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R/TempWindProfileFunctions.R
In TrenchR: Tools for Microclimate and Biophysical Ecology
#' @title Surface Roughness from Empirical Measurements
#'
#' @description The function estimates surface roughness (m) from empirical wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) data collected at a vector of heights (m) \insertCite{Kingsolver2015,Campbell1998,Porter1979}{TrenchR}.
#'
#' @param u_r \code{numeric} wind velocity (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a vector of reference heights.
#'
#' @param zr \code{numeric} vector of reference heights (m).
#'
#' @return \code{numeric} surface roughness (m).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' surface_roughness(u_r = c(0.01, 0.025, 0.05, 0.1, 0.2),
#' zr = c(0.05, 0.25, 0.5, 0.75, 1))
#'
surface_roughness <- function (u_r,
zr) {
stopifnot(zr > 0,
u_r >= 0)
mod1 <- lm(log(zr) ~ u_r)
d <- exp(as.numeric(mod1$coefficients[1])) # Zero Plane displacement:height at which the wind speed is zero
# can also assume d=0.63h (Monteith 1975)
inds <- which(zr - d > 0) # indices of measurements where zr-d>0
z0 <- NA
if(length(inds) > 0){
mod1 <- lm(u_r[inds] ~ log(zr[inds] - d))
b <- as.numeric(mod1$coefficients[1])
n <- as.numeric(mod1$coefficients[2])
z0 <- exp(-b / n)
}
z0
}
#' @title Wind Speed at a Specific Height Under Neutral Conditions
#'
#' @description The function calculates wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a specified height (m) within a boundary layer near the surface. The profile assumes neutral conditions. The velocity profile is the neutral profile described by \insertCite{Sellers1965;textual}{TrenchR}. Function is equations (2) and (3) of \insertCite{Porter1973;textual}{TrenchR}.
#'
#' @param u_r \code{numeric} wind velocity (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @return \code{numeric} windspeed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' wind_speed_profile_neutral(u_r = 0.1,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15)
#'
wind_speed_profile_neutral <- function (u_r,
zr,
z0,
z) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
u_r * log(z / z0 + 1) / log(zr / z0 + 1)
}
#' @title Air Temperature at a Specified Height Under Neutral Conditions
#'
#' @description The function calculates air temperature (C) at a specified height (m) within a boundary layer near the surface. The velocity profile is the neutral profile described by \insertCite{Sellers1965;textual}{TrenchR}. Function is included as equations (2) and (3) of \insertCite{Porter1973;textual}{TrenchR}.
#'
#' @param T_r \code{numeric} air temperature (C) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale to (m).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @references
#' \insertAllCited{}
#'
#' @family microclimate functions
#'
#' @export
#'
#' @examples
#' air_temp_profile_neutral(T_r = 20,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15,
#' T_s = 25)
#'
#'
air_temp_profile_neutral <- function (T_r,
zr,
z0,
z,
T_s) {
stopifnot(zr >= 0,
z0 >= 0,
z >= 0)
(T_r - T_s) * log(z / z0 + 1) / log(zr / z0 + 1) + T_s
}
#' @title Air Temperature Profile using MICRO Routine
#'
#' @description The function estimates air temperature (C) at a specified height (m). Estimates a single, unsegmented temperature profile using the MICRO routine from NicheMapR \insertCite{Kearney2017}{TrenchR}.
#'
#' @param T_r \code{numeric} air temperature (C) at reference height.
#'
#' @param u_r \code{numeric} windspeed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' air_temp_profile(T_r = 20,
#' u_r = 0.1,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15,
#' T_s = 25)
#'
air_temp_profile <- function (T_r,
u_r,
zr,
z0,
z,
T_s) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
k <- von_karman_constant()
# friction velocity
u_star <- k * u_r / log(zr / z0 + 1)
# sublayer Stanton number
S_ts <- 0.62 / (z0 * u_star / 12)^0.45
# bulk Stanton number
S_tb <- 0.64 / log(zr / z0 + 1)
# Temperature at roughness height, z0
T_z0 <- (T_r * S_tb + T_s * S_ts) / (S_tb + S_ts)
# Temperature at local height
# Initial from Ecography paper but fixed in vignette: T_z= T_z0 + (T_r - T_z0)*log(z/z0+1)
T_z0 + (T_r - T_z0) * log(z / z0 + 1) / log(zr / z0 + 1)
}
#' @title Air Temperature at a Specified Height
#'
#' @description The function calculates air temperature (C) at a specified height (m). Estimates a three segment velocity and temperature profile based on user-specified, experimentally determined values for 3 roughness heights and reference heights. Multiple heights are appropriate in heterogenous areas with, for example, a meadow, bushes, and rocks. Implements the MICROSEGMT routine from NicheMapR as described in \insertCite{Kearney2017;textual}{TrenchR}.
#'
#' @param T_r \code{numeric} a vector of air temperatures (C) at the 3 reference heights.
#'
#' @param u_r \code{numeric} a vector of wind speeds (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at the 3 reference heights.
#'
#' @param zr \code{numeric} a vector of 3 reference heights (meters).
#'
#' @param z0 \code{numeric} a vector of 3 experimentally determined roughness heights (meters).
#'
#' @param z \code{numeric} height for air temperature estimation (meters).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @family microclimate functions
#'
#' @export
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' air_temp_profile_segment(T_r = c(25, 22, 20),
#' u_r = c(0.01, 0.025, 0.05),
#' zr = c(0.05, 0.25, 0.5),
#' z0 = c(0.01, 0.15, 0.2),
#' z = 0.3,
#' T_s = 27)
#'
air_temp_profile_segment <- function (T_r,
u_r,
zr,
z0,
z,
T_s){
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
# order roughness and segment heights
zr.ord <- order(zr, decreasing = TRUE)
zr <- zr[zr.ord]
z0 <- z0[zr.ord]
u_r <- u_r[zr.ord]
T_r <- T_r[zr.ord]
# friction velocity
u_star <- 0.4 * u_r / log(zr / z0 + 1) #0.4 is von Karman constant
# sublayer Stanton number
S_ts <- 0.62 / (z0[3] * u_star[2] / 12)^0.45
# bulk Stanton number
S_tb <- 0.64 / log(zr[2] / z0[3] + 1)
# estimate u_Zloc
if (zr[1] <= z) {
us_star <- u_star[1]
z0s <- z0[1]
T_rs <- T_r[1]
zrs <- zr[1]
} else if (zr[1] > z & zr[2] <= z) {
us_star <- u_star[2]
z0s <- z0[2]
T_rs <- T_r[2]
zrs <- zr[2]
} else if (zr[1] > z & zr[2] > z) {
us_star <- u_star[3]
z0s <- z0[3]
T_rs <- T_r[3]
zrs <- zr[3]
}
# Estimate windspeed
u_z <- 2.5 * us_star * log(z / z0s + 1)
# Temperature at roughness height, z0
T_z0 <- (T_rs * S_tb + T_s * S_ts) / (S_tb + S_ts)
# Temperature at local height
T_z0 + (T_rs - T_z0) * log(z / z0s + 1) / log(zrs / z0s + 1)
}
#' @title Wind Speed at a Specified Height
#'
#' @description The function calculates wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a specified height (m). The function estimates a three segment velocity and temperature profile based on user-specified, experimentally determined values for 3 roughness heights and reference heights. Multiple heights are appropriate in heterogenous areas with, for example, a meadow, bushes, and rocks. Implements the MICROSEGMT routine from NicheMapR as described in \insertCite{Kearney2017;textual}{TrenchR}.
#'
#' @param u_r \code{numeric} a vector of wind speeds (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at the 3 reference heights.
#'
#' @param zr \code{numeric} a vector of 3 reference heights (m).
#'
#' @param z0 \code{numeric} a vector of 3 experimentally determined roughness heights (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @return \code{numeric} wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' wind_speed_profile_segment(u_r = c(0.01, 0.025, 0.05),
#' zr = c(0.05, 0.25, 0.5),
#' z0 = c(0.01, 0.15, 0.2),
#' z = 0.3)
#'
wind_speed_profile_segment <- function (u_r,
zr,
z0,
z) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0,
length(u_r) == 3,
length(zr) == 3,
length(z0) == 3)
k <- von_karman_constant()
# order roughness and segment heights so that z1 > z2 > z0
zr.ord <- order(zr, decreasing = TRUE)
zr <- zr[zr.ord]
z0 <- z0[zr.ord]
u_r <- u_r[zr.ord]
# friction velocity
u_star <- k * u_r / log(zr / z0 + 1)
# estimate u_z loc
if (z <= zr[3]) {
us_star <- u_star[3]
z0s <- z0[3]
zrs <- zr[3]
} else if (z > zr[3] & z < zr[2]) {
us_star <- u_star[2]
z0s <- z0[2]
zrs <- zr[2]
} else if (z >= zr[2]) {
us_star <- u_star[1]
z0s <- z0[1]
zrs <- zr[1]
}
#estimate wind speed
0.5 * us_star * log(z / z0s + 1)
}
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TrenchR documentation built on Sept. 14, 2023, 1:07 a.m.
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#' @title Surface Roughness from Empirical Measurements
#'
#' @description The function estimates surface roughness (m) from empirical wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) data collected at a vector of heights (m) \insertCite{Kingsolver2015,Campbell1998,Porter1979}{TrenchR}.
#'
#' @param u_r \code{numeric} wind velocity (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a vector of reference heights.
#'
#' @param zr \code{numeric} vector of reference heights (m).
#'
#' @return \code{numeric} surface roughness (m).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' surface_roughness(u_r = c(0.01, 0.025, 0.05, 0.1, 0.2),
#' zr = c(0.05, 0.25, 0.5, 0.75, 1))
#'
surface_roughness <- function (u_r,
zr) {
stopifnot(zr > 0,
u_r >= 0)
mod1 <- lm(log(zr) ~ u_r)
d <- exp(as.numeric(mod1$coefficients[1])) # Zero Plane displacement:height at which the wind speed is zero
# can also assume d=0.63h (Monteith 1975)
inds <- which(zr - d > 0) # indices of measurements where zr-d>0
z0 <- NA
if(length(inds) > 0){
mod1 <- lm(u_r[inds] ~ log(zr[inds] - d))
b <- as.numeric(mod1$coefficients[1])
n <- as.numeric(mod1$coefficients[2])
z0 <- exp(-b / n)
}
z0
}
#' @title Wind Speed at a Specific Height Under Neutral Conditions
#'
#' @description The function calculates wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a specified height (m) within a boundary layer near the surface. The profile assumes neutral conditions. The velocity profile is the neutral profile described by \insertCite{Sellers1965;textual}{TrenchR}. Function is equations (2) and (3) of \insertCite{Porter1973;textual}{TrenchR}.
#'
#' @param u_r \code{numeric} wind velocity (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @return \code{numeric} windspeed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' wind_speed_profile_neutral(u_r = 0.1,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15)
#'
wind_speed_profile_neutral <- function (u_r,
zr,
z0,
z) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
u_r * log(z / z0 + 1) / log(zr / z0 + 1)
}
#' @title Air Temperature at a Specified Height Under Neutral Conditions
#'
#' @description The function calculates air temperature (C) at a specified height (m) within a boundary layer near the surface. The velocity profile is the neutral profile described by \insertCite{Sellers1965;textual}{TrenchR}. Function is included as equations (2) and (3) of \insertCite{Porter1973;textual}{TrenchR}.
#'
#' @param T_r \code{numeric} air temperature (C) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale to (m).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @references
#' \insertAllCited{}
#'
#' @family microclimate functions
#'
#' @export
#'
#' @examples
#' air_temp_profile_neutral(T_r = 20,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15,
#' T_s = 25)
#'
#'
air_temp_profile_neutral <- function (T_r,
zr,
z0,
z,
T_s) {
stopifnot(zr >= 0,
z0 >= 0,
z >= 0)
(T_r - T_s) * log(z / z0 + 1) / log(zr / z0 + 1) + T_s
}
#' @title Air Temperature Profile using MICRO Routine
#'
#' @description The function estimates air temperature (C) at a specified height (m). Estimates a single, unsegmented temperature profile using the MICRO routine from NicheMapR \insertCite{Kearney2017}{TrenchR}.
#'
#' @param T_r \code{numeric} air temperature (C) at reference height.
#'
#' @param u_r \code{numeric} windspeed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at reference height.
#'
#' @param zr \code{numeric} initial reference height (m).
#'
#' @param z0 \code{numeric} surface roughness (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' air_temp_profile(T_r = 20,
#' u_r = 0.1,
#' zr = 0.1,
#' z0 = 0.2,
#' z = 0.15,
#' T_s = 25)
#'
air_temp_profile <- function (T_r,
u_r,
zr,
z0,
z,
T_s) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
k <- von_karman_constant()
# friction velocity
u_star <- k * u_r / log(zr / z0 + 1)
# sublayer Stanton number
S_ts <- 0.62 / (z0 * u_star / 12)^0.45
# bulk Stanton number
S_tb <- 0.64 / log(zr / z0 + 1)
# Temperature at roughness height, z0
T_z0 <- (T_r * S_tb + T_s * S_ts) / (S_tb + S_ts)
# Temperature at local height
# Initial from Ecography paper but fixed in vignette: T_z= T_z0 + (T_r - T_z0)*log(z/z0+1)
T_z0 + (T_r - T_z0) * log(z / z0 + 1) / log(zr / z0 + 1)
}
#' @title Air Temperature at a Specified Height
#'
#' @description The function calculates air temperature (C) at a specified height (m). Estimates a three segment velocity and temperature profile based on user-specified, experimentally determined values for 3 roughness heights and reference heights. Multiple heights are appropriate in heterogenous areas with, for example, a meadow, bushes, and rocks. Implements the MICROSEGMT routine from NicheMapR as described in \insertCite{Kearney2017;textual}{TrenchR}.
#'
#' @param T_r \code{numeric} a vector of air temperatures (C) at the 3 reference heights.
#'
#' @param u_r \code{numeric} a vector of wind speeds (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at the 3 reference heights.
#'
#' @param zr \code{numeric} a vector of 3 reference heights (meters).
#'
#' @param z0 \code{numeric} a vector of 3 experimentally determined roughness heights (meters).
#'
#' @param z \code{numeric} height for air temperature estimation (meters).
#'
#' @param T_s \code{numeric} surface temperatures (C).
#'
#' @return \code{numeric} air temperature (C).
#'
#' @family microclimate functions
#'
#' @export
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' air_temp_profile_segment(T_r = c(25, 22, 20),
#' u_r = c(0.01, 0.025, 0.05),
#' zr = c(0.05, 0.25, 0.5),
#' z0 = c(0.01, 0.15, 0.2),
#' z = 0.3,
#' T_s = 27)
#'
air_temp_profile_segment <- function (T_r,
u_r,
zr,
z0,
z,
T_s){
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0)
# order roughness and segment heights
zr.ord <- order(zr, decreasing = TRUE)
zr <- zr[zr.ord]
z0 <- z0[zr.ord]
u_r <- u_r[zr.ord]
T_r <- T_r[zr.ord]
# friction velocity
u_star <- 0.4 * u_r / log(zr / z0 + 1) #0.4 is von Karman constant
# sublayer Stanton number
S_ts <- 0.62 / (z0[3] * u_star[2] / 12)^0.45
# bulk Stanton number
S_tb <- 0.64 / log(zr[2] / z0[3] + 1)
# estimate u_Zloc
if (zr[1] <= z) {
us_star <- u_star[1]
z0s <- z0[1]
T_rs <- T_r[1]
zrs <- zr[1]
} else if (zr[1] > z & zr[2] <= z) {
us_star <- u_star[2]
z0s <- z0[2]
T_rs <- T_r[2]
zrs <- zr[2]
} else if (zr[1] > z & zr[2] > z) {
us_star <- u_star[3]
z0s <- z0[3]
T_rs <- T_r[3]
zrs <- zr[3]
}
# Estimate windspeed
u_z <- 2.5 * us_star * log(z / z0s + 1)
# Temperature at roughness height, z0
T_z0 <- (T_rs * S_tb + T_s * S_ts) / (S_tb + S_ts)
# Temperature at local height
T_z0 + (T_rs - T_z0) * log(z / z0s + 1) / log(zrs / z0s + 1)
}
#' @title Wind Speed at a Specified Height
#'
#' @description The function calculates wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at a specified height (m). The function estimates a three segment velocity and temperature profile based on user-specified, experimentally determined values for 3 roughness heights and reference heights. Multiple heights are appropriate in heterogenous areas with, for example, a meadow, bushes, and rocks. Implements the MICROSEGMT routine from NicheMapR as described in \insertCite{Kearney2017;textual}{TrenchR}.
#'
#' @param u_r \code{numeric} a vector of wind speeds (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}) at the 3 reference heights.
#'
#' @param zr \code{numeric} a vector of 3 reference heights (m).
#'
#' @param z0 \code{numeric} a vector of 3 experimentally determined roughness heights (m).
#'
#' @param z \code{numeric} height to scale (m).
#'
#' @return \code{numeric} wind speed (\ifelse{html}{\out{m s<sup>-1</sup>}}{\eqn{m s^-1}{ASCII}}).
#'
#' @family microclimate functions
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' wind_speed_profile_segment(u_r = c(0.01, 0.025, 0.05),
#' zr = c(0.05, 0.25, 0.5),
#' z0 = c(0.01, 0.15, 0.2),
#' z = 0.3)
#'
wind_speed_profile_segment <- function (u_r,
zr,
z0,
z) {
stopifnot(u_r >= 0,
zr >= 0,
z0 >= 0,
z >= 0,
length(u_r) == 3,
length(zr) == 3,
length(z0) == 3)
k <- von_karman_constant()
# order roughness and segment heights so that z1 > z2 > z0
zr.ord <- order(zr, decreasing = TRUE)
zr <- zr[zr.ord]
z0 <- z0[zr.ord]
u_r <- u_r[zr.ord]
# friction velocity
u_star <- k * u_r / log(zr / z0 + 1)
# estimate u_z loc
if (z <= zr[3]) {
us_star <- u_star[3]
z0s <- z0[3]
zrs <- zr[3]
} else if (z > zr[3] & z < zr[2]) {
us_star <- u_star[2]
z0s <- z0[2]
zrs <- zr[2]
} else if (z >= zr[2]) {
us_star <- u_star[1]
z0s <- z0[1]
zrs <- zr[1]
}
#estimate wind speed
0.5 * us_star * log(z / z0s + 1)
}
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