predADTS {spphpr}R Documentation

Prediction Function of the Accumulated Days Transferred to a Standardized Temperature Method

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, 2017b).

Usage

predADTS(S, Ea, AADTS, Year2, DOY, Temp, 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) when the climate data exist

Temp

the mean 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 showing phenological events in early spring often experience several cold days during the development. In this case, Arrhenius' equation (Shi et al., 2017a, 2017b, 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 keep the consistence of the unit used in E_{a} and R, we need to re-assign R to be 1.987\times {10}^{-3} to make 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}. 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\} = \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\} < \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\} > \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 occurence times (day of year) in different years

Note

The entire mean daily temperature data in the spring of each year should be provided. There is a need to note 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, 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(BJMDT)
X1 <- apricotFFD
X2 <- BJMDT
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     <- 14 
AADTS.val  <-  9.607107

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 


[Package spphpr version 0.1.4 Index]