The User Guide is divided into two volumes: 1. Radiation and 2. Astronomy. The second volume also describes functions related to water vapour in the atmosphere.
We load two packages, our ‘photobiology’ and ‘lubridate’, as they will be used in the examples.
library(photobiology)
library(lubridate)
# if installed, we use 'lutz' to lookup time zones from geocodes
eval_lutz <- requireNamespace("lutz", quietly = TRUE)
if (eval_lutz) {library(lutz)}Most organisms, including plants and animals, have circadian internal clocks. These clocks are entrained to the day-night cycle through perception of light. For example, night length informs plants about seasons of the year. This information allows the synchronization of developmental events like flowering to take place at the “right” time of the year.
From the point of view of interactions between light and vegetation, the direction of the direct light beam is of interest. Hence, the position of the sun in the sky is also important for photobiology. This is the reason for the inclusion of astronomical calculations about the sun in this package. On the other hand, such calculations are also highly relevant to other fields including solar energy.
The functions and methods described in this volume return either
values that represent angles or times. In the current version angles are
always expressed in degrees. In the case of times, the unit of
expression, can be changed through parameter unit.out which
accepts the following arguments "datetime",
"hours", "minutes", "seconds".
For backwards compatibility "date" is also accepted as
equivalent to "datetime" but deprecated.
All astronomical computations rely on the algorithms of Meuss (1998), and consequently returned values are very precise. However, these algorithms are computationally rather costly. Contrary to other faster algorithms, they give reliable estimates even for latitudes near the poles.
However, at high latitudes due to the almost tangential path of the sun to the horizon, atmospheric effects that slightly alter the apparent elevation of the sun have much larger effects on the apparent timing of events given that the solar elevation angle changes at a slower rate than at lower latitudes.
The position of the sun at an arbitrary geographic locations and time instant can be described with two angles: elevation above the horizon and azimuth angle relative to the geographic North. If expressed in degrees, solar elevation (\(h\)) varies between -90 and 90 degrees, while being visible when angles are positive and otherwise occluded below the horizon. Azimuth angle (\(\alpha\)) varies clockwise from North between 0 and 360 degrees. Zenith angle (\(z\)), provides the same information as the elevation angle but using the zenith as starting point, consequently taking values between 0 and 180 degrees, such that \(z = 90 - h\). Declination angle describes the angle between the plane of the Equator and the plane of the Earth’s orbit around the sun, and varies with the seasons of the year.
The function sun_angles returns location, civil time,
local solar time, the azimuth in degrees eastwards, elevation in degrees
above the horizon, declination, the equation of time and the hour
angle.
In versions up to 0.9.11 in addition to parameter
geocode most functions also had the redundant formal
parameters lon and lat which were removed in
version 0.9.12. This change may require users’ scripts to be
revised.
In versions 0.9.16 and later the code has been optimized for performance with time vectors, making massive calculations such as the sun position for every minute of the year quite fast (couple of seconds). We keep, however, examples with rather short vectors.
For calculation of the position of the sun we need to supply
geographic coordinates and a time instant. The time instant passed as
argument should be a POSIXct vector, possibly of length
one. The easiest way create date and time constant values is to use
package ‘lubridate’.
The object to be supplied as argument for geocode is a
data frame with variables lon and lat giving
the location on Earth. This matches the return value of functions
tidygeocoder::geo_osm(),
tidygeocoder::geo_google() and
ggmap::geocode(), functions that can be used to find the
coordinates using an address entered as a character string
understood by the OSM or Google maps APIs (Google requires an API key
and registration, while OSM is open). We use the “geocode” for Helsinki,
defined explicitly rather than searched for.
my.geocode <- data.frame(lat = 60.16, lon = 24.93, address = "Helsinki")Be aware that to obtain correct the time zone must be correctly set
for the argument passed to time. To obtain results based on
local time, this time zone needs to be set in the POSIXct
object or passed as a argument to tz. In the examples we
use functions from package ‘lubridate’ for working with times and dates.
The argument passed to parameter time can be a “vector” of
POSIXct values. The returned value is a
data.frame.
The position of the sun at Helsinki, at the given instant in time for time zone Eastern European Time.
sun_angles(time = ymd_hms("2017-06-20 08:00:00", tz = "EET"), geocode = my.geocode)## # A tibble: 1 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2017-06-20 08:00:00 EET 06:38:09 24.9 60.2 Helsin… 85.8 24.9
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesFunctions have defaults for their arguments, but rarely Greenwich will be the location you are interested in. Current UTC time is probably a useful default in some cases.
sun_angles()## # A tibble: 1 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2022-07-22 22:36:40 UTC 22:30:10 0 51.5 Greenw… 338. -15.7
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesA vector of times is accepted as argument, and as performance is optimized for this case, vectorization will markedly improve performance compared to multiple calls to the function. The vector of times can be created on the fly, or stored beforehand.
sun_angles(time = ymd_hms("2014-01-01 0:0:0", tz = "EET") + hours(c(0, 6, 12)),
geocode = my.geocode)## # A tibble: 3 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2014-01-01 00:00:00 EET 23:36:26 24.9 60.2 Helsin… 351. -52.6
## 2 2014-01-01 06:00:00 EET 05:36:19 24.9 60.2 Helsin… 97.0 -22.7
## 3 2014-01-01 12:00:00 EET 11:36:12 24.9 60.2 Helsin… 174. 6.71
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesmy.times <- ymd_hms("2014-01-01 0:0:0", tz = "EET") + hours(c(0, 6, 12))
sun_angles(time = my.times, geocode = my.geocode)## # A tibble: 3 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2014-01-01 00:00:00 EET 23:36:26 24.9 60.2 Helsin… 351. -52.6
## 2 2014-01-01 06:00:00 EET 05:36:19 24.9 60.2 Helsin… 97.0 -22.7
## 3 2014-01-01 12:00:00 EET 11:36:12 24.9 60.2 Helsin… 174. 6.71
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesGeocodes for several locations can be stored in a data frame with multiple rows.
two.geocodes <- data.frame(lat = c(60.16, 65.02),
lon = c(24.93, 25.47),
address = c("Helsinki", "Oulu"))
sun_angles(time = my.times, geocode = two.geocodes)## # A tibble: 6 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2014-01-01 00:00:00 EET 23:36:26 24.9 60.2 Helsin… 351. -52.6
## 2 2014-01-01 06:00:00 EET 05:36:19 24.9 60.2 Helsin… 97.0 -22.7
## 3 2014-01-01 12:00:00 EET 11:36:12 24.9 60.2 Helsin… 174. 6.71
## 4 2014-01-01 00:00:00 EET 23:38:36 25.5 65.0 Oulu 353. -47.9
## 5 2014-01-01 06:00:00 EET 05:38:29 25.5 65.0 Oulu 95.4 -23.0
## 6 2014-01-01 12:00:00 EET 11:38:22 25.5 65.0 Oulu 175. 1.89
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesWhen spectra contain suitable metadata, the position of the sun for the spectral irradiance data measurement can be easily obtained.
sun_angles(time = getWhenMeasured(sun.spct), geocode = getWhereMeasured(sun.spct))## # A tibble: 1 × 12
## time tz solartime longitude latit…¹ address azimuth eleva…²
## <dttm> <chr> <solar_tm> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 2010-06-22 09:51:00 UTC 11:28:54 25.0 60.2 Kumpul… 168. 52.8
## # … with 4 more variables: declination <dbl>, eq.of.time <dbl>,
## # hour.angle <dbl>, distance <dbl>, and abbreviated variable names ¹latitude,
## # ²elevation
## # ℹ Use `colnames()` to see all variable namesIf what is needed is only one of the solar angles, functions
returning vectors instead of data frames can be useful. (In their
current implementation these functions do not have improved
performance compared to sun_angles())
sun_elevation(time = my.times, geocode = my.geocode)## [1] -52.639345 -22.722495 6.710245sun_zenith_angle(time = my.times, geocode = my.geocode)## [1] 142.63935 112.72250 83.28976sun_azimuth(time = my.times, geocode = my.geocode)## [1] 351.04757 96.98377 174.48767Convenience functions sunrise_time(),
sunset_time(), noon_time(),
day_length() and night_length() have all the
same parameter signature and are wrappers on function
day_night(). Function day_night returns a data
frame containing all the quantities returned by the other functions.
These functions are vectorized for their date and
geocode parameters. They use as default location Greenwich
in the U.K., and default time zone “UTC”. The date is given by default
by the current date based on “UTC”. Universal Time Coordinate (“UTC”) is
the reference used to describe differences among time zones and is never
modified by daylight saving time or summer time. The difference between
EET (Eastern European Time) and UTC is +2 hours in winter and with EEST
(Eastern European Summer Time) +3 hours.
Latitude and longitude are passed through a geocode (a
data frame). If the returned value is desired in the local time
coordinates of the argument passed to geocode, the time
zone should match the geographic coordinates. If geocodes contain a
variable "address" it will be copied to the output.
In some of the examples below we reuse the geocode data frames
created above, and we here create a vector of datetime objects differing
in their date. The default time zone of function ymd() is
NULL, so we override it with EET to match the
geocodes for Finnish cities.
dates <- ymd("2015-03-01", tz = "EET") + months(0:5)
dates## [1] "2015-03-01 EET" "2015-04-01 EEST" "2015-05-01 EEST" "2015-06-01 EEST"
## [5] "2015-07-01 EEST" "2015-08-01 EEST"As first example we compute the sunrise time for the current day in Helsinki, with the result returned eithe in UTC or EET coordinates. Time-zone names based on continent and city are also supported, and are to be preferred for past dates and the relationship between time zones and locations are affected by changes in country boundaries and in national laws.
sunrise_time(now("UTC"), geocode = my.geocode)## [1] "2022-07-22 01:37:31 UTC"sunrise_time(now("EET"), geocode = my.geocode)## [1] "2022-07-22 04:37:31 EEST"sunrise_time(now("Europe/Helsinki"), geocode = my.geocode)## [1] "2022-07-22 04:37:31 EEST"Be aware of the behaviour of functions ymd(),
dmy(), ym() and my() from package
‘lubridate’. A function call like
ymd("2015-03-01", tz = "UTC") returns a
POSIXct object while a call like
ymd("2015-03-01") is equivalent to
ymd("2015-03-01", tz = NULL) and returns a
Date object. Date objects do not carry time
zone information in the way POSIXct objects do, and
consequently Dates do not uniquely match a period between
two absolute instants in time, but rather between two instants in local
time. Given these features, it is safer to use POSIXct
objects as arguments to the functions from package ‘photobiology’.
Function today() always returns a Date while
function now() always returns a POSIXct,
independently of the argument passed to their tzone
parameter. Consequently it is preferable to use now(), but
if you do use today() make sure to path the same value as
argument to parameter tzone of today() and to
parameter tz of the functions from package ‘photobiology’.
An instant in time and time zone strictly define a corresponding
date at any location on Earth.
The default for time zone is that of the POSIXct value
passed as argument to parameter date, but this can be
overridden.
sunrise_time(geocode = my.geocode)## [1] "2022-07-22 01:37:31 UTC"sunrise_time(date = now("UTC"), geocode = my.geocode)## [1] "2022-07-22 01:37:31 UTC"sunrise_time(date = now("UTC"), tz = "UTC", geocode = my.geocode)## [1] "2022-07-22 01:37:31 UTC"sunrise_time(date = now("EET"), geocode = my.geocode)## [1] "2022-07-22 04:37:31 EEST"sunrise_time(date = now("EET"), tz = "EET", geocode = my.geocode)## [1] "2022-07-22 04:37:31 EEST"sunrise_time(today("EET"), tz = "EET", geocode = my.geocode)## [1] "2022-07-23 04:39:43 EEST"We can also compute the time of solar noon and of sunset.
noon_time(now("UTC"), geocode = my.geocode)## [1] "2022-07-22 10:26:45 UTC"noon_time(now("EET"), geocode = my.geocode)## [1] "2022-07-22 13:26:45 EEST"sunset_time(now("UTC"), geocode = my.geocode)## [1] "2022-07-22 19:16:00 UTC"sunset_time(now("EET"), geocode = my.geocode)## [1] "2022-07-22 22:16:00 EEST"Functions day_length() and night_length()
return the length of time, by default in hours and fraction.
day_length(dates, geocode = my.geocode)## [1] 10.34596 13.19241 15.90766 18.27962 18.80811 16.97567night_length(dates, geocode = my.geocode)## [1] 13.654040 10.807592 8.092343 5.720384 5.191888 7.024327Southern hemisphere latitudes as well as longitudes to the West of the Greenwich meridian should be supplied as negative numbers.
sunrise_time(dates, geocode = data.frame(lat = 60, lon = 25))## [1] "2015-02-28 07:21:52 EET" "2015-03-31 06:48:41 EEST"
## [3] "2015-04-30 05:20:50 EEST" "2015-05-31 04:10:49 EEST"
## [5] "2015-06-30 04:01:10 EEST" "2015-07-31 04:58:15 EEST"noon_time(dates, geocode = data.frame(lat = 60, lon = 25))## [1] "2015-02-28 12:32:34 EET" "2015-03-31 13:24:14 EEST"
## [3] "2015-04-30 13:17:15 EEST" "2015-05-31 13:17:38 EEST"
## [5] "2015-06-30 13:23:36 EEST" "2015-07-31 13:26:24 EEST"sunrise_time(dates, geocode = data.frame(lat = -60, lon = 25))## [1] "2015-02-28 05:29:25 EET" "2015-03-31 07:46:18 EEST"
## [3] "2015-04-30 08:58:10 EEST" "2015-05-31 10:04:25 EEST"
## [5] "2015-06-30 10:24:25 EEST" "2015-07-31 09:37:27 EEST"noon_time(dates, geocode = data.frame(lat = -60, lon = 25))## [1] "2015-02-28 12:32:34 EET" "2015-03-31 13:24:14 EEST"
## [3] "2015-04-30 13:17:15 EEST" "2015-05-31 13:17:38 EEST"
## [5] "2015-06-30 13:23:36 EEST" "2015-07-31 13:26:24 EEST"The angle used in the twilight calculation can be supplied, either as
the name of a standard definition, or as an angle in degrees (negative
for sun positions below the horizon). Positive angles can be used when
the time of sun occlusion behind a building, mountain, or other obstacle
needs to be calculated. The default for twilight is
"none" meaning that times correspond to the occlusion of
the upper rim of the sun disk below the theoretical horizon.
sunrise_time(ymd("2017-03-21", tz = "EET"),
tz = "EET",
geocode = my.geocode,
twilight = "civil")## [1] "2017-03-20 05:38:58 EET"sunrise_time(ymd("2017-03-21", tz = "EET"),
tz = "EET",
geocode = my.geocode,
twilight = -10)## [1] "2017-03-20 05:05:45 EET"sunrise_time(ymd("2017-03-21", tz = "EET"),
tz = "EET",
geocode = my.geocode,
twilight = +12)## [1] "2017-03-20 08:06:15 EET"Parameter unit.out can be used to obtain the returned
value expressed as time-of-day in hours, minutes, or seconds since
midnight, instead of the default datetime.
sunrise_time(ymd("2017-03-21", tz = "EET"),
tz = "EET",
geocode = my.geocode)## [1] "2017-03-20 06:20:46 EET"sunrise_time(ymd("2017-03-21", tz = "EET"),
tz = "EET",
geocode = my.geocode,
unit.out = "hours")## [1] 6.346365Similarly, the units can also be selected for the values returned by
day_length() and night_length().
day_length(dates, geocode = my.geocode, unit.out = "days")## [1] 0.4310817 0.5496837 0.6628190 0.7616507 0.7836713 0.7073197night_length(dates, geocode = my.geocode, unit.out = "days")## [1] 0.5689183 0.4503163 0.3371810 0.2383493 0.2163287 0.2926803The core function is called day_night() and returns a
data frame containing both the input values and the results of the
calculations. See above for convenience functions useful in the case one
needs only one of the calculated variables. In other cases it is more
efficient to compute the whole data frame and later select the columns
of interest.
day_night(dates[1:3],
geocode = my.geocode)## # A tibble: 3 × 12
## day tz twilight.r…¹ twili…² longi…³ latit…⁴ address sunrise
## <dttm> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 2015-02-28 00:00:00 EET 0 0 24.9 60.2 Helsin… 7.49
## 2 2015-03-31 00:00:00 EET 0 0 24.9 60.2 Helsin… 6.93
## 3 2015-04-30 00:00:00 EET 0 0 24.9 60.2 Helsin… 5.47
## # … with 4 more variables: noon <dbl>, sunset <dbl>, daylength <dbl>,
## # nightlength <dbl>, and abbreviated variable names ¹twilight.rise,
## # ²twilight.set, ³longitude, ⁴latitude
## # ℹ Use `colnames()` to see all variable namesThe default for unit.out is "hours" with
decimal fractions, as seen above. However other useful units like
"seconds", "minutes", and "days"
can be useful.
day_night(dates[1:3],
geocode = my.geocode,
unit.out = "days")## # A tibble: 3 × 12
## day tz twilight.r…¹ twili…² longi…³ latit…⁴ address sunrise
## <dttm> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 2015-02-28 00:00:00 EET 0 0 24.9 60.2 Helsin… 0.312
## 2 2015-03-31 00:00:00 EET 0 0 24.9 60.2 Helsin… 0.289
## 3 2015-04-30 00:00:00 EET 0 0 24.9 60.2 Helsin… 0.228
## # … with 4 more variables: noon <dbl>, sunset <dbl>, daylength <dbl>,
## # nightlength <dbl>, and abbreviated variable names ¹twilight.rise,
## # ²twilight.set, ³longitude, ⁴latitude
## # ℹ Use `colnames()` to see all variable namesFinally it is also possible to have the timing of solar events
returned as POSIXct time values, in which case lengths of
time are still returned as fractional hours.
day_night(dates[1:3],
geocode = my.geocode,
unit.out = "datetime")## # A tibble: 3 × 12
## day tz twilight.rise twilight.set longitude latit…¹ address
## <dttm> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 2015-02-28 00:00:00 EET 0 0 24.9 60.2 Helsin…
## 2 2015-03-31 00:00:00 EET 0 0 24.9 60.2 Helsin…
## 3 2015-04-30 00:00:00 EET 0 0 24.9 60.2 Helsin…
## # … with 5 more variables: sunrise <dttm>, noon <dttm>, sunset <dttm>,
## # daylength <dbl>, nightlength <dbl>, and abbreviated variable name ¹latitude
## # ℹ Use `colnames()` to see all variable namesWhen multiple times and locations are supplied as arguments, the values returned are for all combinations of locations and times.
day_night(dates[1:3],
geocode = two.geocodes)## # A tibble: 6 × 12
## day tz twilight.r…¹ twili…² longi…³ latit…⁴ address sunrise
## <dttm> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 2015-02-28 00:00:00 EET 0 0 24.9 60.2 Helsin… 7.49
## 2 2015-03-31 00:00:00 EET 0 0 24.9 60.2 Helsin… 6.93
## 3 2015-04-30 00:00:00 EET 0 0 24.9 60.2 Helsin… 5.47
## 4 2015-02-28 00:00:00 EET 0 0 25.5 65.0 Oulu 7.68
## 5 2015-03-31 00:00:00 EET 0 0 25.5 65.0 Oulu 6.78
## 6 2015-04-30 00:00:00 EET 0 0 25.5 65.0 Oulu 4.96
## # … with 4 more variables: noon <dbl>, sunset <dbl>, daylength <dbl>,
## # nightlength <dbl>, and abbreviated variable names ¹twilight.rise,
## # ²twilight.set, ³longitude, ⁴latitude
## # ℹ Use `colnames()` to see all variable namesIn field research it is in many cases preferable to sample or measure, and present and plot data based on local solar time. A new class is defined in package ‘photobiology’, with a print method, a constructor, a conversion function and a class query function.
The constructor takes as arguments a POSIXct object
describing and instant in time and a geocode describing the geographic
coordinates.
Paris.geo <- data.frame(lon = 2.352222, lat = 48.85661, address = "Paris")
Paris.time <- ymd_hms("2016-09-30 06:00:00", tz = "UTC")
solar_time(Paris.time, geocode = Paris.geo)## [1] "06:19:28"solar_time(Paris.time, geocode = Paris.geo, unit.out = "datetime")## [1] "2016-09-30 06:19:28 solar"my.solar.t <- solar_time(Paris.time, geocode = Paris.geo)
is.solar_time(my.solar.t)## [1] TRUEis.numeric(my.solar.t)## [1] TRUEmy.solar.d <- solar_time(Paris.time, geocode = Paris.geo, unit.out = "datetime")
is.solar_date(my.solar.d)## [1] TRUEis.timepoint(my.solar.d)## [1] TRUEFunction as_tod() facilitates conversion of R’s time
date objects into a numeric value representing the time of day as
numerical value with a decimal fraction using one of hour, minute or
second as unit of expression. While solar time is based on the
astronomical position of the sun, time of day is based on the time
coordinates for a time zone.
times <- now(tzone = "UTC") + hours(0:6)
times## [1] "2022-07-22 22:36:41 UTC" "2022-07-22 23:36:41 UTC"
## [3] "2022-07-23 00:36:41 UTC" "2022-07-23 01:36:41 UTC"
## [5] "2022-07-23 02:36:41 UTC" "2022-07-23 03:36:41 UTC"
## [7] "2022-07-23 04:36:41 UTC"as_tod(times)## [1] 22.6116138 23.6116138 0.6116138 1.6116138 2.6116138 3.6116138 4.6116138as_tod(times, unit.out = "minutes")## [1] 1356.69683 1416.69683 36.69683 96.69683 156.69683 216.69683 276.69683Solar elevation determines the length of the path of the sun beam
through the Earth’s atmosphere. This affects the solar spectrum at
ground level, specially the UVB region. Function
relative_AM() can be used to calculate an empirical
estimate of this quantity from elevation angles in degrees.
This function is vectorised.
relative_AM(33)## [1] 1.83relative_AM(c(80, 60, 40, 20))## [1] 1.01 1.15 1.55 2.90Evapotranspiration is a measure of the water flux between land and atmosphere expressed as millimeters of water per unit ground area and unit time. One millimeter of evapotranspiration or precipitation is equivalent to one litre per square meter. Evapotranspiration is composed of the evaporation from the soil surface and other wet surfaces plus transpiration from plants (water evaporated inside leaves and diffusing as vapour to the outside of leaves). The condensation of dew represents a negative component.
When not measured, evapotranspiration can be estimated based on energy balance and resistances to mass and heat transport. The Penman-Monteith equation is widely used. One special idealized condition is used to compute reference evapotranspiration (similar to potential evapotranspiration but with a standardized formulation by FAO that is widely used in agriculture).
As implemented the computation of the energy balance is done with
function net_irradiance() and using the value returned by
this function as one argument, reference evapotranspiration is computed
with function ET_ref().
r_net <- net_irradiance(temperature = 20, # C
sw.down.irradiance = 800, # W / m2
water.vp = 1500) # Pa
r_net # W / m2## [1] 546.8251ET_ref(temperature = 20, # C
water.vp = 1500, # Pa
wind.speed = 4, # m / s
net.irradiance = r_net
)## [1] 0.9448297This function returns an estimate of reference evapotranspiration expressed in mm / h. Can be used with hourly means for the inputs or more frequent observations. In all cases the result is expressed as an instantaneous water flux rate expressed per hour.
Function ET_ref_day() should be used when the input data
are daily meeans or less frequent.