Techniques to Predict Agricultural Droughts - Monitoring and Predicting Agricultural Drought: A Global Study - page 44

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In contrast, if the interest lies in drought frequency, then the probability
statements can also be calculated from the same record. For instance, P ( X i
> X 0 ) and P ( X i < X 0 ) express simply the SMS and SMD probabilities,
respectively. These basic probabilities help construct a probabilistic model
that can be used to predict agricultural drought durations ( ¸ en, 1976).
There is no procedure so far for accurately predicting the time of drought
occurrence and durations or areal extent of drought. Although various sub-
jective approaches were used in the past, they all failed. In modern times,
drought estimations are sought on the basis of objective and systematic sci-
entific procedures, and along this line the probability theory provides a con-
venient procedure for drought predictions. These techniques, in general,
are used for depicting the quantitative relationships between the weather
variables and the drought characteristics. For instance, multiple regression
analysis or Monte Carlo simulation techniques are used to answer ques-
tions concerning regional and temporal drought frequencies.
The majority of drought analysis has concentrated on temporal assess-
ments. The first classical approach to statistically analyzing droughts was
evaluating the instantaneously smallest value in a measured sequence of
basic variables such as soil moisture recorded at a single site (Gumbel,
1963). This method gives information on the maximum value of drought
duration magnitude with a prescribed period of time such as 10, 25, 50, or
100 years. Yevjevich (1967) presented the first objective definition of tem-
poral droughts. Applications of the above method have been performed
by Downer et al. (1967), Llamas and Siddiqui (1969), Saldarriaga and
Yevjevich (1970), Millan and Yevjevich (1971), Guerrero-Salazar (1973),
Guerrero-Salazar and Yevjevich (1975), ¸ en (1976, 1977, 1980a) and brief
descriptions have been presented by Dracup et al. (1980). Due to the ana-
lytical difficulties, regional droughts have been studied less. The first study
of regional drought was by Tase (1976), who performed many computer
simulations to explore various drought properties. Different analytical so-
lutions of drought occurrences have been proposed by ¸ en (1980b) through
random field concept. However, these studies are limited in the sense that
they investigate regional drought patterns without temporal considera-
tions.
Below, a systematic approach is presented for the calculation of tem-
poral and regional drought occurrences by simple probability procedures.
Recent improvements in statistical methods have tended to place a new
emphasis on rainfall studies, particularly with respect to a better under-
standing of persistence (continuity of dry spells) effects ( ¸ en, 1989, 1990).

[44],

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Te mporal Drought Models

Statistical theory of runs provides a common basis for objectively defining
and modeling critical drought given a time series (Feller, 1967). A constant
soil moisture truncation level divides the whole series into two complemen-
tary parts: those greater than the truncation level, which are referred to as