Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

Blain, Gabriel Constantino; Meschiatti, Monica Cristina

doi:10.1590/1807-1929/agriambi.v19n12p1129-1135

Cited by 32 publications

(33 citation statements)

References 24 publications

(50 reference statements)

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“…5 mm). As demonstrated by Blain and Meschiatti (2015), this feature may pose an additional difficulty on the use of such distribution in drought early warning system.…”

Section: Cumulative Distribution Functions and Zero Precipitation Valuesmentioning

confidence: 99%

Using the normality assumption to calculate probability‐based standardized drought indices: selection criteria with emphases on typical events

Blain

Ávila

Pereira

2017

Intl Journal of Climatology

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Enhancing the capability of both standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI) for quantifying wet and dry events under distinct climate conditions is of paramount importance. The different recommendations of recent studies regarding the best distribution to calculate the SPEI and the lack of studies addressing the effect of different parameters estimation methods on the SPI motivated us to apply and adapt distinct testing methodologies to select candidate models for calculating these standardized drought indices (SDI). The study is based on two data sets. The first represents a tropical–subtropical region of Brazil. The second comprises the same weather stations that were used for developing the original version of the SPEI. The study also emphasized the performance of the models within the range of typical SDI values [−2.0 : 2.0]. Along with goodness‐of‐fit tests, we calculated the mean absolute errors between the indices values estimated from the candidate distributions, and their corresponding theoretical values derived from the standard normal distribution. The two‐parameter gamma and the generalized extreme value distributions are, respectively, recommended for general use in SPI and SPEI algorithms (1–12‐month timescales). The unbiased probability weighted moments are recommended to estimate the distributions parameters. The study also described a trade‐off between choosing the best model for the central part and for the tails of the distributions. This trade‐off suggests that the methodologies used to select models for the SDI algorithms may have to decide which part of the distribution (central or tails) should be emphasized. The behaviour of the errors among different wet/dry categories showed that both indices were only capable of representing drought and floods in a similar probabilistic way within the range [−2.0 : 2.0]. This feature supports our decision to emphasize model performances within such range.

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“…5 mm). As demonstrated by Blain and Meschiatti (2015), this feature may pose an additional difficulty on the use of such distribution in drought early warning system.…”

Section: Cumulative Distribution Functions and Zero Precipitation Valuesmentioning

confidence: 99%

Using the normality assumption to calculate probability‐based standardized drought indices: selection criteria with emphases on typical events

Blain

Ávila

Pereira

2017

Intl Journal of Climatology

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“…While there is some criticism of the gamma distribution (see, e.g., Guttman, 1999 andBlain andMeschiatti, 2015), it is generally a widely used and recommended index (see, e.g., Svoboda et al (2012)). …”

Section: Spimentioning

confidence: 99%

Characterizing the spatiotemporal variability of groundwater levels of alluvial aquifers in different settings using drought indices

Haas

Birk

2017

Hydrol. Earth Syst. Sci.

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Abstract. To improve the understanding of how aquifers in different alluvial settings respond to extreme events in a changing environment, we analyze standardized time series of groundwater levels (Standardized Groundwater level Index -SGI), precipitation (Standardized Precipitation Index -SPI), and river stages of three subregions within the catchment of the river Mur (Austria). Using correlation matrices, differences and similarities between the subregions, ranging from the Alpine upstream part of the catchment to its shallow foreland basin, are identified and visualized.Generally, river stages exhibit the highest correlations with groundwater levels, frequently affecting not only the wells closest to the river, but also more distant parts of the alluvial aquifer. As a result, human impacts on the river are transferred to the aquifer, thus affecting the behavior of groundwater levels. Hence, to avoid misinterpretation of groundwater levels in this type of setting, it is important to account for the river and human impacts on it.While the river is a controlling factor in all of the subregions, an influence of precipitation is evident too. Except for deep wells found in an upstream Alpine basin, groundwater levels show the highest correlation with a precipitation accumulation period of 6 months (SPI6). The correlation in the foreland is generally higher than that in the Alpine subregions, thus corresponding to a trend from deeper wells in the Alpine parts of the catchment towards more shallow wells in the foreland.Extreme events are found to affect the aquifer in different ways. As shown with the well-known European 2003 drought and the local 2009 floods, correlations are reduced under flood conditions, but increased under drought. Thus, precipitation, groundwater levels and river stages tend to exhibit uniform behavior under drought conditions, whereas they may show irregular behavior during floods. Similarly, correlations are found to be weaker in years with little snow as compared with those with much snow. This is in agreement with typical aquifer response times over 1 month, suggesting that short events such as floods will not affect much of the aquifer, whereas a long-term event such as a drought or snow-rich winter will.Splitting the time series into periods of 12 years reveals a tendency towards higher correlations in the most recent time period from 1999 to 2010. This time period also shows the highest number of events with SPI values below −2. The SGI values behave in a similar way only in the foreland aquifer, whereas the investigated Alpine aquifers exhibit a contrasting behavior with the highest number of low SGI events in the time before 1986. This is a result of overlying trends and suggests that the groundwater levels within these subregions are more strongly influenced by direct human impacts, e.g., on the river, than by changes in precipitation. Thus, direct human impacts must not be ignored when assessing climate change impacts on alluvial aquifers situated in populated valleys.

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“…Ntale and Gan (2003) used Pearson type III (P3) distribution and probability plotting method to improve SPI values. Blain and Meschiatti (2015) provided an alternate procedure to quantify the risk of drought by introducing generalized normal distribution in Standardized Precipitation Index (SPI) model. Blain (2013) proposed a drought index based on generalized extreme value distribution instead of the gamma distribution (McKee et al, 1993).…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Weighted Joint Aggregative Drought Index (PWJADI) criterion for drought monitoring systems

Ali

Hussain

Faisal

et al. 2019

Tellus A: Dynamic Meteorology and Oceanography

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Drought is a complex natural hazard. Its several adverse impacts are prevailing in almost all climatic zones around the world. In this regards, drought monitoring and forecasting play a vital role in making drought mitigation policies. Therefore, several drought monitoring tools based on probabilistic models had been developed for precise and accurate inferences of drought severity and its effects. However, risk of inaccurate determination of drought classes always exists in probabilistic models. To overcome this issue, we proposed a new system based Probabilistic Weighted Joint Aggregative Drought Index (PWJADI) criterion for three multi-scalar drought indices, namely Standardized Precipitation Index (SPI), Standardized Precipitation Temperature Index (SPTI), and Standardized Precipitation Evapotranspiration Index (SPEI) at one-month time scale. By the basic assumption of the Markov chain, the PWJADI is based on the temporal switched weights that are propagated from the transition probability matrix of each temporal classification of drought index. Application of the proposed method is made for three meteorological stations of Pakistan. We found that our proposed model has ability to restructure the drought classes by capturing and bending the information from the historical behaviour of each drought class. Consequently, to make accurate and precise drought mitigation policies, the proposed method may integrate into effective drought monitoring systems.

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Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

Cited by 32 publications

References 24 publications

Using the normality assumption to calculate probability‐based standardized drought indices: selection criteria with emphases on typical events

Using the normality assumption to calculate probability‐based standardized drought indices: selection criteria with emphases on typical events

Characterizing the spatiotemporal variability of groundwater levels of alluvial aquifers in different settings using drought indices

A Probabilistic Weighted Joint Aggregative Drought Index (PWJADI) criterion for drought monitoring systems

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