(1), (2), (3), (4), (5) and (6)) applied on appropriate SHI sequences. The same theorem with the Gamma pdf of flows can be applied to estimate the above parameters on monthly time scale. In both situations, μ, cv, and ρ1 can be used to provide reliable estimates of E(LT) and E(MT) at the truncation level equivalent to the median
flow level over a period of T-year. The drought analysis on weekly time scale becomes complex because of the involved underlying dependence structure and thus the second order Markov chain models are considered for which there is a paucity of close form equations for estimating the second order conditional Ipilimumab in vivo probabilities, viz. qqq and qqp. Therefore, the historical flow records are used to estimate these parameters by the counting method involving see more both the non-standardized flow series and appropriate SHI sequences. Potentially,
there are 3 values (based on the annual, monthly, and weekly time scales) of E(LT) for a T-year drought and consequently 3 values of the expected deficit-volumes, E(DT) that need to be considered for the assessment of volumetric-storage [E(DT) = σE(MT)]. A logical question that naturally arises as to which one of them should be used for planning the drought mitigation measures. To elucidate the point, the case of Torrent river, Canada (station NF02YC001) with the following statistical properties is considered: mean flow equal to 24.50 m3/s; σ equal to 3.68 m3/s (annual), 12.50 m3/s (monthly averaged value), 17.15 m3/s (weekly averaged value); ρ1 equal to 0.0 (annual, assumed as 0.0 in view of negligible dependence), 0.19 (monthly), and 0.73 (weekly). On annual, monthly, and weekly time scales, the values of cv ( Table 1 and Table 2) are respectively 0.15, 0.51 and 1.12 for the computations of E(LT). The values of qq, qqq and qqp were estimated as 0.76 and 0.84 and 0.24 at the median level (i.e. q = 0.5 and SHI0 = −0.32). Using the above statistics, it can be estimated that a 50-year drought is likely to continue for 5 years or 10 months or 33 weeks respectively
when analyzed based on annual, monthly, N-acetylglucosamine-1-phosphate transferase and weekly time scales (by plugging the values of parameters in Equations (1), (2), (3), (4), (5), (6), (7) and (8)). The corresponding values of drought magnitudes can be computed as 0.58 (=3.68 × 5 × c1) billion m3, or 0.32 (=12.50 × 10 × c2) billion m3 or 0.24 (=17.15 × 0.69 × 33 × c3) billion m3. Note c1 (=31.5 × 106), c2 (=2.95 × 106) and c3 (=0.605 × 106) are conversion constants to covert the annual, monthly and weekly flow rates into volumes. It may be borne in mind that for annual and monthly droughts drought intensity, E(I) equal to 1 and for weekly drought E(I) equal to 0.69 (Eq. (6), z0 = SHI0 = −0.32 and corresponding q for normal pdf is 0.37) for use in the relationship E(MT) = E(I) × E(LT).