cc: Keith Briffa <k.briffa@uea.ac.uk>, Edward Cook <drdendro@ldeo.columbia.edu>
date: Mon, 11 Apr 2005 07:33:06 -0400
from: Edward Cook <drdendro@ldeo.columbia.edu>
subject: Re: North American SC-PDSI
to: Gerard van der Schrier <g.schrier@uea.ac.uk>

<x-rich>Hi Gerard,


Thanks for the EOT source code. I will have a go at it and let you
know if I encounter any problems with it. It looks like it won't be a
problem to deal with.


Interesting plot from the Dai data as well. Aside from what appears to
be a calibration period around months 1000-1400, the remainder of the
mins and maxs look like they have been mowed to keep them from getting
too extreme as you suggest. I am afraid that the Dai data are looking
more and more unreliable. At some point, this will need to be brought
up to Dai. Of course, Trenberth will go nuts because his name is on
the publications associated with the data.


Below is an html version of an article written by Ned Guttman that
discusses, among other things, the modified PDSI that does not require
backtracking. Some of the equations and math terms did not translate
from the paper to html, which is why there are occasional gaps in the
rendering. A more accessible description of the modified PDSI can be
found at http://nadss.unl.edu/PDSIReport/pdsi/, which is a fine review
report by Nathan Wells, author of the SC-PDSI. Go to "The Weighted
PDSI" to get a detailed description of the modified PDSI used by NOAA
for operational purposes (see below).


I hope this helps.


Cheers,


Ed


<fontfamily><param>Courier</param><bigger>DETERMINATION OF DROUGHT
FREQUENCIES FOR THE NATIONAL DROUGHT
ATLAS</bigger></fontfamily><fontfamily><param>Times</param><bigger>



</bigger></fontfamily><fontfamily><param>Courier</param><bigger>Nathaniel
B.
Guttman</bigger></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><bigger>National
Climatic Data Center, Asheville,
NC</bigger></fontfamily><fontfamily><param>Times</param><bigger>



</bigger></fontfamily><fontfamily><param>Courier</param><bigger>
1. INTRODUCTION</bigger></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><bigger>
The meaning of the word </bigger><x-tad-smaller>"drought", as used in
the National Drought Atlas, is the condition of widespread and
negative economic, social, and environmental impacts resulting from
less water than expected. The water shortfall can come from a lack of
precipitation, a deficiency in water storage and distribution systems,
or inefficient use of water. "Water management" refers to the planned
intervention of man in the hydrologic cycle of rainfall, runoff and
evapotranspiration in order to enhance water uses and reduce water
hazards. Pertaining to drought, it refers to reducing the adverse
impacts of drought, to planning activities preceding a drought, and to
operational activities during a
drought.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
One indicator of drought that is also used for water management is the
Palmer Drought Severity Index. This index, which was developed over
25 years ago (Palmer, 1965), relates the normal amount of
precipitation that should have occurred in an area to that which
actually did occur. ("Normal" is used in the sense that the moisture
supply satisfied the average or climatically expected percentage of
the absolute moisture requirements of the area.) The index is
relatively independent of time and space. It is a representation of
what Palmer called meteorological drought, i.e., an evaluation of
meteorological anomalies characterized by prolonged and abnormal
moisture deficiencies.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
This article describes the Palmer Drought Index and the data that were
used to compute the Index for the National Drought Atlas. It
discusses the methodologies, assumptions and limitations used to
prepare drought frequencies.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
2. PALMER INDEX



</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger></bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
The Palmer Drought Severity Index
(</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>)
is based on a calculated water balance using methods devised by
Thornthwaite (Thorthwaite and Mather, 1955). For month i, the
weighted moisture anomaly index, , is
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>



</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>where
k is a weighting factor that allows for spatial comparison; P, PE, PR,
PRO, and PL are the actual precipitation, computed potential
evapotranspiration, potential recharge (net gain in soil moisture),
potential runoff, and potential loss of soil moisture, respectively,
for the month; and are, respectively, the coefficients of
evapotranspiration (mean evapotranspiration divided by the mean
potential evapotranspiration), recharge (mean recharge divided by the
mean potential recharge, runoff (mean runoff divided by mean potential
runoff), and loss (mean loss divided by the potential
runoff).</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>A
drought index, , for month i is computed on an incremental basis such
that each successive month is evaluated in terms of its contribution
to the severity of drought. A recursive relationship linking one
month to the next is defined
as</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>




</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Computation
of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> requires
a tracking of the beginning, establishment and ending of wet and dry
spells. In practice, three values of are computed simultaneously
each month. The first, a wetness index , is the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
for a wet spell that might become established. The second, a dryness
index , is the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> for
a dry spell that might become established. The third, , is the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
for any wet or dry spell that has definitely become established, i.e.,
. It is also necessary to determine the percent of moisture required
to end a spell that is actually received, where the end of spell is
defined as
.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>



</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>If
a spell has become established and the percent of moisture needed to
end the spell is zero, then the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
is equal to . This condition also means that and are equal to zero.
If a wet spell is established but dry months occur so that the percent
of moisture needed to end the spell is between 0 and 100, then is
computed along with . If the percentage does not return to zero and
reaches 100 in month m, then the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
for months i through m are the values because the wet spell has
definitely ended and the dry spell has begun. If the percentage does
return to zero in month m, then the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
for months i through m are the values because the established wet
spell has not ended. Similar computations are made for established
dry spells using and . Once an established spell has ended, the value
of equals
zero.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>If
a spell is not established, and are computed simultaneously until
the month i in which either or . At this time a new spell has become
established and the procedure described in the preceding paragraph is
followed. The
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> values
for the months i backward to t are if a wet spell has become
established or if a dry spell has become established. At the point
backwards in time when the appropriate index (wet or dry) is zero, the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
becomes the other index (dry or wet) value until it reaches
zero.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Table
1, taken from Palmer (1965), arbitrarily relates an index value to a
qualitative measure of wetness or dryness. Since Palmer's original
intent was to describe drought, he postulated that an index value of
-4 would spell economic disaster in any region in which the
established economy is significantly dependent upon the weather for
its moisture supply. Values between 0 and -4 represent conditions
that are scaled between normal and economic disaster. The meaning of
positive index values is a mirror image of the meaning of the negative
values. It is based on Palmer's assumption that the abnormal moisture
departures which lead to drought would lead to wet periods if they
were positive instead of
negative.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>The 
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
is a retrospective index because current values depend on future
conditions. It is therefore useful as a climatological indicator but
not as a "real-time" index for making operational decisions. The
necessity for an index that could be used operationally led to a
variation of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> known
as the Palmer Hydrologic Drought Index or PHDI (Karl, 1986). The PHDI
avoids the backtracking problem, and can therefore be used in
"real-time", by selecting as the index value whenever the percent of
moisture needed to end an established spell is between 0 and 100 and
by selecting the nonzero or during the onset of a wet or dry spell.
The
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> and
the PHDI are identical during an established spell. They differ,
however, during the onset and ending of a spell. The PHDI during the
months that a spell is incipient may change sign from month to month
depending on the magnitude of the current month's departure from
normal conditions (i.e., ); the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
values are those for the wet (dry) index for all the incipient months
of a wet (dry) spell that does become established. At the end of a
spell, the sign of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> values
will reverse to signify the end sooner than with the PHDI
values.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
The tendency of the PHDI to switch signs during incipient conditions,
as well as the slow response of the PHDI at the end of a spell, led to
development of the </x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
as a better representation of existing conditions for real-time,
operational use (Heddinghaus and Sabol, 1991). During near normal or
incipient conditions when , the
</x-tad-smaller><bold><x-tad-smaller>modified 
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
is equal to the or with the largest absolute value. During an
established spell, the </x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
is equal to the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>.
During the end of an established spell, the
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
is equal to the weighted average of and if the spell is dry or and
if the spell is wet. The weighting factors are [1-(PCT/100)] for and
(PCT/100) for , where PCT is the percent of moisture needed to end the
spell.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
The National Drought Atlas is intended for use in real-time by water
managers. Because the </x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
values are readily available from the Weekly Weather and Crop
Bulletin, the Weekly Climate Bulletin, or the Climate Analysis
Center's Climate Dial-Up Service, it is the 
</x-tad-smaller><bold><x-tad-smaller>modified</x-tad-smaller></bold><x-tad-smaller>
Palmer Index whose values are summarized in the Atlas.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
3. LIMITATIONS OF THE PALMER INDEX
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Since the index is widely used as a drought assessment tool for water
management and planning activities (Wilhite et al., 1991; Wilhite,
1990; Grigg and Vlachos, 1990; South Carolina Water Resources
Commission, 1987; American Meteorological Society, 1986), it is
important to summarize its limitations. Palmer developed his index
from temperature and precipitation data observed in the Great Plains
(Palmer, 1965). He specifically designed the index to treat the
drought problem in semiarid and dry subhumid climates, and cautioned
that extrapolation beyond these conditions may lead to unrealistic
results. The index is, however, being computed for and used in all 48
contiguous States. Palmer also clearly states that improvements in
the computation of evapotranspiration, determination of the available
water capacity in a layer of soil, and estimation of runoff would
likely lead to better results. Not considered in his development are
conditions such as water supply from areas that are not in proximity
to the location for which the index is computed, snowmelt, or frozen
ground.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Four
previous studies examined the Palmer Index in terms of the various
assumptions and parameterizations inherent in the computation of the
index. Karl (1983) looked at drought durations and found that
increasing the available water capacity in the soil tends to increase
both the length and severity of the more extreme droughts. The effect
is greatest in the Rocky Mountain states and least in the East. For
milder droughts, there is little effect in the East. He also found
that the magnitude of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>,
but not the duration of a drought, is sensitive to the weighting
factor k that allows for spatial comparisons. He concluded that his
sensitivity experiments showed a negligible effect on drought
duration. In a second study, Karl (1986) examined the effect on both
the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller> and
PHDI of the length of the period used to compute the normal climate of
the area, and concluded that at least 50 years of data should be
used. </x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Alley
(1984), in an excellent critique of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>,
documented several limitations of the method for computing the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>.
He noted that the simplistic representation of runoff is very crude,
and that it is difficult to account for the lag between moisture
surplus and streamflow. He advised that extreme caution should be
exercised in using water balance variables such as soil moisture and
evapotranspiration in developing indices of drought. He also advised
that because terms such as "severe" and "extreme" drought are loosely
defined, care should be used when referring to drought severity
classes. Alley determined that the conditional distribution of the
</x-tad-smaller><bold><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
given the value for the previous month may be bimodal, therefore
limiting the use of conventional time series models for describing the
stochastic properties of the index. He was also disturbed by the
effect on the index of the arbitrary thresholds for determining the
beginning and ending of wet and dry spells.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Guttman (1992) examined the sensitivity of monthly time series of the
PHDI to departures from average temperature and precipitation
conditions. He found that an initialization period of up to five
years is necessary before the time series become reliable. He also
found that the effect of temperature departures from average
conditions are, from a practical view, insignificant. The PHDI is,
however, sensitive to precipitation departures from normal. The
results also show that a warmer than normal temperature usually
decreases the PHDI more than a colder than


 normal temperature of the same magnitude increases the PHDI, but
drier than normal conditions tend to decrease the index less than
wetter conditions increase the index. Guttman (1992) suggests that
the distribution of PHDI values may be asymmetric and possibly
bimodal, thereby possibly impacting threshold values used for making
operational decisions.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
4.
DATA</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Monthly </x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
values were computed for 1,036 sites across the contiguous United
States. Time series go back from 1990 (except from 1988 or 1989 for a
few sites) to at least 1930 after allowing for an initialization
period of four years. Computations required not only serially
complete monthly temperature and precipitation data, but also soil
water capacities, coefficients for computing potential
evapotranspiration, and weighting factors. The values of these latter
constants and factors that were used for the at-site computations were
the values on file at the National Climatic Data Center that are
representative of the climatic division in which the site is located.
Although not examined, the use of climatic division values was not
thought to significantly impact the at-site
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
computations. This belief is based on the results of Karl (1983) and
Guttman (1992), on the relatively small area of a climatic division
(there are 344 divisions in the 48 contiguous United States), and on
the assumption that a division is climatologically homogeneous.


</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger></bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Monthly average temperature and total precipitation data were taken
from the National Climatic Data Center's 1,219-station Historical
Climatology Network (Karl et al., 1990). Both unadjusted and adjusted
data are contained in this data set. The unadjusted data are original
observations that have undergone quality assurance checks. Missing
data have not been estimated and remain missing. The adjusted data
are the original observations that have been quality checked and 
</x-tad-smaller><bold><x-tad-smaller>modified</x-tad-smaller></bold><x-tad-smaller>
from the original data, when necessary, to account for non-climatic
effects and biases such as those caused by changes in station
location. Missing data have been estimated so that the data for a
station are essentially serially
complete.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
The estimation and modification techniques are based on the concept of
making corrections from trends and patterns at neighboring stations.
The neighbors are the closest stations within the network, and could
be large distances away. Meteorologically, precipitation is often a
localized phenomenon so that adjustments made on the basis of stations
that are not within the localized area are suspect. It was therefore
decided to use the unadjusted precipitation data for the drought
atlas. The spatial representation of monthly average temperature,
however, is generally a smooth, continuous field so that more
confidence can be placed on temperature adjustments than on
precipitation adjustments. This added confidence, coupled with the
relative insensitivity of the Palmer Index to temperature, led to the
decision to use the serially complete, adjusted temperature data for
the Atlas.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Since the unadjusted precipitation data are not serially complete, the
missing data had to be estimated. In addition, some of the monthly
precipitation totals are the sum of daily values for less than a full
month, i.e., some of the monthly data are partial totals. Because of
the localized nature of precipitation, there is no generalized,
accepted method of obtaining meteorologically reliable estimates of
missing data.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
A simple precipitation estimation procedure was used that is based on
the assumption that, even though precipitation is a localized
phenomenon, an average monthly total over a small area should be
reasonably representative of any site within the area. A missing
total for a given month and year was estimated by averaging the totals
for the month and year for all stations in the National Climatic Data
Center's Summary of the Month digital data base that are within 60
miles of the station with missing data. The number of nearby stations
whose totals were averaged varied from 1 to 87. The number of
stations depends on the density of the station network (most dense in
the Northeast and least dense in the Rocky Mountains) and the year
(fewer stations in the earlier years of the period of record). If
digital data were not available, Climatological Data publications were
examined, and the published recorded or estimated values for the month
and year in question at the Historical Climatology Network station
were used. The publications were also used to obtain a small number
of values to extend the length of record of the temperature records
(the length of record of the temperature data at a site is often
shorter than that of precipitation
data).</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
If a station had a partial precipitation total for a given month and
year, the average of the totals for the nearby stations was computed
and compared to the partial total. The higher of the partial total or
nearby station average was used as the estimate for the total for the
month and year at the station. Almost 13,000 comparisons were made
between a nearby station average and a partial total. The nearby
station average was higher than the partial total for 60 percent of
the comparisons and lower for 40 percent. These percentages
subjectively confirm the difficulty in estimating monthly
precipitation amounts over a small area and add credibility to the
decision to use the unadjusted data from the Historical Climatology
Network.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Note that the number of stations for which the drought index has been
computed is less than the number of stations for which precipitation
probabilities have been computed. It was necessary to eliminate some
stations from the drought computations because of inadequate data.
The inadequacies resulted from the requirement that both temperature
and precipitation data had to be serially complete from 1926 onward.
If either the temperature or precipitation data were not available and
missing data could not be estimated because of lack of digital or
published data from nearby stations, then the 
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
could not be computed.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
5. DROUGHT FREQUENCIES
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Drought is defined as beginning in the month and year when the
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
equals or falls below -1 after having been above -1, and drought
duration is defined as the interval of time for which the
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
remains equal or below -1. Using these definitions, frequencies of
drought beginning in a specified calendar month were tabulated for
fixed durations of 1, 2, 3, 6, 12, 24, 36 and 60
months.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
The method of counting the occurrences of drought is best illustrated
by example. Consider a site with a
</x-tad-smaller><bold><x-tad-smaller>modified
</x-tad-smaller><x-tad-smaller>PDSI</x-tad-smaller></bold><x-tad-smaller>
above -1 from January through February, 1943; at or below -1 for each
month from March 1943 through June 1946; and above -1 from July
through December 1946. For the time period from 1943 through 1946,
there would be 3 occurrences of drought with a 1-month duration
beginning (and ending) in January and February (the years 1944, 1945
and 1946), 4 occurrences in each month March through June (the years
1943, 1944, 1945 and 1946), and 3 occurrences in each month July
through December (the years 1943, 1944 and 1945). There would be 3
occurrences of 6-month droughts beginning in January (the years 1944,
1945 and 1946), 2 occurrences beginning in February (the years 1944
and 1945), and 3 occurrences beginning in each month March through
December (the years 1943, 1944 and 1945).  Multiyear drought
events with fixed durations of 24, 36 or 60 months beginning in a
specified month are non-overlapping. The drought index for a site was
examined from the beginning of the series to determine whether or not
a drought of specified duration had occurred. Once an event was
identified, the series was then examined beginning with the month
after the end of the drought to determine whether or not another
drought had occurred. For

 example, consider a drought beginning in March 1943 and ending in
June 1947 and a second drought beginning in January 1949 and ending in
December 1950. There would be two occurrences of a 24-month drought
beginning in January (January 1944-December 1945 and January
1949-December 1950), one in February (February 1944-January 1946), two
each in March through July (March 1943-February 1945 and March
1945-February 1947, etc.), and one each in August through December
(August 1943-July 1945, etc.). There would also be one occurrence of
36-month droughts beginning in each of the calendar months (January
1944-December 1946, February 1944-January 1947, March 1943-February
1946, etc.). As defined for the Atlas, there were no occurrences of a
drought with a duration of 60
months.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
Drought frequencies are expressed in terms of percentage. The number
of occurrences of droughts of a specified duration was divided by the
number of periods of the specified duration that are contained in the
whole length of record. This quotient was then multiplied by 100 to
obtain a percentage. The use of percentages allows comparisons among
stations with varying lengths of data records. Caution, however,
should be exercised in making comparisons because cyclical, aperiodic
or other climatic conditions may influence the number of droughts in
one time period differently from that in another time period.
</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>
6.
REFERENCES</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Alley,
W.M., 1984: The Palmer Drought Severity Index: Limitations and
assumptions, J. Clim. Appl. Meteor., 23,
1100-1109.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>American
Meteorological Society, 1986: Conference on Climate and Water
Management--A Critical Era, Boston, MA,
154pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Guttman,
N.B., 1992: A sensitivity analysis of the Palmer Hydrologic Drought
Index. Water Resources Bull., in
press.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Karl,
T.R., C.N. Williams, Jr., F.T. Quinlan and T.A. Boden, 1990: United
States Historical Climatology Network (HCN) serial temperature and
precipitation data. ORNL/CDIAC-30, NDP-019/R1, Carbon Dioxide
Information Analysis Center, Oak Ridge National Lab., Oak Ridge, TN,
374pp.



Grigg, N.S. and E.C. Vlachos, 1990: Drought Water Management,
International School for Water Resources, Colorado St. Univ., Ft.
Collins, CO,
252pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Heddinghaus,
T.R. and P. Sabol, 1991: A review of the Palmer Drought Severity
Index and where do we go from here? Proc. 7th Conf. on Applied
Climatology, September 10-13, 1991, American Meteorological Society,
Boston, MA,
242-246.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Karl,
T.R., 1983: Some spatial characteristics of drought duration in the
United States, J. Clim. Appl. Meteor., 22,
1356-1366.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Karl,
T.R., 1986: The sensitivity of the Palmer Drought Severity Index and
Palmer's Z-index to their calibration coefficients including
potential evapotranspiration, J. Clim. Appl. Meteor., 25, 77-86.



Palmer, W.C., 1965: Meteorological Drought. Res. Paper No. 45,
Weather Bureau, Washington, DC,
58pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>South
Carolina Water Resources Commission, 1987: Southeastern Drought
Symposium Proceedings. South Carolina State Climatology Office
Publication G-30, Columbia, SC,
110pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Thornthwaite,
C.W. and J.R. Mather, 1955: The Water Balance. Publ. in Climatology,
8, 1, Drexel Inst. Technology, Lab. Climatology, Centerton, NJ,
102pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Wilhite,
D.A., 1990: Planning for Drought: A Process for State Government.
IDIC Tech. Rep. Series 90-1, International Drought Information
Center, Univ. Nebraska, Lincoln, NE,
52pp.</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>


</bigger></fontfamily><fontfamily><param>Courier</param><x-tad-smaller>Wilhite,
D.A., D.A. Wood and P.A. Kay, 1991: Drought Management and Planning.
IDIC Tech. Rep. Series 91-1, International Drought Information
Center, Univ. Nebraska, Lincoln, NE, 245pp. 

</x-tad-smaller></fontfamily><fontfamily><param>Times</param><bigger>

</bigger></fontfamily>==================================

Dr. Edward R. Cook
Doherty Senior Scholar and
Director, Tree-Ring Laboratory
Lamont-Doherty Earth Observatory
Palisades, New York 10964  USA
Email:	drdendro@ldeo.columbia.edu
Phone:	845-365-8618
Fax:	845-365-8152
==================================


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