The hydrological droughts on daily time scale at low truncation levels

such as Q90, Q95 have Lumacaftor order also been attempted on non-stationary daily flows using the frequency analysis of observed durations and magnitudes (Zelenhasic and Salvai, 1987 and Tallaksen et al., 1997). Although the assessment and prediction of meteorological droughts on weekly time scale have been practiced using the Palmer Drought Severity Index (PDSI) or Standardized Precipitation Index (SPI), in literature only a few studies on the modeling of hydrological droughts on weekly time scale have been reported. The analysis of hydrological droughts on weekly time scale is desirable because effects of droughts are more palpable in agricultural production, municipal water supplies, small-scale hydro generation etc. The development of suitable predictive and assessment tools for hydrologic droughts at weekly time scale would be useful in managing available water resources

and off-setting effects of droughts. This paper attempts to develop suitable methodology to analyze and predict hydrological droughts at weekly time scale. The paper also embodies the results of drought models for comparative purposes at annual and monthly time scales in Canadian BYL719 streamflows. It has been observed (Bonacci, 1993, Woo and Tarhule, 1994, Sharma, 1997 and Sharma, 2000) that in general the drought intensity (I, i.e. MT = I × LT) is poorly Bay 11-7085 correlated to LT. In view of a poor correlation (i.e. near independence) between these

two entities, the above relationship can be expressed in terms of expectations as E(MT) = E(I) × E(LT), which allows the prediction of drought magnitude with a priori knowledge of drought length. The drought intensity (I) can be modeled satisfactorily by the truncated normal distribution of SHI values which are laying below the truncation level. The modeling of drought length or duration (LT) is therefore essential in addressing the issues related to hydrological droughts. In the past, the theorem of extremes of random numbers of random variables ( Todorovic and Woolhiser, 1975; referred to hereafter as the extreme number theorem) has been used to model LT on annual flow series ( Sen, 1980a, Sharma, 1997, Sharma, 1998, Sharma, 2000, Panu and Sharma, 2002 and Panu and Sharma, 2009) and monthly flow series ( Sharma and Panu, 2008). Further, Sharma and Panu (2010) noted that the above theorem breaks down when the SHI sequences are strongly dependent (i.e. lag-1 autocorrelation being above 0.50) to the first order and/or extend to the second or higher order dependence (in case of weekly time scale). The monthly and weekly SHI sequences exhibit this tendency when the rivers are originating in lakes or passing through them. Under these circumstances, a second order Markov chain model tends to recover the analysis for modeling LT.