Calculating the monthly conventional Palmer Drought Severity Index (PDSI) and Self-calibrating PDSI (scPDSI) using the precipitation and potential evapotranspiration.
pdsi(P, PE, AWC = 100, start = NULL, end = NULL, cal_start = NULL,
cal_end = NULL, sc = TRUE)Monthly precipitation series without NA [mm]. Can be a time series.
Monthly potential evapotranspiration corresponding to the precipitation series. Can be calculated by the Penman-Monteith or the Thonthwate equation [mm].
Available soil water capacity of the soil layer [mm]. Default 100 mm.
Integer. Start year of the PDSI to be calculate default 1.
Integer. End year of the PDSI to be calculate.
Integer. Start year of the calibrate period. Default is start year.
Integer. End year of the calibrate period. Default is end year.
Bool. Should use the self-calibrating procedure to calculate the climatical coefficient (K2 and duration coefficients). If not it would use the default parameters of Palmer (1965).
This function return an object of class pdsi.
The object of class pdsi is a list containing the following components:
call: the call to pdsi used to generate the object.
X: time series of the X values, i.e. the Palmer Drought Severity Index (PDSI).
PHDI: time series of the Palmer hydrological drought index (PHDI).
WPLM: time series of the weighted PDSI (WPLM).
inter.vars: An time series matrix containing the intermediate variables,
including P (input precipitation), PE (input potential
evapotranspiration), PR (potential recharge of soil moisture),
PRO (potential runoff), PL (potential loss of soil moisture),
d (water deficiencies), Z (water anomoly index, i.e. Z index),
Prob (probability to end the wet or dry spell), X1, X2 and
X3 (intermediate variables of calculating the X values).
clim.coes: a matrix of the climate coefficients including alpha,
beta, gamma, delta, and K1 coefficient for each month
in a year.
calib.coes: a matrix of the coefficients in the self-calibrating procedure
of scPDSI, including m, b (slope and intercept of the
duration-accumulated Z index plot), p, q (duration factors), and
K2 (ratio to adjust K coefficient) for wet and dry spell, respectively.
Note that the P and PE would be convered from mm to inch in the calculation,
therefore the units of m, b would also be inch correspondingly.
The Palmer Drought Severity Index (PDSI), proposed by Palmer (1965), is a widely used drought indicator to quantify the long-term drought conditions, for an area at a certain time. The PDSI is a semi-physical based drought index calculated using the precipitation and potential evapotranspiration data, based on a simple two-layer bucket water balance model. Conventionally, the constants to calculate the PDSI were firstly empirically derived by using the meteorological records in Kansas and Iowa in middle US with a semi-arid climate conditions, therefore the conventional PDSI usually could not satisfactorily represent the drought conditions for other areas around the world, which also makes spatial comparisons of PDSI values difficult.
For this, Wells et al. (2004) proposed a self-calibrating Palmer Drought Severity Index (scPDSI). The scPDSI could automatically adjust the empirical constants in the PDSI computation with dynamically calculated values. Several works have proved that the scPDSI performs better in spatially comparison than the conventional PDSI. For more details please see the works of Wells et al. (2004).
This function could also calculate the conventional PDSI with revised constants. Before the scPDSI appeared, the PDSI calculation has also been revised focusing on the local climate characteristics in many area around the world. Those constants could be reset by using the global options before calculating the PDSI e.g.:
options(PDSI.coe.K1.1 = 1.6)
And calculation in the PDSI would be: $$Ki0=coeK11 * lg(((PEi+Ri+ROi)/(Pi+Li)+coeK12)/Di)+coeK13$$ $$Ki=coeK2/(\sum Dj*Kj) * Ki$$ $$X[i]=p*X[i-1]+q*Z[i]$$
\(coeK11\), \(coeK12\), \(coeK13\), \(coeK2\), \(p\), and \(q\) are
corresponding to PDSI.coe.K1.1, PDSI.coe.K1.2, PDSI.coe.K1.3,
PDSI.coe.K2, PDSI.p, and PDSI.q, respectively.
For example, in a national standard in China about meteorological drought level (GB/T 20481-2017), the PDSI was revised by re-adjust the constants in the calculation. To use the PDSI based on this standard should set the global options of R as follows:
options(PDSI.coe.K1.1 = 1.6) options(PDSI.coe.K1.3 = 0.4) options(PDSI.coe.K2 = 16.84) options(PDSI.p = 0.755) options(PDSI.q = 1/1.63)
Palmer W., 1965. Meteorological drought. U.s.department of Commerce Weather Bureau Research Paper.
Wells, N., Goddard, S., Hayes, M. J., 2004. A Self-Calibrating Palmer Drought Severity Index. Journal of Climate, 17(12):2335-2351.
# NOT RUN {
library(scPDSI)
data(Lubuge)
P <- Lubuge$P
PE <- Lubuge$PE
sc_pdsi <- pdsi(P, PE, start = 1960)
plot(sc_pdsi) # plot PDSI
plot(sc_pdsi, index = "PHDI") # plot PHDI
plot(sc_pdsi, index = "WPLM") # plot weighted PDSI
# Without self-calibrating.
ori_pdsi <- pdsi(P, PE, start = 1960, sc = FALSE)
plot(ori_pdsi)
# Without self-calibrating and use standards of
# mainland China. (GB/T 20481-2017)
options(PDSI.coe.K1.1 = 1.6)
options(PDSI.coe.K1.3 = 0.4)
options(PDSI.coe.K2 = 16.84)
options(PDSI.p = 0.755)
options(PDSI.q = 1/1.63)
gb_pdsi <- pdsi(P, PE, start = 1960, sc = FALSE)
plot(gb_pdsi)
# }
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