International Journal of Geophysics

Volume 2015, Article ID 520893, 8 pages

http://dx.doi.org/10.1155/2015/520893

## Simple Model for Simulating Characteristics of River Flow Velocity in Large Scale

^{1}Research Cluster for Dynamics and Modeling of Complex Systems, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia^{2}Theoretical Physics Division, Department of Physics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia^{3}Hydrometeorology Division, Department of Geophysics and Meteorology, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia

Received 28 July 2014; Accepted 30 December 2014

Academic Editor: Alexey Stovas

Copyright © 2015 Husin Alatas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We propose a simple computer based phenomenological model to simulate the characteristics of river flow velocity in large scale. We use shuttle radar tomography mission based digital elevation model in grid form to define the terrain of catchment area. The model relies on mass-momentum conservation law and modified equation of motion of falling body in inclined plane. We assume inelastic collision occurs at every junction of two river branches to describe the dynamics of merged flow velocity.

#### 1. Introduction

The complexity of river network has been studied intensively over the past decades in order to describe its pattern formation and dynamics [1]. The evolution of river network pattern has been investigated based on various approaches such as continuum [2–4], stochastic [5], and cellular [6] approaches. On the other hand, one of the most important dynamical characteristics of a river is its flow velocity which corresponds to the water discharge along the river lines. Many different empirical models have been proposed to describe the associated dynamics in various scales and for various purposes as well [7–12]. Recently, Gauckler-Manning-Strickler (GMS) formula based empirical model has been implemented to describe the global river flow in certain area of Europe [9].

In the meantime, one of the theoretical descriptions of dynamics of open/close river channel is given by the so-called Saint Venant equations (SVEs) in one or two dimensions. These spatiotemporal equations are developed on the basis of mass-momentum conservation law in the form of coupled continuity and momentum differential equations of average water discharge and cross-sectional river flow channel functions where both need initial and boundary conditions [7, 13–19]. Recently, one-dimensional SVE has been adopted in a coupled hydrodynamic analysis model to investigate the large scale water discharge dynamics at basin of Yangtze River, China, in the presence of complex river-lake interaction [7].

In general, the river flow dynamics is affected by friction, roughness, slope, and number of rocks. Usually, in SVEs all these parameters are incorporated in the GMS formula which is found empirically to approximate the average flow velocity in short distance [17]. However, solving SVEs to simulate the river flow dynamics in a large scale such as the whole area of catchment area is not an easy task. It can be done by solving either the two-dimensional SVE or the one-dimensional SVE incorporated by junction model with internal boundary conditions [7, 19, 20]. It is likely that, for large scale cases, the calculation to solve the related SVEs based on rigorous semianalytical or numerical methods can be very difficult and probably time consuming. One of the difficult challenges to solve these equations numerically for the corresponding cases is how to determine the corresponding initial conditions [7].

In this report, we propose a simple approach to develop a computer based discrete phenomenological model of river flow velocity. We still rely on mass-momentum conservation law by assuming that an inelastic collision occurs at a river junction. Instead of using GMS formula, to accommodate friction, roughness, and number of rocks in single parameter, here we introduce the notion of effective gravitational acceleration, whereas the flow velocity follows the equation of motion of falling body in inclined plane.

The procedure that we followed to develop the model includes the following: (i) determination of river catchment area in the form of a computational window grid, (ii) development of algorithm for flow velocity model, and (iii) examining the model characteristics with respect to the variations of initial water discharges at headwaters.

To our best knowledge, the proposed model has never been reported elsewhere. We compare our model with field observation data in order to justify the results. It should be emphasized from the beginning that this simple model is an attempt to determine characteristics of river flow velocity and it is not intended to replace SVEs. In principle, however, this model can also provide initial condition of the whole river network which is needed to solve numerically the corresponding time-dependent SVEs.

We considered the catchment area of Ciliwung River (CR) situated in West Java Province, Indonesia, for simulating the model. To define the corresponding terrain we used digital elevation model (DEM) in grid form which is constructed based on free shuttle radar topography mission (SRTM) data provided by USGS [20]. Each grid in DEM represents the average height within the corresponding terrain. We only take into account the surface runoff and exclude the subsurface runoff as well as landscape characteristics of surrounding river lines such as forest canopy, vegetation, land use, and sediment transport.

We organize this report as follows: in Section 2 we discuss the associated DEM of CR catchment area and then this is followed by the explanation of flow velocity model in Section 3. The results of our simulation and its discussion are given in Section 4. We conclude our report by a summary in Section 5. Sections 2–4 discuss consecutively the abovementioned procedure that we followed.

#### 2. DEM of Ciliwung River Catchment Area

The CR is one of the most important rivers in Java Island, Indonesia. It spans over 120 km from Mount Pangrango in West Java to Java Sea, north to the capital city Jakarta. Its catchment area is 149 km^{2}. In recent years, during the rainy season, this river contributes around 30% of flood in Jakarta.

To plot the CR catchment area we used DEM with m^{2} grid resolution and in order to get a more detailed terrain which still can be handled by modest computational facility, the associated DEM was corrected by m^{2} resolution DEM as well as data from field survey. Using GIS software this modified DEM was converted into numbers that can be read by Excel software. Shown in Figure 1(a) is the plot of m^{2} DEM of the corresponding CR river network pattern. It is obvious that water will flow to the lower land due to gravitational force, such that we can use this fact as a rule in our computer code to determine the corresponding river pattern based on the given DEM data after identifying the positions of all headwaters. Therefore, it is clear that the boundaries of all river branches which define a two-dimensional computational window are automatically provided by DEM, where each grid represents the corresponding computational mesh. In Figure 1(b) we give an example of specific small area of the corresponding computational window grid (see figure caption) which is highlighted with grey color grid. The number inside each grid represents DEM value in meter unit at specific position.