# heatload

**Author: David Zelený & Tsung-Yi Lin**

The function uses aspect, slope and latitude of the plot and calculates potential annual direct incident radiation and heat load, according to equations published by McCune & Keon (2002).

Note: prior to 4/16/2019, the definition of this function had a bug and returned incorrect values; thanks to Tsung-Yi Lin (林宗儀) for noticing the problem and fixing it!

**Arguments:**

`aspect`

- aspect of the plot, vector (either in degrees, or radians)`slope`

- the inclination of the plot, vector (either in degrees, or radians)`latitude`

- latitude of the plot, either a vector of the same length as aspect or slope, or a single value (in case that all plots are from the same relatively small region)`method`

- default is “heatload”, alternative is “radiation”`units`

- default is “degrees”, alternative is “radians”`equation`

- the equation number (1, 2 or 3); default is 1 (the most general one). The three equations have slightly different uses.**Eq. 1**(default in the function below) is broadest in the application, covering all slopes <= 90° in steepness at latitudes 0-60°N, but has the lowest precision.**Eq. 2**increases the precision by excluding slopes steeper than 60°, an inconsequential omission for almost all data sets.**Eq. 3**uses only three parameters to produce a slightly stronger model but is applicable only to latitudes 30-60°N (ie not for the tropical and subtropical region).

- heatload.r
# Function "heatload" # Calculates heat load or potential annual direct incident radiation, using the formulas published in # McCune & Keon (2002) based on aspect, slope and latitude. heatload <- function (aspect, slope, latitude, method = 'heatload', units = 'degrees', equation = 1) { if (units == 'degrees') # convert degrees to radians { aspect <- aspect/180*pi slope <- slope/180*pi aspect[slope == 0] <- 0 latitude <- latitude/180*pi } A <- if (method == 'heatload') abs (pi - abs (aspect - (5*pi/4))) else pi - abs (aspect-pi) S <- slope L <- if (length (latitude) == 1) rep (latitude, length (A)) else latitude if (equation == 1) res <- exp (-1.467 +1.582*cos(L)*cos(S) -1.500*cos(A)*sin(S)*sin(L) -0.262*sin(L)*sin(S) +0.607*sin(A)*sin(S)) if (equation == 2) res <- exp (-1.236 +1.350*cos(L)*cos(S) -1.376*cos(A)*sin(S)*sin(L) -0.331*sin(L)*sin(S) +0.375*sin(A)*sin(S)) if (equation == 3) res <- +0.339 +0.808*cos(L)*cos(S) -0.196*sin(L)*sin(S) - 0.482*cos(A)*sin(S) return (res) }

Example of the use on the dataset `grasslands.env`

(acidophilous grasslands in Třebíč region, Czech Republic). The `grasslands.env`

contains variables `aspect`

, `slope`

and `latitude`

, all in degrees. Dataset represents small plots (16-25m2) located on convex outcrops in the agricultural landscape, covered by seminatural grassland vegetation.

source ('http://anadat-r.davidzeleny.net/doku.php/en:customized_functions:heatload?do=export_code&codeblock=0') # reads the function definition from above grasslands.env <- read.delim ('https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/grasslands-env.txt') # loads the file # Calculate heat load and add it to the grasslands.env data.frame: grasslands.env$heatload <- heatload (aspect = grasslands.env$aspect, slope = grasslands.env$slope, latitude = grasslands.env$latitude, equation = 3)