Nonlinear analysis of seasonality and stochasticity of the Indus River

Abstract

One of the world's largest irrigation networks, based on the Indus River system in Pakistan, faces serious scarcity of water in one season and disastrous floods in another. The system is dominated both by monsoon and by snow and glacier dynamics, which confer strong seasonal and inter-annual variability. In this paper two different forecasting methods are utilized to analyse the long-term seasonal behaviour of the Indus River. The study also assesses whether the strong seasonal behaviour is dominated by the presence of low-dimensional nonlinear dynamics, or whether the periodic behaviour is simply immersed in random fluctuations. Forecasts obtained by nonlinear prediction (NLP) and the seasonal autoregressive integrated moving average (SARIMA) methods show that the performance of NLP is relatively better than the SARIMA method. This, along with the low values of the correlation dimension, is indicative of lowdimensional nonlinear behaviour of the hydrological dynamics. A relatively better performance of NLP, using an inverse technique, may also be indicative of the low-dimensional behaviour. Moreover, the embedding dimension of the best NLP forecasts is in good agreement with the estimated correlation dimension. This provides evidence that the nonlinearity inherent in the monthly river flow due to the snowmelt and the monsoon variations dominate over the high-dimensional components and might be exploited for prediction and modelling of the complex hydrological system. Key words forecasting; nonlinear prediction; hydrological time series modelling; identification methods; correlation dimension; seasonality; stochasticity; monsoon; snowmelt; Indus River Analyse non-linéaire de la saisonnalité et de la stochasticité du Fleuve Indus Résumé Un des plus grands réseaux d'irrigation au monde, basé dans le système du Fleuve Indus au Pakistan, fait face à une pénurie d'eau sérieuse pendant une saison et à des inondations catastrophiques pendant une autre. Le système est dominé à la fois par la mousson et par la dynamique de la neige et des glaciers, ce qui lui confère une forte variabilité saisonnière et interannuelle. Dans cet article, le comportement saisonnier de long terme du Fleuve Indus est analysé par deux méthodes de prévision différentes. L'étude évalue également si le fort comportement saisonnier est dominé par la présence de dynamiques non-linéaires de faible dimension, ou si le comportement périodique est simplement noyé dans des fluctuations aléatoires. Les prévisions obtenues par les méthodes de prévision non-linéaire (PNL) et de modèle saisonnier autorégressif à moyenne mobile intégrée (SARIMA) montrent que la performance de PNL est relativement meilleure que celle de SARIMA. Ceci, ainsi que les faibles valeurs de la dimension de corrélation, est indicatif d'un comportement non-linéaire de faible dimension de la dynamique hydrologique. Une performance relativement meilleure de PNL, utilisant une technique inverse, peut aussi être indicative du comportement de faible dimension. De plus, la dimension ...

Impact of complexity on daily and multi-step forecasting of streamflow with chaotic, stochastic, and black-box models

“…For instance, Kędra (2014) investigated discharge dynamics of the Raba River in southern Poland using several independent methods and concluded that underlying dynamics are not random but deterministic. Similar results were recently obtained by Hassan and Ansari (2010), Xu et al (2010), Sivakumar and Singh (2012), Khatibi et al (2012), and Kalteh and Berndtsson (2007). These studies suggested that streamflow dynamics are nonlinear and persistent complexity can be analyzed by a nonlinear chaotic approach to gain new insights.…”

“…In this study, we employed a zeroorder local forecasting model (Farmer and Sidorowich 1987) since it has fewer parameters to estimate in comparison to nth-order polynomial or local differential equations to avoid exponentially growing estimation errors (Hassan and Ansari 2010). This model approximates the local system dynamics by considering all k-neighbors of Y t as:…”

Impact Assessment of Hydroclimatic and Stochastic Variations on Water Stress of Jhelum River Flow Forecast

“…6b) helps to identify the order of autoregressive and existence of moving average components. It is very supportive in finding the seasonal autoregressive integrated moving average SARIMA models [1]. The crosscorrelation analyses shows that the local temperature (Chitral, Gilgit, Skardu) has significant influence on the river flow (Table 2, Fig.…”

“…2). So, the time series methodology does not completely describe the hydrological variation of the Jhelum River like the Indus river flow at the Tarbela station result presented in Hassan & Ansari [1]. This may also observed from Jhelum river flow ACF plot has sharp roll off (in early lag values Fig.…”

“…Pakistan's power generation zones and agronomic structure depends on the accessibility of water resources and a reliable forecast which helps to manage power generation of the country. The monsoon precipitation and melting of glaciers of the northern areas contributes a significant quantity of water to the IRS in summer season [1][2]. Whereas, in the winter season, water from melting of snow/glaciers, fountains and minimum precipitation (extensively lesser than the summer monsoon precipitation season) supports the lowest level of the river [3].…”