This document describes the R-package topoclim, which was originally published in the article Tscholl et al. (2021), Coupling solar radiation and cloud cover data for enhanced temperature predictions over topographically complex mountain terrain. International Journal of Climatology, under review. The package presents an innovative method to estimate air temperature at high spatiotemporal resolution over complex mountain terrain, called the cloud-corrected model. The cloud-corrected model uses a correction factor to include the effects of slope, aspect, cloud cover and solar position on local air temperature estimates. The following document illustrates the principles of the approach by applying it to South Tyrol, a mountainous study area in the inner alps, during April 2019.
You can install the package using:
devtools::install_github('sitscholl/topoclim')The following script also uses the raster, gstat and automap
packages, which can be installed using the code below.
install.packages(c('raster', 'gstat', 'automap'))library(topoclim)
library(raster)The topoclim package includes the following datasets:
- official_stations: A SpatialPointsDataFrame with the location of the official stations
- timeseries: A table with daily measurements of mean temperature and solar insolation from the official stations for the period 2017 until 2019
- rad_longterm: A table with daily measurements of solar insolation for seven stations for several years (up to 32 years)
- h_topo: A RasterStack with incoming solar insolation in kWh/m² for the study area for each month with a resolution of 100m
- h_flat: A RasterStack with incoming solar insolation in kWh/m² for the study area using constant values of 0 for slope and aspect (e.g. on a flat surface) for each month with a resolution of 100m
- dem: A digital elevation model of the study area with a resolution of 100m
Use the syntax ?DatasetName (e.g. ?official_stations) to get more
information about a certain dataset. The following code imports some of
these datasets, that are required to run the cloud-corrected model.
data("official_stations")
data("timeseries")
data("rad_longterm")
h_topo <- stack( system.file('extdata', 'h_topo.tif', package = 'topoclim') )
h_flat <- stack( system.file('extdata', 'h_flat.tif', package = 'topoclim') )
dem <- raster( system.file('extdata', 'dem.tif', package = 'topoclim') )h_topo and h_flat were both calculated using the Solar
Analyst in
ArcGIS,
version 10.6.1. Two separate files were calculated for a single
reference day for each month. For h_topo we set the option
slope_aspect_input_type to FROM_DEM and for h_flat to
FLAT_SURFACE. For model parameters and reference days, please check
the associated article. For the present demonstration, we will only
consider the month of April in 2019, but other timeperiods can also be
calculated by adjusting the parameters in the following script.
test_month <- 4
h_topo <- h_topo[[test_month]]
h_flat <- h_flat[[test_month]]
Incoming solar insolation during April with and without consideration of aspect and slope.
The following sections will illustrate the cloud-corrected model step-by-step. First, the calculation of the lapse-rate model is described, followed by the relative radiation factor, the cloud index, the radiation correction factor and, finally, the cloud-corrected temperature.
The lapse-rate model is a simple linear regression with elevation as explanatory and air temperature as dependent variable. Because it does not consider slope or aspect of a surface, the predictions from the lapse-rate model describe the air temperature of a flat surface across different elevation levels.
#subset timeseries of measurements to period of interest
dateseq <- seq.Date(as.Date('2019-01-01'),
as.Date('2019-12-31'),
by = 'day')
dateseq_i <- which(as.numeric(format(dateseq, '%m')) == test_month)
dateseq_sub <- dateseq[dateseq_i]
timeseries_sub <- subset(timeseries, date %in% dateseq_sub)
timeseries_split <- split(timeseries_sub, timeseries_sub$date)
#join elevation column
lr_split <- lapply(timeseries_split, merge, official_stations@data, by = 'st_id')
#train linear models
lr_fit <- lapply(lr_split, lm, formula = tmean ~ elev)
names(dem) <- 'elev'
#predict
t_flat <- lapply(lr_fit, predict, object = dem)
t_flat <- stack(t_flat)
Predictions from the lapse-rate model for two example days during April 2019.
The relative radiation factor is defined as the ratio between incoming solar insolation on an inclined and flat surface:
d_rad = h_topo / h_flat
We can therefore calculate d_rad by dividing the raster objects
h_topo and h_flat. Because h_flat contains some unrealistic jumps
in pixel values on ridges and mountain tops, it is first smoothed using
a 5x5 pixel filter.
h_flat2 <- focal(h_flat, w = matrix(1, 5, 5), fun = mean)
d_rad <- h_topo / h_flat2
Relative radiation during April.
The cloud index c can be calculated using the following formula:
c = ( h_obs - h_cloud ) / ( h_clear - h_cloud )
The first step is to calculate monthly reference values for maximum and minimum solar insolation. The maximum reference solar insolation is defined as the mean of all insolation measurements above the 95% quantile and the minimum reference insolation as the mean of all insolation measurements below the 95% quantile. Outliers were already removed from this dataset using a 3-sigma test.
h_clear_monthly <- aggregate(list(h_clear = rad_longterm$insolation),
by = rad_longterm[c('st_id', 'month')],
FUN = function(x){
mean(x[x >= quantile(x, .95, na.rm = T)], na.rm = T)
})
h_cloud_monthly <- aggregate(list(h_cloud = rad_longterm$insolation),
by = rad_longterm[c('st_id', 'month')],
FUN = function(x){
mean(x[x <= quantile(x, .05, na.rm = T)], na.rm = T)
})
h_ref_month <- merge(h_clear_monthly, h_cloud_monthly, by = c('st_id', 'month'))From the monthly reference values, the daily reference values h_clear
and h_cloud are estimated via linear interpolation for every station.
This can be accomplished using the function complete_ts(), which is
included in this package. Internally, the function uses the function
na_interpolation() from the package imputeTS.
h_ref_split <- split(h_ref_month, h_ref_month$st_id)
h_ref <- lapply(h_ref_split, complete_ts)
h_ref <- do.call(rbind, h_ref)Because there are only small differences for h_clear and h_cloud
between the single stations, the average values across all stations is
used to calculate the cloud index:
h_ref <- aggregate(h_ref[c('h_clear', 'h_cloud')],
by = h_ref[c('day', 'month')],
FUN = mean)h_obs is calculated by using ordinary kriging together with the
observed insolation from all the official stations. The packages gstat
and automap are used to perform the kriging. This step can take some
time to calculate (ca. 30s per day)
krige_split <- lapply(timeseries_split, merge, x = official_stations, by = 'st_id', all.y = T)h_var <- lapply(krige_split, function(x) {
var <- automap::autofitVariogram(formula = insolation ~ 1,
input_data = x)
return(var$var_model)
})
h_fit <- mapply(gstat::gstat, data = krige_split, model = h_var,
MoreArgs = list(g = NULL, id = 'insol', formula = insolation ~ 1),
SIMPLIFY = F)
h_obs <- lapply(h_fit, raster::interpolate, object = dem)
h_obs <- stack(h_obs)
#kriging can produce negative radiation values for some pixels
h_obs[h_obs < 0] <- 0
names(h_obs) <- names(krige_split)In the last step, the cloud index is computed. In the present example,
we only consider the month of April. There can be some pixels, where the
interpolated value h_obs is higher or lower than our reference values
h_clear and h_cloud, respectively. This would lead to cloud index
values above one or below zero. To avoid this, values above one are
assigned a value of one, and values below zero a value of zero.
h_ref_sub <- subset(h_ref, month == test_month)
c <- (h_obs - h_ref_sub$h_cloud) / (h_ref_sub$h_clear - h_ref_sub$h_cloud)
##Limit to range 0-1
c[c < 0] <- 0
c[c > 1] <- 1
names(c) <- names(krige_split)
The cloud index for two example days during April 2019.
The relative radiation factor and cloud index are both combined to the radiation correction factor:
D_rad = c * d_rad - c
D_rad <- c * d_rad - c
names(D_rad) <- names(krige_split)
The radiation correction factor for two example days during April 2019.
Cloud-corrected air temperature is calculated by combining the predictions from the lapse-rate model with the radiation correction factor, using the following formula:
t_topo = t_flat + ( D_rad * m_rad * |t_flat| )
m_rad is an empirical relationship between air temperature and
incoming solar radiation and describes the change in local air
temperature by an increase/decrease of incoming solar radiation. m_rad
is defined as the slope of the linear regression between observed air
temperature and solar insolation from the official stations with a long
timeseries.
rad_mean <- aggregate(list(rad_mean = rad_longterm$insolation),
by = rad_longterm['st_id'],
FUN = mean, na.rm = T)
tair_mean <- aggregate(list(tmean_mean = rad_longterm$tmean),
by = rad_longterm['st_id'],
FUN = mean, na.rm = T)
perc_diff <- merge(rad_longterm, rad_mean, by = 'st_id', all.x = T)
perc_diff <- merge(perc_diff, tair_mean, by = 'st_id', all.x = T)
perc_diff$tmean_diff <- (perc_diff$tmean - perc_diff$tmean_mean) / perc_diff$tmean_mean
perc_diff$rad_diff <- (perc_diff$insolation - perc_diff$rad_mean) / perc_diff$rad_mean
fit <- lm(tmean_diff ~ rad_diff, data = perc_diff)
m_rad <- fit$coefficients['rad_diff']
round(m_rad, 2)
#> rad_diff
#> 0.93m_rad amounts to 0.93, which means that a change of radiation by 1%
changes local air temperature by 0.93%. Given this value, we can then
calculate the final cloud-corrected air temperature.
t_topo <- t_flat + (D_rad * m_rad * abs(t_flat))
names(t_topo) <- names(krige_split)
Cloud-corrected air temperature for two example days during April 2019.
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