# Function for Implementing the Accumulated Days Transferred to a Standardized Temperature Method Using Minimum and Maximum Daily Temperatures 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). ```r ADTS2( S.arr, Ea.arr, Year1, Time, Year2, DOY, Tmin, Tmax, DOY.ul = 120, fig.opt = TRUE, verbose = TRUE ) ``` ## Arguments - `S.arr`: the candidate starting dates for thermal accumulation (in day-of-year) - `Ea.arr`: the candidate activation free energy values (in kcal $\cdot$ mol${}^{-1}$) - `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 determination of the combination the starting date and activation free energy, and a comparison between the predicted and observed occurrence times - `verbose`: an optional argument allowing users to suppress the printing of computation progress ## 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 $E_{a}$. $\qquad$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 - **mAADTS.mat**: a matrix consisting of the means of the annual accumulated days transferred to a standardized temperature (AADTS) values from the combinations of $S$ and $E_{a}$ - **RMSE.mat**: the matrix consisting of the RMSEs (in days) from different combinations of $S$ and $E_{a}$ - **AADTS.arr**: the AADTS values in different years associated with the smallest value in `RMSE.mat` - **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) - **Ea**: the determined activation free energy value (in kcal$\cdot$mol${}^{-1}$) - **AADD**: the expected AADTS - **RMSE**: the smallest RMSE (in days) in `RMSE.mat` from different combinations of $S$ and $E_{a}$ - **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$-$192 (in Japanese with English abstract). Konno, T., Sugihara, S. (1986) Temperature index for characterizing biological activity in soil and its application to decomposition of soil organic matter. **Bulletin of National Institute for Agro-Environmental Sciences** 1, 51$-$68 (in Japanese with English abstract). Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures. **Agricultural and Forest Meteorology** 240$-$241, 78$-$89. tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001") Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (III) Phenological applications. **Annals of the Entomological Society of America** 110, 558$-$564. tools:::Rd_expr_doi("10.1093/aesa/sax063") ## Author(s) Peijian Shi pjshi@njfu.edu.cn , Zhenghong Chen chenzh64@126.com , Jing Tan jmjwyb@163.com , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca . ## Note The entire minimum and maximum daily temperature data set for the spring of each year should be provided. `AADTS` is represented by the mean of `AADTS.arr` in the output. ## See Also `predADTS2` ## Examples ```r data(apricotFFD) data(BJDAT) X1 <- apricotFFD X2 <- BJDAT Year1.val <- X1$Year Time.val <- X1$Time Year2.val <- X2$Year DOY.val <- X2$DOY Tmin.val <- X2$MinDT Tmax.val <- X2$MaxDT DOY.ul.val <- 120 S.arr0 <- seq(45, 47, by = 1) Ea.arr0 <- seq(20, 24, by = 0.5) cand.res3 <- ADTS2( S.arr = S.arr0, Ea.arr = Ea.arr0, Year1 = Year1.val, Time = Time.val, Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, DOY.ul = DOY.ul.val, fig.opt = TRUE, verbose = TRUE) cand.res3 RMSE.mat0 <- cand.res3$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() ```

ADTS2 function