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

Table 1.

SPI/SPEI/SPTI valuesClassesCumulative probabilities$\ge 2$Extremely Wet (EW)0.977–1.00$1.5 \mathrm{\hspace{0.5em}to\hspace{0.5em}}1.99$Severe Wet (SW)0.933–0.977$1 \mathrm{\hspace{0.5em}to\hspace{0.5em}} 1.49$Moderate Wet (MW)0.841–0.933$.99 \mathrm{\hspace{0.5em}to\hspace{0.5em}} -.99$Normal Drought (ND)0.159–0.841$-1 \mathrm{\hspace{0.5em}to\hspace{0.5em}} -1.49$Moderate Drought (MD0.067–0.159$-1.5 \mathrm{\hspace{0.5em}to\hspace{0.5em}} -1.99$Severe Drought (SD0.023–0.067$\le -2$Extreme Drought (ED)0.000–0.023

Table 2.

TimeSPI $\left(d_{1t}\mathrm{ }\right)$SPEI $\left(d_{2t}\mathrm{ }\right)$SPTI $\left(d_{3t}\mathrm{ }\right)$PWJADI $\left(d_{\mathit{jt}}\mathrm{ }\right)$2$p_{1c/c-1},$$d_{12}$$q_{1c/c-1},$$d_{22}$$r_{1c/c-1},$$d_{32}$$\mathit{max}(p_{1c/c-1},$$q_{1c/c-1},$$r_{1c/c-1}$) $\in \mathrm{ }{d}_{j2}$3$p_{1c/c-1},$$d_{13}$$q_{1c/c-1},$$d_{23}$$r_{1c/c-1},$$d_{33}$$\mathit{max}(p_{1c/c-1},$$q_{1c/c-1},$$r_{1c/c-1}$) $\in \mathrm{ }{d}_{j3}$4$p_{1c/c-1},$$d_{14}$$q_{1c/c-1},$$d_{23}$$r_{1c/c-1},$$d_{34}$$\mathit{max}(p_{1c/c-1},$$q_{1c/c-1},$$r_{1c/c-1}$) $\in \mathrm{ }{d}_{j4}$...............n$p_{1c/c-1},$$d_{1n}$$q_{1c/c-1},$$d_{2n}$$r_{1c/c-1},$$d_{3n}$$\mathit{max}(p_{1c/c-1},$$q_{1c/c-1},$$r_{1c/c-1}$) $\in \mathrm{ }{d}_{\mathit{jn}}$

Table 3.

StationsVariablesJabJanFebMarchAprMayJunJulAugSepOctNovDecAstorRainfallAvg.39.347.378.186.569.825.124.824.923.623.217.028.1Std.35.432.953.350.458.220.321.120.228.230.223.333.7Sk.1.20.71.20.51.21.52.12.03.02.52.12.3Minimum temperatureAvg.−7.3−5.2−0.93.87.411.214.514.610.34.6−0.4−4.6Std.1.91.91.31.31.41.41.21.21.31.01.11.4Sk.−0.30.30.0−0.10.10.8−0.1−0.30.5−0.4−0.10.1Maximum TemperatureAvg.2.94.59.015.019.824.627.226.923.417.711.45.5Std.1.51.72.01.92.31.61.41.51.51.71.71.7Sk.0.70.70.60.10.30.5−0.1−0.40.3−0.4−0.30.2Potential EvapotranspirationAvg.25.933.159.793.3129.6153.2162.8145.4111.074.942.427.6Std.2.94.17.58.412.98.58.69.47.16.23.93.2Sk.−0.40.2−0.40.30.2−0.4−0.90.0−0.70.6−0.10.0ChilasRainfallAvg.5.49.414.823.727.09.617.121.112.67.73.24.7Std.7.312.816.123.226.09.917.821.416.716.87.78.4Sk.2.52.82.11.51.41.22.21.82.35.53.93.7Minimum temperatureAvg.1.23.78.513.618.523.827.126.322.414.77.32.5Std.1.31.21.31.52.21.91.41.51.51.31.11.4Sk.0.10.30.1−0.7−0.2−0.1−0.2−0.80.00.2−0.1−0.1Maximum TemperatureAvg.12.114.620.025.931.137.039.238.534.928.420.713.9Std.1.41.82.01.92.71.91.71.71.61.71.41.3Sk.−0.20.40.30.20.30.5−0.1−0.30.0−0.5−0.2−0.1Potential EvapotranspirationAvg.41.754.094.0133.6177.3205.1210.4188.8145.2103.862.041.7Std.3.95.38.810.215.011.212.310.48.26.74.43.4Sk.−0.6−0.1−0.70.30.54.21.80.71.3−0.10.3−0.1IslamabadRainfallAvg.56.280.189.655.936.366.3276.8314.4119.333.516.332.9Std.46.561.257.653.628.358.0152.3134.583.835.020.241.4Sk.0.71.41.41.91.11.30.90.61.22.01.81.7Minimum temperatureAvg.2.95.610.515.520.324.024.623.721.114.68.13.9Std.1.21.51.61.51.81.20.80.71.21.41.51.4Sk.0.20.1−0.50.20.4−0.10.10.0−0.20.30.5−0.5Maximum TemperatureAvg.17.619.624.330.235.738.635.233.633.430.825.420.0Std.1.52.02.32.22.31.31.71.01.21.21.31.5Sk.−0.20.40.7−0.20.1−0.30.6−0.3−0.2−0.7−0.8−0.1Potential EvapotranspirationAvg.58.671.7115.4160.1209.8219.3182.8158.5141.9119.780.260.6Std.4.77.111.012.214.612.615.98.610.26.14.84.8Sk.−0.1−0.50.2−0.2−0.40.20.2−0.32.61.70.2−0.7

Table 4.

StationsAstorChillasIslamabadDistributionsSPISPEISPTISPISPEISPTISPISPEISPTI2P Beta−853.70−586.86−280.10−400.09−501.31−379.15−649.02−798.62−175.523P Weibull−1248.54−742.71−480.83−802.14−499.76−377.99−957.96−794.19−530.144P Beta−1243.31−745.71−469.79−804.11−596.01−338.36−950.07−999.42−524.50Arcsine−976.81−677.68−272.85−573.72−535.82−334.56−733.50−869.80−276.20Burr−897.92−685.22−347.29−552.51−580.56−333.51−685.97−921.57−349.46Cauchy−1062.66−705.69−367.96−609.06−570.14−266.33−815.15−1039.25−339.64Chi−891.67−592.94−247.93−529.75−505.56−263.65−685.96−804.31−186.58Chi − Square−898.99−593.03−441.42−561.03−505.52−233.31−686.20−803.99−400.85Cosine−955.91−749.20−192.31−420.16−588.46−218.93−691.23−912.17−221.50Curvilinear Trapezoidal−919.08−692.83−375.44−465.58−531.02−200.00−662.30−802.74−347.39Exponential−1184.40−592.94−401.81−541.19−505.52−148.24−685.99−803.98−416.79F−−853.70−588.68−457.56−666.41−501.38−118.30−734.53−799.56−397.90Gamma−1231.37−597.08−477.56−676.12−501.38−97.89−958.03−807.46−529.91Generalized Extreme Value−1136.72−744.03−456.48−710.95−600.36−97.11−910.00−1002.13−429.33Generalized normal−1157.38−741.93−476.01−757.31−596.88−94.60−940.23−1005.17−463.18Gumbel−1111.02−730.27−389.62−575.20−579.37−62.38−837.26−1001.09−355.68Inverse Chi − Square−977.24−597.63−273.05−691.27−505.58−58.44−745.12−808.03−277.75Inverse Gamma−1040.61−598.37−396.36−693.05−501.46−43.66−866.58−809.94−363.11Inverse Gaussian−992.97−586.86−356.23−634.16−501.31−39.21−855.36−798.62−301.65Johnson SB−1154.09−748.91−478.62−753.49−618.70−31.88−937.22−842.69−494.07Johnson SU−1152.55−737.66−471.37−752.90−592.94−23.93−935.91−1040.57−458.60Laplace−1071.73−717.40−382.24−586.94−571.37−23.01−830.09−1064.06−352.81Logistic−1080.45−736.36−365.07−568.66−582.07−16.07−809.03−1023.31−329.32Log − normal−1144.79−597.90−478.07−707.29−501.46−16.00−943.26−808.57−464.28Normal−1076.88−743.47−357.27−559.95−585.227.74−801.45−1008.64−320.81Rayleigh−1099.33−741.32−373.83−563.77−584.0813.94−820.24−987.28−338.22Scaled/shifted t−1075.95−739.20−369.08−620.14−581.0818.20−813.32−1039.68−336.58Skewed − normal−1126.18−743.67−384.42−561.25−603.1633.01−838.66−1006.44−354.71Trapezoidal−1111.66−761.06−361.71−543.75−606.2541.18−820.53−1004.38−336.16Triangular−1116.49−749.46−366.35−539.98−608.48105.68−824.84−1008.51−339.99Uniform−860.67−657.41−274.09−487.34−598.51194.16−739.90−817.55−158.35von Mises−874.06−590.16−364.93−552.56−501.56207.11−649.02−800.34−332.92

Table 5.

StationPairsCorrelationTest-statisticsp-valueAstorSPI vs SPEI0.623321.8912.2e-16SPI vs SPTI0.936173.1362.2e-16SPEI vs SPTI0.777533.9492.2e-16ChilasSPI vs SPEI0.23236.63865.994e-11SPI vs SPTI0.9793133.982.2e-16SPEI vs SPTI0.389211.6972.2e-16IslamabadSPI vs SPEI0.643323.2582.2e-16SPI vs SPTI0.9181115.232.2e-16SPEI vs SPTI0.739529.3632.2e-16

Table 7.

IndexTest Statistics (W)P-ValuesSPI0.805252.2e-16SPEI0.837442.2e-16SPTI0.833332.2e-16PWJADI0.763532.2e-16