Function for Implementing the Accumulated Degree Days Method Using Mean Daily Temperatures

Description

Estimates the starting date (S, in day-of-year) and base tempeature (T_{0}, in {}^{\circ}C) in the accumulated degree days method using mean daily air temperatures (Aono, 1993; Shi et al., 2017a, b).

Usage

ADD(S.pd = NULL, T0.arr, Year1, Time, Year2, DOY, Temp, DOY.ul = 120, 
    fig.opt = TRUE, S.def = 54, verbose = TRUE)

Arguments

Details

The default of S.pd is NULL. In this case, the date associated with the minimum correlation coefficient [between the mean of the mean daily temperatures (from a candidate starting date to the observed occurrence time) and the observed occurrence time] will be determined to be the starting date on the condition that it is smaller than the mininum phenological occurrence time. If the determined date associated with the minimum correlation coefficient is greater than the mininum phenological occurrence time, S.def will be used as the starting date. If S.pd is not NULL, the starting date will be directly set as S.pd irrespective of the minimum correlation coefficient method and the value of S.def. This means that S.pd is superior to S.def in determining the starting date.

\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.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided. AADD is represented by the mean of AADD.arr in the output. When the argument of S.pd is not NULL, the returned value of search.failure will be NA. When the argument of S.pd is NULL, and the minimum correlation coefficient method fails to find a suitable starting date, the argument of S.def is then defined as the determined starting date, i.e., the returned value of S. At the same time, the returned value of cor.coef is defined as NA.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADD

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
T0.arr0    <- seq(-5, 5, by = 0.1) 
S.pd0      <- NULL


  res1 <- ADD( S.pd = S.pd0, T0.arr = T0.arr0, Year1 = Year1.val, Time = Time.val, 
               Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, 
               DOY.ul = DOY.ul.val, fig.opt = TRUE, S.def=54, verbose = TRUE )
  res1

  S0 <- res1$S.arr 
  r0 <- res1$cor.coef.arr
  
  dev.new()
  par1 <- par(family="serif")
  par2 <- par(mar=c(5, 5, 2, 2))
  par3 <- par(mgp=c(3, 1, 0))
  plot( S0, r0, cex.lab = 1.5, cex.axis = 1.5, xlab = "Candidate starting date (day-of-year)", 
        ylab="Correlation coefficient between the mean temperature and FFD", type="l" )
  ind <- which.min(r0)
  points(S0[ind], r0[ind], cex = 1.5, pch = 16)
  text(S0[ind], r0[ind] + 0.1, bquote(paste(italic(S), " = ", .(S0[ind]), sep = "")), cex = 1.5)
  par(par1)
  par(par2)
  par(par3)

  resu1 <- ADD( S.pd = 65, T0.arr = seq(-10, 0, by = 0.1), Year1 = Year1.val, Time = Time.val, 
                Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, 
                DOY.ul = DOY.ul.val, fig.opt = TRUE, S.def = 54, verbose = TRUE )
  resu1

  # graphics.off()

Function for Implementing the Accumulated Degree Days Method Using Minimum and Maximum Daily Temperatures

Description

Estimates the starting date (S, in day-of-year) and base tempeature (T_{0}, in {}^{\circ}C) in the accumulated degree days method using minimum and maximum daily air temperatures (Aono, 1993; Shi et al., 2017a, b).

Usage

ADD2(S.pd = NULL, T0.arr, Year1, Time, Year2, DOY, Tmin, Tmax,  
     DOY.ul = 120, fig.opt = TRUE, S.def = 54, verbose = TRUE)

Arguments

Details

The default of S.pd is NULL. In this case, the date associated with the minimum correlation coefficient [between the mean of the (Tmin + Tmax)/2 values (from a candidate starting date to the observed occurrence time) and the observed occurrence time] will be determined to be the starting date on the condition that it is smaller than the mininum phenological occurrence time. If the determined date associated with the minimum correlation coefficient is greater than the mininum phenological occurrence time, S.def will be used as the starting date. If S.pd is not NULL, the starting date will be directly set as S.pd irrespective of the minimum correlation coefficient method and the value of S.def. This means that S.pd is superior to S.def in determining the starting date.

\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.

Value

Note

The entire minimum and maximum daily temperature data set for the spring of each year should be provided. AADD is represented by the mean of AADD.arr in the output. When the argument of S.pd is not NULL, the returned value of search.failure will be NA. When the argument of S.pd is NULL, and the minimum correlation coefficient method fails to find a suitable starting date, the argument of S.def is then defined as the determined starting date, i.e., the returned value of S. At the same time, the returned value of cor.coef is defined as NA.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADD2

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
T0.arr0    <- seq(3.5, 4, by = 0.1) 
S.pd0      <- NULL


  cand.res1 <- ADD2( S.pd = S.pd0, T0.arr = T0.arr0, Year1 = Year1.val, Time = Time.val, 
                     Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, 
                     DOY.ul = DOY.ul.val, fig.opt = TRUE, S.def=54, verbose = TRUE )
  cand.res1

  S0 <- cand.res1$S.arr 
  r0 <- cand.res1$cor.coef.arr
  
  dev.new()
  par1 <- par(family="serif")
  par2 <- par(mar=c(5, 5, 2, 2))
  par3 <- par(mgp=c(3, 1, 0))
  plot( S0, r0, cex.lab = 1.5, cex.axis = 1.5, xlab = "Candidate starting date (day-of-year)", 
        ylab="Correlation coefficient between the mean temperature and FFD", type="l" )
  ind <- which.min(r0)
  points(S0[ind], r0[ind], cex = 1.5, pch = 16)
  text(S0[ind], r0[ind] + 0.1, bquote(paste(italic(S), " = ", .(S0[ind]), sep = "")), cex = 1.5)
  par(par1)
  par(par2)
  par(par3)

  # graphics.off()

Function for Implementing the Accumulated Degree Days Method Using Mean Daily Temperatures for the Combinations of the Starting Date and Base Temperature

Description

Estimates the starting date (S, in day-of-year) and base temperature (T_{0}, in {}^{\circ}C) in the accumulated degree days (ADD) method using mean daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

ADD3( S.arr, T0.arr, Year1, Time, Year2, DOY, Temp, DOY.ul = 120, 
      fig.opt = TRUE, verbose = TRUE )

Arguments

Details

When fig.opt is equal to TRUE, it will show the contours of the root-mean-square errors (RMSEs) based on different combinations of S and T_{0}.

\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.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided. AADD is represented by the mean of AADD.arr in the output.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADD

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     <- seq(60, 70, by = 1)
T0.arr0    <- seq(-2, 5, by = 1)


  RES1 <- ADD3( S.arr = S.arr0, T0.arr = T0.arr0, Year1 = Year1.val, Time = Time.val, 
                Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, DOY.ul = DOY.ul.val, 
                fig.opt = TRUE, verbose = TRUE)
  RES1

  RMSE.mat0  <- RES1$RMSE.mat
  RMSE.range <- range(RMSE.mat0)

  dev.new()
  par1 <- par(family="serif")
  par2 <- par(mar=c(5, 5, 2, 2))
  par3 <- par(mgp=c(3, 1, 0))
  image( S.arr0, T0.arr0, RMSE.mat0, col = terrain.colors(200), axes = TRUE, 
         cex.axis = 1.5, cex.lab = 1.5, xlab = "Starting date (day-of-year)", 
         ylab = expression(paste("Base temperature (", degree, "C)", sep = "")))
  points( RES1$S, RES1$T0, cex = 1.5, pch = 16, col = 2 )
  contour( S.arr0, T0.arr0, RMSE.mat0, levels = round(seq(RMSE.range[1], 
           RMSE.range[2], len = 20), 4), add = TRUE, cex = 1.5, col = "#696969", labcex = 1.5)
  par(par1)
  par(par2)
  par(par3)

  # graphics.off()

Function for Implementing the Accumulated Degree Days Method Using Minimum and Maximum Daily Temperatures for the Combinations of the Starting Date and Base Temperature

Description

Estimates the starting date (S, in day-of-year) and base temperature (T_{0}, in {}^{\circ}C) in the accumulated degree days (ADD) method using minimum and maximum daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

ADD4( S.arr, T0.arr, Year1, Time, Year2, DOY, Tmin, Tmax, DOY.ul = 120, 
      fig.opt = TRUE, verbose = TRUE )

Arguments

Details

When fig.opt is equal to TRUE, it will show the contours of the root-mean-square errors (RMSEs) based on different combinations of S and T_{0}.

\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.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided. AADD is represented by the mean of AADD.arr in the output.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADD2

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.arr0     <- seq(63, 66, by = 1)
T0.arr0    <- 3.8


  RES2 <- ADD4( S.arr = S.arr0, T0.arr = T0.arr0, Year1 = Year1.val, Time = Time.val, 
                Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, 
                DOY.ul = DOY.ul.val, fig.opt = TRUE, verbose = TRUE)
  RES2


  RESU2 <- ADD4( S.arr = 65, T0.arr = seq(2, 6, by = 1), Year1 = Year1.val, Time = Time.val, 
                 Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, 
                 DOY.ul = DOY.ul.val, fig.opt = TRUE, verbose = TRUE)
  RESU2

  # graphics.off()

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

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

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. 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. 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. 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. 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. 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()

Function for Implementing the Accumulated Developmental Progress Method Using Minimum and Maximum 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 minimum and maximum daily air temperatures (Wagner et al., 1984; Shi et al., 2017a, b).

Usage

ADP2( S.arr, expr, ini.val, Year1, Time, Year2, DOY, Tmin, Tmax, 
      DOY.ul = 120, fig.opt = TRUE, control = list(), verbose = TRUE )

Arguments

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 ADTS2 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}}\sum_{w=1}^{24}\frac{r_{ijw}\left(\mathrm{\mathbf{P}}; T_{ijw}\right)}{24},

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, T_{ijw} represents the estimated mean hourly temperature of the wth hour of the jth day of the ith year (in {}^{\circ}C or K), and r_{ijw} represents the developmental rate (per hour) at T_{ijw}, which is transferred to r_{ij} (per day) by dividing 24. This packages takes the method proposed by Zohner et al. (2020) to estimate the mean hourly temperature 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}r_{ijw}/24 = 100\% (where F \geq S), it follows that F is the predicted occurrence time; when \sum_{j=S}^{F}\sum_{w=1}^{24}r_{ijw}/24 < 100\% and \sum_{j=S}^{F+1}\sum_{w=1}^{24}r_{ijw}/24 > 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

Note

The entire minimum and maximum 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 estimated mean daily air temperatures (= (Tmin + Tmax)/2) from the starting date to the occurrence times, and the fourth column of Rate saves the calculated developmental rates corresponding to the estimated 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. 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. 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. 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. 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. 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. doi:10.1111/geb.13088

See Also

predADP2

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.arr0     <- 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))
}
##############################################################################

#### Provides the initial values of the parameter of Arrhenius' equation #####
ini.val0 <- list( B = 20, Ea = 14 )
##############################################################################

# The usage is similar to that of the "ADP" function. There is only a need to 
#   replace "Temp = Temp.val" with "Tmin = Tmin.val, Tmax = Tmax.val" when using 
#   the "ADP2" function.

Function for Implementing the Accumulated Days Transferred to a Standardized Temperature Method Using Mean Daily Temperatures

Description

Estimates the starting date (S, in day-of-year) and activation free energy (E_{a}, in kcal \cdot mol{}^{-1}) in the accumulated days transferred to a standardized temperature (ADTS) method using mean daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

ADTS( S.arr, Ea.arr, Year1, Time, Year2, DOY, Temp, DOY.ul = 120, 
      fig.opt = TRUE, verbose = TRUE )

Arguments

Details

When fig.opt is equal to TRUE, it will show the contours of the root-mean-square errors (RMSEs) based on different combinations of S and E_{a}.

\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.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided. AADTS is represented by the mean of AADTS.arr in the output.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADTS

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     <- seq(40, 60, by = 1)
Ea.arr0    <- seq(10, 20, by = 1)


  res3 <- ADTS( S.arr = S.arr0, Ea.arr = Ea.arr0, Year1 = Year1.val, Time = Time.val, 
                Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, DOY.ul = DOY.ul.val, 
                fig.opt = TRUE, verbose = TRUE)
  res3

  RMSE.mat0  <- res3$RMSE.mat
  RMSE.range <- range(RMSE.mat0)

  dev.new()
  par1 <- par(family="serif")
  par2 <- par(mar=c(5, 5, 2, 2))
  par3 <- par(mgp=c(3, 1, 0))
  image( S.arr0, Ea.arr0, RMSE.mat0, col = terrain.colors(200), axes = TRUE, 
         cex.axis = 1.5, cex.lab = 1.5, xlab = "Starting date (day-of-year)", 
         ylab = expression(paste(italic(E["a"]), " (kcal" %.% "mol"^{"-1"}, ")", sep = "")))
  points( res3$S, res3$Ea, cex = 1.5, pch = 16, col = 2 )
  contour( S.arr0, Ea.arr0, RMSE.mat0, levels = round(seq(RMSE.range[1], 
           RMSE.range[2], len = 20), 4), add = TRUE, cex = 1.5, col = "#696969", labcex = 1.5)
  par(par1)
  par(par2)
  par(par3)

  resu3 <- ADTS( S.arr = 47, Ea.arr = seq(10, 20, by = 0.5), Year1 = Year1.val, Time = Time.val, 
                 Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, DOY.ul = DOY.ul.val, 
                 fig.opt = TRUE, verbose = TRUE)
  resu3

  # graphics.off()

Function for Implementing the Accumulated Days Transferred to a Standardized Temperature Method Using Minimum and Maximum Daily Temperatures

Description

Estimates the starting date (S, in day-of-year) and activation free energy (E_{a}, in kcal \cdot mol{}^{-1}) in the accumulated days transferred to a standardized temperature (ADTS) method using minimum and maximum daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

ADTS2( S.arr, Ea.arr, Year1, Time, Year2, DOY, Tmin, Tmax, 
       DOY.ul = 120, fig.opt = TRUE, verbose = TRUE )

Arguments

Details

When fig.opt is equal to TRUE, it will show the contours of the root-mean-square errors (RMSEs) based on different combinations of S and E_{a}.

\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.

Value

Note

The entire minimum and maximum daily temperature data set for the spring of each year should be provided. AADTS is represented by the mean of AADTS.arr in the output.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

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. 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. doi:10.1093/aesa/sax063

See Also

predADTS2

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.arr0     <- seq(45, 47, by = 1)
Ea.arr0    <- seq(20, 24, by = 0.5)


  cand.res3 <- ADTS2( S.arr = S.arr0, Ea.arr = Ea.arr0, Year1 = Year1.val, Time = Time.val, 
                      Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val,  
                      DOY.ul = DOY.ul.val, fig.opt = TRUE, verbose = TRUE)
  cand.res3

  RMSE.mat0  <- cand.res3$RMSE.mat
  RMSE.range <- range(RMSE.mat0)

  dev.new()
  par1 <- par(family="serif")
  par2 <- par(mar=c(5, 5, 2, 2))
  par3 <- par(mgp=c(3, 1, 0))
  image( S.arr0, Ea.arr0, RMSE.mat0, col = terrain.colors(200), axes = TRUE, 
         cex.axis = 1.5, cex.lab = 1.5, xlab = "Starting date (day-of-year)", 
         ylab = expression(paste(italic(E["a"]), " (kcal" %.% "mol"^{"-1"}, ")", sep = "")))
  points( cand.res3$S, cand.res3$Ea, cex = 1.5, pch = 16, col = 2 )
  contour( S.arr0, Ea.arr0, RMSE.mat0, levels = round(seq(RMSE.range[1], 
           RMSE.range[2], len = 20), 4), add = TRUE, cex = 1.5, col = "#696969", labcex = 1.5)
  par(par1)
  par(par2)
  par(par3)

  # graphics.off()

Daily Air Temperature Data of Beijing from 1952 to 2012.

Description

The data include the mean, minimum, and maximum daily temperatures (in {}^{\circ}C) of Beijing between 1952 and 2012. Data source: China Meteorological Data Service Centre (https://data.cma.cn/en).

Usage

data(BJDAT)

Details

In the data set, there are seven columns of vectors: Year, Month, Day, DOY, MDT, MinDT, and MaxDT. Year saves the recording years; Month saves the recording months; Day saves the recording days; DOY saves the dates in day-of-year; MDT saves the mean daily temperatures (in {}^{\circ}C) corresponding to DOY; MinDT saves the minimum daily temperatures (in {}^{\circ}C) corresponding to DOY; MaxDT saves the maximum daily temperatures (in {}^{\circ}C) corresponding to DOY.

References

Guo, L., Xu, J., Dai, J., Cheng, J., Wu, H., Luedeling, E. (2015) Statistical identification of chilling and heat requirements for apricotflower buds in Beijing, China. Scientia Horticulturae 195, 138-144. doi:10.1016/j.scienta.2015.09.006

Examples

data(BJDAT)
attach(BJDAT)

x    <- as.numeric( tapply(DOY, DOY, mean) )
y    <- as.numeric( tapply(MDT, DOY, mean) )
y.sd <- as.numeric( tapply(MDT, DOY, sd) )

dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( x, y, cex = 1.5, xlim = c(0, 367), ylim = c(-10, 30), 
      cex.lab = 1.5, cex.axis = 1.5, type = "n", xlab = "Day-of-year", 
      ylab = expression(paste("Mean daily temperature (", degree, "C)", sep="")) )
for(i in 1:length(x)){
  lines(c(x[i], x[i]), c(y[i]-y.sd[i], y[i]+y.sd[i]), col=4)
}
points(x, y, cex = 1.5)
par(par1)
par(par2)
par(par3)

# graphics.off()

First flowering date records of Prunus armeniaca

Description

The data consist of the first flowering date records of Prunus armeniaca at the Summer Palace (39{}^{\circ}54'38'' N, 116{}^{\circ}8'28'' E, 50 m a.s.l.) in Beijing, China between 1963 and 2010 with the exception of 1969-1971, and 1997-2002. Data source: Chinese Phenological Observation Network (Guo et al., 2015).

Usage

data(apricotFFD)

Details

In the data set, there are two columns of vectors: Year and Time. Year saves the recording years; and Time saves the 1963-2010 first flowering dates of Prunus armeniaca (in day-of-year).

References

Guo, L., Xu, J., Dai, J., Cheng, J., Wu, H., Luedeling, E. (2015) Statistical identification of chilling and heat requirements for apricotflower buds in Beijing, China. Scientia Horticulturae 195, 138-144. doi:10.1016/j.scienta.2015.09.006

Examples

data(apricotFFD)
attach(apricotFFD)

dev.new()
par1 <- par(family="serif")
par2 <- par(mar=c(5, 5, 2, 2))
par3 <- par(mgp=c(3, 1, 0))
plot( Year, Time, asp = 1, cex.lab = 1.5, cex.axis = 1.5, 
      xlab = "Year", ylab = "First flowering date (day-of-year)" ) 
par(par1)
par(par2)
par(par3)

# graphics.off()

Prediction Function of the Accumulated Degree Days Method Using Mean Daily Temperatures

Description

Predicts the occurrence times using the accumulated degree days method based on observed or predicted mean daily air temperatures (Aono, 1993; Shi et al., 2017a, b).

Usage

predADD(S, T0, AADD, Year2, DOY, Temp, DOY.ul = 120)

Arguments

Details

In the accumulated degree days (ADD) method (Shi et al., 2017a, b), the starting date (S), the base temperature (T_{0}), and the annual accumulated degree days (AADD, which is denoted by k) are assumed to be constants across different years. Let k_{i} denote the AADD of the ith year, which equals

k_{i} = \sum_{j=S}^{E_{i}}\left(T_{ij}-T_{0}\right),

where E_{i} represents the ending date (in day-of-year), i.e., the occurrence time of a particular phenological event in the ith year, and T_{ij} represents the mean daily temperature of the jth day of the ith year (in {}^{\circ}C). If T_{ij} \le T_{0}, T_{ij} - T_{0} is defined to be zero. In theory, k_{i} = k, i.e., the AADD values of different years are a constant. However, in practice, there is a certain deviation of k_{i} from k that is estimated by \overline{k} (i.e., the mean of the k_{i} values). The following approach is used to determine the predicted occurrence time. When \sum_{j=S}^{F}\left(T_{ij}-T_{0}\right) = \overline{k} (where F \geq S), it follows that F is the predicted occurrence time; when \sum_{j=S}^{F}\left(T_{ij}-T_{0}\right) < \overline{k} and \sum_{j=S}^{F+1}\left(T_{ij}-T_{0}\right) > \overline{k}, the trapezoid method (Ring and Harris, 1983) is used to determine the predicted occurrence time.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity at College Station, Texas. Environmental Entomology 12, 482-486. 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. 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. doi:10.1093/aesa/sax063

See Also

ADD, ADD3

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.val      <- 65
T0.val     <- -0.5 
AADD.val   <- 235.5282

res2 <- predADD( S = S.val, T0 = T0.val, AADD = AADD.val, 
                 Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, 
                 DOY.ul = DOY.ul.val )
res2


ind1  <- res2$Year %in% intersect(res2$Year, Year1.val)
ind2  <- Year1.val %in% intersect(res2$Year, Year1.val)
RMSE1 <- sqrt( sum((Time.val[ind2]-res2$Time.pred[ind1])^2) / length(Time.val[ind2]) ) 
RMSE1 

Prediction Function of the Accumulated Degree Days Method Using Minimum and Maximum Daily Temperatures

Description

Predicts the occurrence times using the accumulated degree days method based on observed or predicted minimum and maximum daily air temperatures (Aono, 1993; Shi et al., 2017a, b).

Usage

predADD2(S, T0, AADD, Year2, DOY, Tmin, Tmax, DOY.ul = 120)

Arguments

Details

In the accumulated degree days (ADD) method (Shi et al., 2017a, b), the starting date (S), the base temperature (T_{0}), and the annual accumulated degree days (AADD, which is denoted by k) are assumed to be constants across different years. Let k_{i} denote the AADD of the ith year, which equals

k_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\frac{\left(T_{ijw}-T_{0}\right)}{24},

where E_{i} represents the ending date (in day-of-year), i.e., the occurrence time of a particular phenological event in the ith year, and T_{ijw} represents the estimated mean hourly temperature of the wth hour of the jth day of the ith year (in {}^{\circ}C). If T_{ijw} \le T_{0}, T_{ijw} - T_{0} is defined to be zero. 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, k_{i} = k, i.e., the AADD values of different years are a constant. However, in practice, there is a certain deviation of k_{i} from k that is estimated by \overline{k} (i.e., the mean of the k_{i} values). The following approach is used to determine the predicted occurrence time. When \sum_{j=S}^{F}\sum_{w=1}^{24}\left(T_{ijw}-T_{0}\right)/24 = \overline{k} (where F \geq S), it follows that F is the predicted occurrence time; when \sum_{j=S}^{F}\sum_{w=1}^{24}\left(T_{ijw}-T_{0}\right)/24 < \overline{k} and \sum_{j=S}^{F+1}\sum_{w=1}^{24}\left(T_{ijw}-T_{0}\right)/24 > \overline{k}, the trapezoid method (Ring and Harris, 1983) is used to determine the predicted occurrence time.

Value

Note

The entire minimum and maximum daily temperature data set for the spring of each year should be provided.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity at College Station, Texas. Environmental Entomology 12, 482-486. 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. 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. doi:10.1093/aesa/sax063

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. doi:10.1111/geb.13088

See Also

ADD2, ADD4

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      <- 65
T0.val     <- 3.8
AADD.val   <- 136.5805


  cand.res2 <- predADD2( S = S.val, T0 = T0.val, AADD = AADD.val, Year2 = Year2.val, 
                         DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, 
                         DOY.ul = DOY.ul.val )
  cand.res2


  ind1  <- cand.res2$Year %in% intersect(cand.res2$Year, Year1.val)
  ind2  <- Year1.val %in% intersect(cand.res2$Year, Year1.val)
  RMSE1 <- sqrt( sum((Time.val[ind2]-cand.res2$Time.pred[ind1])^2) / length(Time.val[ind2]) ) 
  RMSE1 

Prediction Function of the Accumulated Developmental Progress Method Using Mean Daily Temperatures

Description

Predicts the occurrence times using the accumulated developmental progress (ADP) method based on observed or predicted mean daily air temperatures (Wagner et al., 1984; Shi et al., 2017a, b).

Usage

predADP(S, expr, theta, Year2, DOY, Temp, DOY.ul = 120)

Arguments

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}}r_{ij},

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. 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}}\mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ij}}\right),

where T_{ij} represents the mean daily temperature of the jth day of the ith year (in 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.

\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

Note

The entire mean daily temperature data set for the spring of each year should be provided. It should be noted that the unit of Temp 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}}\left[{10}^{12} \cdot \mathrm{exp}\left(B - \frac{E_{a}}{R\,T_{ij}}\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. 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. 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. 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. doi:10.1093/aesa/77.2.208

See Also

ADP

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.val      <- 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))
}

P0 <- c(-4.3787, 15.0431)
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)

res6 <- predADP( S = S.val, expr = Arrhenius.eqn, theta = P0, Year2 = Year2.val, 
                 DOY = DOY.val, Temp = Temp.val, DOY.ul = DOY.ul.val )
res6

ind5 <- res6$Year %in% intersect(res6$Year, Year1.val)
ind6  <- Year1.val %in% intersect(res6$Year, Year1.val)
RMSE3 <- sqrt( sum((Time.val[ind6]-res6$Time.pred[ind5])^2) / length(Time.val[ind6]) ) 
RMSE3 

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

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

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. 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. 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. 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. 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. 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 

Prediction Function of the Accumulated Days Transferred to a Standardized Temperature Method Using Mean Daily Temperatures

Description

Predicts the occurrence times using the accumulated days transferred to a standardized temperature (ADTS) method based on observed or predicted mean daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

predADTS(S, Ea, AADTS, Year2, DOY, Temp, DOY.ul = 120)

Arguments

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 consistence 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.

\qquadAccording to the definition of the developmental rate (r), it is the developmental progress per unit time (e.g., per day, per hour), which equals the reciprocal of the developmental duration D, i.e., r = 1/D. Let T_{s} represent the standard temperature (in K), and r_{s} represent the developmental rate at T_{s}. Let r_{j} represent the developmental rate at T_{j}, an arbitrary temperature (in K). It is apparent that D_{s}r_{s} = D_{j}r_{j} = 1. It follows that

\frac{D_{s}}{D_{j}} = \frac{r_{j}}{r_{s}} = \mathrm{exp}\left[\frac{E_{a}\left(T_{j}-T_{s}\right)}{R\,T_{j}\,T_{s}}\right],

where D_{s}/D_{j} is referred to as the number of days transferred to a standardized temperature (DTS) (Konno and Sugihara, 1986; Aono, 1993).

\qquadIn the accumulated days transferred to a standardized temperature (ADTS) method, the annual accumulated days transferred to a standardized temperature (AADTS) is assumed to be a constant. Let \mathrm{AADTS}_{i} denote the AADTS of the ith year, which equals

\mathrm{AADTS}_{i} = \sum_{j=S}^{E_{i}}\left\{\mathrm{exp}\left[\frac{E_{a}\left(T_{ij}-T_{s}\right)}{R\,T_{ij}\,T_{s}}\right]\right\},

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, and T_{ij} represents the mean daily temperature of the jth day of the ith year (in K). In theory, \mathrm{AADTS}_{i} = \mathrm{AADTS}, i.e., the AADTS values of different years are a constant. However, in practice, there is a certain deviation of \mathrm{AADTS}_{i} from \mathrm{AADTS} that is estimated by \overline{\mathrm{AADTS}} (i.e., the mean of the \mathrm{AADTS}_{i} values). The following approach is used to determine the predicted occurrence time. When \sum_{j=S}^{F}\left\{\mathrm{exp}\left[\frac{E_{a}\left(T_{ij}-T_{s}\right)} {R\,T_{ij}\,T_{s}}\right]\right\} = \overline{\mathrm{AADTS}} (where F \geq S), it follows that F is the predicted occurrence time; when \sum_{j=S}^{F}\left\{\mathrm{exp}\left[ \frac{E_{a}\left(T_{ij}-T_{s}\right)}{R\,T_{ij}\,T_{s}}\right]\right\} < \overline{\mathrm{AADTS}} and \sum_{j=S}^{F+1}\left\{\mathrm{exp}\left[\frac{E_{a}\left(T_{ij}-T_{s}\right)} {R\,T_{ij}\,T_{s}}\right]\right\} > \overline{\mathrm{AADTS}}, the trapezoid method (Ring and Harris, 1983) is used to determine the predicted occurrence time.

Value

Note

The entire mean daily temperature data set for the spring of each year should be provided. It should be noted that the unit of Temp in Arguments is {}^{\circ}C, not K.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity at College Station, Texas. Environmental Entomology 12, 482-486. 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. 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. doi:10.1093/aesa/sax063

See Also

ADTS

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.val      <- 47
Ea.val     <- 15 
AADTS.val  <- 8.5879

res4 <- predADTS( S = S.val, Ea = Ea.val, AADTS = AADTS.val, 
                  Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val, 
                  DOY.ul = DOY.ul.val )
res4

ind3  <- res4$Year %in% intersect(res4$Year, Year1.val)
ind4  <- Year1.val %in% intersect(res4$Year, Year1.val)
RMSE2 <- sqrt( sum((Time.val[ind4]-res4$Time.pred[ind3])^2) / length(Time.val[ind4]) ) 
RMSE2 

Prediction Function of the Accumulated Days Transferred to a Standardized Temperature Method Using Minimum and Maximum Daily Temperatures

Description

Predicts the occurrence times using the accumulated days transferred to a standardized temperature (ADTS) method based on observed or predicted minimum and maximum daily air temperatures (Konno and Sugihara, 1986; Aono, 1993; Shi et al., 2017a, b).

Usage

predADTS2(S, Ea, AADTS, Year2, DOY, Tmin, Tmax, DOY.ul = 120)

Arguments

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 consistence 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.

\qquadAccording to the definition of the developmental rate (r), it is the developmental progress per unit time (e.g., per day, per hour), which equals the reciprocal of the developmental duration D, i.e., r = 1/D. Let T_{s} represent the standard temperature (in K), and r_{s} represent the developmental rate at T_{s}. Let r_{j} represent the developmental rate at T_{j}, an arbitrary temperature (in K). It is apparent that D_{s}r_{s} = D_{j}r_{j} = 1. It follows that

\frac{D_{s}}{D_{j}} = \frac{r_{j}}{r_{s}} = \mathrm{exp}\left[\frac{E_{a}\left(T_{j}-T_{s}\right)}{R\,T_{j}\,T_{s}}\right],

where D_{s}/D_{j} is referred to as the number of days transferred to a standardized temperature (DTS) (Konno and Sugihara, 1986; Aono, 1993).

\qquadIn the accumulated days transferred to a standardized temperature (ADTS) method, the annual accumulated days transferred to a standardized temperature (AADTS) is assumed to be a constant. Let \mathrm{AADTS}_{i} denote the AADTS of the ith year, which equals

\mathrm{AADTS}_{i} = \sum_{j=S}^{E_{i}}\sum_{w=1}^{24}\left\{\frac{1}{24}\,\mathrm{exp}\left[\frac{E_{a}\left(T_{ijw}-T_{s}\right)}{R\,T_{ijw}\,T_{s}}\right]\right\},

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, and 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{AADTS}_{i} = \mathrm{AADTS}, i.e., the AADTS values of different years are a constant. However, in practice, there is a certain deviation of \mathrm{AADTS}_{i} from \mathrm{AADTS} that is estimated by \overline{\mathrm{AADTS}} (i.e., the mean of the \mathrm{AADTS}_{i} values). The following approach is used to determine the predicted occurrence time. When \sum_{j=S}^{F}\sum_{w=1}^{24}\left\{\frac{1}{24}\,\mathrm{exp}\left[\frac{E_{a}\left(T_{ijw}-T_{s}\right)} {R\,T_{ijw}\,T_{s}}\right]\right\} = \overline{\mathrm{AADTS}} (where F \geq S), it follows that F is the predicted occurrence time; when \sum_{j=S}^{F}\sum_{w=1}^{24}\left\{\frac{1}{24}\,\mathrm{exp}\left[ \frac{E_{a}\left(T_{ijw}-T_{s}\right)}{R\,T_{ijw}\,T_{s}}\right]\right\} < \overline{\mathrm{AADTS}} and \sum_{j=S}^{F+1}\sum_{w=1}^{24}\left\{\frac{1}{24}\,\mathrm{exp}\left[\frac{E_{a}\left(T_{ijw}-T_{s}\right)} {R\,T_{ijw}\,T_{s}}\right]\right\} > \overline{\mathrm{AADTS}}, the trapezoid method (Ring and Harris, 1983) is used to determine the predicted occurrence time.

Value

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.

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

Aono, Y. (1993) Climatological studies on blooming of cherry tree (Prunus yedoensis) by means of DTS method. Bulletin of the University of Osaka Prefecture. Ser. B, Agriculture and life sciences 45, 155-192 (in Japanese with English abstract).

Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. Bulletin of National Institute for Agro-Environmental Sciences 1, 51-68 (in Japanese with English abstract).

Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity at College Station, Texas. Environmental Entomology 12, 482-486. 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. 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. doi:10.1093/aesa/sax063

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. doi:10.1111/geb.13088

See Also

ADTS2

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$MinDT
Tmax.val   <- X2$MaxD
DOY.ul.val <- 120
S.val      <- 46
Ea.val     <- 22.3 
AADTS.val  <- 4.911035


  cand.res4 <- predADTS2( S = S.val, Ea = Ea.val, AADTS = AADTS.val, 
                          Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, 
                          Tmax = Tmax.val, DOY.ul = DOY.ul.val )
  cand.res4

  ind3  <- cand.res4$Year %in% intersect(cand.res4$Year, Year1.val)
  ind4  <- Year1.val %in% intersect(cand.res4$Year, Year1.val)
  RMSE2 <- sqrt( sum((Time.val[ind4]-cand.res4$Time.pred[ind3])^2) / length(Time.val[ind4]) ) 
  RMSE2 

Spring Phenological Prediction

Description

Predicts the occurrence times (in day-of-year) of spring phenological events. Three methods, including the accumulated degree days (ADD) method, the accumulated days transferred to a standardized temperature (ADTS) method, and the accumulated developmental progress (ADP) method, were used. See Shi et al. (2017a, 2017b) for details.

Details

The DESCRIPTION file:

Index of help topics:

ADD                     Function for Implementing the Accumulated
                        Degree Days Method Using Mean Daily
                        Temperatures
ADD2                    Function for Implementing the Accumulated
                        Degree Days Method Using Minimum and Maximum
                        Daily Temperatures
ADD3                    Function for Implementing the Accumulated
                        Degree Days Method Using Mean Daily
                        Temperatures for the Combinations of the
                        Starting Date and Base Temperature
ADD4                    Function for Implementing the Accumulated
                        Degree Days Method Using Minimum and Maximum
                        Daily Temperatures for the Combinations of the
                        Starting Date and Base Temperature
ADP                     Function for Implementing the Accumulated
                        Developmental Progress Method Using Mean Daily
                        Temperatures
ADP2                    Function for Implementing the Accumulated
                        Developmental Progress Method Using Minimum and
                        Maximum Daily Temperatures
ADTS                    Function for Implementing the Accumulated Days
                        Transferred to a Standardized Temperature
                        Method Using Mean Daily Temperatures
ADTS2                   Function for Implementing the Accumulated Days
                        Transferred to a Standardized Temperature
                        Method Using Minimum and Maximum Daily
                        Temperatures
BJDAT                   Daily Air Temperature Data of Beijing from 1952
                        to 2012.
apricotFFD              First flowering date records of _Prunus
                        armeniaca_
predADD                 Prediction Function of the Accumulated Degree
                        Days Method Using Mean Daily Temperatures
predADD2                Prediction Function of the Accumulated Degree
                        Days Method Using Minimum and Maximum Daily
                        Temperatures
predADP                 Prediction Function of the Accumulated
                        Developmental Progress Method Using Mean Daily
                        Temperatures
predADP2                Prediction Function of the Accumulated
                        Developmental Progress Method Using Minimum and
                        Maximum Daily Temperatures
predADTS                Prediction Function of the Accumulated Days
                        Transferred to a Standardized Temperature
                        Method Using Mean Daily Temperatures
predADTS2               Prediction Function of the Accumulated Days
                        Transferred to a Standardized Temperature
                        Method Using Minimum and Maximum Daily
                        Temperatures
spphpr                  Spring Phenological Prediction
toDOY                   Function for Transferring a Date to the Value
                        of Day-of-Year

Note

We thank Benjamin Altmann, Lei Chen, Linli Deng, Feng Ge, Wen Gu, Liang Guo, Jianguo Huang, Cang Hui, Konstanze Lauseker, Gadi V.P. Reddy, Di Tang, Yunfeng Yang, Mei Xiao, Lin Wang, and Wangxiang Zhang for their valuable help during the development of this package.

Author(s)

Peijian Shi [aut, cre], Zhenghong Chen [aut], Jing Tan [aut], Brady K. Quinn [aut]

Maintainer: Peijian Shi <pjshi@njfu.edu.cn>

References

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. 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. doi:10.1093/aesa/sax063

Function for Transferring a Date to the Value of Day-of-Year

Description

Transfers the date (from year, month and day) to the value of day-of-year.

Usage

toDOY(Year, Month, Day)

Arguments

Details

The user needs to provide the three separate vectors of Year, Month and Day, rather than providing a single date vector. The arguments can be numerical vectors or character vectors.

Value

The returned value is a vector of transferred dates in day-of-year.

Note

The returned vector, DOY, usually matches with the year vector and the mean daily temperature vector as arguments in other functions, e.g., the ADD function.

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

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. 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. doi:10.1093/aesa/sax063

See Also

BJDAT

Examples

data(BJDAT)
X2   <- BJDAT
DOY2 <- toDOY(X2$Year, X2$Month, X2$Day)
# cbind(X2$DOY, DOY2)