# Prediction Function of the Accumulated Degree Days Method Using Minimum and Maximum Daily Temperatures 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). ```r predADD2(S, T0, AADD, Year2, DOY, Tmin, Tmax, DOY.ul = 120) ``` ## Arguments - `S`: the starting date for thermal accumulation (in day-of-year) - `T0`: the base temperature (in ${}^{\circ}$C) - `AADD`: the expected annual accumulated degree days - `Year2`: the vector of the years recording the climate data for predicting the occurrence times - `DOY`: the vector of the dates (in day-of-year) for which climate data exist - `Tmin`: the minimum daily air temperature data (in ${}^{\circ}$C) corresponding to `DOY` - `Tmax`: the maximum daily air temperature data (in ${}^{\circ}$C) corresponding to `DOY` - `DOY.ul`: the upper limit of `DOY` used to predict the occurrence time ## Details 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 $i$th 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 $i$th year, and $T_{ijw}$ represents the estimated mean hourly temperature of the $w$th hour of the $j$th day of the $i$th 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 $w$th hour of a day, and $T_{\mathrm{min}}$ and $T_{\mathrm{max}}$ represent the minimum and maximum temperatures of the day, respectively. $\qquad$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 $\sum_{j=S}^{F}\sum_{w=1}^{24}\left(T_{ijw}-T_{0}\right)/24 = \overline{k}$ (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. ## Returns - **Year**: the years with climate data - **Time.pred**: the predicted occurrence times (day-of-year) in different years ## 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$-$192 (in Japanese with English abstract). Ring, D.R., Harris, M.K. (1983) Predicting pecan nut casebearer (Lepidoptera: Pyralidae) activity at College Station, Texas. **Environmental Entomology** 12, 482$-$486. tools:::Rd_expr_doi("10.1093/ee/12.2.482") Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures. **Agricultural and Forest Meteorology** 240$-$241, 78$-$89. tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001") Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (III) Phenological applications. **Annals of the Entomological Society of America** 110, 558$-$564. tools:::Rd_expr_doi("10.1093/aesa/sax063") Zohner, C.M., Mo, L., Sebald, V., Renner, S.S. (2020) Leaf-out in northern ecotypes of wide-ranging trees requires less spring warming, enhancing the risk of spring frost damage at cold limits. **Global Ecology and Biogeography** 29, 1056$-$1072. tools:::Rd_expr_doi("10.1111/geb.13088") ## Author(s) Peijian Shi pjshi@njfu.edu.cn , Zhenghong Chen chenzh64@126.com , Jing Tan jmjwyb@163.com , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca . ## Note The entire minimum and maximum daily temperature data set for the spring of each year should be provided. ## See Also `ADD2`, `ADD4` ## Examples ```r data(apricotFFD) data(BJDAT) X1 <- apricotFFD X2 <- BJDAT Year1.val <- X1$Year Time.val <- X1$Time Year2.val <- X2$Year DOY.val <- X2$DOY Tmin.val <- X2$MinDT Tmax.val <- X2$MaxDT DOY.ul.val <- 120 S.val <- 65 T0.val <- 3.8 AADD.val <- 136.5805 cand.res2 <- predADD2( S = S.val, T0 = T0.val, AADD = AADD.val, Year2 = Year2.val, DOY = DOY.val, Tmin = Tmin.val, Tmax = Tmax.val, DOY.ul = DOY.ul.val ) cand.res2 ind1 <- cand.res2$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 ```

predADD2 function