Simultaneous Estimation of Inflow and Channel Roughness
Using 2D Hydraulic Models and Particle Filters

Poster Session: P5

Simultaneous Estimation of Inflow and Channel Roughness
Using 2D Hydraulic Models and Particle Filters
Yeonsu Kim, Yasuto Tachikawa, Michiharu Shiiba, Sunmin Kim, and Kazuaki Yorozu
Hydrology and Water Resources Research Laboratory,
Department of Civil and Earth Resources Engineering, Kyoto University
C1, Nishikyo-ku, Kyoto 615-8540, Japan
E-mail: yeonsu@hywr.kuciv.kyoto-u.ac.jp

The Sequential Importance Resampling (SIR) method
is introduced to a 2D hydraulic model to estimate inflow and Manning roughness coefficient (Manning’sn) simultaneously. The equifinality problem between
the Manning’s n and the inflow is considered using theproposed method. To solve the problem, we introduce
the variance reduction factor and the correction factor in the perturbation step of the proposed method.
The perturbed inflow and Manning’s n are updated
according to the observed water stage with state variables. The result of the proposed method shows good
agreement with the observed discharge, which enable
us to estimate the Manning’s n and inflow discharge at
the same time considering the uncertainties of the existing rating curve. Finally, it showed that the methodology is not only to estimate the appropriate Manning’s n, but also to improve the existing rating curve.
Keywords: 2D hydraulic model, particle filter, discharge
estimation, manning roughness coefficient, rating curve

1. Introduction
Discharge data at the basin outlet are utilized in water resource management, hydrological model calibration,
flood prediction, and so on. These data are obtained bymeasuring the flow velocity or constructing a rating curve,or through the installation of a specific gauging stationsuch as a flume. Among them, a general method uses arating curve, which depicts the relationship between stage
and discharge at the section based on occasional measurements. Even if a rating curve is based on measurement
data, it assumes that the flow is steady state and the channel bed does not change as time passes; which means thedynamic river flow estimation with a rating curve has limitations. Therefore the accuracy of the discharge obtainedby transforming a time-series observed water stage to discharge using the rating curve is uncertain. Baldasassarreand Montari (2009) investigated the uncertainties of thedischarge using a 1D hydraulic model and classified theuncertainty into three categories: one is due to the interpolation and extrapolation of a rating curve; another isdue to the presence of unsteady flow conditions; and the

Journal of Disaster Research Vol.8 No.1, 2013

last one is generated by the seasonal change in the channelroughness.
Therefore, this study aims to present a simultaneous estimation method, which can consider an uncertain Manning’s n with spatial distributions and an uncertain inflow.
We use the 2D dynamic wave model, which can reflect
the effect of river geomorphology and is sensitive to variations in the water stage. The Monte Carlo sequential data
assimilation scheme (the so-called Particle Filters) which
is applicable for non-linear and non-Gaussian systems iscombined with the 2D dynamic wave model. The proposed method is verified through real observed discharge,
and the applicability of the proposed method is confirmedwith another flood event.

2. Methodology
The proposed method builds on the assumption that arating curve and the Manning’s n include uncertainties
and sequential updating of the observed water stage reduces these uncertainties. To understand that framework
in regard to the proposed method, we need to consider thesequential procedure shown in Fig. 1 and structure of it.
With regard to the structure, it consists of a two dimensional dynamic wave model (2D model) and a particle filter (PF). The 2D dynamic wave model calculates variables
inside the calculation domain. The particle filter incorporates noise to the boundary conditions of each 2D model at
the perturbation step before implementing the 2D modeland compares the results against the observed water stage
at the weight calculation step. Concerning the sequential
procedure, the estimation process repeats every one hourbecause we utilize the hourly observed data. At first, theboundary conditions of inflow and the roughness coefficient including uncertainties are incorporated with someerrors at the perturbation step, so the 2D model run withthe various boundary conditions, so called particles. The
2D model is a deterministic model unless many similarsystems run.
simultaneously and independently and the result ofeach particle is evaluated by the updated water stage every updating step. The weight of each particle is calculated against the observed water stage for every updating step, and the weight recursively updates the state vari-193

Kim, Y. et al.

Fig. 2. Comparison of the water stage at Hazukashi stationfrom each deterministic simulation using the event occurredin Sep., 2004.
Fig. 1. Procedure of the proposed estimation process.

ables consecutively. In terms of using a 2D model, channel roughness, inflow, and water stage have the closest
connections with each other for estimating one of them.
Manning’s n is determined by the engineer on the basisof the small number of investigation of the bed material,
vegetation, channel shape, and so on. In addition, the inflow obtained from a rating curve or a hydrological model
involves many uncertainties and the 2D model is highly
nonlinear., Thus, we select the Sequential Importance Resampling (SIR) method for this approach since the resampling step, which entails removing particles with low
weights and duplicating particles with heavier weights
with a brief process, makes the system reflect the variables
more accurately than the typical PFs, Sequential Importance Sampling (SIS).
To verify the proposed method, we apply the method tothe Katsura River located in Kyoto, Japan. Because natural flood event data are affected by many anonymous factors, we designed experiments based on the natural river
reach instead of using the experiment implemented in alaboratory. The experiment implemented with two events.

result and the RMSE against the observed water stage,using the Manning’s n and the modified rating curve obtained from the proposed method improves the estimatedwater stage using the existing rating curve.

4. Conclusion
The proposed method enables estimation of the inflow
and the Manning’s n simultaneously. Using the provided
results from the method, the relationship between the water stage and the discharge at the water stage station could
be constructed. The modified rating curve and Manning’sn of each separated zone obtained from the proposed
method is applied to another event to confirm the reproducibility.
Through the above verifications and application of themethod, we confirm that it is a feasible alternative to thetraditional method, in which the Manning’s n estimatedempirically and the discharge converted from an existing
curve are utilized.
References:

3. Simulation Results
Manning’s n and inflow are simultaneously estimatedby the proposed method. The five parameters, threeroughness values, inflow, and downstream water stage,
which are essential and sensitive factors for hydraulicmodeling, construct one particle. Each particle is disturbed with some errors through the perturbation step.
With various particles, the simulations are implemented.
For the verification, the flood event from 6:00 on October
20 to 14:00 on October 21, 2004 is utilized. The simulation is implemented with 300 particles as 300 particles
are enough to present the stabilized results. To confirm
the reproducibility of another event, the procedure above
applies to another event of September 2004. Fig. 2 shows
the results of the application. As we have seen from the194[1] G. Di Baldassarre, A. Montanari, “Uncertainty in river discharge
observations: a quantitative analysis,” Hydrol. Earth System Sci.,
Vol.13, pp. 913-921, 2009.
[2] T. Nagata, “Hydraulics formulae: Hydraulics worked examples
with CD-ROM,” Hydraulic committee, JSCE, pp. 16-19, 2002.

Journal of Disaster Research Vol.8 No.1, 2013