Palmer Drought Severity Index
(PDSI) algorithm
•The PDSI analyses either a weekly or monthly
water budget
•It assumes that evapotranspiration (ET) occurs
close to the potential monthly ET (PE) until a
certain amount of the available water is
depleted, after which the actual ET is less than
PE.
PDSI algorithm
•The PDSI uses the following equations to
compute the moisture transfer between soil
layers:
Ls = min {Ss, (PE - P)}
P < PE
(1)
Lu = [(PE - P) - Ls] Su/AWC Lu < Su, P < PE (2)
where P is the precipitation, Ls and Lu (Ss and
Su) are the moisture loss (available soil moisture
stored) in the upper or surface and underlying
layer(s) respectively at the start of the month,
and AWC is the combined available field capacity
of all soil layers.
PDSI algorithm
•Palmer (1965) assumed that no runoff occurs
until both layers reach field capacity. He
estimated PE by Thornthwaite’s (1948) method
•Palmer (1965) also computed:
1. the potential recharge (PR) that brings the
soil to field capacity,
2. the potential loss (PL) of soil moisture to ET
during dry periods, and
3. the potential runoff (PRO)
PDSI algorithm
PR=AWC-(Ss + Su)
PL = PLs+ PLu
where
PLs = min{PE,Ss}
PLu = [PE – PLs] Su/AWC
PRO = AWC-PR = Ss + Su
(3)
(4)
PLu < Su
(5)
(6)
(7)
PDSI algorithm
The following four monthly coefficients are
computed using the four potential terms, PE, PR, PRO
and PL:
(8)
(9)
(10)
(11)
where ETj , Lj , Rj, and ROj are monthly mean
evapotranspiration, moisture loss, water recharge,
and runoff respectively, and j = 1, 2, . . ., 12.
PDSI algorithm
•Palmer (1965) computed the ‘climatologically
appropriate for existing conditions’ (CAFEC)
precipitation
(12)
•Palmer (1965) introduced a moisture anomaly
index Z that signifies the departure (D=P- ) of the
monthly weather from the ‘climatically normal’
conditions for j :
Z = Kj*D
(13)
PDSI algorithm
Where Kj is a weighting factor for the month j,
which takes into account the spatial variability of
departures D, such that they are independent of
time and space.
(14)
Dj is the monthly average of dw,j, and Tj is the
ratio of ‘moisture demand’ to ‘moisture supply’:
(15)
PDSI algorithm
•In this final step the Z-index time series is
analysed to develop criteria for the beginning and
end of the periods of drought and a formula for
determining drought severity. The following
empirical expression for drought severity is used:
(16)
where Zj represents the value of the moisture
anomaly index or Z-index for the jth month and Xj
is the value of PDSI for the jth month
PDSI algorithm
The classification of weather based on PDSI (Palmer, 1965) is
shown in the following Table:
PDSI or Z-index
> 4.00
3.00 to 3.99
2.00 to 2.99
1.00 to 1.99
0.50 to 0.99
0.49 to -0.49
-0.50 to -0.99
-1.00 to -1.99
-2.00 to -0.99
-3.00 to-3.99
< -4.00
Weather
Extremely wet
Very wet
Moderately wet
Slightly wet
Incipient wet spell
Near normal
Incipient drought
Mild drought
Moderate drought
Severe drought
Extreme drought