predADTS: Prediction Function of the Accumulated Days Transferred to a...
In spphpr: Spring Phenological Prediction
predADTS R Documentation
Prediction Function of the Accumulated Days Transferred
to a Standardized Temperature Method Using Mean Daily Temperatures
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, b).
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) for which 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 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}}\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} 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}\left\{\mathrm{exp}\left[\frac{E_{a}\left(T_{ij}-T_{s}\right)}
{R\,T_{ij}\,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}\left\{\mathrm{exp}\left[
\frac{E_{a}\left(T_{ij}-T_{s}\right)}{R\,T_{ij}\,T_{s}}\right]\right\} < \overline{\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\} > \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 mean daily temperature data set for the spring of each year should be provided.
It should be noted 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,
Jing Tan jmjwyb@163.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. \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")}
See Also
ADTS
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
Temp.val <- X2$MDT
DOY.ul.val <- 120
S.val <- 47
Ea.val <- 15
AADTS.val <- 8.5879
res4 <- predADTS( S = S.val, Ea = Ea.val, AADTS = AADTS.val,
Year2 = Year2.val, DOY = DOY.val, Temp = Temp.val,
DOY.ul = DOY.ul.val )
res4
ind3 <- res4$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
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| predADTS | R Documentation |
Prediction Function of the Accumulated Days Transferred to a Standardized Temperature Method Using Mean Daily Temperatures
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, b).
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 |
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 |
Temp |
the mean daily air temperature data (in |
DOY.ul |
the upper limit of |
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}}\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} 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}\left\{\mathrm{exp}\left[\frac{E_{a}\left(T_{ij}-T_{s}\right)}
{R\,T_{ij}\,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}\left\{\mathrm{exp}\left[
\frac{E_{a}\left(T_{ij}-T_{s}\right)}{R\,T_{ij}\,T_{s}}\right]\right\} < \overline{\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\} > \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 mean daily temperature data set for the spring of each year should be provided.
It should be noted 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, Jing Tan jmjwyb@163.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. \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")}
See Also
ADTS
Examples
data(apricotFFD)
data(BJDAT)
X1 <- apricotFFD
X2 <- BJDAT
Year1.val <- X1$Year
Time.val <- X1$Time
Year2.val <- X2$Year
DOY.val <- X2$DOY
Temp.val <- X2$MDT
DOY.ul.val <- 120
S.val <- 47
Ea.val <- 15
AADTS.val <- 8.5879
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
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