User Guide: 2 Radiation

Getting started

We load two packages in addition to ‘photobiology’, ‘lubridate’ and ‘magrittr’, as they will be used in the examples.

library(photobiology)

## For news about 'photobiology', please, see http://www.r4photobiology.info/

## For on-line documentation see http://docs.r4photobiology.info/photobiology/

library(lubridate)

## 
## Attaching package: 'lubridate'

## The following object is masked from 'package:base':
## 
##     date

library(magrittr)

Classes

Package ‘photobiology’ defines several classes intended to be used to store different types of spectral data. They are all derived from generic_spct, which in turn is derived from tibble::tibble. Table 1 lists these classes. Attributes are used in objects of these classes to store metadata such as information about units of expression.

Table 1. Classes for spectral data. In addition to the required variables listed in the table, additional arbitrary variables are partly supported—some operations will not include them in returned values to avoid ambiguity and other possible conflicts. In addition to the attributes listed, all spectral objects have attributes multiple.wl, normalized, scaled, when.measured, where.measured, what.measured plus the normal attributes of tibble (and data.frame) objects including comment.

The design imposes the restriction that data from different observations are never present as different data columns, if present, additional data columns represent different properties from the same observation event. In other words, the storage format is tidy as defined by Hadley Wickham. In most cases, one spectral object should correspond to one spectral observation, but some functions are compatible or can be used to create spectral objects where the spectral data from different observations are stored “longitudinally” and “tagged” with a factor with a level for each observation event. These observations must use consistent units of expression and attribute values. This long format is useful, for example, when producing plots with package ‘ggplot2’. If spectra are stored in long form, e.g. for plotting with ‘ggplot2’, attributes are stored as named lists or enforced to be the same across spectra. This allows to reconstruct a collection of spectra from a long-form spectral object preserving most of the metadata.

Data assumptions

A key assumption of the package is that wavelengths are always expressed in nanometres (\(1~\mathrm{nm} = 1 \cdot 10^{-9}\,\mathrm{m}\)). If the data to be analysed use different units for wavelengths, e.g. Ångstrom (\(1~\textrm{Å} = 1 \cdot 10^{-10}\,\mathrm{m}\)), the values need to be re-scaled before creating objects of the spectral classes. The same applies to all spectral quantities, as there is an expectation in every case, of using base SI units for expression. Table 2 lists the units of expression for the different variables and the metadata attributes that may determine variations in the expression of the quantities.

Table 2. Variables used for spectral data and their units of expression. A: as stored in objects of the spectral classes, B: also recognized by the set family of functions for spectra and automatically converted. time.unit accepts in addition to the character strings listed in the table, objects of classes lubridate::duration and period, in addition numeric values are interpreted as seconds. exposure.time accepts these same values, but not the character strings.

Energy irradiance is assumed to be expressed in \(W\,m^{-2}\) and photon irradiances in \(mol^{-1}\,m^{-2}\,s^{-1}\), that is to say using second as unit for time. This is the default, but it is possible to set the unit for time to day in the case of source_spct objects.

The default time unit used is second, but day and exposure can be used by supplying the arguments "day" or "exposure"—The meaning of "exposure" is the total exposure time, in other words, fluence instead of irradiance—to a parameter of the constructor of source_spct objects. In addition to these character constants objects of class lubridate:duration are also accepted.

The attributes are normally set when a spectral object is created, either using default values or with values supplied as arguments to the constructor. However, methods for querying and setting most of these attributes are also available.

If spectral irradiance data is in \(W\,m^{-2}\,nm^{-1}\), and the wavelength in nm, as is the case for many Macam spectroradiometers, the data can be used directly and functions in the package will return irradiances in \(W\,m^{-2}\).

If, for example, the spectral irradiance data output by a spectroradiometer is expressed in \(mW\,m^{-2}\,nm^{-1}\), and the wavelengths are in Ångstrom then to obtain correct results when using any of the packages in the suite, we need to rescale the data when creating a new object.

# not run
my.spct <- source_spct(w.length = wavelength/10, s.e.irrad = irrad/1000)

In the example above, we take advantage of the behaviour of the S language: an operation between a scalar and a vector, is equivalent to applying this operation to each element of the vector. Consequently, in the code above, each value from the vector of wavelengths is divided by 10, and each value in the vector of spectral irradiances is divided by 1000.

Querying the class

Before giving examples of how to construct objects to store spectral data we show how to query the class of an object, and how to query the class of a spectrum. Consistently with R, the package provides is functions for querying the type of spectra objects. The only unusual function name, defined as a synomin for is.generic_spct, is is.any_spct().

is.any_spct(sun.spct)

## [1] TRUE

is.generic_spct(sun.spct)

## [1] TRUE

is.source_spct(sun.spct)

## [1] TRUE

In addition function class_spc() returns directly the spectrum-related class attributes. It filters out from the output of class() the underlying inherited classes.

class_spct(sun.spct)

## [1] "source_spct"  "generic_spct"

class(sun.spct)

## [1] "source_spct"  "generic_spct" "tbl_df"       "tbl"         
## [5] "data.frame"

Construction

There are basically two different approaches to the creation of spectra by users. The first group are constructors similar to the data.frame() constructor, which take vectors as arguments. The second group are constructors that convert list objects, and because of class derivation also data.frame objects, into spectral objects. Constructors in this second group are similar to as.data.frame from base R. In contrast to the data frame constructors, spectral object constructors require the variables or the vector arguments to be suitably named so that they can be recognized.

Here we briefly describe the as constructor functions for spectra. In the first example we create an object to store spectral irradiance data for a ficticious light source, by first creating a data frame, and creating the spectral object as a copy of it. In the example below we supply a single value, 1, for the spectral irradiance. This value gets recycled as is normal in R, but of course in real use it is more usual to supply a vector of the same length as the w.length vector.

my.df <- data.frame(w.length = 400:410, s.e.irrad = 1)
my.spct <- as.source_spct(my.df)
class(my.spct)

## [1] "source_spct"  "generic_spct" "tbl_df"       "tbl"         
## [5] "data.frame"

class(my.df)

## [1] "data.frame"

my.spct

## Object: source_spct [11 x 2]
## Wavelength range 400 to 410 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      400        1.
## 2      401        1.
## 3      402        1.
## 4      403        1.
## # ... with 7 more rows

We can make a `generic_spct’ copy of any spectrum object.

my.g.spct <- as.generic_spct(my.spct)
class(my.g.spct)

## [1] "generic_spct" "tbl_df"       "tbl"          "data.frame"

When constructing spectral objects from numeric vectors the names of the arguments are meaningful and convey information on the nature of the spectral data and basis of expression.

source_spct(w.length = 300:305, s.e.irrad = 1)

## Object: source_spct [6 x 2]
## Wavelength range 300 to 305 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 6 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      300        1.
## 2      301        1.
## 3      302        1.
## 4      303        1.
## 5      304        1.
## 6      305        1.

z <- 300:305
y <- 2
source_spct(w.length = z, s.e.irrad = y)

## Object: source_spct [6 x 2]
## Wavelength range 300 to 305 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 6 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      300        2.
## 2      301        2.
## 3      302        2.
## 4      303        2.
## 5      304        2.
## 6      305        2.

When argument names are not supplied explicitly as above, the names of the variables are used to identify the data vectors.

w.length <- 300:305
s.e.irrad <- 1
source_spct(w.length, s.e.irrad)

## Object: source_spct [6 x 2]
## Wavelength range 300 to 305 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 6 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      300        1.
## 2      301        1.
## 3      302        1.
## 4      303        1.
## 5      304        1.
## 6      305        1.

The different constructors have additional arguments to be used in setting non-default values for the attributes. These arguments have the same name as the attributes. Here we used the data frame created in the first code chunk of this section.

my.d.spct <- as.source_spct(my.df, time.unit = "day")

Argument strict.range can be used to override or make more strict the validation of the data values.

source_spct(w.length = 300:305, s.e.irrad = -1)

## Warning in range_check(x, strict.range = strict.range): Negative spectral
## energy irradiance values; minimum s.e.irrad = -1.00

## Object: source_spct [6 x 2]
## Wavelength range 300 to 305 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 6 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      300       -1.
## 2      301       -1.
## 3      302       -1.
## 4      303       -1.
## 5      304       -1.
## 6      305       -1.

source_spct(w.length = 300:305, s.e.irrad = -1, strict.range = NULL)

## Object: source_spct [6 x 2]
## Wavelength range 300 to 305 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 6 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      300       -1.
## 2      301       -1.
## 3      302       -1.
## 4      303       -1.
## 5      304       -1.
## 6      305       -1.

Finally argument comment can be used to add a comment to the data at the time of construction.

my.cm.spct <- source_spct(w.length = 300:305, s.e.irrad = 1,
                          comment = "This is a comment")
comment(my.cm.spct)

## [1] "This is a comment"

Metadata attributes

Spectral objects have several attributes used to store metadata, such as the time unit used or type of spectral quantity. Some attributes are meaningful for all the classes of spectra defined in the package. These are time of measurement using attribute "when.measured", place of measurement using attribute "where.measured", a user supplied label using attribute "what.measured", and free-text comments. One can set and get comments stored in spectra by means of base R’s comment() and comment() <- functions. Some of the functions in this package append additional information to comments or merge comments.

Functions setWhenMeasured() and getWhenMeasured() are used for setting or getting a date as a POSIXct value. This format is compatible with many functions from package lubridate.

my.spct <- sun.spct
setWhenMeasured(my.spct, NULL)
getWhenMeasured(my.spct)

## [1] NA

setWhenMeasured(my.spct, ymd_hms("2015-10-31 22:55:00", tz = "EET"))
getWhenMeasured(my.spct)

## [1] "2015-10-31 20:55:00 UTC"

Functions setWhereMeasured() and getWhereMeasured() are used for setting or getting a geocode as a data.frame value. This format is compatible with function geocode() from package ggmap. It is also possible, to simply pass latitude and longitude coordinates, as shown below. The returned value is always a data frame with columns "lon" and "lat".

setWhereMeasured(my.spct, NULL)
getWhereMeasured(my.spct)

##   lon lat
## 1  NA  NA

setWhereMeasured(my.spct, lat = 60, lon = -10)
getWhereMeasured(my.spct)

##   lon lat
## 1 -10  60

getWhereMeasured(my.spct)$lon

## [1] -10

my.spct

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 20:55:00 UTC 
## Measured at 60 N, -10 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

Functions setWhatMeasured() and getWhatMeasured() are used for setting or getting a text value.

setWhatMeasured(my.spct, "something")
getWhatMeasured(my.spct)

## [1] "something"

my.spct

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: something 
## Measured on 2015-10-31 20:55:00 UTC 
## Measured at 60 N, -10 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

Similar functions exist for other attributes which are not shared by all spectral classes. Several other attributes of different spectral objects can be used to store metadata in a consistent way. One example is the time unit used to express spectral irradiance. Functions are available for querying and setting the state if these attributes. is_ functions return a logical value, and get functions return the values of the attributes themselves. In addition set functions can be used to set the value attributes. Several of the set functions are very rarely needed in user code, as these attributes are set during construction or as a side effect of applying other functions and/or operators to the objects. Function setBSWFUsed() and other set functions for attributes are examples of those useful to programmers extending the package, but only exceptionally to users. One exception is the case when a wrong value has been assigned by mistake and needs to be overwritten.

For example function is_effective() returns TRUE if the spectral data has been weighted with a BSWF. The corresponding getBSWFUsed() function can be used, in this case to retrieve the name of the BSWF that was used when generating the data. Here we demonstrate with one example, where we use two different waveband objects—constructed on-the-fly with constructor function—, defining a range of wavelengths.

is_effective(sun.spct)

## [1] FALSE

is_effective(sun.spct * waveband(c(400, 700)))

## [1] FALSE

Sometimes it may be desired to change the time unit used for expressing spectral irradiance or spectral response, and this can be achieved with the conversion function convertTimeUnit. This function both converts spectral data to the new unit of expression and sets the time.unit attribute, preserving the validity of the data object.

ten.minutes.spct <-
  convertTimeUnit(sun.spct, time.unit = duration(10, "minutes"))
ten.minutes.spct

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 600s (~10 minutes)
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

getTimeUnit(ten.minutes.spct)

## [1] "600s (~10 minutes)"

Classes

The package defines several classes intended to be used to store collections of different types of spectral data. They are all derived from generic_mspct, which in turn is derived from list. Table 3 lists them.

Table 3. Classes for collections of spectral objects. Objects of class generic_mspct can have member objects of any class derived from generic_spct and can be heterogeneous. Attributes can be queried and set with the normal R methods attr and attributes as well as with functions defined in this package. See table 1 for the attributes used in individual member spectra of collections.

Objects of these classes, except for those of class generic_mspct, can contain members belonging to a single class of spectra. Being all other spectral object classes derived from generic_spct, generic_mspct objects can contain heterogeneous collections of spectra. In all cases, there are no restrictions on the lengths, wavelength range and/or wavelength step size, or attributes other than class of the contained spectra. Mimicking R’s arrays and matrices, a dim attribute is always present and dim methods are provided. These allows the storage of time series of spectral data, or (hyper)spectral image data, or even higher dimensional spectral data. The handling of 1D and 2D spectral collections is already implemented in the summary methods. Handling of 3D and higher dimensional data can be implemented in the future without changing the class definitions. By having implemented dim, also methods ncol and nrow are available as they use dim internally. Array-like subscripting is not implemented.

Construction

two_suns.mspct <- source_mspct(list(sun1 = sun.spct, sun2 = sun.spct))
two_suns.mspct

## Object: source_mspct [2 x 1]
## --- Member: sun1 ---
## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows
## --- Member: sun2 ---
## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows
## 
## --- END ---

mixed.mspct <- generic_mspct(list(filter = clear.spct, source = sun.spct))
class(mixed.mspct)

## [1] "generic_mspct" "list"

lapply(mixed.mspct, class_spct)

## $filter
## [1] "filter_spct"  "generic_spct"
## 
## $source
## [1] "source_spct"  "generic_spct"

two_gen.mspct <- as.generic_mspct(two_suns.mspct)
class(two_gen.mspct)

## [1] "generic_mspct" "list"

str(two_gen.mspct, max.level = 1, give.attr = FALSE)

## List of 2
##  $ sun1:Classes 'source_spct', 'generic_spct', 'tbl_df', 'tbl' and 'data.frame': 522 obs. of  3 variables:
##  $ sun2:Classes 'source_spct', 'generic_spct', 'tbl_df', 'tbl' and 'data.frame': 522 obs. of  3 variables:

one_sun.mspct <- as.source_mspct(sun.spct)
class(one_sun.mspct)

## [1] "source_mspct"  "generic_mspct" "list"

str(one_sun.mspct, max.level = 1, give.attr = FALSE)

## List of 1
##  $ spct_1:Classes 'source_spct', 'generic_spct', 'tbl_df', 'tbl' and 'data.frame':   522 obs. of  3 variables:

x <- matrix(1:100, ncol = 2)
wl <- 501:550 # wavelengths in nanometres
as.filter_mspct(x, wl, "Tpc")

## Object: filter_mspct [1 x 2]
## --- Member: spct_1 ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length    Tfr
##      <dbl>  <dbl>
## 1     501. 0.0100
## 2     502. 0.0200
## 3     503. 0.0300
## 4     504. 0.0400
## # ... with 46 more rows
## --- Member: spct_2 ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length   Tfr
##      <dbl> <dbl>
## 1     501. 0.510
## 2     502. 0.520
## 3     503. 0.530
## 4     504. 0.540
## # ... with 46 more rows
## 
## --- END ---

as.filter_mspct(x, wl, "Tpc", spct.names = c("A", "B"))

## Object: filter_mspct [1 x 2]
## --- Member: A ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length    Tfr
##      <dbl>  <dbl>
## 1     501. 0.0100
## 2     502. 0.0200
## 3     503. 0.0300
## 4     504. 0.0400
## # ... with 46 more rows
## --- Member: B ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length   Tfr
##      <dbl> <dbl>
## 1     501. 0.510
## 2     502. 0.520
## 3     503. 0.530
## 4     504. 0.540
## # ... with 46 more rows
## 
## --- END ---

xrow <- matrix(1:100, nrow = 2, byrow = TRUE)
as.filter_mspct(xrow, wl, "Tpc")

## Object: filter_mspct [1 x 2]
## --- Member: spct_1 ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length    Tfr
##      <dbl>  <dbl>
## 1     501. 0.0100
## 2     502. 0.0200
## 3     503. 0.0300
## 4     504. 0.0400
## # ... with 46 more rows
## --- Member: spct_2 ---
## Object: filter_spct [50 x 2]
## Wavelength range 501 to 550 nm, step 1 nm 
## 
## # A tibble: 50 x 2
##   w.length   Tfr
##      <dbl> <dbl>
## 1     501. 0.510
## 2     502. 0.520
## 3     503. 0.530
## 4     504. 0.540
## # ... with 46 more rows
## 
## --- END ---

two_suns.mat <- as.matrix(two_suns.mspct, "s.e.irrad")
class(two_suns.mat)

## [1] "matrix"

dim(two_suns.mat)

## [1] 522   2

head(dimnames(two_suns.mat)$spct)

## [1] "sun1" "sun2"

head(dimnames(two_suns.mat)$w.length)

## [1] "280"              "280.923076923077" "281.846153846154"
## [4] "282.769230769231" "283.692307692308" "284.615384615385"

head(attr(two_suns.mat, "w.length"))

## [1] 280.0000 280.9231 281.8462 282.7692 283.6923 284.6154

two_suns.row_mat <- as.matrix(two_suns.mat, "s.e.irrad", byrow = TRUE)
class(two_suns.row_mat)

## [1] "matrix"

dim(two_suns.row_mat)

## [1] 522   2

head(dimnames(two_suns.row_mat)$spct)

## [1] "sun1" "sun2"

head(attr(two_suns.row_mat, "w.length"))

## [1] 280.0000 280.9231 281.8462 282.7692 283.6923 284.6154

two_suns.spct <- rbindspct(list(a = sun.spct, b = sun.spct / 2))
two_suns.spct

## Object: source_spct [1,044 x 4]
## containing 2 spectra in long form
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## a label: sunlight, simulated
## b label: sunlight, simulated 
## a measured on 2010-06-22 09:51:00 UTC
## b measured on 2010-06-22 09:51:00 UTC 
## a measured at 60.2091078 N, 24.9647355 E
## b measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 1,044 x 4
##   w.length s.e.irrad spct.idx s.q.irrad
##      <dbl>     <dbl> <fct>        <dbl>
## 1     280.        0. a               0.
## 2     281.        0. a               0.
## 3     282.        0. a               0.
## 4     283.        0. a               0.
## # ... with 1,040 more rows

subset2mspct(two_suns.spct)

## Object: source_mspct [2 x 1]
## --- Member: a ---
## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
## *    <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows
## --- Member: b ---
## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
## *    <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows
## 
## --- END ---

test1.df <- data.frame(w.length = rep(200:210, 2),
                       s.e.irrad = rep(c(1, 2), c(11, 11)),
                       spectrum = factor(rep(c("A", "B"), c(11,11))))
subset2mspct(test1.df, member.class = "source_spct", idx.var = "spectrum")

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
## *    <int>     <dbl>
## 1      200        1.
## 2      201        1.
## 3      202        1.
## 4      203        1.
## # ... with 7 more rows
## --- Member: B ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
## *    <int>     <dbl>
## 1      200        2.
## 2      201        2.
## 3      202        2.
## 4      203        2.
## # ... with 7 more rows
## 
## --- END ---

subset2mspct(test1.df, member.class = "source_spct", idx.var = "spectrum",
             time.unit = "day")

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 86400s (~1 days)
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
## *    <int>     <dbl>
## 1      200        1.
## 2      201        1.
## 3      202        1.
## 4      203        1.
## # ... with 7 more rows
## --- Member: B ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 86400s (~1 days)
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
## *    <int>     <dbl>
## 1      200        2.
## 2      201        2.
## 3      202        2.
## 4      203        2.
## # ... with 7 more rows
## 
## --- END ---

setSourceSpct(test1.df, multiple.wl = 2L)
test1.df

## Object: source_spct [22 x 3]
## containing 2 spectra in long form
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 22 x 3
##   w.length s.e.irrad spectrum
##      <int>     <dbl> <fct>   
## 1      200        1. A       
## 2      201        1. A       
## 3      202        1. A       
## 4      203        1. A       
## # ... with 18 more rows

test2.df <- data.frame(w.length = 200:210, A = 1, B = 2, z = "A")
split2source_mspct(test2.df)

## Warning in split2mspct(x = x, member.class = "source_spct", spct.data.var =
## spct.data.var, : Skipping non-numeric column in x: z

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      200        1.
## 2      201        1.
## 3      202        1.
## 4      203        1.
## # ... with 7 more rows
## --- Member: B ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.e.irrad
##      <int>     <dbl>
## 1      200        2.
## 2      201        2.
## 3      202        2.
## 4      203        2.
## # ... with 7 more rows
## 
## --- END ---

split2source_mspct(test2.df, spct.data.var = "s.q.irrad")

## Warning in split2mspct(x = x, member.class = "source_spct", spct.data.var =
## spct.data.var, : Skipping non-numeric column in x: z

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.q.irrad
##      <int>     <dbl>
## 1      200        1.
## 2      201        1.
## 3      202        1.
## 4      203        1.
## # ... with 7 more rows
## --- Member: B ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 11 x 2
##   w.length s.q.irrad
##      <int>     <dbl>
## 1      200        2.
## 2      201        2.
## 3      202        2.
## 4      203        2.
## # ... with 7 more rows
## 
## --- END ---

split2source_mspct(test2.df, spct.data.var = "s.q.irrad", time.unit = "day")

## Warning in split2mspct(x = x, member.class = "source_spct", spct.data.var =
## spct.data.var, : Skipping non-numeric column in x: z

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 86400s (~1 days)
## 
## # A tibble: 11 x 2
##   w.length s.q.irrad
##      <int>     <dbl>
## 1      200        1.
## 2      201        1.
## 3      202        1.
## 4      203        1.
## # ... with 7 more rows
## --- Member: B ---
## Object: source_spct [11 x 2]
## Wavelength range 200 to 210 nm, step 1 nm 
## Time unit 86400s (~1 days)
## 
## # A tibble: 11 x 2
##   w.length s.q.irrad
##      <int>     <dbl>
## 1      200        2.
## 2      201        2.
## 3      202        2.
## 4      203        2.
## # ... with 7 more rows
## 
## --- END ---

Conversion into a “wide” data frame

Sometimes, when exporting spectral data we may need to convert a collection of spectra into an untidy or wide form data frame. In the example below we use a collection with only two member spectra, but join_mspct() can handle collections of any length.

my.mspct <- source_mspct(list(sun1 = sun.spct, sun2 = sun.spct * 2))
my.df <- join_mspct(my.mspct)
head(my.df)

##   w.length sun1 sun2
## 1 280.0000    0    0
## 2 280.9231    0    0
## 3 281.8462    0    0
## 4 282.7692    0    0
## 5 283.6923    0    0
## 6 284.6154    0    0

Querying the class

is. functions are defined for all the new classes. R’s class method can also be used.

is.source_mspct(two_suns.mspct)

## [1] TRUE

class(two_suns.mspct)

## [1] "source_mspct"  "generic_mspct" "list"

In addition to using class to query the class of the collection, we can use base R’s lapply together with class or class_spct to query the class of each of the members of the collection.

is.filter_mspct(mixed.mspct)

## [1] FALSE

is.any_mspct(mixed.mspct)

## [1] TRUE

class(mixed.mspct)

## [1] "generic_mspct" "list"

lapply(mixed.mspct, class_spct)

## $filter
## [1] "filter_spct"  "generic_spct"
## 
## $source
## [1] "source_spct"  "generic_spct"

lapply(mixed.mspct, class)

## $filter
## [1] "filter_spct"  "generic_spct" "tbl_df"       "tbl"         
## [5] "data.frame"  
## 
## $source
## [1] "source_spct"  "generic_spct" "tbl_df"       "tbl"         
## [5] "data.frame"

Extract, replace and combine

R’s extraction and replacement methods have specializations for collections of spectra and can be used with the same syntax and functionality as for R lists. However they test the class and validity of the returned objects and replacement members.

# not run as this triggers an error when building the vignette with 'devtools'
two_suns.mspct[1]
two_suns.mspct[1:2]

Avoid code like that in the chunk bellow. Collections of spectra are named lists, consequently assigning by position as shown here swaps the values without swapping the names of the slots!

# not run as this triggers an error when building the vignette with 'devtools'
two_suns.mspct[1:2] <- two_suns.mspct[2:1]

two_suns.mspct[[1]]

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

two_suns.mspct$sun1

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

two_suns.mspct[["sun1"]]

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

two_suns.mspct[["sun1"]] <- sun.spct * 2
two_suns.mspct[["sun2"]] <- NULL
two_suns.mspct

## Object: source_mspct [1 x 1]
## --- Member: sun1 ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

As with R’s list objects, can combine collections of spectra with method c() but we can not create new collections from individual spectra using this method.

c(two_suns.mspct, mixed.mspct)

## Object: generic_mspct [3 x 1]
## --- Member: sun1 ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: filter ---
## Object: filter_spct [4 x 2]
## Wavelength range 100 to 5000 nm, step 1 to 4898 nm 
## Label: theoretical fully transparent object 
## 
## # A tibble: 4 x 2
##   w.length   Tfr
##      <dbl> <dbl>
## 1     100.    1.
## 2     101.    1.
## 3    4999.    1.
## 4    5000.    1.
## --- Member: source ---
## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows
## 
## --- END ---

Transform or apply functions

For our apply functions we follow the naming convention used in package plyr, but using ms as prefix for _mspct objects. The apply functions implemented in the ‘photobiology’ package are msmsply, msdply, mslply and msaply which both accept a collection of spectra as first argument and return a collection of spectra, a data frame, a list, or an array respectively (see Table 4).

Table 4. Apply functions for collections of spectra. Key: v., value returned by apply function; f.v., value returned by the applied function (argument .fun). In the table generic_mspct and generic_spct indicate objects of these classes or any class derived from them. The exact class of the collection of spectra object returned will be determined by the class(es) of the values returned by the applied function.

Functions msmsply(), msdply and mslply can be used to apply a function to each member spectrum in a collection. The apply function to use depends on the return value of the applied function.

In the case of msmsply() the applied function is expected to return a transformed spectrum as another object of class generic_spct or a class derived from it. The value returned by msmsply is a collection of spectra, of a type determined by the class(es) of the member spectra in the new collection.

We start with a simple example in which we add a constant to each spectrum in the collection

two.mspct <- source_mspct(list(A = sun.spct * 1, B = sun.spct * 2))
msmsply(two.mspct, `+`, 0.1)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.     0.100
## 2     281.     0.100
## 3     282.     0.100
## 4     283.     0.100
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.     0.100
## 2     281.     0.100
## 3     282.     0.100
## 4     283.     0.100
## # ... with 518 more rows
## 
## --- END ---

and continue with a more complex example in which we trim each spectrum

msmsply(two.mspct, trim_wl, range = c(281, 500), fill = NA)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [525 x 2]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 525 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.       NA 
## 2     281.       NA 
## 3     281.       NA 
## 4     281.        0.
## # ... with 521 more rows
## --- Member: B ---
## Object: source_spct [525 x 2]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 525 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.       NA 
## 2     281.       NA 
## 3     281.       NA 
## 4     281.        0.
## # ... with 521 more rows
## 
## --- END ---

In the second example we pass two arguments by name to the applied function. The number of arguments is not fixed, but the spectrum will be always passed as the first argument to the function.

In the case of msdply() the applied function is expected to return an R object of the same length for each of the member spectra.

msdply(two.mspct, max)

## # A tibble: 2 x 2
##   spct.idx max.wl
##   <fct>     <dbl>
## 1 A          800.
## 2 B          800.

ranges.df <- msdply(two.mspct, range)
ranges.df

## # A tibble: 2 x 3
##   spct.idx min.wl max.wl
##   <fct>     <dbl>  <dbl>
## 1 A          280.   800.
## 2 B          280.   800.

cat(comment(ranges.df))

## Applied function: 'range'.

msdply(two.mspct, range, na.rm = TRUE)

## # A tibble: 2 x 3
##   spct.idx min.wl max.wl
##   <fct>     <dbl>  <dbl>
## 1 A          280.   800.
## 2 B          280.   800.

In the case of mslply() the applied function is expected to return an R object of any length, possibly variable among members.

str(mslply(two.mspct, names))

## List of 2
##  $ A: chr [1:2] "w.length" "s.e.irrad"
##  $ B: chr [1:2] "w.length" "s.e.irrad"
##  - attr(*, "comment")= chr "Applied function: 'names'.\n"

In the case of msaply() the applied function is expected to return an R object of length 1, although a list with dimensions will be returned for longer return values.

str(msaply(two.mspct, max))

##  atomic [1:2] 800 800
##  - attr(*, "comment")= chr "Applied function: 'max'.\n"

str(msaply(two.mspct, range))

##  num [1:2, 1:2] 280 280 800 800
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:2] "1" "2"
##  - attr(*, "comment")= chr "Applied function: 'range'.\n"

For the most common cases for which one would use the apply functions described in the previous section methods and functions for operations on collections of spectra are defined in the package. For example the following statement is equivalent to the second example in the previous section. These are described in a later section and listed in Table 9.

Convolution

By convolution we normally mean the multiplication value by value at matching wavelengths of two spectra. The function described in this section facilitates this and similar operations among collections of spectra. An example use case could be the convolution of spectral irradiance by spectral transmittance for all combinations of light sources and filters in a collection of source spectra and a collection of filter spectra.

Default operator (or function) is that for multiplication, either one or both of the two first arguments must be a collection of spectra. When only one argument is a collection of spectra, the other one can be a spectrum, or even a numeric vector. For multiplication the order of the operands does not affect the returned value. With operators or functions for non-transitive operations the order does matter.

convolve_each(two.mspct, sun.spct)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

convolve_each(sun.spct, two.mspct)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

another_two.mspct <- two.mspct
names(another_two.mspct) <- c("a", "b")
convolve_each(another_two.mspct, two.mspct)

## Object: source_mspct [2 x 2]
## --- Member: a_A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: a_B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: b_A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: b_B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

The function convolve_each will use other operators or functions and even pass additional named arguments when these are supplied as arguments.

convolve_each(two.mspct, sun.spct, oper = `+`)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

Metadata attributes

Some of the set and get functions used with attributes have method definitions for collections of spectra. Some examples follow.

getWhenMeasured(two.mspct)

## # A tibble: 2 x 2
##   spct.idx when.measured      
##   <fct>    <dttm>             
## 1 A        2010-06-22 09:51:00
## 2 B        2010-06-22 09:51:00

setWhenMeasured(two.mspct, ymd("2015-10-31", tz = "EET"))
getWhenMeasured(two.mspct)

## # A tibble: 2 x 2
##   spct.idx when.measured      
##   <fct>    <dttm>             
## 1 A        2015-10-30 22:00:00
## 2 B        2015-10-30 22:00:00

setWhenMeasured(two.mspct,
                list(ymd_hm("2015-10-31 10:00", tz = "EET"),
                     ymd_hm("2015-10-31 11:00", tz = "EET")))
getWhenMeasured(two.mspct)

## # A tibble: 2 x 2
##   spct.idx when.measured      
##   <fct>    <dttm>             
## 1 A        2015-10-31 08:00:00
## 2 B        2015-10-31 09:00:00

two.mspct

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 08:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 09:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

Other methods available are getWhereMeasured and setWhereMeasured, and getWhatMeasured and setWhatMeasured.

Functions when.measured2tb(), geocode2tb(), lon2tb(), lat2tb() and what.measured2tb() extract these same attributes from collection members into a tibble or data frame. In contrast to the “get” methods described above, if an existing data frame or tibble with a matching number of rows is passed as second argument, the values for the attribute are saved into a new column appended at the right edge of the tibble or data frame.

when_measured2tb(two.mspct)

## # A tibble: 2 x 2
##   spct.idx when.measured      
##   <fct>    <dttm>             
## 1 A        2015-10-31 08:00:00
## 2 B        2015-10-31 09:00:00

By default the new column is named after the name of the attribute, but this default can be overridden by the user.

when_measured2tb(two.mspct, col.names = c(when.measured = "time"))

## # A tibble: 2 x 2
##   spct.idx time               
##   <fct>    <dttm>             
## 1 A        2015-10-31 08:00:00
## 2 B        2015-10-31 09:00:00

Function add_attr2tb() adds one or more columns with attributes to a tibble or data frame. We here also demonstrate that because the data frame object is passed to the first positional argument, we can use a pipe.

q_irrad(two.mspct) %>%
  add_attr2tb(two.mspct, 
              col.names = c("lon", "lat", "when.measured"))

## # A tibble: 2 x 5
##   spct.idx q_irrad_Total   lon   lat when.measured      
##   <fct>            <dbl> <dbl> <dbl> <dttm>             
## 1 A              0.00126  25.0  60.2 2015-10-31 08:00:00
## 2 B              0.00251  25.0  60.2 2015-10-31 09:00:00

We can set the desired names for the columns if we wish them to be something else than the default.

q_irrad(two.mspct) %>%
  add_attr2tb(two.mspct, 
              col.names = c(lon = "longitude", 
                            lat = "latitude", 
                            when.measured = "time"))

## # A tibble: 2 x 5
##   spct.idx q_irrad_Total longitude latitude time               
##   <fct>            <dbl>     <dbl>    <dbl> <dttm>             
## 1 A              0.00126      25.0     60.2 2015-10-31 08:00:00
## 2 B              0.00251      25.0     60.2 2015-10-31 09:00:00

Construction

When defining a waveband which uses a SWF, a function can be supplied either based on energy effectiveness, on photon effectiveness, or one function for each one. If only one function is supplied the other one is built automatically, but if performance is a concern it is better to provide two separate functions. Another case when you might want to enter the same function twice, is if you are using an absorptance spectrum as SWF, as the percent of radiation absorbed will be independent of whether photon or energy units are used for the spectral irradiance.

To create a waveband object we use constructor function waveband, and optionally giving a name to it. We will use these objects in many of the examples below, so you will need to run the code chunk bellow to be able to reproduce those examples. It should be noted that waveband constructors for the most frequently used wavelength-range definitions are provided by package ‘photobiologyWavebands’.

PAR.wb <- waveband(c(400, 700), wb.name = "PAR")
UVA.wb <- waveband(c(315, 400), wb.name = "UVA")
UVB.wb <- waveband(c(280, 315), wb.name = "UVB")
UVC.wb <- waveband(c(100, 280), wb.name = "UVC")
UV.wb  <- waveband(c(100, 400), wb.name =  "UV")
UV_bands.lst <- list(UVC.wb, UVB.wb, UVA.wb)

When including a BSWF, we can supply, one or two versions of functions returning the weights as a function of wavelength. Several such functions are defined in package ‘photobiologyWavebands’ as well as waveband constructors using them. Here we show how a waveband can be defined based on a SWF, using the CIE definition for the erythemal spectral weighting function. Although the constructor is smart enough to derive the missing function when only one function is supplied, performance may suffer unless two performance-optimized function are provided, one for energy-based effect and a second one for photon-based effect.

CIE_e_fun <-
function(w.length){
    CIE.energy <- numeric(length(w.length))
    CIE.energy[w.length <= 298] <- 1
    CIE.energy[(w.length > 298) & (w.length <= 328)] <-
      10^(0.094*(298-w.length[(w.length > 298) & (w.length <= 328)]))
    CIE.energy[(w.length > 328) & (w.length <= 400)] <-
      10^(0.015*(139-w.length[(w.length > 328) & (w.length <= 400)]))
    CIE.energy[w.length > 400] <- 0
    return(CIE.energy)
}

CIE.wb <- waveband(c(250, 400), weight = "SWF",
                   SWF.e.fun = CIE_e_fun, SWF.norm = 298)

The first argument to waveband() does not need to be a numeric vector of length two. Any R object of a class that supplies a range() method definition that can be interpreted as a range of wavelengths in nanometres can be used. As a consequence, when wanting to construct a waveband covering the whole range of a spectrum one can simply supply the spectrum as argument, or to construct an non-weighed waveband which covers exactly the same range of wavelengths as an existing effective (weighted) waveband, one can supply a waveband object as an argument.

waveband(sun.spct)

## Total 
## low (nm) 280 
## high (nm) 800 
## weighted none

An “empty” waveband is returned by some functions as a “null” value.

waveband()

## range.NA.NA 
## low (nm) NA 
## high (nm) NA 
## weighted none

Querying the class

The function is.waveband can the used to query any R object. This function returns a logical value.

is.waveband(PAR.wb)

## [1] TRUE

Above, we demonstrate that PAR.wb is a waveband object, the function photobiologyWavebands::PAR() is a waveband constructor returning a waveband object. See package ‘photobiologyWavebands’ for details on pre-defined waveband constructors for frequently used wavelength ranges and biological spectral weighting functions (BSWFs).

Retrieving properties

The function is_effective can the used to query any R object.

is_effective(waveband(c(400,500)))

## [1] FALSE

Construction

wavebands <- list(waveband(c(300,400)), waveband(c(400,500)))
wavebands

## [[1]]
## range.300.400 
## low (nm) 300 
## high (nm) 400 
## weighted none 
## 
## [[2]]
## range.400.500 
## low (nm) 400 
## high (nm) 500 
## weighted none

split_bands(c(200, 225, 300))

## $wb1
## range.200.225 
## low (nm) 200 
## high (nm) 225 
## weighted none 
## 
## $wb2
## range.225.300 
## low (nm) 225 
## high (nm) 300 
## weighted none

split_bands(c(200, 225, 300), length.out = 2)

## $wb1
## range.200.250 
## low (nm) 200 
## high (nm) 250 
## weighted none 
## 
## $wb2
## range.250.300 
## low (nm) 250 
## high (nm) 300 
## weighted none

split_bands(sun.spct, length.out = 2)

## $wb1
## range.280.540 
## low (nm) 280 
## high (nm) 540 
## weighted none 
## 
## $wb2
## range.540.800 
## low (nm) 540 
## high (nm) 800 
## weighted none

split_bands(PAR.wb, length.out = 2)

## $wb1
## range.400.550 
## low (nm) 400 
## high (nm) 550 
## weighted none 
## 
## $wb2
## range.550.700 
## low (nm) 550 
## high (nm) 700 
## weighted none

split_bands(c(200, 800), length.out = 3)

## $wb1
## range.200.400 
## low (nm) 200 
## high (nm) 400 
## weighted none 
## 
## $wb2
## range.400.600 
## low (nm) 400 
## high (nm) 600 
## weighted none 
## 
## $wb3
## range.600.800 
## low (nm) 600 
## high (nm) 800 
## weighted none

split_bands(list(A = c(200, 300), B = c(400, 500), C = c(250, 350)))

## $A
## range.200.300 
## low (nm) 200 
## high (nm) 300 
## weighted none 
## 
## $B
## range.400.500 
## low (nm) 400 
## high (nm) 500 
## weighted none 
## 
## $C
## range.250.350 
## low (nm) 250 
## high (nm) 350 
## weighted none

split_bands(list(c(100, 150, 200), c(800, 825)))

## $wb.a
## range.100.150 
## low (nm) 100 
## high (nm) 150 
## weighted none 
## 
## $<NA>
## range.150.200 
## low (nm) 150 
## high (nm) 200 
## weighted none 
## 
## $wb.b
## range.800.825 
## low (nm) 800 
## high (nm) 825 
## weighted none

split_bands(UV_bands.lst, length.out  =  2)

## $wb.a
## range.100.190 
## low (nm) 100 
## high (nm) 190 
## weighted none 
## 
## $<NA>
## range.190.280 
## low (nm) 190 
## high (nm) 280 
## weighted none 
## 
## $wb.b
## range.280.297.5 
## low (nm) 280 
## high (nm) 298 
## weighted none 
## 
## $<NA>
## range.297.5.315 
## low (nm) 298 
## high (nm) 315 
## weighted none 
## 
## $wb.c
## range.315.357.5 
## low (nm) 315 
## high (nm) 358 
## weighted none 
## 
## $<NA>
## range.357.5.400 
## low (nm) 358 
## high (nm) 400 
## weighted none

split_bands(list(c(100, 150, 200), c(800, 825)), length.out = 1)

## $wb.a
## range.100.200 
## low (nm) 100 
## high (nm) 200 
## weighted none 
## 
## $wb.b
## range.800.825 
## low (nm) 800 
## high (nm) 825 
## weighted none

Printing

The print() method for spectra is based on the method defined in package ‘tibble’, consequently, it is possible to use the options from this package to control printing. In the code chunk below, tibble.print_max, the number of rows in the spectral object above which only tibble.print_min rows are printed, are both set to 5, instead of the default 20 and 10, to avoid excessive clutter in our examples.

options(tibble.print_max = 4)
options(tibble.print_min = 4)

For explicit calls to print() its argument n can be used to control the number of lines printed. If n is set to Inf the whole spectrum is always printed. The output differs from that of the print() method from package ‘dplyr’ in that additional metadata specific to spectra are shown.

print(sun.spct, n = 3)

Specialized print() methods for collections of spectra and for waveband objects are also defined.

Summary

The summary() method for spectra is based on base R’s summary() method for data frames, and accepts the same arguments. The main difference is that the attributes containing metadata and dimensions of the original spectrum object are copied to the summary object.

summary(sun.spct)

Specialized print() methods for summaries of spectra are defined. The output differs from that of the print() method from base R in that additional metadata specific to spectra are shown.

Handling NAs

Functions na.omit() and na.exclude are implemented for all spectral classes. These methods test for NAs only the spectral data, not wavelength. They set the "na.action" attribute in the same way as the corresponding methods for data frames. In the case of na.fail(), na.pass() and na.action(), the methods from base R, can be used with spectra.

na.omit(sun.spct)

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

na.exclude(sun.spct)

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

Binary operators

All of R’s built-in maths operators have definitions for spectra. It is possible to sum, subtract, multiply and divide spectra. These operators can be used even if the spectral data is on different arbitrary sets of wavelengths. Operators by default return values expressed in energy units. Only certain operations are meaningful for a given combination of objects belonging to different classes, and meaningless combinations return NA also issuing a warning (see Table 5). By default operations are carried out on spectral energy irradiance for source_spct objects and transmittance for filter_spct objects.

Table 5. Binary operators and their operands. Validity and class of result. All operations marked \Y' are allowed, those marked’ are forbidden and return NA and issue a warning. Operators %/% and %% follow /.

sun.spct * sun.spct

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

When meaningful, operations between different spectra are also allowed. For example, it is possible to simulate the effect of a filter on a light source by multiplying (or convolving) the two spectra.

sun.spct * polyester.spct

## Object: source_spct [533 x 2]
## Wavelength range 280 to 800 nm, step 0.07692308 to 1 nm 
## Time unit 1s
## 
## # A tibble: 533 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     281.        0.
## 4     282.        0.
## # ... with 529 more rows

If we have two layers of the filter, this can be approximated using either of these two statements.

sun.spct * polyester.spct * polyester.spct

## Object: source_spct [533 x 2]
## Wavelength range 280 to 800 nm, step 0.07692308 to 1 nm 
## Time unit 1s
## 
## # A tibble: 533 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     281.        0.
## 4     282.        0.
## # ... with 529 more rows

sun.spct * polyester.spct^2

## Object: source_spct [533 x 2]
## Wavelength range 280 to 800 nm, step 0.07692308 to 1 nm 
## Time unit 1s
## 
## # A tibble: 533 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     281.        0.
## 4     282.        0.
## # ... with 529 more rows

Operators are also defined for operations between a spectrum and a numeric vector (with normal recycling).

sun.spct * 2

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

2 * sun.spct

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

sun.spct * c(0,1)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

There is one special case, for chroma_spct: if the numeric operand has length three, containing three named values x, y and z, the corresponding value is used for each of the chromaticity columns in the chroma_spct. Un-named values or differently named values are not treated specially.

Operators are also defined for operations between an spectrum and a waveband object. The next to code chunks demonstrate how the class of the result depends on whether the waveband object describes a range of wavelengths or a range of wavelengths plus a BSWF.

sun.spct * UVB.wb

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

sun.spct * CIE.wb

And of course these operations can be combined into more complex statements, including parentheses, when needed. The example below estimates the difference in effective spectral irradiance according to the CIE98 definition, between sunlight and sunlight filtered with a polyester film. Of course, the result is valid only for the solar spectral data used, which corresponds to Southern Finland.

sun.spct * CIE.wb - sun.spct * polyester.spct * CIE.wb

## Object: source_spct [133 x 2]
## Wavelength range 280 to 400 nm, step 0.07692308 to 1 nm 
## Time unit 1s
## Data weighted using 'range.250.400.wtd' BSWF
## 
## # A tibble: 133 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     281.        0.
## 4     282.        0.
## # ... with 129 more rows

Unary operators and maths functions

Many common maths functions, as well as unary minus and plus, are implemented for spectral objects (see Table 6).

Table 6. Unary operators and maths functions for spectra. Classes for which they are implemented and class of the result. All operations marked Y are allowed, those marked N are not implemented and return NA and issue a warning. Additional supported functions: log2, log10, sin, cos, tan, asin, acos, atan, sinpi, cospi, tanpi, signif, floor, ceiling, trunc, sign, abs.

-sun.spct

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

sqrt(sun.spct)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

Options

Table 7 lists all the recognized options affecting maths operators and functions, and their default values. Within the suite all functions have a default value which is used when the options are undefined. Options are set using base R’s function options, and queried with functions options and getOption.

Table 7. Options used in the ‘r4photobiology suite’ and recognized by methods, operators and functions in the ‘photobiology’ package. Option names, accepted and default values, and the purpose of the options are given.

The behaviour of the operators defined in this package depends on the value of two global options. For example, if we would like the operators to operate on spectral photon irradiance and return spectral photon irradiance instead of spectral energy irradiance, this behaviour can be set, and will remain active until unset or reset. It is possible to change options using base R’s function options() as shown in the next code chunk. The other options listed in the Table above can be set similarly, while to unset any option, they can be given a NULL value.

options(photobiology.radiation.unit = "photon")
sun.spct * UVB.wb

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.q.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

options(photobiology.radiation.unit = "energy")
sun.spct * UVB.wb

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

However using convenience functions is easier. The chunk above can be rewritten as below.

photon_as_default()
sun.spct * UVB.wb

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.q.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

energy_as_default()
sun.spct * UVB.wb

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

Furthermore, it is possible to temporarily change the options for the evaluation of a single, possibly compound, R expression using a different syntax, reminiscent of that of R’s with().

using_photon(sun.spct * UVB.wb)

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.q.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

using_energy(sun.spct * UVB.wb)

## Object: source_spct [37 x 2]
## Wavelength range 280 to 315 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## 
## # A tibble: 37 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 33 more rows

Manipulating spectra

Sometimes, especially for plotting, we may want to row-bind spectra. When the aim is that the returned object retains its class and other attributes like the time unit. Package ‘photobiology’ provides function rbinspct for row-binding spectra, with the necessary checks for consistency of the bound spectra.

# STOPGAP
shade.spct <- sun.spct

By default an ID factor named spct.idx is added allow to identify the source of the observations after the binding. If the supplied list has named members, then these names are used as factor levels. If a character value is supplied to as idfactor argument, this is used as name for the factor.

rbindspct(list(sun.spct, shade.spct))

## Object: source_spct [1,044 x 4]
## containing 2 spectra in long form
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## spct_1 label: sunlight, simulated
## spct_2 label: sunlight, simulated 
## spct_1 measured on 2010-06-22 09:51:00 UTC
## spct_2 measured on 2010-06-22 09:51:00 UTC 
## spct_1 measured at 60.2091078 N, 24.9647355 E
## spct_2 measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 1,044 x 4
##   w.length s.e.irrad spct.idx s.q.irrad
##      <dbl>     <dbl> <fct>        <dbl>
## 1     280.        0. spct_1          0.
## 2     281.        0. spct_1          0.
## 3     282.        0. spct_1          0.
## 4     283.        0. spct_1          0.
## # ... with 1,040 more rows

rbindspct(list(A = sun.spct, B = shade.spct), idfactor = "site")

## Object: source_spct [1,044 x 4]
## containing 2 spectra in long form
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## A label: sunlight, simulated
## B label: sunlight, simulated 
## A measured on 2010-06-22 09:51:00 UTC
## B measured on 2010-06-22 09:51:00 UTC 
## A measured at 60.2091078 N, 24.9647355 E
## B measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 1,044 x 4
##   w.length s.e.irrad site  s.q.irrad
##      <dbl>     <dbl> <fct>     <dbl>
## 1     280.        0. A            0.
## 2     281.        0. A            0.
## 3     282.        0. A            0.
## 4     283.        0. A            0.
## # ... with 1,040 more rows

Special Extract methods for spectral objects have been implemented. These are used by default and preserve the attributes used by this package, except when the returned value is a single column from the spectral object.

sun.spct[1:10, ]

## Object: source_spct [10 x 3]
## Wavelength range 280 to 288.30769 nm, step 0.9230769 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 10 x 3
##   w.length s.e.irrad s.q.irrad
## *    <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 6 more rows

sun.spct[1:10, 1]

##  [1] 280.0000 280.9231 281.8462 282.7692 283.6923 284.6154 285.5385
##  [8] 286.4615 287.3846 288.3077

sun.spct[1:10, 1, drop = TRUE]

##  [1] 280.0000 280.9231 281.8462 282.7692 283.6923 284.6154 285.5385
##  [8] 286.4615 287.3846 288.3077

sun.spct[1:10, "w.length", drop = TRUE]

##  [1] 280.0000 280.9231 281.8462 282.7692 283.6923 284.6154 285.5385
##  [8] 286.4615 287.3846 288.3077

In contrast to trim_spct, subset never interpolates or inserts hinges. On the other hand, the subset argument accepts any logical expression and can be consequently used to do subsetting, for example, based on factors. Both subset() and trim() methods preserve attributes.

subset(sun.spct, s.e.irrad > 0.2)

## Object: source_spct [475 x 3]
## Wavelength range 324 to 800 nm, step 1 to 3 nm 
## Time unit 1s
## 
## # A tibble: 475 x 3
##   w.length s.e.irrad   s.q.irrad
## *    <dbl>     <dbl>       <dbl>
## 1     324.     0.208 0.000000562
## 2     325.     0.217 0.000000589
## 3     326.     0.277 0.000000756
## 4     327.     0.285 0.000000779
## # ... with 471 more rows

subset(sun.spct, w.length > 600)

## Object: source_spct [200 x 3]
## Wavelength range 601 to 800 nm, step 1 nm 
## Time unit 1s
## 
## # A tibble: 200 x 3
##   w.length s.e.irrad  s.q.irrad
## *    <dbl>     <dbl>      <dbl>
## 1     601.     0.630 0.00000316
## 2     602.     0.631 0.00000317
## 3     603.     0.636 0.00000321
## 4     604.     0.658 0.00000332
## # ... with 196 more rows

subset(sun.spct, c(TRUE, rep(FALSE, 99)))

## Object: source_spct [6 x 3]
## Wavelength range 280 to 779 nm, step 99 to 100 nm 
## Time unit 1s
## 
## # A tibble: 6 x 3
##   w.length s.e.irrad  s.q.irrad
## *    <dbl>     <dbl>      <dbl>
## 1     280.     0.    0.        
## 2     379.     0.413 0.00000131
## 3     479.     0.754 0.00000302
## 4     579.     0.647 0.00000313
## 5     679.     0.580 0.00000329
## 6     779.     0.471 0.00000307

R’s Extract methods $ and [[ can be used to extract whole columns. Replace methods $<- and [<- have definitions for spectral objects, which allow their safe use. They work identically to those for data frames but check the validity of the spectra after the replacement.

Conversions between radiation units

The functions e2q and q2e can be used on source spectra to convert spectral energy irradiance into spectral photon irradiance and vice versa. A second optional argument sets the action with "add" and "replace" as possible values. By default these functions use normal reference semantics.

e2q(sun.spct, "add")

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

e2q(sun.spct, "replace")

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.q.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

For filter_spct objects functions T2A and A2T allow conversion between spectral transmittance and spectral absorbance and vice versa.

Normalizing a spectrum

Function normalize permits normalizing a spectrum to a value of one at an arbitrary wavelength (nm) or to the wavelength of either the maximum or the minimum spectral value. It supports the different spectral classes, we use a source_spct object as an example.

normalize(sun.spct)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Spectral data normalized to 1 at 451 nm 
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

Which is equivalent to supplying "max" as argument to norm, it is also possible to give a range within which the maximum should be searched.

normalize(sun.spct, range = PAR.wb, norm = "max")

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Spectral data normalized to 1 at 451 nm 
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

It is also possible to normalize to an arbitrary wavelength within the range of the data, even if it is not one of the wavelength values present in the spectral object, as interpolation is used when needed.

normalize(sun.spct, norm = 600.3)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Spectral data normalized to 1 at 600.3 nm 
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

The normalization status of a spectral object can be tested with method is_normalized() and the normalization used can be recalled with method getNormalized().

my.spct <- normalize(sun.spct)
is_normalized(my.spct)

## [1] TRUE

getNormalized(my.spct)

## [1] 451

Once a spectrum is normalized, summary methods that return values in absolute units such as irrad(), will trigger an error if applied. Ratios and similar summaries that are invariant with respect to normalization can be calculated.

Applying method fscale() removes the normalization and clears the corresponding attribute where the normalization information is stored. This attribute also can be cleared with method setNormalized(), but this is rarely valid or of any use.

Rescaling a spectrum

Function fscale() rescales a spectrum by dividing each spectral data value by a value calculated with a function (f) selected by a character string (“total” or “mean”), or an actual R function which can accept the spectrum object supplied as its first argument. Additional named arguments can be also passed.

fscale(sun.spct)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Rescaled to 'mean' = 1
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

fscale(sun.spct, f = "total")

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Rescaled to 'total' = 1
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

fscale(sun.spct, range = PAR.wb, f = irrad)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Rescaled to 'a user supplied R function' = 1
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

fscale(sun.spct, range = PAR.wb, f = q_irrad, target = 800e-6)

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## Rescaled to 'a user supplied R function' = 8e-04
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

In the third example, the spectral data is rescaled so that the corresponding photosynthetically-active irradiance is equal to one.

The normalization status of a spectral object can be tested with method is_normalized() and the normalization used can be recalled with method getNormalized().

my.spct <- fscale(sun.spct)
is_scaled(my.spct)

## [1] TRUE

getScaled(my.spct)

## $multiplier
## [1] 1.932188
## 
## $f
## [1] "mean"
## 
## $range
## [1] 280 800
## 
## $target
## [1] 1

Once a spectrum is scaled, summary methods that return values in absolute units such as irrad(), will trigger a warning if applied. Ratios and similar summaries that are invariant with respect to normalization do not trigger warnings.

Applying method normalize() removes the scaling and clears the corresponding attribute where the scaling information is stored. This attribute also can be cleared with method setScaled(), and this can be useful is some cases such as when irradiance has been measured separately from the emission spectrum.

Shifting the zero of the spectral data scale

Function fshift() shifts the zero of the scale of a spectrum by subtracting from each spectral data value a value calculated with a function (f) selected by a character string (“mean”, “min” or “max”), or an actual R function which can accept the spectrum object supplied as its first argument. The range argument selects a region of the spectrum to be used as reference in the calculation of the summary.

fshift(sun.spct, range = UVB.wb, f = "mean")

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.   -0.0184
## 2     281.   -0.0184
## 3     282.   -0.0184
## 4     283.   -0.0184
## # ... with 518 more rows

fshift(sun.spct, range = c(280,290), f = "min")

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows

In the first example, the spectral data shifted so that the mean spectral irradiance becomes zero for the UV-B region. In the second example the minimum value in the range of wavelengths between 280~nm and 290~nm is used as zero reference for the scale.

Replacing off-range spectral data values

Method clean() should be used with care as off-range values stem almost always from calibration errors or measuring noise. This function allows one to replace such values, but in many cases a zero shift or rescaling could be the option to be preferred. Even when the off-range values are the result of random noise, replacing them with the boundary values can cause bias, by censoring the data. Here we create artificial off-range values by subtracting a constant from each spectrum.

clean(sun.spct - 0.01, range = c(280.5, 282))

## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.   -0.0100
## 2     281.    0.    
## 3     282.    0.    
## 4     283.   -0.0100
## # ... with 518 more rows

clean(polyester.spct - 0.053)

## Warning in range_check_Tfr(x, strict.range = strict.range): Off-range
## transmittance values [-0.050..0.873] instead of [0..1]

## Object: filter_spct [611 x 2]
## Wavelength range 190 to 800 nm, step 1 nm 
## Label: clear polyester film, 125um thick 
## 
## # A tibble: 611 x 2
##   w.length   Tfr
##      <int> <dbl>
## 1      190    0.
## 2      191    0.
## 3      192    0.
## 4      193    0.
## # ... with 607 more rows

Wavelength interpolation

Converting spectra available at a given set of wavelengths values to a different one, is frequently needed when operating with several spectra of different origin. One can increase the apparent resolution by interpolation, and reduce it by local averaging or smoothing and resampling. The same function works on all spct objects, interpolating every column except w.length and replacing in this last column the old wavelength values with the new ones supplied as argument. The optional argument fill.value control what value is assigned to wavelengths in the new data that are outside the range of the old wavelengths.

interpolate_wl(sun.spct, seq(400, 500, by = 0.1))

## Object: source_spct [1,001 x 3]
## Wavelength range 400 to 500 nm, step 0.1 nm 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 1,001 x 3
##   w.length s.e.irrad  s.q.irrad
##      <dbl>     <dbl>      <dbl>
## 1     400.     0.608 0.00000203
## 2     400.     0.610 0.00000204
## 3     400.     0.612 0.00000205
## 4     400.     0.614 0.00000205
## # ... with 997 more rows

Trimming and clipping

clip_wl(sun.spct, range = c(400, 402))

## Object: source_spct [3 x 3]
## Wavelength range 400 to 402 nm, step 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 3 x 3
##   w.length s.e.irrad  s.q.irrad
## *    <dbl>     <dbl>      <dbl>
## 1     400.     0.608 0.00000203
## 2     401.     0.626 0.00000210
## 3     402.     0.650 0.00000218

clip_wl(sun.spct, range = c(400, NA))

## Object: source_spct [401 x 3]
## Wavelength range 400 to 800 nm, step 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 401 x 3
##   w.length s.e.irrad  s.q.irrad
## *    <dbl>     <dbl>      <dbl>
## 1     400.     0.608 0.00000203
## 2     401.     0.626 0.00000210
## 3     402.     0.650 0.00000218
## 4     403.     0.621 0.00000209
## # ... with 397 more rows

clip_wl(sun.spct, range = UVA.wb)

## Object: source_spct [86 x 3]
## Wavelength range 315 to 400 nm, step 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 86 x 3
##   w.length s.e.irrad   s.q.irrad
## *    <dbl>     <dbl>       <dbl>
## 1     315.     0.113 0.000000297
## 2     316.     0.102 0.000000270
## 3     317.     0.149 0.000000394
## 4     318.     0.141 0.000000376
## # ... with 82 more rows

clip_wl(sun.spct, range = c(100, 200))

## Object: source_spct [0 x 3]
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 0 x 3
## # ... with 3 variables: w.length <dbl>, s.e.irrad <dbl>, s.q.irrad <dbl>

trim_wl(sun.spct, c(282.5, NA))

## Object: source_spct [520 x 3]
## Wavelength range 282.5 to 800 nm, step 0.2692308 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 520 x 3
##   w.length s.e.irrad s.q.irrad
## *    <dbl>     <dbl>     <dbl>
## 1     282.        0.        0.
## 2     283.        0.        0.
## 3     284.        0.        0.
## 4     285.        0.        0.
## # ... with 516 more rows

clip_wl(sun.spct, c(282.5, NA))

## Object: source_spct [519 x 3]
## Wavelength range 282.76923 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 519 x 3
##   w.length s.e.irrad s.q.irrad
## *    <dbl>     <dbl>     <dbl>
## 1     283.        0.        0.
## 2     284.        0.        0.
## 3     285.        0.        0.
## 4     286.        0.        0.
## # ... with 515 more rows

trim_wl(sun.spct, PAR.wb)

## Object: source_spct [301 x 3]
## Wavelength range 400 to 700 nm, step 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 301 x 3
##   w.length s.e.irrad  s.q.irrad
## *    <dbl>     <dbl>      <dbl>
## 1     400.     0.608 0.00000203
## 2     401.     0.626 0.00000210
## 3     402.     0.650 0.00000218
## 4     403.     0.621 0.00000209
## # ... with 297 more rows

trim_wl(sun.spct, c(281.5, NA), fill = NA)

## Object: source_spct [524 x 3]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 524 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.       NA        NA 
## 2     281.       NA        NA 
## 3     281.       NA        NA 
## 4     282.        0.        0.
## # ... with 520 more rows

trim_wl(sun.spct, c(275, NA), fill = 0)

## Object: source_spct [529 x 3]
## Wavelength range 275 to 800 nm, step 1.023182e-12 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 529 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     275.        0.        0.
## 2     276.        0.        0.
## 3     277.        0.        0.
## 4     277.        0.        0.
## # ... with 525 more rows

trim_wl(sun.spct, c(281.5, NA), fill = NA)

## Object: source_spct [524 x 3]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 524 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.       NA        NA 
## 2     281.       NA        NA 
## 3     281.       NA        NA 
## 4     282.        0.        0.
## # ... with 520 more rows

trim_wl(sun.spct, c(281.5, NA), fill = NA, use.hinges = FALSE)

## Object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.       NA        NA 
## 2     281.       NA        NA 
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 518 more rows

trim2overlap(two.mspct)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 08:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
## *    <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 09:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
## *    <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

extend2extremes(two.mspct, fill = 0)

## Object: source_mspct [2 x 1]
## --- Member: A ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 08:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## --- Member: B ---
## Object: source_spct [522 x 2]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm 
## Label: sunlight, simulated 
## Measured on 2015-10-31 09:00:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 522 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 518 more rows
## 
## --- END ---

Convolving weights

It is very instructive to look at weighted spectral data to understand how effective irradiances are calculated. Plotting effective spectral irradiance data can be very instructive when analysing the interaction of photoreceptors and ambient radiation. It can also illustrate the large effect that small measuring errors can have on the estimated effective irradiances or exposures when SWFs have a steep slope.

sun.spct * CIE.wb

## Object: source_spct [122 x 2]
## Wavelength range 280 to 400 nm, step 0.9230769 to 1 nm 
## Time unit 1s
## Data weighted using 'range.250.400.wtd' BSWF
## 
## # A tibble: 122 x 2
##   w.length s.e.irrad
##      <dbl>     <dbl>
## 1     280.        0.
## 2     281.        0.
## 3     282.        0.
## 4     283.        0.
## # ... with 118 more rows

Tagging with bands and colours

We call tagging, to the process of adding reference information to spectral data. For example we can add a factor indicating regions or bands in the spectrum. We can add also information on the colour, as seen by humans, for each observed value, or for individual regions or bands of the spectrum. In most cases this additional information is used for annotations when plotting the spectral data.

tag(sun.spct, PAR.wb)

## Object: source_spct [524 x 6]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Time unit 1s
## 
## # A tibble: 524 x 6
##   w.length s.e.irrad s.q.irrad wl.color wb.color wb.f 
##      <dbl>     <dbl>     <dbl> <chr>    <chr>    <fct>
## 1     280.        0.        0. #000000  <NA>     <NA> 
## 2     281.        0.        0. #000000  <NA>     <NA> 
## 3     282.        0.        0. #000000  <NA>     <NA> 
## 4     283.        0.        0. #000000  <NA>     <NA> 
## # ... with 520 more rows

tag(sun.spct, UV_bands.lst)

## Object: source_spct [524 x 6]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Time unit 1s
## 
## # A tibble: 524 x 6
##   w.length s.e.irrad s.q.irrad wl.color wb.color wb.f 
##      <dbl>     <dbl>     <dbl> <chr>    <chr>    <fct>
## 1     280.        0.        0. #000000  black    UVB  
## 2     281.        0.        0. #000000  black    UVB  
## 3     282.        0.        0. #000000  black    UVB  
## 4     283.        0.        0. #000000  black    UVB  
## # ... with 520 more rows

tg.sun.spct <- tag(sun.spct, PAR.wb)
attr(tg.sun.spct, "spct.tags")

## $valid
## [1] TRUE
## 
## $time.unit
## [1] "second"
## 
## $wb.key.name
## [1] "Bands"
## 
## $wl.color
## [1] TRUE
## 
## $wb.color
## [1] TRUE
## 
## $wb.num
## [1] 1
## 
## $wb.colors
## [1] "#735B57"
## 
## $wb.names
## [1] "PAR"
## 
## $wb.list
## $wb.list[[1]]
## PAR 
## low (nm) 400 
## high (nm) 700 
## weighted none

wb2tagged_spct(UV_bands.lst)

## Object: generic_spct [8 x 12]
## Wavelength range 100 to 400 nm, step 9.947598e-13 to 180 nm 
## 
## # A tibble: 8 x 12
##   w.length counts   cps s.e.irrad s.q.irrad   Tfr   Rfl s.e.response
##      <dbl>  <dbl> <dbl>     <dbl>     <dbl> <dbl> <dbl>        <dbl>
## 1    100.0     0.    0.        0.        0.    0.    0.           0.
## 2    100.      0.    0.        0.        0.    0.    0.           0.
## 3    280.      0.    0.        0.        0.    0.    0.           0.
## 4    280.      0.    0.        0.        0.    0.    0.           0.
## # ... with 4 more rows, and 4 more variables: wl.color <chr>,
## #   wb.color <chr>, wb.f <fct>, y <dbl>

wb2rect_spct(UV_bands.lst)

## Object: generic_spct [3 x 15]
## Wavelength range 190 to 357.5 nm, step 60 to 107.5 nm 
## 
## # A tibble: 3 x 15
##   w.length counts   cps s.e.irrad s.q.irrad   Tfr   Rfl s.e.response
##      <dbl>  <dbl> <dbl>     <dbl>     <dbl> <dbl> <dbl>        <dbl>
## 1     190.     0.    0.        0.        0.    0.    0.           0.
## 2     298.     0.    0.        0.        0.    0.    0.           0.
## 3     358.     0.    0.        0.        0.    0.    0.           0.
## # ... with 7 more variables: wl.color <chr>, wb.color <chr>,
## #   wb.name <chr>, wb.f <fct>, wl.high <dbl>, wl.low <dbl>, y <dbl>

tg.sun.spct

## Object: source_spct [524 x 6]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Time unit 1s
## 
## # A tibble: 524 x 6
##   w.length s.e.irrad s.q.irrad wl.color wb.color wb.f 
##      <dbl>     <dbl>     <dbl> <chr>    <chr>    <fct>
## 1     280.        0.        0. #000000  <NA>     <NA> 
## 2     281.        0.        0. #000000  <NA>     <NA> 
## 3     282.        0.        0. #000000  <NA>     <NA> 
## 4     283.        0.        0. #000000  <NA>     <NA> 
## # ... with 520 more rows

is_tagged(tg.sun.spct)

## [1] TRUE

untg.sun.spct <- untag(tg.sun.spct)
is_tagged(untg.sun.spct)

## [1] FALSE

is_tagged(untg.sun.spct)

## [1] FALSE

untag(tg.sun.spct, byref = TRUE)

## Object: source_spct [524 x 3]
## Wavelength range 280 to 800 nm, step 1.023182e-12 to 1 nm 
## Time unit 1s
## 
## # A tibble: 524 x 3
##   w.length s.e.irrad s.q.irrad
##      <dbl>     <dbl>     <dbl>
## 1     280.        0.        0.
## 2     281.        0.        0.
## 3     282.        0.        0.
## 4     283.        0.        0.
## # ... with 520 more rows

is_tagged(untg.sun.spct)

## [1] FALSE

Summary

Specialized definitions of summary and the corresponding print methods are available for spectral objects. Attributes "what.measured", "when.measured" and "where.measured" are included in the summary print out only if set in the spectral object summarized.

summary(sun.spct)

## Summary of object: source_spct [522 x 3]
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
##     w.length       s.e.irrad        s.q.irrad        
##  Min.   :280.0   Min.   :0.0000   Min.   :0.000e+00  
##  1st Qu.:409.2   1st Qu.:0.4115   1st Qu.:1.980e-06  
##  Median :539.5   Median :0.5799   Median :2.929e-06  
##  Mean   :539.5   Mean   :0.5160   Mean   :2.407e-06  
##  3rd Qu.:669.8   3rd Qu.:0.6664   3rd Qu.:3.154e-06  
##  Max.   :800.0   Max.   :0.8205   Max.   :3.375e-06

summary(two_suns.spct)

## Warning in setWhenMeasured.summary_generic_spct(z,
## getWhenMeasured(object)): Length of 'when.measured' does not match spectrum
## object

## Summary of object: source_spct [1,044 x 4]
## containing  2  spectra in long form
## Wavelength range 280 to 800 nm, step 0.9230769 to 1 nm
## a label: sunlight, simulated
## b label: sunlight, simulated 
## a measured on 2010-06-22 09:51:00 UTC
## b measured on 2010-06-22 09:51:00 UTC 
## a measured at 60.2091078 N, 24.9647355 E
## b measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
##     w.length       s.e.irrad      spct.idx   s.q.irrad        
##  Min.   :280.0   Min.   :0.0000   a:522    Min.   :0.000e+00  
##  1st Qu.:409.0   1st Qu.:0.2471   b:522    1st Qu.:1.159e-06  
##  Median :539.5   Median :0.3494            Median :1.580e-06  
##  Mean   :539.5   Mean   :0.3870            Mean   :1.806e-06  
##  3rd Qu.:670.0   3rd Qu.:0.5799            3rd Qu.:2.928e-06  
##  Max.   :800.0   Max.   :0.8205            Max.   :3.375e-06

Wavelength

wl_range(sun.spct)

## [1] 280 800

wl_min(sun.spct)

## [1] 280

wl_max(sun.spct)

## [1] 800

wl_midpoint(sun.spct)

## [1] 540

wl_expanse(sun.spct)

## [1] 520

wl_stepsize(sun.spct)

## [1] 0.9230769 1.0000000

filters.mspct <- filter_mspct(list(none = clear.spct,
                                   pet = polyester.spct,
                                   yellow = yellow_gel.spct))
wl_range(filters.mspct)

## # A tibble: 3 x 3
##   spct.idx min.wl max.wl
##   <fct>     <dbl>  <dbl>
## 1 none       100.  5000.
## 2 pet        190.   800.
## 3 yellow     190.   800.

Peaks and valleys

peaks(sun.spct, span = 51)

## Object: source_spct [3 x 2]
## Wavelength range 451 to 747 nm, step 44 to 252 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 3 x 2
##   w.length s.e.irrad
## *    <dbl>     <dbl>
## 1     451.     0.820
## 2     495.     0.790
## 3     747.     0.503

valleys(sun.spct, span = 51)

## Object: source_spct [9 x 2]
## Wavelength range 358 to 761 nm, step 30 to 72 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 9 x 2
##   w.length s.e.irrad
## *    <dbl>     <dbl>
## 1     358.     0.254
## 2     393.     0.242
## 3     431.     0.414
## 4     487.     0.651
## # ... with 5 more rows

peaks(sun.spct, span = 51, unit.out = "photon")

## Object: source_spct [7 x 2]
## Wavelength range 451 to 754 nm, step 36 to 90 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 7 x 2
##   w.length  s.q.irrad
## *    <dbl>      <dbl>
## 1     451. 0.00000309
## 2     495. 0.00000327
## 3     531. 0.00000337
## 4     621. 0.00000336
## # ... with 3 more rows

peaks(sun.spct, span = 21)

## Object: source_spct [18 x 2]
## Wavelength range 354 to 774 nm, step 11 to 51 nm 
## Label: sunlight, simulated 
## Measured on 2010-06-22 09:51:00 UTC 
## Measured at 60.2091078 N, 24.9647355 E 
## Time unit 1s
## 
## # A tibble: 18 x 2
##   w.length s.e.irrad
## *    <dbl>     <dbl>
## 1     354.     0.376
## 2     366.     0.449
## 3     378.     0.497
## 4     416.     0.676
## # ... with 14 more rows

msmsply(filters.mspct, peaks, span = 11)

## Object: filter_mspct [3 x 1]
## --- Member: none ---
## Object: filter_spct [0 x 2]
## Label: theoretical fully transparent object 
## 
## # A tibble: 0 x 2
## # ... with 2 variables: w.length <dbl>, Tfr <dbl>
## --- Member: pet ---
## Object: filter_spct [8 x 2]
## Wavelength range 453 to 648 nm, step 6 to 76 nm 
## Label: clear polyester film, 125um thick 
## 
## # A tibble: 8 x 2
##   w.length   Tfr
## *    <int> <dbl>
## 1      453 0.926
## 2      503 0.926
## 3      579 0.921
## 4      609 0.919
## # ... with 4 more rows
## --- Member: yellow ---
## Object: filter_spct [5 x 2]
## Wavelength range 642 to 755 nm, step 8 to 64 nm 
## Label: yellow theatrical 'gel', Rosco supergel no. 312, 'canary yellow' 
## 
## # A tibble: 5 x 2
##   w.length   Tfr
## *    <int> <dbl>
## 1      642 0.898
## 2      706 0.901
## 3      714 0.901
## 4      744 0.902
## 5      755 0.902
## 
## --- END ---

Irradiance

irrad(sun.spct)

##    Total 
## 269.1249 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

irrad(sun.spct, PAR.wb)

##      PAR 
## 196.6343 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

irrad(sun.spct, c(400, 700))

##  range.400.700 
##       196.6343 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

e_irrad(sun.spct, PAR.wb) # W m-2

##      PAR 
## 196.6343 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

q_irrad(sun.spct, PAR.wb) * 1e6 # umol s-1 m-2

##      PAR 
## 894.1352 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "photon irradiance total"

irrad(sun.spct, PAR.wb, time.unit = "hour")

##      PAR 
## 707883.4 
## attr(,"time.unit")
## [1] "hour"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

irrad(sun.daily.spct, PAR.wb, time.unit = "second")

##      PAR 
## 92.16251 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

e_irrad(sun.spct, UV_bands.lst) # W m-2

##        UVB        UVA 
##  0.6445105 27.9842061 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

irrad(sun.spct, UV_bands.lst, quantity = "total")

##        UVB        UVA 
##  0.6445105 27.9842061 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

irrad(sun.spct, UV_bands.lst, quantity = "average")

##        UVB        UVA 
## 0.01841458 0.32922595 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance average"

irrad(sun.spct, UV_bands.lst, quantity = "contribution")

##         UVB         UVA 
## 0.002394838 0.103982226 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance contribution"

irrad(sun.spct, UV_bands.lst, quantity = "relative")

##        UVB        UVA 
## 0.02251273 0.97748727 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance relative"

irrad(sun.spct, UV_bands.lst, quantity = "contribution.pc")

##        UVB        UVA 
##  0.2394838 10.3982226 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance contribution.pc"

irrad(sun.spct, UV_bands.lst, quantity = "relative.pc")

##       UVB       UVA 
##  2.251273 97.748727 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance relative.pc"

irrad(sun.spct, PAR.wb, time.unit = duration(8, "hours"))

##     PAR 
## 5663067 
## attr(,"time.unit")
## [1] "28800s (~8 hours)"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

fluence(sun.spct, PAR.wb, exposure.time = duration(8, "hours"))

##     PAR 
## 5663067 
## attr(,"radiation.unit")
## [1] "energy fluence (J m-2)"
## attr(,"exposure.duration")
## [1] "28800s (~8 hours)"

names(filters.mspct)

## [1] "none"   "pet"    "yellow"

two_suns.mspct <- source_mspct(list(sun1 = sun.spct, sun2 = sun.spct))
q_irrad(two_suns.mspct, 
        w.band = list(PAR = waveband(c(400,700))),
        attr2tb = c(when.measured = "time", lon = "lon", lat = "lat"))

## # A tibble: 2 x 5
##   spct.idx      PAR time                  lon   lat
##   <fct>       <dbl> <dttm>              <dbl> <dbl>
## 1 sun1     0.000894 2010-06-22 09:51:00  25.0  60.2
## 2 sun2     0.000894 2010-06-22 09:51:00  25.0  60.2

filtered_sun <- convolve_each(filters.mspct, sun.spct)
irrad(filtered_sun, list(UVA.wb, PAR.wb))

## # A tibble: 3 x 3
##   spct.idx irrad_UVA irrad_PAR
##   <fct>        <dbl>     <dbl>
## 1 none       28.0         197.
## 2 pet        23.0         181.
## 3 yellow      0.0373      107.

irrad(convolve_each(filters.mspct, sun.spct), list(UVA.wb, PAR.wb))

## # A tibble: 3 x 3
##   spct.idx irrad_UVA irrad_PAR
##   <fct>        <dbl>     <dbl>
## 1 none       28.0         197.
## 2 pet        23.0         181.
## 3 yellow      0.0373      107.

filtered_sun <- msmsply(filters.mspct, `*`, sun.spct)
irrad(filtered_sun, list(UVA.wb, PAR.wb))

## # A tibble: 3 x 3
##   spct.idx irrad_UVA irrad_PAR
##   <fct>        <dbl>     <dbl>
## 1 none       28.0         197.
## 2 pet        23.0         181.
## 3 yellow      0.0373      107.

Fluence

fluence(sun.spct, exposure.time = duration(1, "hours"))

##    Total 
## 968849.6 
## attr(,"radiation.unit")
## [1] "energy fluence (J m-2)"
## attr(,"exposure.duration")
## [1] "3600s (~1 hours)"

fluence(sun.spct, exposure.time = 3600) # seconds

## converting 'time.unit' 3600 into a lubridate::duration

##    Total 
## 968849.6 
## attr(,"radiation.unit")
## [1] "energy fluence (J m-2)"
## attr(,"exposure.duration")
## [1] 3600

q_fluence(sun.spct, PAR.wb, exposure.time = duration(25, "minutes"))

##      PAR 
## 1.341203 
## attr(,"radiation.unit")
## [1] "photon fluence (mol m-2)"
## attr(,"exposure.duration")
## [1] "1500s (~25 minutes)"

Photon and energy ratios

q_ratio(sun.spct, UVB.wb, PAR.wb)

##  UVB: PAR(q:q) 
##    0.001873724 
## attr(,"radiation.unit")
## [1] "q:q ratio"

q_ratio(sun.spct, list(UVC.wb, UVB.wb, UVA.wb, UV.wb))

##       UVB: Total(q:q)       UVA: Total(q:q)  UV.tr.lo: Total(q:q) 
##           0.001334593           0.067567343           0.068901936 
## attr(,"radiation.unit")
## [1] "q:q ratio"

q_ratio(sun.spct, UVB.wb, list(UV.wb, PAR.wb))

##  UVB: UV.tr.lo(q:q)       UVB: PAR(q:q) 
##         0.019369458         0.001873724 
## attr(,"radiation.unit")
## [1] "q:q ratio"

qe_ratio(sun.spct, list(UVB.wb, PAR.wb))

##    q:e( UVB)    q:e( PAR) 
## 2.599434e-06 4.547199e-06 
## attr(,"radiation.unit")
## [1] "q:e ratio"

q_ratio(filtered_sun, list(UVB.wb, UVA.wb, PAR.wb))

## # A tibble: 3 x 4
##   spct.idx `q_ratio_UVB:Total(q:q)` `q_ratio_UVA:Total~ `q_ratio_PAR:Tota~
##   <fct>                       <dbl>               <dbl>              <dbl>
## 1 none                   0.00133               0.0676                0.712
## 2 pet                    0.0000370             0.0614                0.720
## 3 yellow                 0.00000254            0.000134              0.684

Normalized difference indexes

Individual spectra

These indexes are frequently used to summarize reflectance data, for example in remote sensing the NDVI (normalized difference vegetation index). Here we give an unusual example to demonstrate that function normalized_diff_ind() can be used to calculate, or define any similar index.

normalized_diff_ind(sun.spct,
                    waveband(c(400, 700)), waveband(c(700, 1100)),
                    irrad)

## NDI  irrad  [ 400.700 ] - [ 700.1100 ] 
##                              0.6352382

Transmittance, reflectance, absorptance and absorbance

transmittance(polyester.spct, list(UVB.wb, UVA.wb, PAR.wb))

##         UVB         UVA         PAR 
## 0.007671429 0.782682353 0.920245000 
## attr(,"Tfr.type")
## [1] "total"
## attr(,"radiation.unit")
## [1] "transmittance average"

reflectance(green_leaf.spct, waveband(c(600, 700)))

##  range.600.700 
##       0.089647 
## attr(,"Rfr.type")
## [1] "total"
## attr(,"radiation.unit")
## [1] "reflectance average"

irrad(sun.spct * polyester.spct, list(UVB.wb, UVA.wb, PAR.wb, wb.trim = TRUE)) /
  irrad(sun.spct, list(UVB.wb, UVA.wb, PAR.wb, wb.trim = TRUE))

##        UVB        UVA        PAR 
## 0.02506541 0.82127856 0.92059898 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy irradiance total"

transmittance(filters.mspct, w.band = list("Tfr(UVA)" = UVA.wb, "Tfr(PAR)" = PAR.wb))

## # A tibble: 3 x 3
##   spct.idx `Tfr(UVA)` `Tfr(PAR)`
##   <fct>         <dbl>      <dbl>
## 1 none        1.000        1.000
## 2 pet         0.783        0.920
## 3 yellow      0.00160      0.566

transmittance(filters.mspct,
              w.band = list(Tfr = waveband(c(350, 550))),
              attr2tb = "what.measured")

## # A tibble: 3 x 3
##   spct.idx   Tfr what.measured                                            
##   <fct>    <dbl> <chr>                                                    
## 1 none     1.000 theoretical fully transparent object                     
## 2 pet      0.913 clear polyester film, 125um thick                        
## 3 yellow   0.178 yellow theatrical 'gel', Rosco supergel no. 312, 'canary~

transmittance(filters.mspct, 
              list("Tfr(UVA)" = UVA.wb, "Tfr(PAR)" = PAR.wb),
              attr2tb = "what.measured")

## # A tibble: 3 x 4
##   spct.idx `Tfr(UVA)` `Tfr(PAR)` what.measured                            
##   <fct>         <dbl>      <dbl> <chr>                                    
## 1 none        1.000        1.000 theoretical fully transparent object     
## 2 pet         0.783        0.920 clear polyester film, 125um thick        
## 3 yellow      0.00160      0.566 yellow theatrical 'gel', Rosco supergel ~

Integrated response

response(photodiode.spct)

##    Total 
## 24.40478 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy response total"

e_response(photodiode.spct, list(UVB.wb, UVA.wb))

##  UVB.tr.lo        UVA 
##   0.346462   5.981818 
## attr(,"time.unit")
## [1] "second"
## attr(,"radiation.unit")
## [1] "energy response total"

sensors <- response_mspct(list(GaAsP = photodiode.spct,
                               CCD = ccd.spct))
response(sensors, list(UVB.wb, UVA.wb, PAR.wb), quantity = "contribution")

## # A tibble: 2 x 4
##   spct.idx response_UVB.tr.lo response_UVA response_PAR.tr.hi
##   <fct>                 <dbl>        <dbl>              <dbl>
## 1 GaAsP                0.0142       0.245               0.741
## 2 CCD                  0.0215       0.0634              0.411

Integration over wavelengths

When we need to integrate some numeric variable stored in a spectral object we can use functions integrate_spct or average_spct.

integrate_spct(sun.spct)

##      e.irrad      q.irrad 
## 2.691249e+02 1.255336e-03

average_spct(sun.spct)

##      e.irrad      q.irrad 
## 5.175479e-01 2.414107e-06