A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL<sup>1</sup>

Cruise, J. F.; Arora, Kishore

doi:10.1111/j.1752-1688.1990.tb01382.x

Cited by 33 publications

(19 citation statements)

References 35 publications

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“…Even though the methodological framework was not yet clarified, in the past few authors highlighted some points which direct attention to the different meaning and application of the two steps. A very good illustration is provided by Cruise and Arora (1990) who noticed that the threshold level for physical declustering often had to be raised significantly to meet exponentially based tests on the POT distribution (Lang et al, 1999).…”

Section: Review Discussionmentioning

confidence: 99%

A two-step framework for over-threshold modelling of environmental extremes

Bernardara

Mazas

Kergadallan

et al. 2014

Nat. Hazards Earth Syst. Sci.

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Abstract. The evaluation of the probability of occurrence of extreme natural events is important for the protection of urban areas, industrial facilities and others. Traditionally, the extreme value theory (EVT) offers a valid theoretical framework on this topic. In an over-threshold modelling (OTM) approach, Pickands' theorem, (Pickands, 1975) states that, for a sample composed by independent and identically distributed (i.i.d.) values, the distribution of the data exceeding a given threshold converges through a generalized Pareto distribution (GPD). Following this theoretical result, the analysis of realizations of environmental variables exceeding a threshold spread widely in the literature. However, applying this theorem to an auto-correlated time series logically involves two successive and complementary steps: the first one is required to build a sample of i.i.d. values from the available information, as required by the EVT; the second to set the threshold for the optimal convergence toward the GPD. In the past, the same threshold was often employed both for sampling observations and for meeting the hypothesis of extreme value convergence. This confusion can lead to an erroneous understanding of methodologies and tools available in the literature. This paper aims at clarifying the conceptual framework involved in threshold selection, reviewing the available methods for the application of both steps and illustrating it with a double threshold approach.

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Section: Review Discussionmentioning

confidence: 99%

A two-step framework for over-threshold modelling of environmental extremes

Bernardara

Mazas

Kergadallan

et al. 2014

Nat. Hazards Earth Syst. Sci.

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“…Such is the commonly selected exponential distribution (e.g. Shane & Lynn, 1964;Kirby, 1969;Cruise & Arora, 1990;Katz et al, 2002;Smith, 2003;Koutsoyiannis, 2004Koutsoyiannis, , 2005. For this distribution, the standard deviation of the intervals is equal to the mean, and the skewness coefficient's value is 2.…”

Section: Transformation Of Probabilities To Recurrence Intervalsmentioning

confidence: 98%

Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences

Ben‐Zvi

Azmon

2010

Hydrological Sciences Journal

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Citation Ben-Zvi, A. & Azmon, B. (2010) Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences. Hydrol. Sci J. 55(4), 565-577.Abstract This article paves a way for assessing flood risk by the use of two-parameter distributions, for the intervals between threshold exceedences rather than by the traditional exponential distribution. In a case study, the apparent properties of intervals between exceedences of runoff events differ from those anticipated for exponentially distributed series. A procedure is proposed to relate two statistical parameters of the intervals to threshold discharges. It considers partial duration series (PDS) with thresholds equal to all high enough observed discharges. To avoid unnecessary assumptions on the behaviour of those parameters and effects of dependence between parameters for different PDS, a non-parametric trend-free pre-whitened scheme is applied. It leads to power-law relationships between a discharge and the mean and standard deviation of the intervals between its exceedences. Predicted mean inter-exceedence intervals, for the highest observed discharges at the stations, are closer to the observational periods than those predicted by GEV distributions fitted to AMS, and by GP distributions to fitted PDS. In the present case, the latter predictions are longer than the observational periods whereas some of the predicted mean inter-exceedences are shorter than the corresponding observational periods and some others are longer.Relations directes des débits á la moyenne et à l'écart-type des intervalles entre leurs dépassements de seuils Résumé Cet article ouvre une voie d'estimation du risque de crue par l'utilisation de lois de distribution à deux paramètres appliquées aux intervalles de temps entre dépassements de seuils plutôt que par la traditionnelle utilisation d'une loi de distribution exponentielle. Sur une étude de cas, il apparaît que les propriétés découlant de l'utilisation d'intervalles entre dépassements de seuils diffèrent de celles que l'on peut attendre de séries exponentiellement distribuées. On propose une procédure permettant de relier les deux paramètres statistiques aux seuils de dèbits utilisés. On considère des séries tronquées selon des seuils égaux à des débits suffisamment élevés et pour éviter d'inutiles hypothàses concernant le comportement des paramètres et leur dépendance au seuil de troncature, on applique une procédure non-paramétrique préalable d'élimination des tendances et des bruits colorés. Cela conduit à une dépendance algébrique entre le débit et la moyenne et l'écart-type de l'intervalle entre les dépassements de seuils retenus. Pour les débits les plus importants des stations étudiées, les intervalles de temps entre dépassements de seuils prévus sont plus proches des observations que ceux prévus par une loi GEV ajustée sur les séries de maximums annuels. Dans les cas étudiés, ces derniéres prévisions sont systématiquement plus longues que les intervalles observés, alors que pour la n...

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“…Relatively hot summers and precipitation distributed throughout the year are typical of subtropical humid climates. Although precipitation does occur throughout the year, the Gulf of Mexico region is known to receive more precipitation during winter months than summer [21]. In fact, the records show that the annual mean precipitation at Belle Mina is 1,453 mm, of which only 297 mm occurs during the growing season (Belle Mina rain gauge record from 2000 to 2009).…”

Section: Study Sitementioning

confidence: 99%

“…The second constraint serves to connect the first moment in probability space to the mean water content of the soil column in physical space. The Shannon entropy is given by [65]: (21) where f(x) is the probability density function (pdf) of the variable. Maximizing I in Equation (21) for the uniform pdf subject to the constraints above, Chiu [64] developed the 1-D profile of a variable decreasing monotonically from the surface down using the method of Lagrange multipliers (put into soil moisture terms by Al-Hamdan and Cruise [59]): (22) The Lagrange multipliers (λ's) can be solved from application of the constraints and boundary conditions (surface effective saturation, Θ 0 and mean effective saturation value of the soil column ), z is calculation depth, and L is total depth of the column.…”

Section: Development Of Soil Moisture Profiles From Alexi Awmentioning

confidence: 99%

A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields

et al. 2013

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Biophysical crop simulation models are normally forced with precipitation data recorded with either gauges or ground-based radar. However, ground-based recording networks are not available at spatial and temporal scales needed to drive the models at many critical places on earth. An alternative would be to employ satellite-based observations of either precipitation or soil moisture. Satellite observations of precipitation are currently not considered capable of forcing the models with sufficient accuracy for crop yield predictions. However, deduction of soil moisture from space-based platforms is in a more advanced state than are precipitation estimates so that these data may be capable of forcing the models with better accuracy. In this study, a mature two-source energy balance model, the Atmosphere Land Exchange Inverse (ALEXI) model, was used to deduce root zone soil moisture for an area of North Alabama, USA. The soil moisture estimates were used in turn to force the state-of-the-art Decision Support System for Agrotechnology Transfer (DSSAT) crop simulation model. The study area consisted of a mixture of rainfed and irrigated cornfields. The results indicate that the model forced with the ALEXI moisture estimates produced yield simulations that compared favorably with observed yields and with the rainfed model. 3332The data appear to indicate that the ALEXI model did detect the soil moisture signal from the mixed rainfed/irrigation corn fields and this signal was of sufficient strength to produce adequate simulations of recorded yields over a 10 year period.

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A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL¹

Cited by 33 publications

References 35 publications

A two-step framework for over-threshold modelling of environmental extremes

A two-step framework for over-threshold modelling of environmental extremes

Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences

A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields

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A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL1

Cited by 33 publications

References 35 publications

A two-step framework for over-threshold modelling of environmental extremes

A two-step framework for over-threshold modelling of environmental extremes

Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences

A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields

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Product

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A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL¹