# Kudryavtsev model: An alternative solution to the Stefan problem was proposed
# by Kudryavtsev et al. (1974) for estimating maximum annual depth of thaw propagation
# and the mean annual temperature at the base of the active layer (equivalent to
# the temperature at the top of permafrost, or TTOP)
# TTOP: refers to the temperature at the top of the permafrost or at the bottom of the seasonally frozen layer.
# cot: coefficient of thermal conductivity during thawing
# cof: coefficient of thermal conductivity during freezing
TTOP_Kudryavtsev <- function(Year, AirTempName, GroundTempName, MinGTName, MaxGTName, data=QTP_ATM, SID){
cot <- Station_Info$COT[Station_Info$SID==SID]
cof <- Station_Info$COF[Station_Info$SID==SID]
magst <- sapply(Year, function(Year) tryCatch({
MAGST(Year = Year, AirTempName = AirTempName, GroundTempName = GroundTempName, data = data, SID=SID)
}, error = function ( e ) {magst<- NA}
, warning = function ( e ) {magst<- NA}
), simplify=T)
temp_amp_ann <- sapply(Year, function(Year) tryCatch({
Temp_Ampl_Annual(Year = Year, MinTempName=MinGTName, MaxTempName=MinGTName, data = data, SID=SID)
}, error = function ( e ) {temp_amp_ann<- NA}
, warning = function ( e ) {temp_amp_ann<- NA}
), simplify=T)
ttop_numerator <- tryCatch({
(0.5*magst*(cot+cof))+(temp_amp_ann*(cot-cof)/pi)*
((magst*asin(magst/temp_amp_ann)/temp_amp_ann)+sqrt(1-(magst^2/temp_amp_ann^2)))
}, error = function ( e ) {ttop_numerator<- NA}
, warning = function ( e ) {ttop_numerator<- NA}
)
ttop <- ifelse (ttop_numerator < 0, ttop_numerator/cof, ttop_numerator/cot)
names(ttop) <- Year
return(ttop)
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.