Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value

Abstract

Partial duration series modelling is a robust tool with which to model hydrologic extremes, but because of several technical problems it remains underused. The most important obstacle is the choice of the threshold value, a matter that is currently under investigation by several authors.The truncation value affects the basic assumptions of the model, including arrival times and exceedance magnitudes. This paper considers changes in parameter and quantile estimates as a function of the threshold value (sampling variability). Simulated and real data were used to test the consistency of the model, and a new modelling procedure based on increasing threshold censoring is proposed to overcome these problems. Poisson arrivals and Generalized Pareto exceedances were assumed, and the suitability of this model at different threshold values has been also addressed.

Partial duration series distributions of the European dry spell lengths for the second half of the twentieth century

“…The selection of the appropriate truncation value to obtain the set of long and independent PDS events remains an open question (Beguería 2005 ;Ben-Zvi 2009 ;Mailhot et al 2013 ). A common truncation threshold for Europe, whatever the rain gauge considered, is justified in the manuscript.…”

“…Figure 3a, Lana et al ( 2006a , b ) for the Iberian Peninsula and northeastern Spain. In these papers, it was shown by means of excess plots (Beguería 2005 ) that the 95th percentile is a good common truncation value for these regions. At present, the excess plot method has been applied to define a truncation level for every DSL series.…”

“…The criterion to establish this threshold is nowadays an open problem. A review of the results obtained for the 267 rain gauges, after applying the mean-excess plot technique (Beguería 2005 ;Lana et al 2006a ), permits to ascertain that a wide range of thresholds would be necessary for the different rain gauges. This result should be expected, given the strong climatic differences between northern and southern latitudes or between Atlantic and Mediterranean domains.…”

Broad-scale ecosystem services of European wetlands—overview of the current situation and future perspectives under different climate and water management scenarios

“…swamps and marshes), which depend on a natural pattern of inundation, the "bankfull flow approach" was applied at representative grid cells to indicate important high-flow events (Schneider et al 2010). In this approach, bankfull flow was estimated by applying the partial duration series of river flows fitted with a Generalized Pareto Distribution (Davison and Smith 1990) and an increasing threshold censoring procedure (Begueria 2005). The underlying 42-year time series of daily discharge data was modelled by WaterGAP and a return period of 0.92 years was employed as a best estimate of bankfull flow (Dunne and Leopold 1978).…”

Comparative Study between POT and AMS Flood Frequency Analysis Models under Changing Environment

“…超定量(POT 或 PDS)抽样两种方法获得 [3] 。其中基于 AMS 抽样的洪水频率分析较常用， 样本长度与实测资 料年数相等。基于 POT 序列的洪水频率分析(POT 模 型)， 是以大于指定门限值的洪峰流量为样本进行分析 [2,4] 。在利用实测资料描述洪水特征上，POT 抽样既反 映洪水量级又反映洪水发生过程，比 AMS 抽样具有 更多物理相关性 [5] 。 关于超定量发生次数和样本分布。超定量的年发 生次数为随机数，在洪水频率分析应用中多假设该序 列服从泊松分布 [6][7][8][9] ；此外还有学者对比分析二项分 布、负二项分布和泊松分布，并给出利用分散指数检 验超定量发生次数服从何种分布的方法 [10,11] 。在拟合 POT 样本方面，近十几年来多采用广义 Pareto(GP)分 布 [12,13] ，作为 POT 模型经典分布的指数分布为 GP 分 布在形状参数为 0 时的特殊情况。 POT 样本选取的关键在于洪峰独立性判别和门 限值的选取 [5] 。POT 模型优点众多，但却未得到广泛 应用，原因可能是 POT 样本选取尚无统一标准 [3] 。目 前样本独立性判别标准主要有美国水资源协会标准、 Cunnane 标准和王善序提出的判别标准 [4] 。门限值选 取的主要方法包括年均超定量发生次数 n 法 [14,15] 、超 定量样本均值法、分散指数法和 Rosbjerg 提出的门限 值选取方法 [5] 。Lang 等 [5] 概括了上述方法并提出门限 值选择建议：通过超定量样本均值法和分散指数法确 定门限值区间，并选择满足 n > 2 或 3 的较大门限值， 该方法综合考虑了门限值选取需注意的问题。年均超 定量发生次数有不同的建议值，Cunnane [14] 认为用指 数分布时 n 应大于 1.65， 我国学者在进行 POT 模型分 析的时候，多通过试算将 n 控制在 2~3 [2,8,9,12] 。董爱红 [13] 分析了用 GP 分布拟合 POT 序列时， 设计值和分布 …”