FAO approach
The empirical formula for estimating the minimum temperature is \(T_{min} = a * T + b * T_{dew} + c\). For calculating the coefficientes \(a, b\) and \(c\) we call buildFAO(dw,temp,tmin).
library(frost)
# We create random data
x1 <- rnorm(100,mean=2,sd=5)
x2 <- rnorm(100,mean=1,sd=3)
y <- rnorm(100,mean=0,sd=2)
buildFAO(dw = x2,temp=x1,tmin=y)
#> An object of class "FAOFrostModel"
#> Slot "a":
#> [1] -0.0212634
#>
#> Slot "b":
#> [1] -0.0740061
#>
#> Slot "c":
#> [1] 0.001168745
#>
#> Slot "Tp":
#> [1] 0.3317844864 -0.1203190410 0.1334290382 -0.3938878717 -0.2030806995
#> [6] -0.2088475442 0.0804456769 -0.1744633209 -0.1957718598 0.0588446032
#> [11] 0.2632287624 -0.2228468080 0.1215774881 0.4719427731 -0.1423961768
#> [16] -0.1435656329 -0.0758006193 0.0345275459 0.1401422384 0.6020580379
#> [21] -0.5073168322 -0.2820275982 -0.5226070432 -0.5769375646 0.1280641615
#> [26] -0.3662330462 0.1391154147 -0.6708894581 -0.4895895194 -0.1722829655
#> [31] -0.0695250598 -0.1756239850 -0.0872101766 0.1390127722 -0.0005958758
#> [36] 0.2652138776 -0.0434716468 0.1967849373 0.2652703453 -0.1558650866
#> [41] -0.1066094171 0.1745030187 -0.7380950223 0.1602548837 0.0720685542
#> [46] -0.4800011487 0.0764527009 -0.1480798262 -0.5191671329 -0.3912491983
#> [51] -0.1289594306 -0.2819242139 0.3713357002 -0.0125856482 -0.0406952249
#> [56] 0.0654154839 -0.0351323419 -0.3376009628 -0.2372115041 -0.2859484620
#> [61] 0.0035973849 -0.5202481760 -0.1018946862 -0.0354233941 -0.3291166095
#> [66] 0.2196682326 -0.0292289184 0.0537502268 -0.0366203356 -0.2551508203
#> [71] 0.2536956400 -0.2082472934 -0.1164544875 -0.4770960625 0.1605930654
#> [76] 0.2770897280 0.2249430002 0.4600066331 -0.0378402288 -0.4587163548
#> [81] -0.1986482800 0.0187932855 -0.4230999062 0.0080105413 0.2939677758
#> [86] -0.3154599637 -0.4807873439 0.2103869843 0.2168626502 0.0633279822
#> [91] 0.0230896725 -0.6855424752 -0.5377790054 -0.2349990500 -0.3839017339
#> [96] -0.0287641200 -0.2677175810 -0.0748641863 -0.1884836957 -0.3402656205
#>
#> Slot "Rp":
#> [1] -2.946754461 -2.990855346 -0.981263480 2.516562788 0.726690087
#> [6] -0.086809612 -0.468997847 -1.123860170 -0.479698948 -3.427662377
#> [11] 0.970614304 -0.879594924 -0.431102340 -0.869586682 -0.344517161
#> [16] -0.920845110 -1.996718978 -1.804556714 -1.495413190 2.281998587
#> [21] 2.257782594 -0.445316644 -2.028999346 0.035697483 -0.170255421
#> [26] -2.445870245 4.393099644 3.463141584 -3.314101266 1.850888883
#> [31] 3.111068006 2.562302716 0.026822201 -0.201477439 -1.355424433
#> [36] 3.139400998 -1.547350607 -3.292997780 3.414485141 0.417355197
#> [41] -1.806778415 -3.893292122 0.231301768 -0.893700052 2.927112424
#> [46] -0.241529550 -2.354713082 1.400030592 -0.694058452 1.463345186
#> [51] 1.117268406 -0.785009918 2.256686838 1.061800308 0.491175208
#> [56] -0.666057978 -3.077604140 0.765013576 2.586458304 1.217978001
#> [61] 1.673285916 -0.378955032 -2.131789410 -2.543909929 -0.500089643
#> [66] 2.987069585 -0.413285515 -0.611616426 -2.077630309 0.341797510
#> [71] 0.098434003 -0.319203250 -0.563209483 -0.594499335 0.001201451
#> [76] -2.346730284 -0.291429626 2.904629142 1.681730634 -0.501577676
#> [81] 0.672932394 0.099048611 -1.303365574 0.836510646 1.447024722
#> [86] -1.750576402 0.264627862 1.243011567 -0.201711260 1.488691604
#> [91] 1.398884790 3.505885395 1.197625026 -4.853958863 3.576546638
#> [96] -0.621231481 -0.813832298 -0.261545322 0.460537194 0.977365835
#>
#> Slot "r2":
#> [1] 0.02121489
# data example taken from FAO Book
t0 <- c(3.2,0.8,0.2,2.6,4.4,5.2,2.7,1.2,4.5,5.6) # temperature 2 hours after sunset
td <- c(-4.2,-8.8,-6.5,-6.2,-6.1,2.6,-0.7,-1.7,-1.2,0.1) # dew point 2 hours after sunset
tn <- c(-3.1,-5,-6.3,-5.4,-4,-2.5,-4.8,-5,-4.4,-3.3)
out <- buildFAO(dw = td,temp=t0,tmin=tn)
# We use the results of the model to have the coefficients for the formula
current_temp <- 10
current_dw <- 2
ptmin <- predFAO(out,current_temp,current_dw)
cat("The predicte minimum temperature is ",ptmin," °C")
#> The predicte minimum temperature is -0.7409219 °C
# We plot the temperature trend, we have 12 hours until sunrise
getTrend(Tmin = ptmin ,t2 = current_temp,n = 12,plot=TRUE) # in °C degress
#> x y
#> 1 3 6.6034223
#> 2 4 5.1965137
#> 3 5 4.1169548
#> 4 6 3.2068445
#> 5 7 2.4050213
#> 6 8 1.6801177
#> 7 9 1.0135000
#> 8 10 0.3930274
#> 9 11 -0.1897332
#> 10 12 -0.7409219
We can plot an estimated temperature trend during a frost night, calculated using the FAO recomendation.
library(frost)
getTrend(Tmin = 22.2,t2 = 33.7,n = 15) # in °F degress
#> x y
#> 1 3 30.51047
#> 2 4 29.18933
#> 3 5 28.17558
#> 4 6 27.32095
#> 5 7 26.56800
#> 6 8 25.88729
#> 7 9 25.26131
#> 8 10 24.67866
#> 9 11 24.13142
#> 10 12 23.61383
#> 11 13 23.12154
#> 12 14 22.65116
#> 13 15 22.20000
getTrend(Tmin = -5.45,t2 = 0.95,n = 15, plot=TRUE) # in °C degress
#> x y
#> 1 3 -0.8250406
#> 2 4 -1.5602865
#> 3 5 -2.1244606
#> 4 6 -2.6000813
#> 5 7 -3.0191115
#> 6 8 -3.3979438
#> 7 9 -3.7463161
#> 8 10 -4.0705731
#> 9 11 -4.3751219
#> 10 12 -4.6631713
#> 11 13 -4.9371438
#> 12 14 -5.1989211
#> 13 15 -5.4500000
We can use the output of plotTrend to plot using other libraries such as ggplot2.
library(frost)
var <- getTrend(Tmin = -5.45,t2 = 0.95,n = 15) # in °C degress
require(ggplot2)
#> Loading required package: ggplot2
# just plotting points
ggplot(var,aes(x=x,y=y)) + geom_point(color="blue")
# add trend line
ggplot(var,aes(x=x,y=y)) + geom_point() + geom_smooth(color="red")
#> `geom_smooth()` using method = 'loess' and formula 'y ~ x'
