In ijlyttle/groundTemp: Make models of ground temperature

library(ggvis)
library(dplyr)
library(lubridate)
library(groundTemp)

The first step of the ground-temperature modeling process is to fit a sinusoid to an air-temperature dataset. This gives us a model for the surface temperature.

The form of the sinusoid:

[T(t, 0) = {T_0} + \Delta {T_0}\sin \left( {\frac{{2\pi (t - {t_0})}}{{\Delta {t_0}}} - \frac{\pi }{2}} \right)]

Symbol | Description | Units :-------: | :-------------- | :---- $T$ | Temperature | °C
$T_0$ | Temperature, annual mean | °C
$\Delta T_0$ | Temperature, annual amplitude | °C
$t$ | time, from 1970-01-01 UTC | s $t_0$ | time when surface-temperature is at its minimum | s $\Delta t_0$ | duration of a tropical year | s

Here's a year of temperature data:

ggvis_temp <- 
  wx_2011 %>%
  ggvis(x = ~instant, y = ~tmp_db) %>%
  layer_points(fill := "blue", fillOpacity := 0.1, size := 20) 


ggvis_temp

Let's get the coefficients:

surface_temp_coef <- surface_temp_coef(wx_2011$instant, wx_2011$tmp_db)

surface_temp_coef

Here it is, as a table:

Symbol | Name | Value ------:|:-----|:----- $T_0$ | temp_ref | r surface_temp_coef$temp_ref $\Delta T_0$ | dtemp_ref | r surface_temp_coef$dtemp_ref $t_0$ | time_ref | r surface_temp_coef$time_ref

We can now use this information to estimate and plot the surface temperature. We will make a function, for now, but we will show how do build the function in a later vignette.

surface_temp <- function(instant){

  dtime <- as.numeric(instant) - as.numeric(surface_temp_coef$time_ref)

  phase <- 2*pi*dtime/tropical_year$dtime_ref - pi/2 

  surface_temp_coef$temp_ref +
    surface_temp_coef$dtemp_ref*sin(phase)

}

df_surface <- 
  data_frame(
    instant = ymd("2011-01-01", tz = "America/New_York") + seq(0, 365)*ddays(1),
    tmp_db = surface_temp(instant)
  )

We superimpose the line for the surface-temperature model.

ggvis_temp %>%
  layer_paths(stroke := "red", strokeWidth := 2, data = df_surface) 

Now that we have the coefficients for the surface-temperature, the next step is to incorporate the thermal-diffusivity of the ground-material.

ijlyttle/groundTemp documentation built on May 18, 2019, 3:41 a.m.