Flow routing with unknown rating curves using a state-space reservoir-cascade-type formulation

Abstract

A discrete version of the Kalinin-Milyukov-Nash-cascade is formulated for operational forecasting of stream stages when no information of rating curves is available. Model performance is slightly reduced in comparison to flow routing results using accurate, single-valued stage-discharge relationships. However, when only inaccurate rating curves are available, the present approach may yield superior forecasts. Since in practice the accuracy of the employed rating curves, used to convert stage measurements into discharge values for flow routing, may be somewhat uncertain, application of the present technique is recommended for rating-curve falsification. The method allows for stage predictions using physically based flow routing in rivers where flow rates are unknown or the available rating curves are inaccurate. The technique can also be used without modification for streams with tributaries. q

The Use of Machine Learning for the Synthesis of Stream Discharge – Gage Height Rating Curves

“…Most recent work on rating curves has involved the development of rating curves based on channel geometry without any gage height vs. discharge measurements (Kean and Smith 2005;Szilagyi et al 2005;Perumal et al 2007Perumal et al , 2010, the use of parameters in addition to gage height to predict discharge (Sahoo and Ray 2006;Weijs et al 2013), the methodology and accuracy of developing rating curves based on gage height vs. discharge measurements (Morlot et al 2014;Singh et al 2014;Coxon et al 2015) and the use of remote discharge measurements to develop rating curves (Birkhead and James 1998). We are not aware of any other previous work besides that of the authors (Stuart and Emerman 2012;Rundall et al 2015) on the development of rating curves based on the statistics of the existing rating curve database.…”

Discrete state-space approximation of the continuous Kalinin–Milyukov–Nash cascade of noninteger storage elements

“…On the other hand, most flow routing techniques: (a) do not require information on the channel and floodplain geometry; (b) require only simplified (i.e. nonlooped) rating curves; (c) are linear in nature, which is fortunate for the propagation of errors in the stage and discharging values, and; (d) as long as the routing method is linear, it can even be used without discharge (but including stage) measurements as was demonstrated by Szilagyi et al (2005).…”

“…Camacho and Lees, 1999;Keefer and McQuivey, 1974;Kontur, 1977;Kundzewicz and Dooge, 1985;O'Connor, 1976;Perumal, 1994;Szolgay, 1991Szolgay, , 2004, the discrete linear cascade model (DLCM) (Szollosi-Nagy, 1982, 1989Szilagyi, 2003Szilagyi, , 2004Szilagyi et al, 2005) stands out for several reasons: (a) it is equivalent to the discretized form of the continuous, spatially discrete, kinematic wave equation (Szollosi-Nagy, 1989); (b) it is specifically formulated to deal with discrete data whether in a pulse-or sample-data system framework; (c) it is discretely coincident, which means that for identical inputs (as between the discrete and continuous models), it gives identical outputs at discrete time increments; (d) it does not require numerical iterations (so numerical stability is not an issue) because it is written in a state-space form with the state-and input-transition matrices given explicitly; (e) since it is in a state-space form, linear filtering techniques, such as the Kalman filter (1960), can directly be applied; and last but not the least, (f) with it, the inverse problem of finding the input sequence to a given output sequence (which often is needed to fill data gaps in a streamflow series) is a simple algebraic manipulation.…”