Stochastic Water Resources Technology

Kottegoda, N. T.

doi:10.1007/978-1-349-03467-3

Cited by 181 publications

(104 citation statements)

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“…The seasonality must be removed before performing the long-range dependence analysis. A classical approach, which is followed here, consists of estimating and subtracting a periodic deter- For the sake of comparison, instead of using the STL procedure, we also performed the model estimation on a series which was deseasonalized by applying the classical harmonic regression method [Kottegoda, 1980, Sample data (m3/s) Figure 9. Sample probability density of the deseasonalized Lake Maggiore mean daily inflows series (1943-1994) versus the "best fitted" Gaussian probability density function.…”

Section: Lake Maggiore Mean Daily Inflowsmentioning

confidence: 99%

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Montanari¹,

Rosso²,

Taqqu³

1997

Water Resources Research

267

199

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Abstract. Since Hurst [1951] detected the presence of long-term persistence in hydrologic data, new estimation methods and long-memory models have been developed. The lack of flexibility in representing the combined effect of short and long memory has been the major limitation of stochastic models used to analyze hydrologic time series. In the present paper a fractionally differenced autoregressive integrated moving average (FARIMA) model is considered. In contrast to using traditional ARIMA models, this approach allows the modeling of both short-and long-term persistence in a time series. A framework for identification and estimation is presented. The data do not have to be Gaussian. The resulting model, which replicates the sample probability density of the data, can be used for the generation of long synthetic series. An application to the monthly and daily inflows of Lake Maggiore, Italy, is presented. Once a suitable model is chosen, this method gives a more accurate estimate of H. In this paper, the fractionally differenced autoregressive integrated moving average models (FARIMA, see section 3) are considered because they account for both the short-and long-memory components that are present in many hydrologic long-memory processes. An identification procedure consisting of several steps is introduced in order to determine the most suitable model. This method is then applied to daily flows to Lake Maggiore, Italy. For purposes of comparison we also apply it to monthly flows to Lake Maggiore and to monthly rainfall in Genoa, Italy. A stochastic simulation of the non-Gaussian observations is also performed.In the next section the determination of the Hurst exponent from observed hydrologic time series is discussed. Although heuristic graphical methods can detect the presence of long memory, they are not capable of estimating its intensity with a sufficient degree of accuracy. Therefore, in section 3 a stochastic modeling framework is introduced in order to combine long-memory effects with the traditional identification and estimation approach of autoregressive integrated moving average (ARIMA) models. The application of the model to daily (and monthly) flows is discussed in the section 4. An application to monthly rainfall is also presented in order to assess the flexibility of the proposed approach when modeling data not affected by persistence. Detecting Long Memory in Hydrologic Time SeriesThe relative simplicity of the heuristic estimation methods for H has made them popular as diagnostic tools. Their purpose is only to detect long memory and to provide a rough estimate of the value of the H exponent; they are not able to supply any additional information concerning the spectral density function of the data. Among the methods found in the literature, the best known is the R/S statistic, which was introduced by Hurst [1951]. Other methods have been proposed. 1035

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Section: Lake Maggiore Mean Daily Inflowsmentioning

confidence: 99%

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Montanari¹,

Rosso²,

Taqqu³

1997

Water Resources Research

267

199

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“…Similarly, the periodogram exhibits quite a corresponding pattern in terms of the periodicity. However, as noted by Kottegoda [1], interpretation is difficult as it provides unexpected peaks. From Figure 11(b), the sample spectra from the different sections of the rainfall data may resemble each other in their overall aspects.…”

Section: Assessment Of Stochastic Characteristics and Findingsmentioning

confidence: 99%

“…This significance is informed more largely due to the variability and oscillatory behaviour of hydrological sequences. Against this backdrop therefore, as noted by Kottegoda [1], the lack of complete understanding of the physical processes involved and the consequent uncertainties in the magnitudes and frequencies of future events highlight the importance of time series analysis. Thus, the main objective of any time series analysis is to understand the mechanism that generates the data and also, but not necessarily, to produce likely future sequences over a short period of time.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Characteristics and Modelling of Monthly Rainfall Time Series of Ilorin, Nigeria

Ahaneku¹,

Otache²

2014

OJMH

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The analysis of time series is essential for building mathematical models to generate synthetic hydrologic records, to forecast hydrologic events, to detect intrinsic stochastic characteristics of hydrologic variables as well to fill missing and extend records. To this end, this paper examined the stochastic characteristics of the monthly rainfall series of Ilorin, Nigeria vis-à-vis modelling of same using four modelling schemes. The Decomposition, Square root transformation-deseasonalisation, Composite, and Periodic Autoregressive (T-F) modelling schemes were adopted. Results of basic analysis of the stochastic characteristics revealed that the monthly series does not show any discernible presence of long-term trend, though there is a seeming inter-decadal annual variation. The series exhibits strong seasonality throughout its length, both in the moments and autocorrelation and significantly intermittent. Based on assessment of the respective models, the performance of the different modelling schemes can be expressed in this order: T-F > Composite > Square root transformation-Deseasonalised > Decomposition. Considering the results obtained, modelling of monthly rainfall series in the presence of serial correlation between months should be based on the establishment of conditional probability framework. On the other hand, in view of the inadequacy of these modelling schemes, because of the autoregressive model components in the coupling protocol, nonlinear deterministic methods such as Artificial Neural Network, Wavelet models could be viable complements to the linear stochastic framework.

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“…Ces modèles à mémoire longue incluent les modèles « bruit Gaussien » (MANOELBROT et WALLIS, 1969a , b, c), de « ligne brisée»» (MEJIA et al, 1972), «niveau variable» (BOES et SALAS, 1978;BALLERINI et BOES, 1985), et « autorégressif et moyennes mobiles sur différen-ces fractionnaires »» (GRANGER, 1980 ;GRANGER et JOYEUX, 1980 ;HOSKING, 1981HOSKING, , 1984HOSKING, , 1985Ll et McLEOD, 1986). Plusieurs de ces modèles à mémoire longue sont aussi présentés dans des ouvrages d'hydrologie stochastique (KOTTEGODA, 1980 ;SALAS et al, 1980 ;BRASS et RODRIGUEZ-ITURBE, 1984 ; HIPEL et MCLEOD, 1990). Un avantage des modèles FARMA sur les autres modèles est que leurs structures d'autocorrélation sont capables de mettre en évidence un comportement de « mémoire à court terme » semblable à ceux des modèles ARMA mais aussi un comportement de « mémoire à long terme »>.…”

Section: Introductionunclassified

Développements récents dans la modélisation de la persistance à long terme

Jimenez¹,

Hipel²,

McLeod³

2005

rseau

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Afin de modéliser efficacement la persistance dans les séries chronologiques rencontrées en hydrologie, des développements récents autour du modèle fractionnaire auto-régressif à moyenne mobile (FARMA) (fractional autoregressive-moving average model) sont présentés. On s'intéresse particulièrement ici à de nouvelles procédures permettant d'estimer les paramètres du modèle FARMA d'une manière efficace au point de vue calcul. Pour obtenir les distributions d'échantillons des estimateurs des paramètres à partir de petits échantillons, une technique faisant appel au bootstrap peut être utilisée. Des applications pratiques à des séries de débits en rivière, de précipitations et de températures, montrent l'utilité des modèles FARMA.In order to model effectively persistence in hydrologic tune series, recent developments in fractional autoregressive-moving average (FARMA) models are presented. A time series possesses persistence or long memory if it has an autocorrelation structure that attenuates slowly to zero with increasing lags. Based on the controversy surrounding the Hurst phenomenon, some hydrologists claim that it is important to employ stochastic models which have the ability to model long memory when it is present in a given time series. Fractional Gaussian noise models and approximations thereof were developed within the field of hydrology in order to be able to model long memory. However, a particularly flexible set of models having the capability to describe long memory is the FARMA family of models, which constitutes a direct generalization of autoregressive integrated moving average (ARIMA) models.In particular, like an ARIMA model, a FARMA model contains autoregressive and moving average parameters. Whereas the differencing operator d is restricted to be zero or take on positive integer values in an ARIMA model, the parameter d in a FARMA model can have real values and is estimated along with the other model parameters. For a specified range of values for the d parameter, a FARMA model has long memory. Besides reviewing the background and main theoretical properties of FARMA models, simulation and forecasting techniques are presented. Additionally, procedures for estimating the parameters of a FARMA model are given and a bootstrapping technique is described to obtain the small sample distributions of the estimated parameters.To explain how to apply FARMA models in practice and demonstrate their usefulness, they are fitted to riverflow, precipitation and temperature time series

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Stochastic Water Resources Technology

Cited by 181 publications

References 0 publications

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Stochastic Characteristics and Modelling of Monthly Rainfall Time Series of Ilorin, Nigeria

Développements récents dans la modélisation de la persistance à long terme

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