Droughts adversely impact rural and urban communities, industry, primary production and, thus, a country's economy. Drought monitoring is directed to detecting the onset, persistence and severity of the drought. In this study, meteorological drought indices such as the Standardized Precipitation Index (SPI), the Reconnaissance Drought Index (RDI) and deciles were assessed to investigate how well these indices reflect drought conditions in Victoria, Australia. The Theory of Runs was also used to identify the drought deficit. The study uses 55 years (1955–2010) of monthly precipitation and reference evapotranspiration data for five selected meteorological stations in Victoria, Australia. Results show that drought characterization using SPI and RDI provides a standardized classification of severity thus exhibiting advantages over deciles. As RDI considers both rainfall and potential evapotranspiration in calculations, it could be sensitive to climatic variability. For characterizing agricultural droughts, the application of the RDI is recommended. The use of the SPI was shown to be satisfactory for assessing and monitoring meteorological droughts. The SPI was also successful in detecting the onset and the end of historical droughts for the selected events.

INTRODUCTION

Drought differs from other natural hazards such as cyclones and floods as it is a slow on-setting, creeping phenomenon (WMO 2006). It is difficult to determine when the drought begins and, likewise, when it ends, as urban, agricultural and industrial sectors recover from droughts differently. Monitoring droughts and forecasting persistence always present unique research challenges; however, it is essential as droughts become more common and more severe due to climate change impacts (Mishra & Singh 2009; Alexander et al. 2009). There are four types of droughts, commonly classified as meteorological, agricultural, hydrological and socio-economic (Wilhite & Glantz 1985). In contrast to meteorological droughts, the other three types of droughts occur less frequently because it usually takes weeks or months before precipitation deficiencies begin to produce soil moisture deficiencies, declines in streamflow, reduced reservoir levels and lower groundwater tables. Thus, for drought monitoring and early warning, meteorological drought indices (DI) provide the best initial assessment. Once meteorological indices indicate the onset of a drought, other non-meteorological indices could provide complementary additional information to the relevant sectors, describing severity and impact.

In Australia, several significant droughts have occurred in the recent past, including 1963–1968, 1972–1973, 1982–1983 and 1991–1995, costing the Australian economy billions of dollars (BoM 2011). South-eastern Australia (Victoria, parts of New South Wales and South Australia) experienced low rainfall from 1997 to 2009, known as the ‘Big Dry’ (Ummenhofer et al. 2009; Potter et al. 2010; Verdon-Kidd & Kiem 2010). The 12-year prolonged dry period saw four major drought years beginning in late 1997, 2002, 2006 and 2008 (Gergis et al. 2012). In 2010, even though widespread above-average rainfall fell across most of Australia, the long-term rainfall deficiencies affecting large parts of Southern Australia had still not ended (National Climate Centre 2010). The dry period had wiped out crops, decimated livestock numbers, drained rivers and dams, compromised water-dependent ecosystems and created conditions suitable for catastrophic bushfires. Tan & Rhodes (2008) reported 2006 annual inflow into four major water harvesting reservoirs supplying the greater Melbourne area to be the lowest on record, resulting in adverse socio-economic and industry impacts due to shortage of water and the imposition of restrictions.

DI have been commonly used to quantify rainfall deficits, soil moisture and water availability and to assess drought severity (Morid et al. 2006; Mishra & Singh 2010). Many different meteorological DI have been developed. Palmer (1965) first introduced the Palmer Drought Severity Index (PDSI) in the United States. Despite its widespread use, the PDSI has many limitations (Hayes 2003); other limitations are also discussed in Alley (1984), Hayes et al. (1999), Heim (2002), Mo & Chelliah (2006), Dai (2011) and van der Schrier et al. (2011). Other indices that have been used widely include percent of normal, deciles (commonly used in Australia (Gibbs & Maher 1967)) and the Standardized Precipitation Index (SPI) (McKee et al. 1993). Apart from the indices, stochastic analysis including the Theory of Runs (ToR) has also been successfully applied for characterization of droughts (Yevjevich 1967; Paulo & Pereira 2006). Tsakiris et al. (2007) proposed a new Reconnaissance Drought Index (RDI) which makes use of precipitation and potential evapotranspiration (PET) deficits simultaneously.

From the many indices used, the SPI has found widespread application for describing and comparing actual drought events (Mishra & Desai 2005; Paulo et al. 2005; Nalbantis & Tsakiris 2009; Khalili et al. 2011). The SPI was developed for the purpose of defining and monitoring droughts (McKee et al. 1993). In addition, after a comprehensive review, the World Meteorological Organization recommended the use of SPI to determine meteorological droughts and to complement local meteorological DI then in use (Hayes et al. 2011).

In addition, the RDI proposed by Tsakiris & Vangelis (2005) as a meteorological drought index is applied in this study to test its applicability. It makes use of precipitation and PET simultaneously as temperature, wind and relative humidity are also important factors in characterizing drought. In addition to these two DI, the ToR is applied to determine the best rainfall threshold level and to quantify the number of droughts and their characteristics.

In Australia, deciles are used to assess the status of rainfall deficiency (BoM 2007). Despite the advantages, deciles do not detect the essential characteristics of droughts (e.g., severity and intensity). However, the deciles method is also applied in this study to test its performance. Recently, Barua et al. (2012) developed a new drought index, namely the Nonlinear Aggregated Drought Index (NADI). NADI uses factor analysis and is complex, and has been recently developed using hydro-meteorological data from the Yarra River catchment, Victoria. However, it is yet to be tested in other regions.

The ease of application was also a factor in finalizing which indices to test and compare. This paper assesses how well the SPI, RDI and deciles can define the historical droughts in Victoria based on the data from the selected rainfall stations and ToR to identify drought properties. The results obtained by applying these three DI are presented and discussed. The SPI was also applied to identify the initiation and end of historical droughts.

METHOD

Study area

The State of Victoria in Australia has a varied climate ranging from semi-arid and hot in the north-west (300 mm/annum), to temperate and cool along the coast (1,800 mm/annum). Victoria has been split into 15 rainfall districts with relatively similar rainfall patterns (BoM 2007). The locations of the five rainfall stations selected for this study and their details are shown in Figure 1 and Table 1, respectively. Station 76031 is located in north-west Victoria in the region of Mildura, and has a long history of agriculture and irrigation. Stations 77051 and 79011 are in the Wimmera–Mallee regions of western Victoria and cover the dryland farming area. Station 81013 is located in the Goulburn Valley region, also part of the Murray–Darling Basin; this region is one of the most productive areas in Australia and mostly irrigated. Station 86071 is within the Yarra River catchment and located in the urbanized areas. Due to the wide climatic differences prevailing in the State, the selected stations represent both drier and wetter regions of Victoria.

Table 1

Description of rainfall stations

Station Station name Mean annual rainfall (mm) Latitude (°S) Longitude (°E) AHD (m) % of missing rainfall 
76031 Mildura Airport 293 − 34.24 142.1 50 – 
77051 Rainbow (Werrap (Oak-Lea)) 349 − 35.94 141.9 83 0.8 
79011 Edenhope (Post Office) 576 − 37.03 141.2 162 1.4 
81013 Dookie Agricultural College 554 − 36.37 145.7 185 0.5 
86071 Melbourne Regional Office 650 − 37.80 144.9 31 – 
Station Station name Mean annual rainfall (mm) Latitude (°S) Longitude (°E) AHD (m) % of missing rainfall 
76031 Mildura Airport 293 − 34.24 142.1 50 – 
77051 Rainbow (Werrap (Oak-Lea)) 349 − 35.94 141.9 83 0.8 
79011 Edenhope (Post Office) 576 − 37.03 141.2 162 1.4 
81013 Dookie Agricultural College 554 − 36.37 145.7 185 0.5 
86071 Melbourne Regional Office 650 − 37.80 144.9 31 – 
Figure 1

Locations of the study site.

Figure 1

Locations of the study site.

Rainfall and PET data

Mean annual rainfall for the five selected stations ranges from 293 to 650 mm. Rainfall data from 1955–2010 were used for the analysis and were downloaded from the Bureau of Meteorology (BoM) web site (http://www.bom.gov.au/climate/data/). Two commonly used data in-filling methods, namely the arithmetic mean and the normal ratio method were applied to calculate the missing monthly rainfall data. Data from a station's nearest neighbours were used to make the estimations. If the average annual rainfall at each of the adjacent stations differed from the average at the missing data station by ±10%, the equation used was an expression of an estimate based on the average precipitation at all stations. In contrast, if the difference between the average annual rainfall at any of the adjacent stations and the missing data station was greater than 10%, a normal ratio was used. The percentage of missing data is reported in Table 1. Figure 2 shows mean monthly temperature and precipitation for all stations. Overall, rainfall is at a maximum in late winter and early spring (i.e., July–October) and at a minimum in summer or early autumn (i.e., December–March). Similar to precipitation, temperatures in Victoria also fluctuate both on a seasonal and daily basis. High temperatures in summer (December–February) range from 24 °C to 30 °C. Mean annual rainfall is between 550 mm and 650 mm in Stations 79011, 81013 and 86071 while Stations 76031 and 77051 receive below 350 mm.

Figure 2

Mean monthly precipitation and temperature for all stations.

Figure 2

Mean monthly precipitation and temperature for all stations.

Reference evapotranspiration for these stations has been calculated using the adapted Penman–Monteith equation recommended by the United Nations Food and Agriculture Organization given in Equation (1) (Webb 2010). Daily wind speed, air temperature, humidity and solar radiation data were obtained from the BoM in Australia (BoM 2012) 
formula
1
where Australian is the reference evapotranspiration (mm day−1), is the slope of the saturation vapour pressure curve (kPa°C−1), is the net radiation at the crop surface (MJm−2day−1), is the soil heat flux density (MJm−2 day−1), is the psychometric constant (kPa°C−1), is the mean daily air temperature at a height of 2 m (°C), is the wind speed at a height of 2 m (ms−1), is the mean saturation vapour pressure (kPa) and is the actual vapour pressure (kPa). The computation of followed the method described in Chapter 4 in Allen et al. (1998).

Drought indices

Standardized Precipitation Index

The SPI was designed by McKee et al. (1993) at Colorado State University to quantify the precipitation deficit for multiple time scales (i.e., 1, 3, 6, 12, 24 and 48 months). The SPI is basically the transformation of the precipitation time series into a standardized normal distribution. The computation of the SPI index requires the following steps (McKee et al. 1993; Wu et al. 2007):
  • (1) Fit a cumulative probability distribution function (PDF) (usually gamma distribution) on aggregated monthly (k) precipitation series (say k = 3, 6 and 12 months in this study). The gamma PDF (g(x)) is defined as

 
formula
2
where β is a scale parameter, α is a shape parameter, which can be estimated using method of maximum likelihood, is the precipitation amount and is the gamma function at α. The estimated parameters can be used to find the cumulative PDF of observed precipitation events for the given month and particular time scale. The cumulative distribution function (CDF) is obtained by integrating Equation (2) 
formula
3
where 
formula
4
 
formula
5
 
formula
6
n = number of precipitation observations and refers to the sample mean of the data.

  • (2) Transform the CDF to the CDF of the standard normal distribution with zero mean and unit variance, which is given as follows: 
    formula
    7

This transformed probability is the SPI. A positive value of SPI indicates that precipitation is above average and a negative value denotes below average precipitation.

A drought event is defined here as a period in which the SPI is continuously negative and reaching a value of −1.0 or less (McKee et al. 1993; Paulo & Pereira 2006). The duration (D) is defined by the time between the beginning and the end (−ve SPI values); the magnitude is calculated by the sum of the SPI for every month from the initiation to the end of each drought event, and the intensity is the ratio between the magnitude and the duration of the event.

Reconnaissance Drought Index

Tsakiris & Vangelis (2005) proposed meteorological droughts to be conceptualized as water deficits representing the water balance deficit between input (precipitation) and output (reference evapotranspiration). The initial value () of RDI for a certain period, indicated by a certain month (k) during a year, could be determined as 
formula
8
where and are the precipitation and PET of the jth month of the year. Although this equation can be calculated starting from any month of the year, this study considered January (k = 1) as the starting month and not October, the month normally used in several Mediterranean countries and in the Middle East region.
The RDI can be expressed as normalized RDI (RDIn) and Standardized RDI (RDIst). The RDIn is computed using the following equation: 
formula
9
The RDIst is computed following a similar procedure to the one that is used for the calculation of the SPI. The equation is as follows: 
formula
10
where is ln , is its arithmetic mean and is its standard deviation.

In this study, the RDI is fitted to a gamma PDF similar to the one used for SPI. Therefore, the RDIst could be computed following a similar procedure described for SPI and the values compared to the same threshold values as SPI (Table 2).

Table 2

Classifications scale for SPI values

SPI values Category 
0 to −0.99 Near normal 
− 1.0 to −1.49 Moderate drought 
− 1.5 to −1.99 Severe drought 
− 2 and less Extreme drought 
SPI values Category 
0 to −0.99 Near normal 
− 1.0 to −1.49 Moderate drought 
− 1.5 to −1.99 Severe drought 
− 2 and less Extreme drought 

Theory of Runs

Probabilistic features of drought have been investigated extensively since Yevjevich (1967) proposed the use of the run concept as a method to identify and characterize drought events and their statistical properties in an objective way. Although ToR is not a drought index, it could be used along with other DI in identifying drought parameters. A drought event is identified as a period in which the rainfall time series is consecutively less than the critical threshold level, yc (Figure 3).

Figure 3

Characteristics of local drought events with the ToR (Paulo & Pereira 2006).

Figure 3

Characteristics of local drought events with the ToR (Paulo & Pereira 2006).

In this study, the identification of the critical rainfall threshold level was based on the SPI drought class threshold (SPI = −1). Therefore, the rainfall threshold level, (i.e., a rainfall below the mean corresponding to the standard deviation) was selected. This threshold level was also used in past studies by Ben-Zvi (1987) and Paulo & Pereira (2006). ToR can be computed for 3-, 6- and 12-month time scales.

Deciles

Gibbs & Maher (1967) suggested another drought-monitoring technique by arranging monthly precipitation data into deciles. The deciles are commonly used by the BoM to assess the status of rainfall deficiency throughout Australia. This technique divides the distribution of occurrences over a long-term precipitation record into tenths of the distribution, and each of these one-tenth slices is called a decile. The deciles are grouped into five classifications as shown in Table 3. The first decile is the rainfall amount not exceeded by the lowest 10% of the precipitation occurrences. The second decile is the precipitation amount not exceeded by the lowest 20% of occurrences, and so on, until the tenth decile which is the largest one-tenth of precipitation amounts within the long-term record.

Table 3

Decile classification

Value Classification 
Deciles 1–2: lowest 20% Much below normal 
Deciles 3–4: next lowest 20% Below normal 
Deciles 5–6: middle 20% Near normal 
Deciles 7–8: next highest 20% Above normal 
Deciles 9–10: highest 20% Much above normal 
Value Classification 
Deciles 1–2: lowest 20% Much below normal 
Deciles 3–4: next lowest 20% Below normal 
Deciles 5–6: middle 20% Near normal 
Deciles 7–8: next highest 20% Above normal 
Deciles 9–10: highest 20% Much above normal 

In the current study, a station is considered to be suffering from drought if the sum of the observed precipitation falls within the two lowest deciles (deciles 1 and 2) of the historical distribution of 3-, 6- or 12-month totals, as suggested by Kinninmonth et al. (2000) and Keyantash & Dracup (2002).

RESULTS AND DISCUSSION

Drought characteristics

The SPI, RDI and deciles were applied to data from all five stations at 3-, 6- and 12-month time scales. The three methods were applied to rainfall and evapotranspiration data from 1955 to 2010. For meaningful comparison, all three indices were calculated starting at the beginning of each year for all time scales. For the ToR and deciles, the threshold values for all stations are tabulated in Table 4. It is worthwhile noting that the values vary for each station. The threshold value is critical when estimating the water shortage, especially during a drought spell or when designing water storage systems.

Table 4

The threshold values (mm) for each station using ToR and deciles in different time scales (3-, 6- and 12-month)

  ToR Deciles 
Station 12 12 
76031 23 68 191 31 73 202 
77051 24 91 247 31 95 270 
79011 43 174 472 40 175 492 
81013 47 155 384 53 168 397 
86071 75 212 508 77 210 503 
  ToR Deciles 
Station 12 12 
76031 23 68 191 31 73 202 
77051 24 91 247 31 95 270 
79011 43 174 472 40 175 492 
81013 47 155 384 53 168 397 
86071 75 212 508 77 210 503 

Droughts identified using all three indices for Station 86071 on 3-, 6- and 12-month time scales are shown in Figures 456, respectively. For the 3-month time scale using the RDI, eight drought events were identified during a period from 1955 to 2010. For the SPI, nine droughts were identified with one additional moderate drought event in the year 1976 with SPI at −1.16. Deciles showed 11 observed precipitation totals falling within the two lowest deciles of the historical distribution.

Figure 4

Droughts identified using (a) SPI and RDI and (b) deciles on 3-month time scale for Station 86071.

Figure 4

Droughts identified using (a) SPI and RDI and (b) deciles on 3-month time scale for Station 86071.

Figure 5

Droughts identified using (a) SPI and RDI and (b) deciles on 6-month time scale for Station 86071.

Figure 5

Droughts identified using (a) SPI and RDI and (b) deciles on 6-month time scale for Station 86071.

Figure 6

Droughts identified using (a) SPI and RDI and (b) deciles on 12-month time scale for Station 86071.

Figure 6

Droughts identified using (a) SPI and RDI and (b) deciles on 12-month time scale for Station 86071.

For the 6-month time scale, the SPI showed drought events increasing from eight to ten. However, the RDI identified only eight drought events over the period. It identified similar years of drought as the SPI did, except there were no droughts detected in the years 1983 (−0.84) and 2008 (−0.82). Similar to the 3-month time scale result, deciles identified 11 drought events giving the greatest number of droughts from all the indices. The threshold value obtained for this time scale was 210 mm.

For the 12-month time scale, in addition to Station 86071, the droughts identified for the other stations are tabulated in Table 5 for comparison. The years when drought occurred were slightly different from one station to the other. This is due to the variation in precipitation and other meteorological data for each location. For Station 76031, the SPI and RDI indices showed similar behaviour in detecting years of drought, except in 2002. However, while SPI does not indicate drought in 2002, RDI showed the severity to be just below the threshold level of −1.08. The 1982 and 2006 droughts are shown to be the worst among all droughts based on the results of all indices. In contrast, Station 77051 identified the 1967 drought to be the most severe, followed by the 1982 and 2006 droughts; RDI gave one additional year of drought in the year 1990 for this station. For Station 79011, the results of the SPI and RDI indices show similarities in detecting drought events. The 2006 drought was the worst amongst all of them.

Table 5

Droughts identified at 12-month time scale for all stations

Stations Year SPI RDI Deciles 
76031 1959 −1.15 −1.07 
 1967 −1.96 −1.91 
 1972 −1.58 −1.49 
 1982 −2.07 −1.99 
 1994 −1.4 −1.34 
 1998 −1.39 −1.36 
 2001 −1.04 −1.07 
 2002 – −1.08 
 2004 −1.23 −1.28 
 2006 −2.04 −2.06 
 2008 – – 
77051 1967 −2.79 −2.68 
 1972 − – 
 1977 −1.23 −1.11 
 1982 −2.72 −2.6 
 1990 – −1 
 1994 −1.42 −1.37 
 1997 – – 
 2002 −1.72 −1.78 
 2004 − – 
 2006 −2.31 −2.34 
 2008 −1.03 −1.06 
79011 1959 −1.81 −1.63 
 1961 −1.02 −1.18 
 1967 –2.33 −2.27 
 1969 – – 
 1982 −1.82 −1.83 
 1994 −1.07 −1.13 
 1997 −1.35 −1.46 
 2002 −1.53 −1.44 
 2005 – – 
 2006 −2.79 −2.78 
 2008 – – 
81013 1957 – – 
 1961 −1.02 −1 
 1967 −1.56 −1.54 
 1972 −1.6 −1.51 
 1976 – – 
 1982 −2.37 −2.27 
 1994 −1.52 −1.45 
 1997 −1.13 −1.12 
 2002 −1.76 −1.81 
 2006 −2.54 −2.52 
 2009 −1.18 −1.34 
86071 1967 −2.54 −2.43 
 1976 −1.18 −1.15 
 1982 −1.63 −1.65 
 1994 −1.18 −1.24 
 1997 −2.24 −2.35 
 2002 −1.87 −1.76 
 2003 −1 – 
 2006 −1.48 −1.38 
 2007 −1.38 −1.46 
 2008 −1.38 −1.27 
 2009 −1.24 −1.35 
Stations Year SPI RDI Deciles 
76031 1959 −1.15 −1.07 
 1967 −1.96 −1.91 
 1972 −1.58 −1.49 
 1982 −2.07 −1.99 
 1994 −1.4 −1.34 
 1998 −1.39 −1.36 
 2001 −1.04 −1.07 
 2002 – −1.08 
 2004 −1.23 −1.28 
 2006 −2.04 −2.06 
 2008 – – 
77051 1967 −2.79 −2.68 
 1972 − – 
 1977 −1.23 −1.11 
 1982 −2.72 −2.6 
 1990 – −1 
 1994 −1.42 −1.37 
 1997 – – 
 2002 −1.72 −1.78 
 2004 − – 
 2006 −2.31 −2.34 
 2008 −1.03 −1.06 
79011 1959 −1.81 −1.63 
 1961 −1.02 −1.18 
 1967 –2.33 −2.27 
 1969 – – 
 1982 −1.82 −1.83 
 1994 −1.07 −1.13 
 1997 −1.35 −1.46 
 2002 −1.53 −1.44 
 2005 – – 
 2006 −2.79 −2.78 
 2008 – – 
81013 1957 – – 
 1961 −1.02 −1 
 1967 −1.56 −1.54 
 1972 −1.6 −1.51 
 1976 – – 
 1982 −2.37 −2.27 
 1994 −1.52 −1.45 
 1997 −1.13 −1.12 
 2002 −1.76 −1.81 
 2006 −2.54 −2.52 
 2009 −1.18 −1.34 
86071 1967 −2.54 −2.43 
 1976 −1.18 −1.15 
 1982 −1.63 −1.65 
 1994 −1.18 −1.24 
 1997 −2.24 −2.35 
 2002 −1.87 −1.76 
 2003 −1 – 
 2006 −1.48 −1.38 
 2007 −1.38 −1.46 
 2008 −1.38 −1.27 
 2009 −1.24 −1.35 

Nine droughts were detected using the SPI and RDI for Station 81013. Again, the 1982 and the 2006 droughts were found to be the most severe compared to other droughts. For Station 86071, the 2003 drought was the only difference between RDI and the other two indices. However, it was a very slight difference as the SPI gave a severity of −1 and deciles showed the sum of the precipitations falls in the second decile. Similarly to Station 77051, the 1967 drought was the most severe amongst all the years. The longest duration of a drought was found at this station and was for four successive years from 2006 to 2009 detected by all three indices (Figure 6).

Overall, the 1967 and 1982 droughts, which are said to be the most widespread droughts in the State of Victoria (BoM 2011), were confirmed to be so based on the results of the current study for all stations. Furthermore, all stations suffered from droughts in 2006. Table 6 summarizes the number of drought events and classifications that occurred in all five locations during the study periods, as discussed above. It also depicts the maximum intensity of droughts and maximum deficits for all five stations calculated for each period over 3-, 6- and 12-month time scales. As discussed earlier, the SPI and RDI identified almost the same number of drought events during each drought period but with slightly different severity, as shown in Table 6. Overall, on the 3-month time scale, Stations 76031, 77051 and 79011 gave comparable numbers of drought for these two indices, while for the 6-month time scale, Stations 76031, 77051 and 81013 showed similarities. Last but not least, for the 12-month time scale, Stations 76031, 79011 and 81013 gave similar results in identifying the number of drought events. Station 76031, which is the driest station, showed comparable results between SPI and RDI. It is also important to note that the intensity values obtained from the SPI and RDI methods were not directly comparable as each method calculated the droughts differently.

Table 6

Drought properties based on the SPI, RDI and ToR analysis

  SPI RDI ToR 
Stations No. of drought events Max intensity No. of drought events Max intensity Max deficit (mm) 
 Moderate Severe Extreme  Moderate Severe Extreme   
76031 – −3.11 (1965) −3.05 (1965) 19.5 (1965) 
77051 −3.25 (1986) −3.22 (1986) 21.1 (1986) 
79011 – −1.82 (1986) – −1.8 (2009) 16 (1986) 
81013 – −3.28 (1965) −3.24 (1965) 40.6 (1965) 
86071 −2.51 (1965) −2.51 (1965) 51 (1965) 
76031 – −1.88 (2004) – −1.8 (2004) 23.2 (2004) 
77051 −2.52 (1967) −2.41(1967) 48.3 (1967) 
79011 −2.33 (1967) −2.87 (1976) 67.1 (1967) 
81013 −2.3 (1976) −2.7 (1976) 51.4 (1976) 
86071 −2.29 (2009) −2.68 (1976) 85.3 (2009) 
76031 −2.07 (1982) −2.06 (2006) 65 (1982) 
77051 −2.79 (1967) −2.68 (1967) 126 (1967) 
79011 −2.79 (2006) −2.78 (2006) 164 (2006) 
81013 −2.54 (2006) −2.52 (2006) 177 (2006) 
86071 −2.54 (1967) −2.43 (1967) 171 (1967) 
  SPI RDI ToR 
Stations No. of drought events Max intensity No. of drought events Max intensity Max deficit (mm) 
 Moderate Severe Extreme  Moderate Severe Extreme   
76031 – −3.11 (1965) −3.05 (1965) 19.5 (1965) 
77051 −3.25 (1986) −3.22 (1986) 21.1 (1986) 
79011 – −1.82 (1986) – −1.8 (2009) 16 (1986) 
81013 – −3.28 (1965) −3.24 (1965) 40.6 (1965) 
86071 −2.51 (1965) −2.51 (1965) 51 (1965) 
76031 – −1.88 (2004) – −1.8 (2004) 23.2 (2004) 
77051 −2.52 (1967) −2.41(1967) 48.3 (1967) 
79011 −2.33 (1967) −2.87 (1976) 67.1 (1967) 
81013 −2.3 (1976) −2.7 (1976) 51.4 (1976) 
86071 −2.29 (2009) −2.68 (1976) 85.3 (2009) 
76031 −2.07 (1982) −2.06 (2006) 65 (1982) 
77051 −2.79 (1967) −2.68 (1967) 126 (1967) 
79011 −2.79 (2006) −2.78 (2006) 164 (2006) 
81013 −2.54 (2006) −2.52 (2006) 177 (2006) 
86071 −2.54 (1967) −2.43 (1967) 171 (1967) 

The correlation between the SPI and RDI indices were calculated and deemed to be satisfactory (Table 7) for all stations and time scales. The values ranged from 0.980 to 0.997. Station 76031 obtained the highest coefficient while Station 79011 showed the lowest. A similar result was found in Asadi Zarch et al. (2011), where SPI and RDI are more correlative in a dry climate than in a humid (wet) climate. As shown in Figure 2, Stations 79011 and 86071 receive more monthly rainfall with lower average temperature compared to the others. It also shows that the correlation decreased with an increase in time scale. This is most probably due to the variability of monthly PET and the rainfall data when longer time scales were considered. The correlations were also tested for SPI and RDI values calculated starting with a month different to January. This still gave similar results.

Table 7

Correlation coefficient of the SPI and RDI for all stations in different time scales

  Time scales 
Stations 12 
76031 0.997 0.994 0.994 
77051 0.997 0.990 0.994 
79011 0.988 0.980 0.985 
81013 0.997 0.992 0.993 
86071 0.995 0.980 0.991 
  Time scales 
Stations 12 
76031 0.997 0.994 0.994 
77051 0.997 0.990 0.994 
79011 0.988 0.980 0.985 
81013 0.997 0.992 0.993 
86071 0.995 0.980 0.991 

Detecting the onset and end of droughts using SPI

The SPI was further applied to define the initiation (onset) and end of droughts in Victoria. The onset of drought times for different time scales (3, 6 and 12 months) obtained were compared with the recorded 1982 and 2002 droughts as shown in Table 8. The 1982–83 event had recorded drought periods between April 1982 and February 1983 (Gibbs 1984) based on the deciles method.

Table 8

Comparison of the recorded onset of the 1982–83 (April 82–February 83) and 2002–03 (April 2002–January 2003) drought events with the results obtained from the SPI

  1982–1983 2002–2003 
Stations Initiation End Initiation End 
3-month     
76031 November 81 July 83 November 01 July 03 
77051 November 81 March 83 December 01 January 03 
79011 November 81 February 83 January 02 December 02 
81013 November 81 March 83 May 01 April 03 
86071 October 81 June 83 March 02 December 03 
6-month   
76031 January 82 September 83 January 01 January 03 
77051 January 82 June 83 January 02 January 03 
79011 January 82 April 83 March 02 January 03 
81013 January 82 May 83 May 01 May 03 
86071 December 81 August 83 September 01 December 03 
12-month   
76031 May 82 November 83 February 01 September 03 
77051 May 82 October 83 February 01 July 03 
79011 July 82 August 83 March 02 May 03 
81013 June 82 August 83 May 01 October 03 
86071 December 81 December 83 July 01 December 03 
  1982–1983 2002–2003 
Stations Initiation End Initiation End 
3-month     
76031 November 81 July 83 November 01 July 03 
77051 November 81 March 83 December 01 January 03 
79011 November 81 February 83 January 02 December 02 
81013 November 81 March 83 May 01 April 03 
86071 October 81 June 83 March 02 December 03 
6-month   
76031 January 82 September 83 January 01 January 03 
77051 January 82 June 83 January 02 January 03 
79011 January 82 April 83 March 02 January 03 
81013 January 82 May 83 May 01 May 03 
86071 December 81 August 83 September 01 December 03 
12-month   
76031 May 82 November 83 February 01 September 03 
77051 May 82 October 83 February 01 July 03 
79011 July 82 August 83 March 02 May 03 
81013 June 82 August 83 May 01 October 03 
86071 December 81 December 83 July 01 December 03 

Figure 7 shows an example of SPI for Station 77051 for all time scales for the 1982–83 drought. The 3-month time scale started in November 1981 and ended in March 1983, and the duration became longer for the 6-month time scale because of less fluctuation in the SPI values given that the computation is based on a 6-month moving cumulative rainfall. As the time period is lengthened, the SPI responds more slowly to changes in precipitation, and periods with the SPI being negative and positive become fewer in number but longer in duration. The 6-month time scale showed the drought starting in January 1982 lasting until June 1983. For the 12-month time scale, the drought commenced in May 1982, which was 1 month late than recorded, and ended in September 1983.

Figure 7

Onset and end of drought obtained from the SPI on (a) 3-month, (b) 6-month and (c) 12-month time scales for Station 77051.

Figure 7

Onset and end of drought obtained from the SPI on (a) 3-month, (b) 6-month and (c) 12-month time scales for Station 77051.

The onset time of the drought for other stations, as shown in Table 8, varied with the time scale used to calculate the index. For all five locations, the 3-month time scale showed the onset of the drought during the same time of the year in October–November. They show the onset of a mild drought from the beginning of the year followed by severe drought commencing later around June–July that year. The 6-month time scale indicated a drought two to three months in advance of the recorded drought. In contrast, with the exception of Station 86071, the 12-month time scale showed the onset later, in May–July, in that year. This might be because, as the time period is lengthened to 12 months, the SPI responds more slowly to changes in precipitation. Shorter or longer time scales may reflect different lags in the response to precipitation anomalies.

The 2002–2003 drought lasted from April 2002 to January 2003 (BoM 2003). Figure 8 shows the onset and end of drought for the 2002–2003 drought for all time scales. On the 3-month time scale, the SPI showed the onset of the drought starting from December 2001 and lasting until January 2003, showing the duration of the drought to be 14 months. For the 6-month time scale, it showed the onset two months earlier than the recorded drought that started from January 2002 ending in January 2003. For all five locations and for all time scales, the SPI showed the onset of the droughts well, as shown in Table 8. Based on the results it could be concluded that the SPI method would satisfactorily identify meteorological drought events in Victoria, Australia.

Figure 8

Onset and end of drought for 2002–2003 on (a) 3-month, (b) 6-month and (c) 12-month time scales for Station 77051.

Figure 8

Onset and end of drought for 2002–2003 on (a) 3-month, (b) 6-month and (c) 12-month time scales for Station 77051.

Why is it important to apply DI in Australia

To date, there are no DI applied across Australia by any Commonwealth agency except the Bureau of Meteorology (BoM) which uses deciles to assess the status of rainfall deficiency throughout Australia. A similar situation existed in the USA until the National Integrated Drought Information System Act was passed in 2006 (Public Law 109-430) addressing major droughts across America, which locked in SPI to legally define drought. In Australia, state-based agencies are responsible for operational decision-making using independently derived indices to assist operational planning.

For example, Melbourne Water Corporation responsible for supplying four million people across the metropolis, uses ‘total system storage triggers’ to impose various water restriction levels. The implementation of water restriction is directly related to the severity of an evolving drought, and thus the water authority has to identify how severe a particular drought event is before planning the appropriate response. Therefore, the adaptation of SPI, which is applied in this current study, could provide essential information on droughts (e.g., lead time, duration, magnitude, the onset and end of the drought, etc.) which would help organizations to plan responses and drought impact mitigation actions.

CONCLUSIONS

This study was designed to evaluate three popular indices for the assessment of drought occurrences using data from five rainfall stations across Victoria, Australia. Theory of Runs (ToR) was then used to obtain drought deficit. The SPI and deciles require only rainfall data which are usually available in most countries for many locations, while the RDI method needed evapotranspiration and rainfall for its computation. Although the decile method is commonly used in Australia, it has a few limitations. One of the disadvantages is that it does not indicate the onset and end of droughts which are important features of drought monitoring. Another limitation is that droughts are defined arbitrarily based on a selected threshold and hence would be different from one location to the other. In contrast, SPI and RDI do not rely on arbitrary selection of threshold values and the classification of when a drought occurs is clear and is set objectively. They are also applied consistently across jurisdiction (States) as the methodology has inbuilt standardization of the specific indices.

The SPI was able to identify the onset and end of meteorological droughts successfully when applied to the data. It was shown to be a good indicator and is worthy of further study to examine its use for drought monitoring and early warning, especially in other eastern states of Australia. On the other hand, utilization of the RDI might be beneficial for characterizing agricultural droughts, given that the RDI includes PET apart from precipitation in the calculation, providing an indicative deficit in soil moisture. As all three indices were calculated starting at the beginning of each year for all time scales, looking at different time scales is also necessary for comparison. In this study it was shown that the indices calculated at a longer time scale (i.e., 12 months) provided better results as the longer time scale reflected better historical drought events.

ACKNOWLEDGEMENTS

The authors would like to thank the BoM in Australia for providing precipitation data and Tun Hussein Onn University of Malaysia (UTHM) for providing scholarship support to the first author. Valuable comments and recommendations from the editor and anonymous reviewers are greatly appreciated.

REFERENCES

REFERENCES
Alexander
L. V.
Tapper
N.
Zhang
X.
Fowler
H. J.
Tebaldi
C.
Lynch
A.
2009
Climate extremes: progress and future directions
.
Int. J. Climatol.
29
(
3
),
317
319
.
Allen
R. G.
Pereira
L. S.
Raes
D.
Smith
M.
1998
Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56. Available at
:
Alley
W. M.
1984
The Palmer drought severity index: limitations and assumptions
.
J. Climate Appl. Meteorol.
23
,
1100
1109
.
Asadi Zarch
M.
Malekinezhad
H.
Mobin
M.
Dastorani
M.
Kousari
M.
2011
Drought monitoring by Reconnaissance Drought Index (RDI) in Iran
.
Water Resour. Manage.
25
(
13
),
3485
3504
.
Ben-Zvi
A.
1987
Indices of hydrological drought in Israel
.
J. Hydrol.
92
(
1–2
),
179
191
.
BoM (Bureau of Meteorology)
2003
Drought statement
.
Australian BoM, Melbourne, VA
.
Available at: http://www.bom.gov.au/announcements/ (accessed May 2013)
.
BoM (Bureau of Meteorology)
2007
Climate statistics for Australian Locations
.
Australian BoM, Melbourne, VA
.
Available at
: (
accessed 21 October 2013
).
BoM (Bureau of Meteorology)
2011
Living with Drought. Australian BoM, Melbourne, VA
.
Available at
: (
accessed November 2011
).
BoM (Bureau of Meteorology)
2012
Climate Data Online. Australian BoM, Melbourne, VA
.
Available at
: (
accessed 21 October 2013
).
Dai
A.
2011
Characteristics and trends in various forms of the Palmer Drought severity index during 1900–2008
.
J. Geophys. Res.
116
(
D12
),
D12115
.
Gergis
J.
Gallant
A.
Braganza
K.
Karoly
D.
Allen
K.
Cullen
L.
D'Arrigo
R.
Goodwin
I.
Grierson
P.
McGregor
S.
2012
On the long-term context of the 1997–2009 ‘Big Dry’ in South–Eastern Australia: insights from a 206-year multi-proxy rainfall reconstruction
.
Clim. Change
111
(
3–4
),
923
944
.
Gibbs
W. J.
Maher
J. V.
1967
Rainfall deciles as drought indicators
.
Bureau of Meteorology (BoM) Bulletin No 48. BoM, Melbourne, VA
.
Hayes
M. J.
2003
Drought indices
.
Available at
: (
accessed 2 May 2011
).
Hayes
M. J.
Svoboda
M.
Wilhite
D. A.
Vanyarkho
O. V.
1999
Monitoring the 1996 drought using the SPI
.
Bull. Amer. Meteor. Soc.
80
,
429
438
.
Heim
R. R.
Jr
2002
A review of twentieth-century drought indices used in the United States
.
Bull. Amer. Meteor. Soc.
83
(
8
),
1149
1165
.
Keyantash
J.
Dracup
J. A.
2002
The quantification of drought: an evaluation of drought indices
.
Bull. Amer. Meteor. Soc.
83
(
8
),
1167
1180
.
Khalili
D.
Farnoud
T.
Jamshidi
H.
Kamgar-Haghighi
A.
Zand-Parsa
S.
2011
Comparability analyses of the SPI and RDI Meteorological Drought Indices in different climatic zones
.
Water Resour. Manage.
25
(
6
),
1737
1757
.
Kinninmonth
W. R.
Voice
M. E.
Beard
G. S.
de Hoedt
G. C.
Mullen
C. E.
2000
Australian Climate Services for Drought Management. Drought: A Global Assessment
(
D. A. Wilhite, ed.).
Routledge
, pp.
210
222
.
McKee
T. B.
Doesken
N. J.
Kleist
J.
1993
The relationship of drought frequency and duration to time scales. Proceedings of Eighth Conference on Applied Climatology, 17–22 January
,
American Meteorological Society
,
Boston, MA
.
Mishra
A.
Desai
V.
2005
Drought forecasting using stochastic models
.
Stoch. Environ. Res. Risk A.
19
(
5
),
326
339
.
Mishra
A. K.
Singh
V. P.
2009
Analysis of drought severity-area-frequency curves using a general circulation model and scenario uncertainty
.
J. Geophys. Res.
114
(
D6
),
D06120
.
Mishra
A. K.
Singh
V. P.
2010
A review of drought concepts
.
J. Hydrol.
391
(
1–2
),
202
216
.
Morid
S.
Smakhtin
V.
Moghaddasi
M.
2006
Comparison of seven meteorological indices for drought monitoring in Iran
.
Int. J. Climatol.
26
(
7
),
971
985
.
Nalbantis
I.
Tsakiris
G.
2009
Assessment of hydrological drought revisited
.
Water Resour. Manage.
23
(
5
),
881
897
.
National Climate Centre
2010
Australia's wettest September on record but it is not enough to clear long-term rainfall deficits
.
Special Climate Statement 22
.
Palmer
W. C.
1965
Meteorological Drought
.
Research Paper No. 45
. US Department of Commerce Weather Bureau
,
Washington, DC
.
Paulo
A. A.
Pereira
L. S.
2006
Drought concepts and characterization
.
Water Int.
31
(
1
),
37
49
.
Paulo
A. A.
Ferreira
E.
Coelho
C.
Pereira
L. S.
2005
Drought class transition analysis through Markov and Loglinear models, an approach to early warning
.
Agric. Water Manage.
77
(
1–3
),
59
81
.
Tan
K. S.
Rhodes
B. G.
2008
Implications of the 1997–2006 Drought on Water Resources Planning for Melbourne. In: Proceedings of Water Down Under 2008, Engineers Australia, Causal Productions
, pp.
2016
2027
.
Tsakiris
G.
Vangelis
H.
2005
Establishing a drought index incorporating evapotranspiration
.
Europ. Water
9/10
,
3
11
.
Tsakiris
G.
Pangalou
D.
Vangelis
H.
2007
Regional drought assessment based on the Reconnaissance Drought Index (RDI)
.
Water Resour. Manage.
21
(
5
),
821
833
.
Ummenhofer
C. C.
England
M. H.
McIntosh
P. C.
Meyers
G. A.
Pook
M. J.
Risbey
J. S.
Gupta
A. S.
Taschetto
A. S.
2009
What causes southeast Australia's worst droughts?
Geophys. Res. Lett.
36
(
4
),
L04706
.
van der Schrier
G.
Jones
P. D.
Briffa
K. R.
2011
The sensitivity of the PDSI to the Thornthwaite and Penman-Monteith parameterizations for potential evapotranspiration
.
J. Geophys. Res.
116
(
D3
),
D03106
.
Verdon-Kidd
C. D.
Kiem
A. S.
2010
Quantifying drought risk in a nonstationary climate
.
J. Hydrometeor.
11
,
1019
1031
.
Webb
C. P.
2010
Bureau of Meteorology
Reference Evapotranspiration Calculations: 20
.
Wilhite
D. A.
Glantz
M. H.
1985
Understanding the drought phenomenon: the role of definitions
.
Water Int.
10
(
3
),
111
120
.
WMO (World Meteorological Organization)
2006
Drought Monitoring and Early Warning: Concepts, Progress and Future Challenges
.
WMO Publication
No. 1006. WMO, Geneva, Switzerland
.
Wu
H.
Svoboda
M. D.
Hayes
M. J.
Wilhite
D. A.
Wen
F.
2007
Appropriate application of the standardized precipitation index in arid locations and dry seasons
.
Int. J. Climatol.
27
(
1
),
65
79
.
Yevjevich
V.
1967
An objective approach to definitions and investigations of Continental Hydrologic Drought
.
Hydrology Paper No. 23
.
Colorado State University
,
Fort Collins, CO
.