Least Squares Estimation of Constants in a Linear Recession Model

James, L. Douglas; Thompson, William O.

doi:10.1029/wr006i004p01062

Cited by 31 publications

(22 citation statements)

References 5 publications

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“…Consider, for instance, the AR with exogenous variables (ARX) model of flow in a small, rainfall-driven coastal catchment developed by Farahmand et al (2007). The AR predictor (prior streamflow) empirically captures the effects of physical water storage within the catchment by soils, wetlands, channel storage, and so forth, and can be tied back to the physical concept of a hydrograph recession constant (James and Thompson, 1970;Tallaksen, 1995) and indeed to a governing differential equation (Fleming, 2007). By the same token, the exogenous predictor employed in the model (rainfall) obviously captures the physical driving forces behind streamflow generation.…”

Section: Approaches To Hydrological Modellingmentioning

confidence: 99%

Streamflow Modelling: A Primer on Applications, Approaches and Challenges

2012

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This article examines the current practice of streamflow modelling, a field under development for over a century. A sample of the wide range of assessment and planning applications of streamflow models is presented. The diversity in the use of these models is mirrored in the diversity of model complexity, and modelling approaches ranging from empirical to physically based and from lumped to fully distributed are described with examples. Predictions derived from hydrological models are subject to many sources of error; these are discussed along with methods for error minimization or anticipation. Model error is generally quantified using an ensemble of forecasts meant to sample the range of predictive uncertainty. This ensemble can be used to generate reliable probabilistic forecasts of hydrological quantities if all sources of error are accounted for. To date, applications of ensemble methods in streamflow forecasting have typically focused on only one or two error sources. A challenge will be to develop ensemble streamflow forecasts that sample a wider range of predictive uncertainty.

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Section: Approaches To Hydrological Modellingmentioning

confidence: 99%

Streamflow Modelling: A Primer on Applications, Approaches and Challenges

2012

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“…Although in general it is desirable to use weighted least-squares when the error are correlated (James and Thompson, 1970), the weighted procedure may produce estimates that are more variable than the unweighted estimates because the weights are functions of the parameter to be estimated (James and Thompson, 1970;Tallaksen, 1995). A much simpler least-squares approach is to ignore the correlations in the recorded flows and simply use, as the estimates of 1 and 2 , the solution to the 'normal equations' (James and Thompson, 1970). Combining the relationship between 1 , 2 , K b and K i implied by Equations (9) and (10) yields…”

Section: Non-linear Reservoirmentioning

confidence: 99%

Models for recession flows in the upper Blue Nile River

Mishra¹,

Hata²,

Abdel-Hadi³

2004

Hydrological Processes

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Abstract:Stream-flow recessions are commonly characterized by the exponential equation or in the alternative power form equation of a single linear reservoir. The most common measure of recession is the recession constant K, which relates to the power function form of the recession equation for a linear reservoir. However, in reality it can be seen that the groundwater dynamics of even the simplest of aquifers may behave in a non-linear fashion. In this study three different storage-outflow algorithms; single linear, non-linear and multiple linear reservoir were considered to model the stream-flow recession of the upper Blue Nile. The recession parameters for the linear and non-linear models were derived by the use of least-squares regression procedures. Whereas, for the multiple linear reservoir model, a second-order autoregressive AR (2) model was applied first in order to determine the parameters by the least-squares method. The modelling of the upper Blue Nile recession flow performed shortly after the wet season, when interflow and bank storage may be contributing considerably to the river flow, showed that the non-linear reservoir model simulates well with the observed counterparts. The variation related to preceding flow on a recession parameter of the non-linear reservoir remains significant, which was obtained by stratification of the recession curves. Although a similar stratification did not show any systematic variation on the recession parameters for the linear and multiple linear reservoir models.

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“…This model was used by James and Thompson (1970) and Vogel and Kroll (1991) for modelling baseflow recessions and found successful, hence it was chosen to use here as a comparison model to gauge accuracy of the ANN model developed in this study. The recession curve or baseflow is considered in this study to be the flow period between Q1Oct to Q3May in Fig.…”

Section: Autoregressive Model Of the Recession Curvementioning

confidence: 99%

Comparison of artificial neural networks and autoregressive model for inflows forecasting of Roseires Reservoir for better prediction of irrigation water supply in Sudan

Abdellatif

Osman

Elkhidir

2015

International Journal of River Basin Management

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The Blue Nile River is utilised in the Sudan as main source of irrigation water. However, the river has a long dry low flow season (October to May), which necessitates use of regulations and rules to manage its water use during this period. This depends on use of accurate lead time forecasts of inflows to the reservoirs built along the river. Thus a reliable and tested forecasting tool is needed to provide inflow forecast, with sufficient lead

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Least Squares Estimation of Constants in a Linear Recession Model

Cited by 31 publications

References 5 publications

Streamflow Modelling: A Primer on Applications, Approaches and Challenges

Streamflow Modelling: A Primer on Applications, Approaches and Challenges

Models for recession flows in the upper Blue Nile River

Comparison of artificial neural networks and autoregressive model for inflows forecasting of Roseires Reservoir for better prediction of irrigation water supply in Sudan

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