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 |
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 |
DOY.ul |
the upper limit of |
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.
\qquad
According 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).
\qquad
In 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 i
th 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 i
th year, and T_{ij}
represents the mean daily temperature of the
j
th day of the i
th 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
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