# Function for Implementing the Accumulated Degree Days Method Using Minimum and Maximum Daily Temperatures 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). ```r ADD2(S.pd = NULL, T0.arr, Year1, Time, Year2, DOY, Tmin, Tmax, DOY.ul = 120, fig.opt = TRUE, S.def = 54, verbose = TRUE) ``` ## Arguments - `S.pd`: the pre-determined starting date for thermal accumulation (in day-of-year) - `T0.arr`: the candidate base temperatures (in ${}^{\circ}$C) - `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 - `Tmin`: the minimum daily air temperature data (in ${}^{\circ}$C) corresponding to `DOY` - `Tmax`: the maximum daily air temperature data (in ${}^{\circ}$C) corresponding to `DOY` - `DOY.ul`: the upper limit of `DOY` used to predict the occurrence time - `fig.opt`: an optional argument to draw the figures associated with the determinations of the starting date and base temperature, and a comparison between the predicted and observed occurrence times - `S.def`: a mandatory defintion of the starting date when (i) `S.pd` is NULL and (ii) the minimum correlation coefficient method fails to find a suitable starting date - `verbose`: an optional argument allowing users to suppress the printing of computation progress ## 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. $\qquad$The 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. $\qquad$The numerical value of `DOY.ul` should be greater than or equal to the maximum `Time`. ## Returns - **S.arr**: the candidate starting dates (in day-of-year), whose default ranges from the minimum `DOY` to min(`DOY.ul`, the maximum `DOY`) - **cor.coef.arr**: the candidate correlation coefficients between the mean of the (`Tmin` + `Tmax`)/2 values (from a candidate starting date to the observed occurrence time) and the observed occurrence time - **cor.coef**: the minimum correlation coefficient, i.e., min(`cor.coef.arr`) - **search.failure**: a value of 0 or 1 of showing whether the starting date is successfully determined by the minimum correlation coefficient method when `S.pd = NULL`, where 0 represents success and 1 represents failure - **mAADD.arr**: an vector saving the interannual mean of the annual acccumulated degree days (AADD) values for each of the candidate base temperatures - **RMSE.arr**: a vector saving the candidate root-mean-square errors (in days) between the observed and predicted occurrence times for each of the candidate base temperatures - **AADD.arr**: the annual accumulated degree days (AADD) values 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) - **T0**: the determined base temperature (in ${}^{\circ}$C) - **AADD**: the expected annual accumulated degree days - **RMSE**: the smallest RMSE (in days) from the different candidate base temperatures - **unused.years**: the years that have phenological records but lack climate data ## 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$-$192 (in Japanese with English abstract). Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures. **Agricultural and Forest Meteorology** 240$-$241, 78$-$89. tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001") Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (III) Phenological applications. **Annals of the Entomological Society of America** 110, 558$-$564. tools:::Rd_expr_doi("10.1093/aesa/sax063") ## Author(s) Peijian Shi pjshi@njfu.edu.cn , Zhenghong Chen chenzh64@126.com , Jing Tan jmjwyb@163.com , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca . ## Note The entire minimum and maximum daily temperature data set for the spring of each year should be provided. `AADD` is represented by the mean of `AADD.arr` in the output. When the argument of `S.pd` is not `NULL`, the returned value of `search.failure` will be `NA`. When the argument of `S.pd` is `NULL`, and the minimum correlation coefficient method fails to find a suitable starting date, the argument of `S.def` is then defined as the determined starting date, i.e., the returned value of `S`. At the same time, the returned value of `cor.coef` is defined as `NA`. ## See Also `predADD2` ## Examples ```r data(apricotFFD) data(BJDAT) X1 <- apricotFFD X2 <- BJDAT Year1.val <- X1$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() ```

ADD2 function