ANALYSIS OF METEOROLOGICAL DROUGHTS IN TANZANIA
P. 0. Box 3056 Dar es Salaam, Tanzania
2.0 DATA AND METHODOLOGY 2.1 Data
2.1.1 Data Sources
Instrumental rainfall data for the period 1963 - 1994 from 66 rainfall stations in Tanzania distributed over lo x lo grids covering the whole country was collected and analyzed. Double mass curves were used to fill in gaps of missing data. Neighboring stations that had data were used to estimate missing data for those stations without data. However the double mass curve approach seemed to perform well in areas with uniform rainfall and perform poorly in dry areas and seasons.
Ogallo (1980) used principal component analysis (PCA) to regionalize East African rainfall. His study indicated that Tanzania rainfall could be categorized into seven regions Stations in these regions were thus used to check for homogeneity in time since the method group’s stations that are homogenous in space. The Spear-man’s rank correlation method is used applying 95%
significance level. The advantage of this method is that it spots trend without assuming anything about the mathematical configuration of the trend.
An F-test and t-test at 95% significance level tested stability of the Variance and mean respectively.
The stability of the mean indicates the absence of trend in the rainfall series that was split into two halves for the stability test.
2.2 METHODOLOGY
A drought indicator includes crop yields, run-off, evapotranspiration, temperature, soil moisture rainfaIl as well as other socio - economic activities. However, rainfall data is readily available compared to the other parameters and has therefore been used in this study to analyze drought patterns and subsequently develop a method for forecasting droughts in this country.
2.2.1 Rainfall Intensity Index
Standardized inter-annual and seasonal area, averaged rainfall anomalies were calculated to define the annual or seasonal intensity of rainfall deficiency. The intensity index (Zij) is expressed as follows: -
Zij=(Xij-xj)lSj (1)
where Xij is the observed annual or seasonal rainfall total at station j, and in year i, whereas x j and Sj are mean and standard deviation respectively.
Computed negative values of Zij represent years of rainfall deficiency. These values are used to group the observed inter-annual/seasonal rainfall anomalies into three categories as follows:-
Zij 2 -x j/Sj No significant drought - 1 X j/Sj 5 Zij < - 1 X j&j Moderate drought
2 5
Zij<-1 X j /Sj Severe drought 2
The above grouping assumes that crop yields will not be severely depressed when at least 80% of the normally expected rainfall is received. This implies that severe crop yields are to be expected during moderate drought conditions while total crop failure may occur in severe drought events. It should be noted here that rainfall is not the only parameter used in drought definition. Krishinan (1979) asserted that crop water status is highly dynamic parameter since it depends on soil conditions and micro-environment, among many others.
Drought prone areas were singled out by considering stations in the homogeneous regions for which probability of a drought occurring is greater or equal to 25%. Area average rainfall was then computed for the drought prone zone following the homogenous regions covered by the prone zone.
Several characteristics of droughts were then investigated as follows:
Drought Distribution (annual and seasonal)
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Time and space distributions of the drought categories were examined using the rainfall intensity index grouping shown above.
Duration
Assuming that the annual/seasonal rainfall is an independent variable, the probability of the n-length of an n-year drought was calculated using the formula given by Yevjevich (1967) as shown below: -
F (n) = qpnl
(2)
where p = probability of annual/seasonal rainfall being above the truncation level q = probability of annual/seasonal rainfall being below the truncation level.
n = duration of drought years = run length Persistence
4
The inter-annual or seasonal persistence of drought occurrences were investigated using the persistence ratio (Rb) as given by Besson (Books and Carruthers, 1953)1-P (3)
Rb = ______ _ 1 l- p’
where p = probability of occurrence of an event(drought)
p’ = probability that the event will occur immediately after the occurrence of such an event.
W
Auto correlation function (ACF) as given by Wei, 1990 was computed for the annual and seasonal rainfall to compare the persistence of droughts with those obtained by Benson (1953) as shown above (equation 3).(F(!) - Pm) (Pt + k) - Pm) t=1
ACF(k) = ________________________________
n
(P(t) - Pm)2 t=1
(4)
where P(t) = the annual/seasonal rainfall in year t.
Pm = the mean annual/seasonal rainfall P(t+k) = the annual/seasonal rainfall in year (t+k) K = lag in years
N = the number of years in the series
The 95% confidence limits were used to check whether the ACF’s significantly deviated from zero, a manifestation of persistence.
Severity
Inter-annual and seasonal drought severity was examined using the definition proposed by Yevjevich 1967 which says that “The sums of deviations are the run sum of negative deviations for a given run length in case of droughts, and indicate the deficiency of water supply or the severity of drought”.
2.2.2 Spectral analysis
Theory of power spectrum is found in many standard textbooks such as Blackman and Tukey (1958), Brier and Panofsky (1958), Jenkins and Watts (1968) and Chatfield (1980). It will suffice only to mention the steps that are normally followed in this type of analysis.
First steps involve the computation of serial covariance of a given series. The unsmoothed spectral estimates are then obtained directly from the serial covariance. Final estimates of the spectral density are found by smoothing technique. This study utilized the Parzen smoothing technique.
Ogallo, 1980 has shown that choice of this smoothing window was based on the fact that “leakage”
at all frequency bands is minimum.