On the use of Standardized Precipitation Index ... - Wiley Online Library

METEOROLOGICAL APPLICATIONS Meteorol. Appl. 16: 381–389 (2009) Published online 17 April 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/met.136

On the use of Standardized Precipitation Index (SPI) for drought intensity assessment M. Naresh Kumar,a * C. S. Murthy,b M. V. R. Sesha Saib and P. S. Royb a

Software Development & Database Systems Group, National Remote Sensing Centre, Hyderabad 500 625, India b Remote Sensing & GIS Applications Area, National Remote Sensing Centre, Hyderabad 500 625, India

ABSTRACT: Monthly rainfall data from June to October for 39 years were used to compute Standardized Precipitation Index (SPI) values based on two parameter gamma distribution for a low rainfall and a high rainfall districts of Andhra Pradesh state, India. Comparison of SPI with actual rainfall and rainfall deviation from the mean indicated that SPI values under-estimate the intensity of dryness/wetness when the rainfall is very low/very high, respectively. As a result, the SPI in the worst drought years of 2002 and 2006 in the low rainfall district indicated only moderate dryness instead of extreme dryness. SPI values of the high rainfall district showed slightly better stretching in both positive and negative directions, compared to that of the low rainfall district. Further, the SPI values of longer time scales (2, 3 and 4 months) showed an extended range compared to that of 1 month, but the sensitivity in drought years has not improved significantly. Normality tests were conducted based on Shapiro-Wilk statistic, p-values and absolute value of the median to ascertain whether non-normality of SPI is a possible reason. Although the results confirmed normal distribution, the scatter plot indicated deviation of the cumulative probability distribution of SPI from normal probability in the lower and upper ranges. Therefore, it is suggested that SPI as a stand alone indicator needs to be interpreted with caution to assess the intensity of drought. Further investigations should include sensitivity of SPI to the estimated shape and scale at lower and upper bounds of the gamma distribution and use of other distributions, such as Pearson III, to standardize the computational procedures, before using SPI as a substitute to the rainfall deviations from normal, for drought intensity assessment. Copyright  2009 Royal Meteorological Society KEY WORDS

standardized precipitation index (SPI); meteorological drought; rainfall deviations; normality tests; gamma distribution

Received 18 July 2008; Revised 17 December 2008; Accepted 13 January 2009

1.

Introduction

Meteorological drought is the earliest and the most explicit event in the process of occurrence and progression of drought conditions. Rainfall is the primary driver of meteorological drought. There are numerous indicators based on rainfall that are being used for drought monitoring (Smakhtin and Hughes, 2007). Deviation of rainfall from normal i.e. long term mean, is the most commonly used indicator for drought monitoring. On the basis of rainfall deviations, four categories are used in India for monitoring and evaluating the rainfall patterns across the country during the monsoon season; ±20% deviation as normal, −20 to −60% deviation as deficit, less than −60% deviation as scanty and greater than 20% deviation as excess (www.imd.gov.in). Meteorological drought is declared based on rainfall deviations measured using the season’s total actual rainfall and long term mean rainfall. If the total season’s rainfall is less than 75% of the long term mean, the meteorological sub-division is categorized to be under drought. Severe * Correspondence to: M. Naresh Kumar, Software Development & Database Systems Group, National Remote Sensing Centre, Hyderabad 500 625, India. E-mail: nareshkumar [email protected] Copyright  2009 Royal Meteorological Society

drought occurs when the season’s rainfall is less than 25% of normal (www.imd.gov.in). The deviation criteria for declaring drought vary. In South Africa, less than 70% of normal precipitation is considered as drought and such a situation for two consecutive years indicates severe drought (Bruwer, 1990). In Poland, rainfall deviation from a multi-year mean (equivalent to the longterm mean) forms the criterion for drought monitoring (www.imgw.pl). Although rainfall deviation from the long-term mean continues to be a widely adopted indicator for drought intensity assessment because of its simplicity, the application of this indicator is strongly limited by its inherent nature of dependence on mean. Rainfall deviations cannot be applied uniformly to different areas having different amounts of mean rainfall since a high rainfall area and a low rainfall area can have the same rainfall deviation for two different amounts of actual rainfall. Therefore, rainfall deviations across space and time need to be interpreted with utmost care. Standardized Precipitation Index (SPI) expresses the actual rainfall as standardized departure from rainfall probability distribution function and, hence, this index has gained importance in recent years as a potential

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drought indicator permitting comparisons across space and time. Computation of SPI requires long term data on precipitation to determine the probability distribution function which is then transformed to normal distribution with mean of zero and standard deviation of one. Thus, the values of SPI are expressed in standard deviations with positive SPI values indicating greater than median precipitation and negative values indicating less than median precipitation (Edwards and McKee, 1997). Since SPI values fit a typical normal distribution, these values lie within one standard deviation at approximately 68% of the time, within two standard deviations 95% of the time and within three standard deviations 98% of the time. In recent years SPI has been increasingly used for assessment of drought intensity in many countries (Vicente-Serrano et al., 2004; Wilhite et al., 2005; Wu et al., 2006). Homogeneous climatic zones were derived using SPI in Mexico (Giddings et al., 2005). Time series analysis of SPI indicated decrease in SPI values during 1970–1999 in the southern Amazon region, reflecting an increase in dry conditions (Li et al., 2007). The interpretation of drought at different time scales using SPI has also been proved to be superior to the Palmer Drought Severity Index (Guttman, 1998). Goodrich and Ellis (2006) have used both SPI and yearly values of the Palmer Drought Severity Index to rank the years according to drought severity. Smakhtin and Hughes (2007), developed software to compute and apply different rainfall based indicators including SPI for quantitative assessment of meteorological drought, and McKee et al. (1993) suggested the SPI ranges corresponding to different severity levels of drought (Table I). The present study analyses the response of seasonal SPI values to drought situation vis-`a-vis comparison of SPI with actual rainfall and rainfall deviation from normal in a low rainfall and a high rainfall district. The main objective was to investigate whether SPI can perform as a better indicator for drought intensity assessment than conventional and widely adopted rainfall deviations. Computation of SPI using two parameter gamma distribution and evaluation of SPI as a drought indicator in two districts having contrasting rainfall patterns constitute the subject of the current research paper. Section 2 describes the study area and methodology. The results and discussion in Section 3 explain the relationship between SPI and rainfall deviation (Section 3.1), sensitivity of SPI in drought and normal years (Section 3.2), SPI of longer time scales (Section 3.3), impact of record length on SPI (Section 3.4), agreement of results of the present study Table I. Drought categories from SPI (source: McKee et al., 1993). SPI

Drought category

0 to −0.99 −1.00 to −1.49 −1.5 to −1.99 −2.00 or less

Mild drought Moderate drought Severe drought Extreme drought

Copyright  2009 Royal Meteorological Society

with that of earlier studies (Section 3.5) and normality tests on SPI (Section 3.6). The discussion is summarized with conclusion and recommendation in Section 4.

2.

Study area and methodology

Two districts of the state of Andhra Pradesh (India), Ananthpur and Khammam, representing low and high rainfall areas, respectively, were selected. The total geographic area of Ananthpur district is 19 135 sq km and that of Khammam district is 15 809 sq km. Monthly actual rainfalls and corresponding normal values from June to October for 39 years (1969–2007), collected from the Directorate of Economics and Statistics, Government of Andhra Pradesh, India, were used as input data in the analysis. The rainfall pattern of these two districts (Table II) indicates that Ananthpur district has a season’s total normal, i.e. long-term average rainfall, of 449 mm, whereas Khammam district has 997 mm of rainfall. Ananthpur district has been declared by the state administration as a chronic drought prone area because of its low rainfall with high inter-annual variability. In India, there are 185 districts in 13 states, occupying 120 million hectares of geographic area identified as drought prone areas (Murthy et al., 2008). Khammam district is not a drought prone district because of its stable and higher rainfall pattern. Thus, the two districts with contrasting rainfall patterns were selected for analyzing the behaviour of SPI. Computation of SPI with time series data, at a monthly scale, was carried out based on the two parameter gamma distribution function. The rainfall data were transformed into log normal values followed by computation of U statistics, shape and scale parameters of the gamma distribution. The resulting parameters were then used to find the incomplete gamma cumulative probability of an observed precipitation event. The incomplete gamma cumulative probability was then converted to gamma probabilities after including the occurrences of zero precipitation events. The gamma probabilities were transformed in to standardized normal distribution using equi-probability transformation techniques (Abramowitz and Stegun, 1965). Although the transformation can be achieved through analytical methods a statistical method following Edwards and McKee (1997) was employed. Table II. Rainfall pattern in the study area districts. Month

June July August September October Total

District normal rainfall (mm) Ananthpur

Khammam

64 67 89 118 111 449

132 314 280 165 106 997

Meteorol. Appl. 16: 381–389 (2009) DOI: 10.1002/met

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ON THE USE OF STANDARDIZED PRECIPITATION INDEX FOR DROUGHT INTENSITY ASSESSMENT

The detailed computation procedure is furnished in the appendix. Rainfall deviation from normal was calculated as:

3 2 1

Normal rainfall × 100

(1)

The lowest value of the rainfall deviation is −100%, reflecting the occurrence of zero rainfall and the uppermost value can not be defined. If the actual rainfall is twice the amount of normal rainfall, the rainfall deviation is 100% and the actual rainfall is thrice the amount of normal, the rainfall deviation is 200% and so on.

3.

Results and discussion

The analysis was focused on understanding the sensitivity of SPI to actual rainfall/rainfall deviation and the behaviour of SPI in drought and normal years. The SPI-based drought classes proposed by McKee et al. (1993), were adopted in this study (Table I), because of their wider applicability to different regions of climatology such as Mexico (Giddings, 2005), Greece (Loukas et al., 2004), Iran (Morid et al., 2006), European Alps (Bartolini et al., 2008), Portugal (Paulo et al., 2005), Europe (Lloyd and Saunders, 2002), Poland (Łab¸edzki et al., 2005), mountainous Mediterranean basin (VicenteSerrano et al., 2004), Slovenia (Ceglar et al., 2008), Colorado, North Dakota, Iowa, Kansas, Nebraska, South Dakota, and Wyoming (Wu et al., 2006), Eastern China (Bordi et al., 2004), Northeast of Thailand (Wattanakij et al., 2006) and South Africa (Rouault and Richard, 2003). As suggested by McKee et al. (1993, 1995), SPI represents wetter and drier climates in a similar way. 3.1. SPI versus rainfall deviation Scatter plots between SPI and rainfall deviation were drawn for July and August separately (Figures 1 and 2). Rainfall deviations included both positive (actual rainfall 3 2

SPI

1 0 -1 -2 -3 -100

-50

0

50

100

150

200

250

300

350

400

Rainfall Deviation %

Figure

1. SPI versus rainfall deviation for Ananthpur (diamond) and Khammam (hexagram).


July –

SPI

Rainfall deviation = (Actual rainfall − Normal rainfall)/

0 -1 -2 -3 -100

-50

0

50

100

150

200

250

300

350

400


Figure

2. SPI versus rainfall deviation for August – Ananthpur (Diamond) and Khammam (hexagram).

is greater than normal) and negative (actual rainfall is less than normal) deviations. July and August are critical from an agriculture point of view. While July rainfall is critical for the sowing of crops, August rainfall is vital for the growth of different crops. The rainfall pattern in these two months plays a greater role in the occurrence of agricultural drought. It is evident from Figures 1 and 2, particularly in the low rainfall district of Ananthpur, that very high negative deviations (−60 to −80%) representing very low rainfall events were associated with the SPI values of −1.00 to −1.50 in most of the cases despite the fact that such a severe dryness should correspond to the SPI of −2.00 and below. Similarly, negative rainfall deviations of −40 to −60%, which represent significant reduction from normal rainfall, corresponded to the SPI values of −0.5 to −1.0 indicating mild or less significant dryness. In the high rainfall district of Khammam, SPI values assumed slightly lower values for the negative rainfall deviations, a better representation of dryness compared to the previous low rainfall district. Thus, there was a relation between SPI and negative rainfall deviations, but the magnitude of SPI values did not indicate the severity of drought situation. Positive rainfall deviations were found to be associated with positive SPI values indicating wetness in both the months, but the extent of positive deviations and the corresponding positive values of SPI have not indicated the same degree of wetness. For example, the rainfall deviation of 50–100% which implies that actual rainfall is 150–200% of normal, has resulted in the SPI values of 0.5–1.00 signifying only normal or slightly wet situation. Similarly, 100–200% deviations have resulted in the SPI values of around 1.5 indicating only moderate wetness in the low rainfall Ananthpur district. Again, in the high rainfall Khammam district the SPI values were found to be on the higher side (>2.0), for the events of excess rainfall. Thus, the SPI values of high rainfall district showed wider range in both positive and negative directions compared to that of the low rainfall district. Actual values of very low and very high rainfall events and associated SPI values are shown in Table III to Meteorol. Appl. 16: 381–389 (2009) DOI: 10.1002/met

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Month

Year Actual rainfall Rainfall deviation (mm) from normal (%)

June

1988 1984 2004 2001 1987 1991 2007 1996

13 15 18 19 84 131 141 145

−72 −68 −72 −70 79 179 130 209

−1.694 −1.532 −1.316 −1.250 1.057 2.007 2.175 2.247

July

1997 1972 1991 1984 2005 1988 1989

10 14 19 137 145 158 280

−82 −74 −66 158 116 182 400

−1.676 −1.389 −1.107 1.489 1.592 1.753 2.977

August

1972 1984 2004 1969 1998 2000

6 13 15 156 166 171

−92 −84 −83 98 131 92

−2.263 −1.671 −1.562 1.308 1.418 1.471

September 1969 1994 2003 1974 2001 1988 1981

27 30 46 231 244 265 283

−80 −75 −61 75 107 117 114

−2.028 −1.908 −1.384 1.299 1.418 1.602 1.753

October

39 43 197 208 226 248

−58 −55 105 124 104 167

−1.495 −1.366 1.234 1.353 1.541 1.757

1976 1997 1991 1989 2001 1975

SPI

3.2.

SPI of drought and normal years

In the low rainfall district of Ananthpur, 2002 and 2006 were the worst drought years and 2000 was a normal year as declared by the State administration. Peanut (Arachis hypogea) is the principal crop of this district, occupying more than 80% of cultivated area. The intensity of drought situation is clearly understood from crop production statistics published by the Government: the yield of peanut crop was 67 kg ha−1 in 2006, 355 kg ha−1 in 2002 and 1118 kg ha−1 in 2000. To understand the sensitivity of SPI and its agreement with rainfall deviations, a comparison of SPI and rainfall deviations, pertaining to drought years and normal year, was performed (Figures 3 and 4). Both SPI and rainfall deviations exhibited the same trend, with the normal year showing higher values and the two drought years showing smaller values, much lower than normal. The rainfall deviations were significant, ranging from −40 to −80% signifying the severity of drought situation in most of the months during 2002 and 2006. Positive rainfall deviations indicating excess rainfall in most of the months reflected the normal season in the year 2000. The values of SPI in the drought year 2002 ranged between 0 and −0.1 in most of the months. In the drought year 2006, SPI was lowest at −1.5 in August, around −1.0 in July and October and around −0.05 in September. By applying SPI classes of drought intensity 2.0 1.5 1.0 0.5 SPI

Table III. Very low rainfall events not associated with a very low SPI and very high rainfall not associated with a very high SPI.

0.0 June

July

August

September

October

-0.5 -1.0 -1.5 -2.0


Figure 3. SPI of drought versus normal years for June to October, circle: 2002 (drought year), cross: 2006 (drought year) and triangle: 2000 (normal year).

120 deviation from normal rainfall %

bring more clarity to the inter-relations between SPI and rainfall. Even the very small amount of rainfall that was certainly insufficient to maintain enough soil moisture for agriculture resulted in the SPI values of around −1.5 which otherwise should represent extreme dryness with the values around −2.0 and below. Similarly, excess rainfall events had an SPI around 1.5. This trend of very low rainfall events not resulting in very low SPI values and very high rainfall events not resulting in very high SPI values was evident in all the five months. Therefore, from the foregoing analysis, it is evident that the SPI values were over estimated for low rainfall levels and underestimated for high rainfall levels in the study area districts with the discrepancy more pronounced in the low rainfall district. In the high rainfall district, the stretching of SPI values both on positive and negative sides was better than that of the low rainfall district.

100 80 60 40 20 0 -20

June

Jluy

August

September

October

-40 -60 -80 -100

Figure 4. Percentage deviation of rainfall from normal for drought and normal years, circle: 2002 (drought year), cross: 2006 (drought year) and triangle: 2000 (normal year). Meteorol. Appl. 16: 381–389 (2009) DOI: 10.1002/met


proposed by McKee et al. (1993), the worst drought years of 2002 and 2006 in the study area district represented only mild to moderate drought situations. Thus, the drought intensity was underestimated by SPIbased classes, mainly due to the over estimation of SPI values at very low rainfall events as discussed in the previous section. Even in a good year such as 2000, which had recorded the highest peanut crop yield, the SPI values were around 1.0 indicating normal situation, as a result of underestimation of SPI at high rainfall events.

3.3. Longer time scale The longer time scale, 2-, 3- and 4-months rainfall, data were used for computing the SPI values to understand their behaviour in contrast to 1-month SPI values. The comparison of SPI and rainfall deviations was carried out for the low rainfall district Ananthpur (Figure 5). The values of SPI were −2 and below for rainfall deviations less than −50%, whereas the SPI values tend to be greater than 2 for the high rainfall events. Thus, the SPI values of longer time scale were better stretched reaching beyond −2 and +2 range compared to 1-month SPI values. Longer time scale SPI values during drought and normal years (shown in Table IV) indicated that even in drought years of 2002 and 2006 the SPI values were still around −1.5 indicating only moderate dryness. Although the range of values has improved with longer time scale SPI, the sensitivity in drought years to represent dryness has not improved significantly.

3 2

3.4. Record length The impact of record length was studied by analyzing the SPI values of different periods for 21 years (1969–1989), 22 years (1969–1990), 23 years (1969–1991) and so on up to 39 years (1969–2007) of data for the two study districts and for July and August separately. SPI calculation for each incremental year from the initial 21–39 years period resulted in 19 SPI values. Maximum and minimum SPI were identified from these 19 values for each month and were plotted separately as shown in Figure 6. The negligible difference between maximum and minimum SPI as the record length increases from 21 years (the corresponding period is 1969–1989) to 39 years (the corresponding period is 1969–2007), indicated that the SPI was stable and not influenced by record length. As a result, SPI-based interpretation remains consistent. These results are in agreement with the findings of Wu et al. (2005). This property of SPI makes it a robust indicator, one that is not influenced by the record length. 3.5. Agreement of results with earlier studies The results of the present study were in agreement with the findings of the earlier studies to some extent. Wu et al. (2006) revealed that the application of SPI of short time scales in arid regions as well as the areas with distinct dry season failed to detect the occurrence of drought situation. This behaviour of SPI was attributed to its non-normal distribution caused by higher frequency of no rain cases. Histograms of drought frequency classes derived by Morid et al. (2006), showed that percent normal rainfall has a higher frequency in extreme drought and severe drought, whereas SPI had higher frequency in normal class. This result indicated that for the cases where large negative deviations representing very low

1 SPI

385

2.5 2.0

0

1.5 SPI

-1

1.0

-2 0.5

-3 -100

-50

0

50

100

150

200

0.0

250

Khammam-August Khammam-July


Anantpur-August Anantpur-July

-0.5

Figure 5. SPI versus rainfall deviation for Ananthpur district, July + August (diamond), July + August + September (star), June–September (hexagram).

Figure 6. Minimum SPI (gridded bar) and maximum SPI (dotted bar) computed for data ranging from 21 to 39 years for Khammam and Ananthpur districts.

Table IV. SPI of longer time scales in drought and normal years. Year

Situation on ground

June + July

July + August

August + September

June + July + August

July + August + September

June– September

2000 2002 2006

Normal Drought Drought

0.352 −1.173 −0.145

1.126 −1.2 −1.85

0.538 −1.424 −1.358

1.293 −1.407 −1.063

0.403 −1.635 −1.582

0.522 −1.717 −1.135



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M. N KUMAR ET AL.

0.75 0.50 0.25 0.10 0.05 0.02 0.01 -2

-1

0

1

2

3

SPI

Figure 7. Probability plot for July – SPI of Ananthpur district (diamond) with its normal (dashed line) and SPI of Khammam district (pentagram) with its normal (solid line). This figure is available in colour online at www.interscience.wiley.com/ma

Tests of normality

Non-normal distribution caused by the occurrence of zero rainfall events was found to be responsible for the distorted SPI values in low and uncertain rainfall areas (Wu et al., 2006). If the rainfall during the specified period is nil, then it is called a zero rainfall period or event. However, in the data sets of the current study there was no zero rainfall. Three tests of normality suggested by Wu et al. (2006), the Shapiro-Wilk statistic (w), pvalues and absolute value of the median were carried out to verify the normality of SPI. The calculated values of these three parameters are shown in Table V. A nonnormal distribution should have ‘w’ value less than 0.96, p-value less than 0.10 and median >0.05. By applying these criteria it was found that the SPI values for all the months conform to the normal distribution in both the study area districts. Normal probability of SPI and its comparison with standard normal probability for July and August, for the two districts separately, is shown in Figures 7 and 8. It can be observed that the SPI probability deviates from the normal line in the lower ranges and upper ranges of SPI in both the districts. The non-normality observed in these two specific ranges of SPI was incidentally associated with the under or over estimation of SPI as revealed in previous sections. The normality of SPI was not fulfilled in all ranges of SPI, although the majority of SPI values run close to the normality line. As a result, it may be necessary to undertake normality tests in different ranges of SPI separately.

0.99 0.98 0.95 0.90 Probability

3.6.

0.99 0.98 0.95 0.90 Probability

rainfall exist, the corresponding SPI values tend to be on higher side reducing the intensity of dryness. Interpretation of 1-month SPI can lead to misleading assessment, as there are many examples where there is no perfect agreement between rainfall deviations and SPI values. Actual precipitation of 15.2 mm against the normal value of 2.5 mm leads to a SPI of +3.11. Similarly 371.9 mm of precipitation, which is above the normal by 211.6 mm, gave rise to an SPI value of 1.97. In another station, 24.9 mm of precipitation against 10.4 mm of normal (which is 239% of normal), resulted in an SPI value of 1.43. During February of 1996, SPI value of −1.76 was recorded over Southeastern Plains Climate Division in New Mexico representing zero rainfall situations (www.drought.unl.edu/monitor).

0.75 0.50 0.25 0.10 0.05 0.02 0.01 -2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

SPI

Figure 8. Probability plot for August – SPI of Ananthpur district (diamond) with its normal (dashed line) and SPI of Khammam district (pentagram) with its normal (solid line). This figure is available in colour online at www.interscience.wiley.com/ma

4.

Summary and conclusion

The actual rainfall expressed as percent deviation from normal (long-term average) is the most commonly used drought indicator, although it has limited use for spatial comparison due to its dependence on the mean. The Standardized Precipitation Index (SPI) expresses the actual rainfall as a standardized departure from rainfall probability distribution function. This index has gained importance in recent years as a potential drought indicator since it permits comparisons across time and space. In this study, the SPI values of different years were analyzed with actual rainfall as well as rainfall deviation from normal in a low rainfall and a high rainfall districts.

Table V. Measured values of parameters for testing normality of SPI from June to October in the study districts. District

Parameters Measured

June

July

August

September

October

Ananthpur

w value p-value median

0.954 0.170 0.023

0.956 0.170 0.171

0.973 0.165 0.117

0.973 0.165 0.109

0.961 0.168 0.085

Khammam

w value p-value median

0.948 0.172 0.041

0.978 0.164 0.003

0.966 0.167 0.182

0.969 0.166 0.188

0.981 0.163 0.057



387


The objective was to evaluate whether SPI can be a better drought indicator than the widely used rainfall deviations. Scatter plots of rainfall deviations vs. SPI indicated less sensitivity of SPI to low rainfall events. Very low or very high rainfall have not corresponded to very low (−2.0 or less) or very high (+2.0 or more) SPI values. Thus, SPI values underestimated the dryness and wetness caused by very low and very high rainfall, respectively. As a result, the worst drought years of 2002 and 2006 in the study area district were classified as only moderate dryness based on the SPI classes proposed by McKee et al. (1993). SPI values of the high rainfall district indicated an enhanced range of values, −2.0 or less for very low rainfall and +2.0 or more for high rainfall, compared to that of the low rainfall district. To determine whether non-normality of the SPI was a possible reason, a normality test was conducted for SPI values based on the Shapiro-Wilk statistic (w), pvalues and absolute value of the median as suggested by Wu et al. (2006), and the results confirmed normal distribution of the SPI. However, a visual inspection of the normal probability plot of the SPI indicated deviation from the normal line in the lower and upper ranges of the SPI values. The selective non-normality in the lower and upper ranges of the SPI could be responsible for the underestimation of dryness/wetness in these ranges. Although the statistical nature of the SPI permits comparisons across space and time better than rainfall deviations, the drought intensity at a given location was found to be more sensitive to rainfall deviations than the SPI. Since rainfall and its variations are very critical in low rainfall districts, SPI values should assume wider range to represent the degree of wetness or dryness resulting in better assessment of drought situation. In this context, the use of other statistical distributions such as Pearson-III, as suggested by Guttman (1999), for SPI computation needs to be investigated for improving the sensitivity of SPI. Further, the impact of shape and scale at lower and upper bounds of gamma estimate on SPI is also an important issue that needs to be investigated. Therefore, it is strongly recommended that there is a need to standardize the computational procedures, before making SPI as a substitute indicator for the rainfall deviations for drought intensity assessment.

Acknowledgements We express our sincere thanks to Dr. V. Jayaraman, Director, National Remote Sensing Centre, for his constant encouragement and guidance. Thanks are also due to Dr. R. S. Dwivedi, Group Director, Land Resources Group, for his suggestions. The cooperation offered by the officials of Directorate of Economics and Statistics, Government of Andhra Pradesh, India for providing the data needed for the study is duly acknowledged.

Appendix Appendix for Computation of SPI. Procedure and Formula for Computation of SPI 1. The transformation of the precipitation value in to standardized precipitation index (SPI) has the purpose of: a. Transforming the mean of the precipitation value adjusted to 0; b. Standard deviation of the precipitation is adjusted to 1.0; and c. Skewness of the existing data has to be readjusted to zero. When these goals have been achieved the standardized precipitation index can be interpreted as mean 0 and standard deviation of 1.0. 2. Mean of the precipitation can be computed as:

Mean = X =

X

N

(A.1)

where N is the number of precipitation observations. In EXCEL the mean is computed as Mean = Average (first : last) 3. The standard deviation for the precipitation is computed as: (X − X)2 (A.2) s= N In EXCEL the standard deviation is computed as s = stdevp (first : last)

Table A1. Appendix data. Calculation of standardized precipitation index. Statistics

Rainfall

ln

gamma

t transform

SPI

Mean (A.1) Standard Deviation (A.2) Skewness (A.3) U (A5) Shape (A.6) Scale (A.7)

61.981 52.2187 2.2196

4.12684 (A.4)

(A.9)

(A.11)

−0.0111 0.99760 0.766445


0.2846 1.90981 32.4544


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4. The skewness of the given precipitation is computed as:

Skew =

X−X N (N − 1)(N − 2) s

3

(A.3)

5. The precipitation is converted to lognormal values and the statistics U , shape and scale parameters of gamma distribution are computed: log mean = X ln = ln X ln(X) U = Xln − N

shapeparameter = β = scaleparameter = α =

(A.4) (A.5)

1+

1+

4U X β

4U 3

(A.6) (A.7)

The Equations (A.1)–(A.8) is computed using built functions provided by EXCEL software. The resulting parameters are then used to find the cumulative probability of an observed precipitation event. The cumulative probability is given by:

G(x) =

x

−x x a−1 e β dx

0

β α (α)

(A.8)

Since the gamma function is undefined for x = 0 and a precipitation distribution may contain zeros, the cumulative probability becomes: H (x) = q + (1 − q)G(x)

(A.9)

where q is the probability of zero. The cumulative probability H (x) is then transformed to the standard normal random variable Z with mean zero and variance of one, which is the value of the SPI following Edwards and McKee (1997); we employ the approximate conversion provided by Abramowitz and Stegun (1965) as an alternative: 

 c0 + c1 t+   c2 t 2  Z = SP I = −  t − 1 + d t + d t 2  0 < H (x) ≤ 0.5 1 2 +d3 t 3   c0 + c1 t+   c2 t 2  0.5 t − Z = SP I = +    1 + d1 t

+d2 t 2 + d3 t 3 < H (x) ≤ 1 Copyright  2009 Royal Meteorological Society

(A.10)

Table A2. Appendix data (continued) Year

Rainfall

Log rainfall

gamma

t Transform

1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

28 30 29 14 27 50 124 39 69 77 47 34 78 58 29 137 75 27 10 158 280 42 19 55 41 45 112 56 10 112 38 55 21 21 41 108 145 21 55

3.3322 3.4012 3.3673 2.6391 3.2958 3.9120 4.8203 3.6636 4.2341 4.3438 3.8501 3.5264 4.3567 4.0604 3.3673 4.9200 4.3175 3.2958 2.3026 5.0626 5.6348 3.7377 2.9444 4.0073 3.7136 3.8067 4.7185 4.0254 2.3026 4.7185 3.6376 4.0073 3.0445 3.0534 3.7062 4.6821 4.9767 3.0445 4.0146

0.2375 0.2611 0.2493 0.0825 0.2257 0.4843 0.9052 0.3657 0.6526 0.7089 0.4533 0.3081 0.7154 0.5612 0.2493 0.9317 0.6956 0.2257 0.0469 0.9602 0.9985 0.3994 0.1342 0.5334 0.3883 0.4321 0.8724 0.5428 0.0469 0.8724 0.3544 0.5334 0.1564 0.1585 0.3849 0.8593 0.9443 0.1564 0.5371

1.6956 1.6388 1.6668 2.2338 1.7253 1.2042 2.1706 1.4183 1.4541 1.5711 1.2579 1.5345 1.5854 1.2835 1.6668 2.3167 1.5424 1.7253 2.4736 2.5393 3.6144 1.3549 2.0041 1.2346 1.3756 1.2955 2.0292 1.2510 2.4736 2.0292 1.4405 1.2346 1.9262 1.9193 1.3819 1.9806 2.4033 1.9262 1.2412

Where, t = ln

1 0 < H (x) ≤ 0.5 H (x)2 1 t = ln 0.5 (1.0 − H (x))2

< H (x) ≤ 1.0

(A.11)

c0 = 2.515517 c1 = 0.802583 c2 = 0.010328 d1 = 1.432788 d2 = 0.189269 d3 = 0.001308

(A.12) Meteorol. Appl. 16: 381–389 (2009) DOI: 10.1002/met


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