Real-Time RIV (RRIV) Estimation
Monday, 25 April 2011
The RIV and RIVC routines in CAPTAIN allow for recursive estimation but only ‘off-line’: i.e. they cannot be applied in ‘on-line’ situations in real-time. The main reason for this is that refined IV estimation involves iterative processing based on all of the data. However, a prototype real-time RIV (RRIV) routine is being developed where the iteration is implemented at each recursive step, which can involve one or more new samples of the input-output data. This prototype is being developed as a CAPTAIN routine rriv but an early version is demonstrated in Chapter 10 of Young (2011).
Fig. 1 This is Figure 10.1 of chapter 10 of Young (2011): RRIV estimation results for the simulated time variable parameter system
One application of RRIV analysis is for real-time adaptive forecasting of river flow and the RRIV algorithm has been applied to generate one-day-ahead forecasts of flow in the humid Leaf River basin (1944 square km.) located north of Collins, Mississippi, USA. In this case, a rather atypical [1 7 0] TF model is identified between the effective rainfall and flow (see Young, 2012) but the [1 7 1] TF also explains the data quite well and is used for adaptive forecasting because it allows for true, one-day-ahead forecasts. The left panel in Fig.2 shows these forecasts for a short section of the data, with the forecasting error in the upper panel. These forecasts are an immediate output of the RRIV algorithm but the RRIV estimates could be used by a separate Kalman Filter-based forecasting engine. The associated RRIV estimates of the denominator polynomial (bottom) and the most significant numerator parameter (top).
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Fig. 2 One-day-ahead forecasting results for the Leaf River: forecasts (left panel) and associated TVP estimates from RRIV (rightpanel).
P. C. Young (2011) Recursive Estimation and Time Series Analysis: an Introduction for the Student and Practitioner, Springer-Verlag.
P. C. Young (2012) Hypothetico-Inductive Data-Based Mechanistic Modeling of Hydrological Systems. Submitted for publication.