Hamill TM, Bates GT, Whitaker JS, Murray DR, Fiorino M, Galarneau Jr. TJ, Zhu Y, Lapenta W (2013). NOAA's second-generation global medium-range ensemble reforecast data set. Bulletin of the American Meteorological Society, 94(10), 1553–1565. doi: 10.1175/BAMS-D-12-00014.1.

## load data and omit missing values
data("IbkTemperature", package = "lmSubsets")
IbkTemperature <- na.omit(IbkTemperature)

## fit a simple climatological model for the temperature
## with a linear trend and annual/bi-annual harmonic seasonal pattern
CLIM <- lm(temp ~ time + sin + cos + sin2 + cos2,
  data = IbkTemperature)

## fit a simple MOS with 2-meter temperature forecast in addition
## to the climatological model
MOS0 <- lm(temp ~ t2m + time + sin + cos + sin2 + cos2,
  data = IbkTemperature)

## graphical comparison and MOS summary
plot(temp ~ time, data = IbkTemperature, type = "l", col = "darkgray")
lines(fitted(MOS0) ~ time, data = IbkTemperature, col = "darkred")
lines(fitted(CLIM) ~ time, data = IbkTemperature, lwd = 2)
MOS0

## best subset selection of remaining variables for the MOS
## (i.e., forcing the regressors of m1 into the model)
MOS1_all <- lmSubsets(temp ~ ., data = IbkTemperature,
  include = c("t2m", "time", "sin", "cos", "sin2", "cos2"))
plot(MOS1_all)
image(MOS1_all, size = 8:20)
## -> Note that soil temperature and maximum temperature are selected
## in addition to the 2-meter temperature

## best subset selection of all variables
MOS2_all <- lmSubsets(temp ~ ., data = IbkTemperature)
plot(MOS2_all)
image(MOS2_all, size = 2:20)
## -> Note that 2-meter temperature is not selected into the best
## BIC model but soil-temperature (and maximum temperature) are used instead

## refit the best BIC subset selections
MOS1 <- refit(lmSelect(MOS1_all))
MOS2 <- refit(lmSelect(MOS2_all))

## compare BIC
BIC(CLIM, MOS0, MOS1, MOS2)

## compare RMSE
sqrt(sapply(list(CLIM, MOS0, MOS1, MOS2), deviance)/
  nrow(IbkTemperature))

## compare coefficients
cf0 <- coef(CLIM)
cf1 <- coef(MOS0)
cf2 <- coef(MOS1)
cf3 <- coef(MOS2)
names(cf2) <- gsub("^x", "", names(coef(MOS1)))
names(cf3) <- gsub("^x", "", names(coef(MOS2)))
nam <- unique(c(names(cf0), names(cf1), names(cf2), names(cf3)))
cf <- matrix(NA, nrow = length(nam), ncol = 4,
  dimnames = list(nam, c("CLIM", "MOS0", "MOS1", "MOS2")))
cf[names(cf0), 1] <- cf0
cf[names(cf1), 2] <- cf1
cf[names(cf2), 3] <- cf2
cf[names(cf3), 4] <- cf3
print(round(cf, digits = 3), na.print = "")