Volcano Hazard Management Using Digital Elevation Model
Estimation of Velocity and Quantity of Mudflow
In hydraulic flow routing the equation of motion for an open channel mudflow are
¶Q/¶t + (¶QV/¶x)+ gA(¶y/¶ x) =gA (Sx- Sf) (1)
where, x - the longitudinal distance along the meandering channel, t - time, A - wet cross sectional area, y - flow depth, V - average velocity (over cross - sectional wetted area), Q - the Quantity of discharge (=VA), S
x- channel slope (S
x = tan
q = bed slope), S
f - Term which takes into account energy dissipation.
For the case with zero lateral inflow, the friction slope is
Sf = S -¶ y/¶x-V/g ¶V/¶x-1/g ¶V/¶t (2)
where, S
f - Slope friction, S - Bed slope,
¶y/
¶x - Surface slope of flow materials, V/g
¶V/
¶x - Convective acceleration, 1/g
¶V/
¶t -Temporal acceleration.
The kinematic wave method assumes that the inertia terms of Eq.(2) are negligible and that the friction equals the bed slope S. Momentum conservation is approximated by assuming steady uniform flow, and routing is accomplished by combining the continuity equation. Typically either the manning or Chezy equation is used to find the velocity. The Chezy (3) and Manning (4) equations are:
V= CÖRS (3)
V=(1.486/n) R2/3 S1/2 (4)
where C and n are friction coefficients, S is the friction slope, and R is the hydraulic radius (area divided by wetted perimeter). Both give velocity in meters per second if area and wetted perimeters are input using square meter and meter units. The applicability of the manning formula to hyper concentrated flows has been used successfully by Laenen and Hansen (1988), Takahashi (1985), Public Work Research Institute(1988) and Vignaux and Weir (1990).
The channel geometry (flow depth and width, cross sectional area, wetted perimeter, hydraulic radius and slope) was calculated using the DEM. In nature, the flow paths do not have a perfect shape of triangular or trapezoidal. Therefore, in this study each cross-section was examined carefully and assumed to fit either to triangular, trapezoidal, circular or rectangular shape. The most appropriate formulae were selected in accordance to the channel shape for calculating the area (A), wetted perimeter (P), hydraulic radius (R) and top width (B).
The Manning coefficient of n can be predicted using Strickler equation. The Strickler equation to predict n is
n = 0.41 D 1/6 (5)
where, D - is the median grain size (m).
The mudflow grain size assumed is 2 mm (USGS1998). The calculated n is 0.15 (This co-efficient is well agree with the viscous co-efficient of lahar found by Macedonio et al (1992) for muddy flow and by Costa (1997) for hydraulic modeling for lahar hazard study at Cascades volcanoes. The velocity and quantity of discharge are calculated for various flow depths using manning formula in the Microsoft excel.
Table 1 shows the velocity of mudflow for 60,000 m3 and 90,000 m3 of lake water discharge. The calculated velocity for 90,000 m3 of discharge is shown in italic.
Results and Discussion
Mudflow path
Analysis of flow path and visualization of the terrain will lead to the understanding of the mudflow origin and flow direction of the mud. This is shown in Figure 2 where two major mudflow paths were derived from DEM. Mudflow is most likely to flow on the west and Northwest of Kawah Ijen volcanic flank. Flow path A (Banyoeputih river) originates from Ijen Crater's outlet and flows towards the west of the volcano flank. It passes West of Mt. Blade and crosses in between Blawan- Kidoel and Kaligedang areas. Pelanggan and Blawan settlements that are located in Blawan Kidoel area are in proximity to the major mudflow route. Thus, any mudflow hazard from Kawah Ijen would affect the people and properties of these settlements. Whilst, flow path B starts from the Northeast of Ijen volcano's flank and in proximity to Blaoe settlement that is located approximately 0.25 km from this flow path. This shows that the mudflow hazard originated from Kawah Ijen would seriously affect this settlement area. The flow path crosses the Kaligedang area and flows into Sengon River. In accordance to the satellite image of this area, there are valuable natural forest and horticulture plantations like tea and coffee in Blawan Kidoel and Kaligedang areas. Obviously, these resources would be destroyed by vigorously moving mudflow. These two major mudflow paths identified from DEM are also exactly coinciding with the mudflow hazard map prepared by volcano survey team of Indonesia in 1990 (Sumberdaya, 1990).
