predADP2: Prediction Function of the Accumulated Developmental Progress...
In spphpr: Spring Phenological Prediction
predADP2 R Documentation
Prediction Function of the Accumulated Developmental Progress Method Using Minimum and Maximum Daily Temperatures
Description
Predicts the occurrence times using the accumulated developmental progress (ADP)
method based on observed or predicted minimum and maximum daily air temperatures
(Wagner et al., 1984; Shi et al., 2017a, b).
Usage
predADP2(S, expr, theta, Year2, DOY, Tmin, Tmax, DOY.ul = 120)
Arguments
S
the starting date for thermal accumulation (in day-of-year)
expr
a user-defined model that is used in the accumulated developmental progress (ADP) method
theta
a vector saves the numerical values of the parameters in expr
Year2
the vector of the years recording the climate data for predicting the occurrence times
DOY
the vector of the dates (in day-of-year) for which climate data exist
Tmin
the minimum daily air temperature data (in {}^{\circ}C) corresponding to DOY
Tmax
the maximum daily air temperature data (in {}^{\circ}C) corresponding to DOY
DOY.ul
the upper limit of DOY used to predict the occurrence time
Details
Organisms exhibiting phenological events in early spring often experience several cold days
during their development. In this case, Arrhenius' equation (Shi et al., 2017a, b,
and references therein) has been recommended to describe the effect of the absolute temperature
(T in Kelvin [K]) on the developmental rate (r):
r = \mathrm{exp}\left(B - \frac{E_{a}}{R\,T}\right),
where E_{a} represents the activation free energy (in kcal \cdot mol{}^{-1});
R is the universal gas constant (= 1.987 cal \cdot mol{}^{-1} \cdot K{}^{-1});
B is a constant. To maintain consistency between the units used for E_{a} and R, we need to
re-assign R to be 1.987\times {10}^{-3}, making its unit 1.987\times {10}^{-3}
kcal \cdot mol{}^{-1} \cdot K{}^{-1} in the above formula.
\qquadIn the accumulated developmental progress (ADP) method, when the annual accumulated developmental
progress (AADP) reaches 100%, the phenological event is predicted to occur for each year.
Let \mathrm{AADP}_{i} denote the AADP of the ith year, which equals
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\frac{r_{ijw}}{24},
where E_{i} represents the ending date (in day-of-year), i.e., the occurrence time of a pariticular
phenological event in the ith year. r_{ijw} is the developmental rate (per hour), which is
transferred to r_{ij} (per day) by dividing 24. If the temperature-dependent developmental rate follows
Arrhenius' equation, the AADP of the ith year is equal to
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\left\{\frac{1}{24}\mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ijw}}\right)\right\},
where T_{ijw} represents the estimated mean hourly temperature of the wth hour of the
jth day of the ith year (in K). This packages takes the method proposed by
Zohner et al. (2020) to estimate the mean hourly temperature (T_{w}) for each of 24 hours:
T_{w} = \frac{T_{\mathrm{max}} - T_{\mathrm{min}}}{2}\, \mathrm{sin}\left(\frac{w\pi}{12}-
\frac{\pi}{2}\right)+\frac{T_{\mathrm{max}} + T_{\mathrm{min}}}{2},
where w represents the wth hour of a day, and T_{\mathrm{min}} and T_{\mathrm{max}}
represent the minimum and maximum temperatures of the day, respectively.
\qquadIn theory, \mathrm{AADP}_{i} = 100\%,
i.e., the AADP values of different years are a constant 100%. However, in practice, there is
a certain deviation of \mathrm{AADP}_{i} from 100%. The following approach
is used to determine the predicted occurrence time.
When \sum_{j=S}^{F}\sum_{w=1}^{24}\left(r_{ijw}/24\right) = 100\% (where F \geq S), it follows that F is
the predicted occurrence time; when \sum_{j=S}^{F}\sum_{w=1}^{24}\left(r_{ijw}/24\right) < 100\% and
\sum_{j=S}^{F+1}\sum_{w=1}^{24}\left(r_{ijw}/24\right) > 100\%, the trapezoid method (Ring and Harris, 1983)
is used to determine the predicted occurrence time.
\qquadThe argument of expr can be any an arbitrary user-defined temperature-dependent
developmental rate function, e.g., a function named myfun,
but it needs to take the form of myfun <- function(P, x){...},
where P is the vector of the model parameter(s), and x is the vector of the
predictor variable, i.e., the temperature variable.
Value
Year
the years with climate data
Time.pred
the predicted occurrence times (day-of-year) in different years
Note
The entire minimum and maximum daily temperature data set for the spring of each year should be provided.
It should be noted that the unit of Tmin and Tmax in Arguments is {}^{\circ}C, not K.
In addition, when using Arrhenius' equation to describe r, to reduce the size of B
in this equation, Arrhenius' equation is multiplied by {10}^{12} in calculating the
AADP value for each year, i.e.,
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\left[{10}^{12} \cdot \frac{1}{24} \cdot \mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ijw}}\right)\right].
Author(s)
Peijian Shi pjshi@njfu.edu.cn, Zhenghong Chen chenzh64@126.com,
Jing Tan jmjwyb@163.com, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
References
Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity
at College Station, Texas. Environmental Entomology 12, 482-486. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ee/12.2.482")}
Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming:
Contrasting effects of rising winter low temperatures and early spring temperatures.
Agricultural and Forest Meteorology 240-241, 78-89. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001")}
Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing
temperature-dependent developmental rates of insects: (III) Phenological applications.
Annals of the Entomological Society of America 110, 558-564. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/aesa/sax063")}
Wagner, T.L., Wu, H.-I., Sharpe, P.J.H., Shcoolfield, R.M., Coulson, R.N. (1984) Modelling insect
development rates: a literature review and application of a biophysical model.
Annals of the Entomological Society of America 77, 208-225. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/aesa/77.2.208")}
Zohner, C.M., Mo, L., Sebald, V., Renner, S.S. (2020) Leaf-out in northern ecotypes of wide-ranging
trees requires less spring warming, enhancing the risk of spring frost damage at cold limits.
Global Ecology and Biogeography 29, 1056-1072. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/geb.13088")}
See Also
ADP2
Examples
data(apricotFFD)
data(BJDAT)
X1 <- apricotFFD
X2 <- BJDAT
Year1.val <- X1$Year
Time.val <- X1$Time
Year2.val <- X2$Year
DOY.val <- X2$DOY
Tmin.val <- X2$MinDT
Tmax.val <- X2$MaxDT
DOY.ul.val <- 120
S.val <- 46
# Defines a re-parameterized Arrhenius' equation
Arrhenius.eqn <- function(P, x){
B <- P[1]
Ea <- P[2]
R <- 1.987 * 10^(-3)
x <- x + 273.15
10^12*exp(B-Ea/(R*x))
}
P0 <- c(8.220327, 22.185942)
T2 <- seq(-10, 20, len = 2000)
r2 <- Arrhenius.eqn(P = P0, x = T2)
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( T2, r2, cex.lab = 1.5, cex.axis = 1.5, pch = 1, cex = 1.5, col = 2, type = "l",
xlab = expression(paste("Temperature (", degree, "C)", sep = "")),
ylab = expression(paste("Developmental rate (", {day}^{"-1"}, ")", sep="")) )
par(par1)
par(par2)
par(par3)
cand.res6 <- predADP2( S = S.val, expr = Arrhenius.eqn, theta = P0, Year2 = Year2.val,
DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, DOY.ul = DOY.ul.val )
cand.res6
ind5 <- cand.res6$Year %in% intersect(cand.res6$Year, Year1.val)
ind6 <- Year1.val %in% intersect(cand.res6$Year, Year1.val)
RMSE3 <- sqrt( sum((Time.val[ind6]-cand.res6$Time.pred[ind5])^2) / length(Time.val[ind6]) )
RMSE3
spphpr documentation built on April 11, 2025, 6:11 p.m.
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| predADP2 | R Documentation |
Prediction Function of the Accumulated Developmental Progress Method Using Minimum and Maximum Daily Temperatures
Description
Predicts the occurrence times using the accumulated developmental progress (ADP) method based on observed or predicted minimum and maximum daily air temperatures (Wagner et al., 1984; Shi et al., 2017a, b).
Usage
predADP2(S, expr, theta, Year2, DOY, Tmin, Tmax, DOY.ul = 120)
Arguments
S |
the starting date for thermal accumulation (in day-of-year) |
expr |
a user-defined model that is used in the accumulated developmental progress (ADP) method |
theta |
a vector saves the numerical values of the parameters in |
Year2 |
the vector of the years recording the climate data for predicting the occurrence times |
DOY |
the vector of the dates (in day-of-year) for which climate data exist |
Tmin |
the minimum daily air temperature data (in |
Tmax |
the maximum daily air temperature data (in |
DOY.ul |
the upper limit of |
Details
Organisms exhibiting phenological events in early spring often experience several cold days
during their development. In this case, Arrhenius' equation (Shi et al., 2017a, b,
and references therein) has been recommended to describe the effect of the absolute temperature
(T in Kelvin [K]) on the developmental rate (r):
r = \mathrm{exp}\left(B - \frac{E_{a}}{R\,T}\right),
where E_{a} represents the activation free energy (in kcal \cdot mol{}^{-1});
R is the universal gas constant (= 1.987 cal \cdot mol{}^{-1} \cdot K{}^{-1});
B is a constant. To maintain consistency between the units used for E_{a} and R, we need to
re-assign R to be 1.987\times {10}^{-3}, making its unit 1.987\times {10}^{-3}
kcal \cdot mol{}^{-1} \cdot K{}^{-1} in the above formula.
\qquadIn the accumulated developmental progress (ADP) method, when the annual accumulated developmental
progress (AADP) reaches 100%, the phenological event is predicted to occur for each year.
Let \mathrm{AADP}_{i} denote the AADP of the ith year, which equals
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\frac{r_{ijw}}{24},
where E_{i} represents the ending date (in day-of-year), i.e., the occurrence time of a pariticular
phenological event in the ith year. r_{ijw} is the developmental rate (per hour), which is
transferred to r_{ij} (per day) by dividing 24. If the temperature-dependent developmental rate follows
Arrhenius' equation, the AADP of the ith year is equal to
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\left\{\frac{1}{24}\mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ijw}}\right)\right\},
where T_{ijw} represents the estimated mean hourly temperature of the wth hour of the
jth day of the ith year (in K). This packages takes the method proposed by
Zohner et al. (2020) to estimate the mean hourly temperature (T_{w}) for each of 24 hours:
T_{w} = \frac{T_{\mathrm{max}} - T_{\mathrm{min}}}{2}\, \mathrm{sin}\left(\frac{w\pi}{12}-
\frac{\pi}{2}\right)+\frac{T_{\mathrm{max}} + T_{\mathrm{min}}}{2},
where w represents the wth hour of a day, and T_{\mathrm{min}} and T_{\mathrm{max}}
represent the minimum and maximum temperatures of the day, respectively.
\qquadIn theory, \mathrm{AADP}_{i} = 100\%,
i.e., the AADP values of different years are a constant 100%. However, in practice, there is
a certain deviation of \mathrm{AADP}_{i} from 100%. The following approach
is used to determine the predicted occurrence time.
When \sum_{j=S}^{F}\sum_{w=1}^{24}\left(r_{ijw}/24\right) = 100\% (where F \geq S), it follows that F is
the predicted occurrence time; when \sum_{j=S}^{F}\sum_{w=1}^{24}\left(r_{ijw}/24\right) < 100\% and
\sum_{j=S}^{F+1}\sum_{w=1}^{24}\left(r_{ijw}/24\right) > 100\%, the trapezoid method (Ring and Harris, 1983)
is used to determine the predicted occurrence time.
\qquadThe argument of expr can be any an arbitrary user-defined temperature-dependent
developmental rate function, e.g., a function named myfun,
but it needs to take the form of myfun <- function(P, x){...},
where P is the vector of the model parameter(s), and x is the vector of the
predictor variable, i.e., the temperature variable.
Value
Year |
the years with climate data |
Time.pred |
the predicted occurrence times (day-of-year) in different years |
Note
The entire minimum and maximum daily temperature data set for the spring of each year should be provided.
It should be noted that the unit of Tmin and Tmax in Arguments is {}^{\circ}C, not K.
In addition, when using Arrhenius' equation to describe r, to reduce the size of B
in this equation, Arrhenius' equation is multiplied by {10}^{12} in calculating the
AADP value for each year, i.e.,
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\left[{10}^{12} \cdot \frac{1}{24} \cdot \mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ijw}}\right)\right].
Author(s)
Peijian Shi pjshi@njfu.edu.cn, Zhenghong Chen chenzh64@126.com, Jing Tan jmjwyb@163.com, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
References
Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity
at College Station, Texas. Environmental Entomology 12, 482-486. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ee/12.2.482")}
Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming:
Contrasting effects of rising winter low temperatures and early spring temperatures.
Agricultural and Forest Meteorology 240-241, 78-89. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001")}
Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing
temperature-dependent developmental rates of insects: (III) Phenological applications.
Annals of the Entomological Society of America 110, 558-564. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/aesa/sax063")}
Wagner, T.L., Wu, H.-I., Sharpe, P.J.H., Shcoolfield, R.M., Coulson, R.N. (1984) Modelling insect
development rates: a literature review and application of a biophysical model.
Annals of the Entomological Society of America 77, 208-225. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/aesa/77.2.208")}
Zohner, C.M., Mo, L., Sebald, V., Renner, S.S. (2020) Leaf-out in northern ecotypes of wide-ranging
trees requires less spring warming, enhancing the risk of spring frost damage at cold limits.
Global Ecology and Biogeography 29, 1056-1072. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/geb.13088")}
See Also
ADP2
Examples
data(apricotFFD)
data(BJDAT)
X1 <- apricotFFD
X2 <- BJDAT
Year1.val <- X1$Year
Time.val <- X1$Time
Year2.val <- X2$Year
DOY.val <- X2$DOY
Tmin.val <- X2$MinDT
Tmax.val <- X2$MaxDT
DOY.ul.val <- 120
S.val <- 46
# Defines a re-parameterized Arrhenius' equation
Arrhenius.eqn <- function(P, x){
B <- P[1]
Ea <- P[2]
R <- 1.987 * 10^(-3)
x <- x + 273.15
10^12*exp(B-Ea/(R*x))
}
P0 <- c(8.220327, 22.185942)
T2 <- seq(-10, 20, len = 2000)
r2 <- Arrhenius.eqn(P = P0, x = T2)
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( T2, r2, cex.lab = 1.5, cex.axis = 1.5, pch = 1, cex = 1.5, col = 2, type = "l",
xlab = expression(paste("Temperature (", degree, "C)", sep = "")),
ylab = expression(paste("Developmental rate (", {day}^{"-1"}, ")", sep="")) )
par(par1)
par(par2)
par(par3)
cand.res6 <- predADP2( S = S.val, expr = Arrhenius.eqn, theta = P0, Year2 = Year2.val,
DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, DOY.ul = DOY.ul.val )
cand.res6
ind5 <- cand.res6$Year %in% intersect(cand.res6$Year, Year1.val)
ind6 <- Year1.val %in% intersect(cand.res6$Year, Year1.val)
RMSE3 <- sqrt( sum((Time.val[ind6]-cand.res6$Time.pred[ind5])^2) / length(Time.val[ind6]) )
RMSE3
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