macroBiome (version 0.4.0)

cliAvgDlySolIrrPoints: Estimator for Daily Solar Irradiance/Irradiation

Description

Calculates monthly averages of daily solar irradiance/irradiation under cloudless-sky conditions, for a given latitude, elevation and year. In addition, it also optionally computes monthly means for daylength (accumulated hours of daylight), for a given latitude, elevation and year. In addition to monthly averages, daily values can also be directly access.

Usage

cliAvgDlySolIrrPoints(
  lat,
  elv = NULL,
  year = 2000,
  aprchSIM = c("Solar123", "SPLASH"),
  aprchTR = c("daily", "hourly"),
  daily = FALSE,
  mlyOpVar = c("R_E")
)

Value

If daily values are also requested (daily = TRUE), the function returns a list of lists with daily and monthly data. If daily = FALSE, the return object is a list with the monthly means. The character vector 'mlyOpVar' determines for which variables the monthly averages are calculated. Daily values also become available only for this/these variable(s). Each matrix in the list of daily data consists of 365 or 366 columns, while monthly data are available, of course, as 12-column matrices. The former are accessible in the list 'dly', while the latter can be found in the list labelled as 'mly'. Here, matrices with monthly data contain averages of the daily values. See the argument 'mlyOpVar' for the content of matrices.

Arguments

lat

'numeric' vector with the latitude coordinates (in decimal degrees)

elv

'numeric' vector with the elevation values (in meters above sea level)

year

'numeric' vector with values of the year (using astronomical year numbering)

aprchSIM

'character' vector of length 1 that indicates the formula used to estimate the value of solar irradiance/irradiation for a specific day. Valid values are as follows:
(a) 'Solar123' - in this approach, first, the mean hourly solar irradiance under cloudless-sky conditions is calculated as proposed by Yin (1997b), with a minor modification, using the daytime means of optical air mass and cosine zenith; the former is computed as recommended by Yin (1997b), while the latter is estimated by using Eq 5 of Yin (1997a); however, in contrast to the original approach, where the solar constant was fixed at \(4.9212 MJ m^{-2} hr^{-1}\), according to Yin (1999), its value is corrected by calendar day for the variable ellipticity of the Earth's orbit, by using the scheme of Brock (1981); in the calculations, the values of solar declination and daylength are derived by using the approach of Brock (1981);
(b) 'SPLASH' - in this approach, first, under varying orbital parameters, the daily solar radiation at the top of the atmosphere is calculated (\(H_{0}\), Eq 7 in Davis et al. (2017)), and then this value is multiplied by the atmospheric transmittivity to obtain the value of daily surface radiation; in this case as well, cloudless conditions are assumed, i.e., the transmission coefficient is taken into account with an universal value of 0.75, however, its value is modified as a function of elevation, by using the scheme of Allen (1996); the daylength is calculated via Eq 1.6.11 in Duffie and Beckman (1991), using the sunset hour angle (\(h_{s}\), Eq 8. in Davis et al. (2017)); finally, the mean hourly surface radiation is derived as the quotient of the daily surface radiation and the daylength.

aprchTR

'character' vector of length 1 that indicates that the daily solar irradiance/irradiation is estimated with a daily or hourly time resolution. Valid values are as follows:
(a) 'daily' - it is calculated as a daily amount (in \(MJ m^{-2} dy^{-1}\));
(b) 'hourly' - it is estimated as an hourly mean (in \(MJ m^{-2} hr^{-1}\)).

daily

'logical' scalar that indicates whether or not daily values should also be computed.

mlyOpVar

'character' vector of at least one length that indicates the variable(s) for which monthly time series are to be calculated. Valid values are as follows:
(a) 'R_E' - monthly averages of daily solar irradiance/irradiation under cloudless-sky conditions (depending on the time resolution in \(MJ m^{-2} dy^{-1}\) or \(MJ m^{-2} hr^{-1}\));
(b) 'DL' - monthly means for daylength (accumulated hours of daylight) (in hours).

Details

To estimate the monthly averages of relative sunshine duration, Yin (1999) uses estimated values of the mean hourly solar irradiance under cloudless-sky conditions ('R_E_MJ.m2.hr1'), which is calculated via the scheme of Yin (1997b), with some minor modifications. Furthermore, in the approach proposed by Yin (1999), the monthly means of daylength ('DL_moa_hr') is used to estimate monthly averages of daily potential evapotranspiration. The solar irradiance model presented by Yin (1997b) and slightly modified by Yin (1999) is labelled 'Solar123' here.
The approach 'SPLASH' uses a different radiation model, which is based on the procedure described by Davis et al. (2017). The approach used here differs from the base scheme only in that it takes into account changes in orbital parameters of the Earth over time. Temporal variability of orbital parameters is considered through the implementation of the procedure as proposed by Berger and Loutre (1991). In the SPLASH algorithm, the daily top-of-the-atmosphere solar radiation is computed as twice the integral of the extraterrestrial radiation flux realized from local solar noon to sunset (see Davis et al. 2017). Using this physical amount, the daily solar radiation at the surface of the Earth under clear-sky conditions ('R_E_MJ.m2.dy1') can be easily estimated. The hourly mean surface radiation is finally obtained as the quotient of this integrated value and the daylength.
In the both approach, the daylength is computed by using the sunset hour angle, however, due to differences in the calculation of the solar declination, the results obtained by the two procedures differ. The approach 'Solar123' gives time-independent results, while using the approach 'SPLASH', varying results over time are obtained through the variable orbital parameters.
The two radiation models therefore differ significantly both in terms of conceptual frameworks and assumptions. The approach 'Solar123' converts hourly mean values into daily amounts, while in the approach 'SPLASH', the integrated daily values are transformed to hourly averages. However, in terms of atmospheric transmittivity, both models consider the universal value of 0.75 as a basic value. To conclude, depending on the scope of application, both methods can give valid results, but for paleo-climatological and paleo-environmental studies, the approach 'SPLASH' is clearly recommended.

References

Allen RG (1996) Assessing integrity of weather data for reference evapotranspiration estimation. J Irrig Drain Eng 122(2):97–106. tools:::Rd_expr_doi("10.1061/(ASCE)0733-9437(1996)122:2(97)")

Berger A, Loutre MF (1991) Insolation values for the climate of the last 10 million years. Quat Sci Rev 10(4):297-317. tools:::Rd_expr_doi("10.1016/0277-3791(91)90033-Q")

Brock TD (1981) Calculating solar radiation for ecological studies. Ecol Model 14(1–2):1-19. tools:::Rd_expr_doi("10.1016/0304-3800(81)90011-9")

Davis TW, Prentice IC, Stocker BD, Thomas RT, Whitley RJ, Wang H, Evans BJ, Gallego-Sala AV, Sykes MT, Cramer W (2017) Simple process-led algorithms for simulating habitats (SPLASH v.1.0): robust indices of radiation, evapotranspiration and plant-available moisture. Geosci Model Dev 10(2):689–708. tools:::Rd_expr_doi("10.5194/gmd-10-689-2017")

Duffie JA, Beckman WA (1991) Solar Engineering of Thermal Processes. Second Edition. Wiley-Interscience, New York, NY

Yin X (1997a) Calculating daytime mean relative air mass. Agric For Meteorol 87(2-3):85-90. tools:::Rd_expr_doi("10.1016/S0168-1923(97)00029-4")

Yin X (1997b) Optical Air Mass: Daily Integration and its Applications. Meteorol Atmos Phys 63(3-4):227-233. tools:::Rd_expr_doi("10.1007/BF01027387")

Yin X (1999) Bright Sunshine Duration in Relation to Precipitation, Air Temperature and Geographic Location. Theor Appl Climatol 64(1–2):61–68. tools:::Rd_expr_doi("10.1007/s007040050111")

Examples

library(graphics)

# Monthly average of the mean hourly solar irradiance under cloudless-sky conditions at sea level,
# in June 2000 along a meridian, according to the two different radiation models
lats <- seq(-90, 90, 10)
models <- c("Solar123", "SPLASH")
R_E_moa_MJ.m2.hr1 <- matrix(nrow = 2, ncol = length(lats), dimnames = list(models, lats))
R_E_moa_MJ.m2.hr1[1, ] <- cliAvgDlySolIrrPoints(lats, elv = 0,
    aprchTR = "hourly")$R_E_moa_MJ.m2.hr1[, "Jun"]
R_E_moa_MJ.m2.hr1[2, ] <- cliAvgDlySolIrrPoints(lats, elv = 0, aprchSIM = "SPLASH",
    aprchTR = "hourly")$R_E_moa_MJ.m2.hr1[, "Jun"]
cols <- c("black", "green")
matplot(t(R_E_moa_MJ.m2.hr1), type = "l", lwd = 2, col = cols, xaxt = "n",
    xlab = "Geographical latitude (degrees)",
    ylab = "Mean hourly solar irradiance (MJ m-2 hr-1)")
axis(1, at = seq(1, ncol(R_E_moa_MJ.m2.hr1)), labels = colnames(R_E_moa_MJ.m2.hr1))
legend(1, 2, legend = rownames(R_E_moa_MJ.m2.hr1), col = cols, lty = 1 : 2, lwd = 2, xpd = TRUE)

# \donttest{
# Daylength at latitude 75N in the year 2000, according to the two different radiation models
DL_hr <- matrix(nrow = 2, ncol = 366, dimnames = list(c("Solar123", "SPLASH"), seq(1, 366)))
DL_hr[1, ] <- cliAvgDlySolIrrPoints(75., 0., daily = TRUE, mlyOpVar = "DL")$dly$DL_hr
DL_hr[2, ] <- cliAvgDlySolIrrPoints(75., 0., aprchSIM = "SPLASH", daily = TRUE,
    mlyOpVar = "DL")$dly$DL_hr
cols <- c("black", "green")
matplot(t(DL_hr), type = "l", lwd = 2, col = cols, xaxt = "n", xlab = "Day number in the year",
    ylab = "Daylength (hr)")
axis(1, at = seq(1, ncol(DL_hr)), labels = colnames(DL_hr))
legend(1, 20, legend = rownames(DL_hr), col = cols, lty = 1 : 2, lwd = 2, xpd = TRUE)
# }