predADTS2: Prediction Function of the Accumulated Days Transferred to a...

In spphpr: Spring Phenological Prediction

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

S	the starting date for thermal accumulation (in day-of-year)
Ea	the activation free energy (in kcal \cdot mol{}^{-1})
AADTS	the expected annual accumulated days transferred to a standardized temperature
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

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

Year	the years with climate data
Time.pred	the predicted occurrence times (day-of-year) in different years

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 [e-mail], Zhenghong Chen [e-mail], Jing Tan [e-mail], Brady K. Quinn [e-mail].

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ee/12.2.482")}

Shi, P., Chen, Z., Reddy, G.V.P., Hui, C., Huang, J., Xiao, M. (2017a) Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures. Agricultural and Forest Meteorology 240-241, 78-89. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.agrformet.2017.04.001")}

Shi, P., Fan, M., Reddy, G.V.P. (2017b) Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (III) Phenological applications. Annals of the Entomological Society of America 110, 558-564. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/aesa/sax063")}

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. \Sexpr[results=rd]{tools:::Rd_expr_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 

spphpr documentation built on April 11, 2025, 6:11 p.m.