ADP: Function for Implementing the Accumulated Developmental...
In spphpr: Spring Phenological Prediction
ADP R Documentation
Function for Implementing the Accumulated Developmental Progress Method Using Mean Daily Temperatures
Description
Estimates the starting date (S, in day-of-year) and the parameters of
a developmental rate model in the accumulated developmental progress (ADP)
method using mean daily air temperatures (Wagner et al., 1984; Shi et al., 2017a, b).
Usage
ADP( S.arr, expr, ini.val, Year1, Time, Year2, DOY, Temp, DOY.ul = 120,
fig.opt = TRUE, control = list(), verbose = TRUE )
Arguments
S.arr
the candidate starting dates for thermal accumulation (in day-of-year)
expr
a user-defined model that is used in the accumulated developmental progress (ADP) method
ini.val
a vector or a list that saves the initial values of the parameters in expr
Year1
the vector of the years in which a particular phenological event was recorded
Time
the vector of the occurrence times (in day-of-year) of a particular phenological event across many years
Year2
the vector of the years recording the climate data corresponding to the occurrence times
DOY
the vector of the dates (in day-of-year) for which climate data exist
Temp
the mean daily air temperature data (in {}^{\circ}C) corresponding to DOY
DOY.ul
the upper limit of DOY used to predict the occurrence time
fig.opt
an optional argument to draw the figures associated with the temperature-dependent developmental rate curve,
the mean daily temperatures versus years, and a comparison between the predicted and observed occurrence times
control
the list of control parameters for using the optim function in the stats package
verbose
an optional argument allowing users to suppress the printing of computation progress
Details
It is better not to set too many candidate starting dates, as doing so will be time-consuming. If expr
is selected as Arrhenius' equation, S.arr can be selected as the S obtained from the output of
the ADTS function. Here, expr can be other nonlinear temperature-dependent
developmental rate functions (see Shi et al. [2017b] for details). Further, 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.
\qquadThe function does not require that Year1 is the same as unique(Year2),
and the intersection of the two vectors of years will be kept. The unused years that have phenological
records but lack climate data will be showed in unused.years in the returned list.
\qquadThe numerical value of DOY.ul should be greater than or equal to the maximum Time.
\qquad Let r represent the temperature-dependent developmental rate, i.e.,
the reciprocal of the developmental
duration required for completing a particular phenological event, at a constant temperature.
In the accumulated developmental progress (ADP) method, when the annual accumulated developmental
progress (AADP) reaches 100%, the phenological event is predicted to occurr for each year.
Let \mathrm{AADP}_{i} denote the AADP of the ith year, which equals
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}r_{ij}\left(\mathrm{\mathbf{P}}; T_{ij}\right),
where S represents the starting date (in day-of-year), E_{i} represents the ending date
(in day-of-year), i.e., the occurrence time of a pariticular phenological event in the ith year,
\mathrm{\mathbf{P}} is the vector of the model parameters in expr,
and T_{ij} represents the mean daily temperature of the jth day of the ith
year (in {}^{\circ}C or K). In 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}r_{ij} = 100\% (where F \geq S), it follows that F is
the predicted occurrence time; when \sum_{j=S}^{F}r_{ij} < 100\% and
\sum_{j=S}^{F+1}r_{ij} > 100\%, the trapezoid method (Ring and Harris, 1983)
is used to determine the predicted occurrence time. Let \hat{E}_{i} represent the predicted
occurrence time of the ith year. Assume that there are n-year phenological records.
When the starting date S and the temperature-dependent developmental rate model are known,
the model parameters can be estimated using the Nelder-Mead optiminization method
(Nelder and Mead, 1965) to minimize the root-mean-square error (RMSE) between the observed and predicted
occurrence times, i.e.,
\mathrm{\mathbf{\hat{P}}} = \mathrm{arg}\,\mathop{\mathrm{min}}\limits_{
\mathrm{\mathbf{P}}}\left\{\mathrm{RMSE}\right\} = \mathrm{arg}\,\mathop{\mathrm{min}}\limits_{
\mathrm{\mathbf{P}}}\sqrt{\frac{\sum_{i=1}^{n}\left(E_{i}-\hat{E}_i\right){}^{2}}{n}}.
Because S is not determined, a group of candidate S values (in day-of-year) need to
be provided. Assume that there are m candidate S values, i.e., S_{1}, S_{2}, S_{3},
\cdots, S_{m}. For each S_{q} (where q ranges between 1 and m), we can obtain
a vector of the estimated model parameters, \mathrm{\mathbf{\hat{P}}}_{q}, by minimizing
\mathrm{RMSE}_{q} using the Nelder-Mead optiminization method. Then we finally selected
\mathrm{\mathbf{\hat{P}}} associated with \mathrm{min}\left\{\mathrm{RMSE}_{1},
\mathrm{RMSE}_{2}, \mathrm{RMSE}_{3}, \cdots, \mathrm{RMSE}_{m}\right\}
as the target parameter vector.
Value
TDDR
the temperature-dependent developmental rate matrix consisting of the year,
day-of-year, mean daily temperature and developmental rate columns
MAT
a matrix consisting of the candidate starting dates and the estimates of
candidate model parameters with the corresponding RMSEs
Dev.accum
the calculated annual accumulated developmental progresses in different years
Year
The overlapping years between Year1 and Year2
Time
The observed occurrence times (day-of-year) in the overlapping years
between Year1 and Year2
Time.pred
the predicted occurrence times in different years
S
the determined starting date (day-of-year)
par
the estimates of model parameters
RMSE
the RMSE (in days) between the observed and predicted occurrence times
unused.years
the years that have phenological records but lack climate data
Note
The entire mean daily temperature data set for the spring of each year should be provided.
In TDDR, the first column of Year saves the years, the second column
of DOY saves the day-of-year values, the third column of Temperature
saves the mean daily air temperatures calculated between the starting date to the occurrence times,
and the fourth column of Rate saves the calculated developmental rates
corresponding to the mean daily temperatures.
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
Nelder, J.A., Mead, R. (1965) A simplex method for function minimization.
Computer Journal 7, 308-313. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/comjnl/7.4.308")}
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")}
See Also
predADP
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
Temp.val <- X2$MDT
DOY.ul.val <- 120
S.arr0 <- 47
#### Defines a re-parameterized Arrhenius' equation ###########################
Arrhenius.eqn <- function(P, x){
B <- P[1]
Ea <- P[2]
R <- 1.987 * 10^(-3)
x <- x + 273.15
10^12*exp(B-Ea/(R*x))
}
##############################################################################
#### Provides the initial values of the parameter of Arrhenius' equation #####
ini.val0 <- list( B = 20, Ea = 14 )
##############################################################################
res5 <- ADP( S.arr = S.arr0, expr = Arrhenius.eqn, ini.val = ini.val0, Year1 = Year1.val,
Time = Time.val, Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val,
DOY.ul = DOY.ul.val, fig.opt = TRUE, control = list(trace = FALSE,
reltol = 1e-12, maxit = 5000), verbose = TRUE )
res5
TDDR <- res5$TDDR
T <- TDDR$Temperature
r <- TDDR$Rate
Y <- res5$Year
DP <- res5$Dev.accum
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
Ind <- sort(T, index.return=TRUE)$ix
T1 <- T[Ind]
r1 <- r[Ind]
plot( T1, r1, cex.lab = 1.5, cex.axis = 1.5, pch = 1, cex = 1.5, col = 2, type = "l",
xlab = expression(paste("Mean daily temperature (", degree, "C)", sep = "")),
ylab = expression(paste("Calculated developmental rate (", {day}^{"-1"}, ")", sep = "")) )
par(par1)
par(par2)
par(par3)
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( Y, DP * 100, xlab = "Year",
ylab = "Accumulated developmental progress (%)",
ylim = c(50, 150), cex.lab=1.5, cex.axis = 1.5, cex = 1.5 )
abline( h = 1 * 100, lwd = 1, col = 4, lty = 2 )
par(par1)
par(par2)
par(par3)
# graphics.off()
spphpr documentation built on April 11, 2025, 6:11 p.m.
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| ADP | R Documentation |
Function for Implementing the Accumulated Developmental Progress Method Using Mean Daily Temperatures
Description
Estimates the starting date (S, in day-of-year) and the parameters of
a developmental rate model in the accumulated developmental progress (ADP)
method using mean daily air temperatures (Wagner et al., 1984; Shi et al., 2017a, b).
Usage
ADP( S.arr, expr, ini.val, Year1, Time, Year2, DOY, Temp, DOY.ul = 120,
fig.opt = TRUE, control = list(), verbose = TRUE )
Arguments
S.arr |
the candidate starting dates for thermal accumulation (in day-of-year) |
expr |
a user-defined model that is used in the accumulated developmental progress (ADP) method |
ini.val |
a vector or a list that saves the initial values of the parameters in |
Year1 |
the vector of the years in which a particular phenological event was recorded |
Time |
the vector of the occurrence times (in day-of-year) of a particular phenological event across many years |
Year2 |
the vector of the years recording the climate data corresponding to the occurrence times |
DOY |
the vector of the dates (in day-of-year) for which climate data exist |
Temp |
the mean daily air temperature data (in |
DOY.ul |
the upper limit of |
fig.opt |
an optional argument to draw the figures associated with the temperature-dependent developmental rate curve, the mean daily temperatures versus years, and a comparison between the predicted and observed occurrence times |
control |
the list of control parameters for using the |
verbose |
an optional argument allowing users to suppress the printing of computation progress |
Details
It is better not to set too many candidate starting dates, as doing so will be time-consuming. If expr
is selected as Arrhenius' equation, S.arr can be selected as the S obtained from the output of
the ADTS function. Here, expr can be other nonlinear temperature-dependent
developmental rate functions (see Shi et al. [2017b] for details). Further, 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.
\qquadThe function does not require that Year1 is the same as unique(Year2),
and the intersection of the two vectors of years will be kept. The unused years that have phenological
records but lack climate data will be showed in unused.years in the returned list.
\qquadThe numerical value of DOY.ul should be greater than or equal to the maximum Time.
\qquad Let r represent the temperature-dependent developmental rate, i.e.,
the reciprocal of the developmental
duration required for completing a particular phenological event, at a constant temperature.
In the accumulated developmental progress (ADP) method, when the annual accumulated developmental
progress (AADP) reaches 100%, the phenological event is predicted to occurr for each year.
Let \mathrm{AADP}_{i} denote the AADP of the ith year, which equals
\mathrm{AADP}_{i} = \sum_{j=S}^{E_{i}}r_{ij}\left(\mathrm{\mathbf{P}}; T_{ij}\right),
where S represents the starting date (in day-of-year), E_{i} represents the ending date
(in day-of-year), i.e., the occurrence time of a pariticular phenological event in the ith year,
\mathrm{\mathbf{P}} is the vector of the model parameters in expr,
and T_{ij} represents the mean daily temperature of the jth day of the ith
year (in {}^{\circ}C or K). In 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}r_{ij} = 100\% (where F \geq S), it follows that F is
the predicted occurrence time; when \sum_{j=S}^{F}r_{ij} < 100\% and
\sum_{j=S}^{F+1}r_{ij} > 100\%, the trapezoid method (Ring and Harris, 1983)
is used to determine the predicted occurrence time. Let \hat{E}_{i} represent the predicted
occurrence time of the ith year. Assume that there are n-year phenological records.
When the starting date S and the temperature-dependent developmental rate model are known,
the model parameters can be estimated using the Nelder-Mead optiminization method
(Nelder and Mead, 1965) to minimize the root-mean-square error (RMSE) between the observed and predicted
occurrence times, i.e.,
\mathrm{\mathbf{\hat{P}}} = \mathrm{arg}\,\mathop{\mathrm{min}}\limits_{
\mathrm{\mathbf{P}}}\left\{\mathrm{RMSE}\right\} = \mathrm{arg}\,\mathop{\mathrm{min}}\limits_{
\mathrm{\mathbf{P}}}\sqrt{\frac{\sum_{i=1}^{n}\left(E_{i}-\hat{E}_i\right){}^{2}}{n}}.
Because S is not determined, a group of candidate S values (in day-of-year) need to
be provided. Assume that there are m candidate S values, i.e., S_{1}, S_{2}, S_{3},
\cdots, S_{m}. For each S_{q} (where q ranges between 1 and m), we can obtain
a vector of the estimated model parameters, \mathrm{\mathbf{\hat{P}}}_{q}, by minimizing
\mathrm{RMSE}_{q} using the Nelder-Mead optiminization method. Then we finally selected
\mathrm{\mathbf{\hat{P}}} associated with \mathrm{min}\left\{\mathrm{RMSE}_{1},
\mathrm{RMSE}_{2}, \mathrm{RMSE}_{3}, \cdots, \mathrm{RMSE}_{m}\right\}
as the target parameter vector.
Value
TDDR |
the temperature-dependent developmental rate matrix consisting of the year, day-of-year, mean daily temperature and developmental rate columns |
MAT |
a matrix consisting of the candidate starting dates and the estimates of candidate model parameters with the corresponding RMSEs |
Dev.accum |
the calculated annual accumulated developmental progresses in different years |
Year |
The overlapping years between |
Time |
The observed occurrence times (day-of-year) in the overlapping years
between |
Time.pred |
the predicted occurrence times in different years |
S |
the determined starting date (day-of-year) |
par |
the estimates of model parameters |
RMSE |
the RMSE (in days) between the observed and predicted occurrence times |
unused.years |
the years that have phenological records but lack climate data |
Note
The entire mean daily temperature data set for the spring of each year should be provided.
In TDDR, the first column of Year saves the years, the second column
of DOY saves the day-of-year values, the third column of Temperature
saves the mean daily air temperatures calculated between the starting date to the occurrence times,
and the fourth column of Rate saves the calculated developmental rates
corresponding to the mean daily temperatures.
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
Nelder, J.A., Mead, R. (1965) A simplex method for function minimization.
Computer Journal 7, 308-313. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/comjnl/7.4.308")}
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")}
See Also
predADP
Examples
data(apricotFFD)
data(BJDAT)
X1 <- apricotFFD
X2 <- BJDAT
Year1.val <- X1$Year
Time.val <- X1$Time
Year2.val <- X2$Year
DOY.val <- X2$DOY
Temp.val <- X2$MDT
DOY.ul.val <- 120
S.arr0 <- 47
#### 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))
}
##############################################################################
#### Provides the initial values of the parameter of Arrhenius' equation #####
ini.val0 <- list( B = 20, Ea = 14 )
##############################################################################
res5 <- ADP( S.arr = S.arr0, expr = Arrhenius.eqn, ini.val = ini.val0, Year1 = Year1.val,
Time = Time.val, Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val,
DOY.ul = DOY.ul.val, fig.opt = TRUE, control = list(trace = FALSE,
reltol = 1e-12, maxit = 5000), verbose = TRUE )
res5
TDDR <- res5$TDDR
T <- TDDR$Temperature
r <- TDDR$Rate
Y <- res5$Year
DP <- res5$Dev.accum
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
Ind <- sort(T, index.return=TRUE)$ix
T1 <- T[Ind]
r1 <- r[Ind]
plot( T1, r1, cex.lab = 1.5, cex.axis = 1.5, pch = 1, cex = 1.5, col = 2, type = "l",
xlab = expression(paste("Mean daily temperature (", degree, "C)", sep = "")),
ylab = expression(paste("Calculated developmental rate (", {day}^{"-1"}, ")", sep = "")) )
par(par1)
par(par2)
par(par3)
dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( Y, DP * 100, xlab = "Year",
ylab = "Accumulated developmental progress (%)",
ylim = c(50, 150), cex.lab=1.5, cex.axis = 1.5, cex = 1.5 )
abline( h = 1 * 100, lwd = 1, col = 4, lty = 2 )
par(par1)
par(par2)
par(par3)
# graphics.off()
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