Using idealized temperature curves for guidance, this function interpolated hourly temperature data.
interpolate_gaps_hourly(
hourtemps,
latitude = 50,
daily_temps = NULL,
interpolate_remaining = TRUE,
return_extremes = FALSE,
minimum_values_for_solving = 5,
runn_mean_test_length = 5,
runn_mean_test_diff = 5,
daily_patch_max_mean_bias = NA,
daily_patch_max_stdev_bias = NA
)data frame containing interpolated temperatures for all hours within the interval defined by the first and last day of the hourtemps input.
data.frame containing hourly temperatures. This has to contain columns c("Year","Month","Day","Hour","Temp").
the geographic latitude (in decimal degrees) of the location of interest
list of (chillR compliant) daily temperature data sets for patching gaps in the record.
boolean parameter indicating whether gaps remaining after the daily record has been patched (or after solving temperature equations, if (daily_temps==NULL)) should be linearly interpolated.
boolean parameters indicating whether daily minimum and maximum temperatures used for the interpolation should be part of the output table. Defaults to FALSE.
integer specifying the minimum number of hourly temperature values that must be available for the solving function to be applied. Must be greater than 1 (otherwise you get an error). Since according to the idealized temperature curves used here, a given daily extreme temperature is related to hourly temperatures of about a 12-hour period, values above 12 are not useful. Note that relatively large numbers for this parameter raise the reliability of the interpolated values, but they restrict the number of missing values in a day, for which the procedure produces results.
integer specifying the length of the period, for which a running mean test for is applied to daily records after the solving procedure. This aims to remove spurious values that can sometimes arise during solving. This test checks for all daily minimum and maximum temperature values, if they differ from the mean of the surrounding values by more than runn_mean_test_diff. If this is the case, they are set to NA, and have to be filled by other means (from proxy data or by interpolation). Defaults to 5, which means each value is compared to the mean of the 2 previous and 2 following days.
integer specifying the maximum tolerable difference between solved daily extreme temperature values and the mean for the surrounding days. See description of runn_mean_test_length for more details. Defaults to 5.
maximum acceptable mean difference between the daily extreme temperatures of daily temperature records used as proxy and daily extreme temperatures in the dataset that is to be interpolated. If the bias between stations is greater than this, the station is not considered a useful proxy and not used for filling gaps.
maximum acceptable standard deviation of the difference between the daily extreme temperatures of daily temperature records used as proxy and daily extreme temperatures in the dataset that is to be interpolated. If the bias between stations is greater than this, the station is not considered a useful proxy and not used for filling gaps.
Eike Luedeling
Many agroclimatic metrics are calculated from hourly temperature data. chillR provides functions for generating hourly data from daily records, which are often available. Small gaps in such daily records can easily be closed through linear interpolation, with relatively small errors, so that complete hourly records can be generated. However, many sites have recorded actual hourly temperatures, which allow much more accurate site-specific assessments. Such records quite often have gaps, which need to be closed before calculating most agroclimatic metrics (such as Chill Portions). Linear interpolation is not a good option for this, because daily temperature curves are not linear. Moreover, when gaps exceed a certain number of hours, important featured would be missed (e.g. interpolating between temperatures at 8 pm and 8 am may miss all the cool hours of the day, which would greatly distort chill estimates).
This function solves this problem by using an idealized daily temperature curve as guide to the interpolation of hourly temperature data.
These are the steps: 1) produce an idealized temperature curve for the site (which requires site latitude as an input), assuming minimum and maximum temperatures of 0 and 1 degrees C, respectively. The calculations are based on equations published by Spencer (1971), Almorox et al. (2005) and Linvill (1990, though I modified these slightly to produce a smooth curve). This curve describes the expected relationship of the temperature for the respective hour with minimum and maximum temperatures of the same, previous or next day (depending on the time of day), according to idealized temperature curve. At this point, however, these daily minimum or maximum temperatures aren't known yet.
2) determine minimum and maximum temperatures for each day. For each minimum and maximum daily temperature, the expected relationships between hourly temperatures and daily extremes determined in step 1, combined with the hourly temperatures that were observed can be interpreted as an overdetermined set of equations that define these temperatures. Since few days will follow the ideal curve precisely, and there are usually more than two equations that define the same daily temperature extreme value, these equations can only be solved numerically. This is implemented with the qr.solve function, which can provide estimates of the minimum and maximum temperatures for all days from the available hourly records.
3) interpolate gaps in the record of estimated daily temperature extremes. There can be days, when the number of recorded hourly temperatures isn't sufficient for inferring daily minimum or maximum temperatures. The resulting gaps are closed by linear interpolation (this may produce poor results if gaps are really large, but this isn't currently addressed).
4) compute an idealized daily temperature curve for all days, based on estimated daily temperature extremes (using the make_hourly_temperatures function).
5) calculate deviation of recorded temperatures from idealized curve.
6) linearly interpolate deviation values using the interpolate_gaps function.
7) add interpolated deviation values to idealized temperature curve.
Linvill DE, 1990. Calculating chilling hours and chill units from daily maximum and minimum temperature observations. HortScience 25(1), 14-16.
Spencer JW, 1971. Fourier series representation of the position of the Sun. Search 2(5), 172.
Almorox J, Hontoria C and Benito M, 2005. Statistical validation of daylength definitions for estimation of global solar radiation in Toledo, Spain. Energy Conversion and Management 46(9-10), 1465-1471)
Winters_gaps<-make_JDay(Winters_hours_gaps[1:2000,])
colnames(Winters_gaps)[5:6]<-c("Temp","original_Temp")
interp<-interpolate_gaps_hourly(hourtemps=Winters_gaps,latitude=38.5)
#plot results: interpolated temperatures are shown in red, measured temperatures in black.
plot(interp$weather$Temp[1:120]~c(interp$weather$JDay[1:120]+
interp$weather$Hour[1:120]/24),type="l",
col="RED",lwd=2,xlab="JDay",ylab="Temperature")
lines(interp$weather$Temp_measured[1:120]~c(interp$weather$JDay[1:120]+
interp$weather$Hour[1:120]/24),lwd=2)
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