《Water Resources Management》刊登“预测干旱等级：加拿大水文干旱的简单模型”

作者：T. C. Sharma, U. S. Panu

刊物：《Water Resources Management》2013年, 第27卷3期, 649-664页

关键词：赤字量，干旱强度，干旱等级，马尔可夫链，标准化水文指数，截断正态分布

摘要：乘法公式干旱程度(M) = 干旱强度(I)×干旱持续时间(L)被用作预测某个时间段内水文干旱程度的最大理论值E(M_T)。预测的E(M_T)值是根据SHI（标准化水文指数，相当于标准正态变量）年度和月度的径流时间序列推算出的。假定I（干旱强度）的概率分布函数（pdf）遵循正态分布。采用旱期某些特定的时间段作为干旱时长(L_c)，干旱时长可以用预期的最长（极端）持续时间E(L_T)和旱期平均持续时间(L_m)以及可能涉及到的参数ø（范围0-1）的线性组合表述。假定干旱等级（赤字总和，M）遵循一个基于M的实测行为的伽马概率分布函数。模型 M = I × L 通过两个近似值被引用，即调用。Type-1只涉及到I 的平均值，Type-2包含I的平均值和方差。通过合适序列的马尔可夫链模型（MC）获得E(L_T)结果是年际时间尺度下的0阶马尔可夫链(MC-0)。在月时间尺度上，用滞后-1的自相关低值(ρ < 0.3)的SHI序列的0阶马尔可夫链和ρ > 0.3的SHI序列的1阶马尔可夫链(MC-1)代表E(L_T)。在低临界值(q ≤ 0.2)，E(M_T) = E(I) × E(L_T)不考虑极数定理，赤字总和(M)的概率分布函数(pdf)得出满意的结果.

Predicting Drought Magnitudes: A Parsimonious Model for Canadian Hydrological Droughts

Authors: T. C. Sharma, U. S. Panu

Journal: Water Resources Management, February 2013, Volume 27, Issue 3, pp 649-664

Keywords: Deficit-volume, Drought intensity, Drought magnitude, Markov chain, Standardized hydrological index, Truncated normal distribution

Abstract: A multiplicative relationship, drought magnitude (M) = drought intensity (I) × drought duration or length (L) is used as a basis for predicting the largest expected value of hydrological drought magnitude, E(M_T) over a period of T-year (or month). The prediction of E(M_T) is carried out in terms of the SHI (standardized hydrological index, tantamount to standard normal variate) sequences of the annual and monthly streamflow time series. The probability distribution function (pdf) of I (drought intensity) was assumed to follow a truncated normal. The drought length (L_c) was taken as some characteristic duration of the drought period, which is expressible as a linear combination of the expected longest (extreme) duration, E(L_T) and the mean duration, L_m of droughts and is estimated involving a parameter ø (range 0 to 1). The drought magnitude (deficit-sum, M) has been assumed to follow a gamma pdf, in view of the observed behavior of M. The model M = I × L has been invoked via two approximations, viz. Type-1 involves only mean of I and Type-2 involves both mean and variance of I through the theorem of extremes of random numbers of random variables. The E(L_T) were obtained using the Markov chain (MC) model of an appropriate order, which turned out to be zero order Markov chain (MC-0) at the annual time scale. At the monthly time scale, the E(L_T) was best represented by MC-0 for SHI sequences with low value of lag-1 autocorrelation (ρ < 0.3) and first order Markov chain (MC-1) for SHI sequences with ρ > 0.3. At low cutoff levels (q ≤ 0.2), the trivial relationship E(M_T) = E(I) × E(L_T) i.e. without considerations of the extreme number theorem and the pdf of M yielded satisfactory results.

原文链接：http://link.springer.com/article/10.1007/s11269-012-0207-x