Discussions and Closures Closure to “Meteorological Drought Quantification with Standardized Precipitation Anomaly Index for the Regions with Strongly Seasonal and Periodic Precipitation” by Kironmala Chanda and Rajib Maity DOI: 10.1061/(ASCE)HE.1943-5584.0001236 Kironmala Chanda 1 and Rajib Maity 2 1 Ph.D. Student, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India. E-mail: kironmala .iitkgp@gmail.com 2 Associate Professor, Dept. of Civil Engineering, Indian Institute of Tech- nology Kharagpur, Kharagpur, West Bengal 721302, India (correspond- ing author). E-mail: rajib@civil.iitkgp.ernet.in; rajibmaity@gmail.com At the outset, the writers would like to thank Javad Bazrafshan (discusser) for writing a discussion on the original paper. The origi- nal paper proposes a new method for meteorological drought quan- tification, named as standardized precipitation anomaly index (SPAI), which is applicable for periodic (seasonal) and nonperiodic precipitation series. Thus, SPAI is shown to be more general, and standardized precipitation index (SPI) is a special case of it. The discusser has mentioned some issues which, the writers feel, have resulted because of some misinterpretations of the working princi- ple of SPAI. These issues, though already discussed in the original paper, are further clarified point by point in this closure. 1. First of all, the writers would like to state that Eq. (1) in the original paper is not related to the SPAI computation in any manner. It simply represents the expression of a mixed probabil- ity distribution. Thus, the discusser has wrongly referred to Eq. (1) while discussing the anomaly calculation in the SPAI methodology. Per Eq. (5) in the original paper, anomaly is cal- culated by deduction of the monthwise means from the respec- tive precipitation values. The expression is reproduced as y ij ¼ðx ij - ¯ x j Þ ð1Þ where y ij = precipitation anomaly for the ith year and jth time step of the year; x ij = precipitation for the ith year and jth time step of the year; and ¯ x j = long-term mean precipitation of the jth time step of the year. The discusser wrongly equates the standard deviation of the entire anomaly series (S y ) with the standard deviation of the raw precipitation series (S x ) in the equation shown in Eq. (4) of the discussion paper. The variable ¯ x j is the long-term mean precipi- tation of the jth time step of the year and is not the same as ¯ x (which is the long-term mean precipitation of the entire raw pre- cipitation series). Thus, S y ≠ S x . This can be shown as S y ¼ P n i¼1 P m j¼1 ðx ij - ¯ x j - 0Þ 2 n × m - 1 ¼ P n i¼1 P m j¼1 ðx ij - ¯ x j Þ 2 n × m - 1 ≠ S x ð2Þ This may be checked directly using actual data. For example, for the monthly precipitation series of Gangetic West Bengal (GWB), India, which has been used in the original paper, the standard deviation of the entire raw precipitation series is S x ¼ 138.9 mm, whereas the standard deviation of the entire anomaly series is S y ¼ 65.3 mm. Thus, the proof shown by the discusser does not hold, and the conclusion that “SPAI (like the SPI) can be calculated using the statistical parameters obtained from the raw precipitation data rather than the anomaly series” is wrong. Further, while attempting to prove the aforementioned state- ment/conclusion of the discussion paper, the discusser assumes that precipitation anomalies follow the normal distribution, which is not necessarily true. In fact, it has been found in an- other paper that t-location scale distribution is a suitable param- etric distribution that can describe the anomaly series for Indian precipitation (Chanda and Maity 2016). 2. The design of SPAI is such that a given anomaly value in both low and high precipitation months will produce an identical SPAI value. This is because a single probability distribution is fitted to all the anomaly values rather than 12 monthwise dis- tributions used in case of SPI. It has been demonstrated that this property makes it easier to interpret SPAI values than SPI values. The value of the SPAI is sufficient to indicate whether water stress is faced by the community or not, whereas for SPI, a combination of the index value and the climatology of the location for that particular month when it occurs is required to understand the water stress faced by the society. In Fig. 2(a) in the original paper, the minimum value of January SPAI observed during the study period in Gangetic West Bengal, India is -0.15 (corresponding to a precipitation of zero), and the maximum value of the same is 1.37 (corre- sponding to a precipitation of 108 mm). If the precipitation in January is even larger, say 150 mm (which is 12 times the mean value of 12.16 mm), then an appropriately large SPAI value (1.68) will obviously result. On the drier side, it is not possible to get any rainfall lower than zero. Thus, it is only natu- ral that the severity of precipitation deficits would potentially be less than the severity of precipitation surpluses in dry months because there is a physical limit to the maximum negative anomaly possible (the mean rainfall of the month), whereas there is theoretically no limit to the maximum positive anomaly. This fact must not confused as a shortcoming of SPAI method- ology; rather, the SPAI quantifies the deficit and surplus in a manner relevent to the society in a monsoon-dominated clima- tology where lack of rainfall in dry months is not at all harmful for the society. The discusser states that “the severity of precipitation deficits would potentially be less than the severity of precipitation sur- pluses in dry months. ” However, this is not true in general. In a region which receives low rainfall throughout the year, such as the arid regions of the middle east, a lack of precipitation in a certain month will of course produce large negative SPAI values indicating serious implications for the society. This can be demonstrated with data generated for 30 years having very low monthly mean rainfall values of 10.34, 7.84, 7.13, 10.58, 11.51, 13.23, 15.19, 13.34, 11.47, 9.53, 9.93, and 8.90 mm, re- spectively. In this low rainfall climatic regime, for a particular January month, if there is no rainfall, then the corresponding SPAI value is obtained as -2.77 indicating very severe drought. Similarly, if the January rainfall is 20.67 mm, then the SPAI value is 2.39 which adequately reflects the large surplus. Thus, in this case, severity of precipitation deficits would not be less © ASCE 07016004-1 J. Hydrol. Eng. J. Hydrol. Eng., 2016, 21(5): 07016004 Downloaded from ascelibrary.org by Rajib Maity on 05/06/16. Copyright ASCE. For personal use only; all rights reserved.