Figure 4.9. Reconstruction of river channels at about 9-10 kyr, 7 kyr, 3.5-4.5 kyr, 2.5-3 kyr, and 0.6-1 kyr ago along the western Hsiukuluan canyon. In each reconstruction the active fluvial channel at that time has the same color as the corresponding river terraces in Figure 4.7. At any given time, the paleochannels must lie within the confines of the valley sides, defined by the valley walls rising above the corresponding terraces (bold solid lines). Terraces that might have formed along tributary channels do not appear in the reconstructions.
to be the result of the lack of constraints on both the Monkey Hill and Chimei loops.
listed in Table 4.2.
The cumulative uplift U(x, t) at point x since the formation of the terraces at time t, with respect to the Longitudinal Valley, can be written as [Lavé and Avouac, 2000]:
U(x, t) = I(x, t) + D(x, t) + P(x, t), (4.1) where I(x, t) is the incision deduced from the terrace, D(x, t) is the change in local base level, and P(x, t) is the change in elevation at point x due to possible geomorphic contributions of the river, such as changes in river gradient and sinuosity. It has been shown that the geomorphic contribution is dominated by changes in river sinuosity, since the gradient of rivers tends to stay relatively constant (see discussion in Lavé and Avouac [2000]).
Therefore, the rock uplift rate would be approximately equal to the bedrock incision rate if the following three assumptions are true: 1) There is no change in climate, or the changes did not create significant river pattern change such as aggradation or incision.
2) There is no significant change in river base level, or the change did not create major changes in accommodation space. 3) The sinuosity of the river stayed relatively constant so that there is no local aggradation or incision.
Periods of climatic fluctuation have been documented for the Holocene in many places of Taiwan [e.g., Kuo and Liew, 2000]. In fact, many small but locally extensive aggradational terraces are present among several small drainages along the eastern slope of the Coastal Range [Hsieh et al., 1994]. These terraces are considered to be the results of three particularly wet periods in eastern Taiwan, about 6 kyr, 4kyr, and 1 kyr ago [M.-L.
Hsieh, unpublished data]. However, such a record is not present in Hsiukuluan canyon.
Not only are there no major aggradational terraces, but also there is no extensive terrace development in any of these periods. We believe that the large drainage area and the long segment of the river upstream from the canyon, in the Longitudinal Valley, damped out any effects of climate change.
The late Quaternary sea level history around Taiwan has been studied intensively
[Chen, 1993; Chen and Liu, 1996, 2000]. According to the ages of emerged corals on the island of Penghu, a stable island in the Taiwan Strait, sea level rose to its highest Holocene level at about 4.7 kyr ago, about 2.4 m above the modern sea level [Chen and Liu, 1996]. The sea level has subsequently dropped slowly to its current position.
Therefore there is no significant base level change for Hsiukuluan canyon in the past 4.7 kyr. Although there were base level changes before 4.7 kyr ago, if the slope of the river valley was similar to the slope of the ocean floor right after the river enters the sea, the changes might not have created much difference in accommodation space [e.g., Miall, 1991; Schumm, 1993]. The similarity of the incision rates before and after 4 kyr ago in Hsiukuluan canyon suggests that this may be the case.
Since our paleo-Hsiukuluan reconstructions show that there have been no significant sinuosity changes of the river course, and since there appear to have been no changes in base level, we are confident that the bedrock incision rates we have obtained for Hsiukuluan canyon are similar to the local rock uplift rates. Because the rock uplift of the Coastal Range should be the result of the upthrusting of the Longitudinal Valley fault, we will, therefore, use these rates to figure out the characteristics of the fault and its Holocene slip rate.
Figure 4.10 shows the terrace surfaces and straths of all river terraces of the western part of Hsiukuluan canyon along with the ages we obtained that were projected to the plane perpendicular to the general trend of the Longitudinal Valley fault. Upon first inspection, it appears that among the terraces that have similar ages, those further upstream are higher above the current riverbed than those farther to the east and closer to the coast. This indicates that the incision rate is higher closer to the Longitudinal Valley fault and decreases to the east. However, because the terraces are not continuous, these ages only provide us local incision rates. Thus, we decided to use two different methods to obtain a continuous incision rate profile along the entire river valley.
Figure 4.10. All of the river terraces, together with the sampling sites and the current Hsiukuluan riverbed, projected along a N80°W direction. Each color represents a single terrace. Solid dots represent terrace surface measurements from the DEM, and short bars represent terraces straths measured by laser range finder. All ages are calibrated ages (2σ) in cal BP.
4.5.1 Shear stress profile along Hsiukuluan canyon
The first method we employed uses the geometry of the Hsiukuluan River to calculate the river bed shear stress, which is related to the incision rate. Although many hydrologic parameters are highly simplified in this method, it generally yields a reasonably accurate result for regular rivers. A detailed discussion of the following calculations can be found in Lavé and Avouac [2001].
The incision rate (i) along a river is related to the shear stress (τ) at the base of the river channel:
i = K (τ − τb), (4.2) where τb is the critical shear stress above which bedrock incision starts to occur and K is an erodability constant, related to factors such as bedrock lithology. Most of the
bedrock incision occurs during major floods, such as those that occur in the typhoon season of Taiwan. For the Hsiukuluan River, we can assume that the width of the river is much larger than the depth of the river even during that period of time. Therefore, the shear stress can be simplified as
τ = ρghS, (4.3)
where ρ is the density of water, h is the depth of the river during floods, and S is the gradient of the river.
On the other hand, the river flux (Q) of a river can be calculated as
Q = vhW, (4.4) where v is the velocity of the flow and W is the width of the channel. Most of the Hsiukuluan drainage basin lies in eastern Central Range, and no large tributary joins this segment of the river. As a result, the river flux Q is approximately a constant along the entire segment.
Furthermore, the flow velocity is related to the geometry and slope of the channel, as shown in many hydrologic equations. Again, since we assume that the width of the river is much larger than the depth of the river, this equation can be simplified as
v = 1/N × h2/3 × S1/2, (4.5) where N is the roughness coefficient [e.g., Chang, 1988], related to the grain size of the bed load. Combining equations (4.4) and (4.5), we get
h = (N × Q/W × S-1/2)3/5. (4.6) Putting equation (4.6) back into equation (4.3), we can get the shear stress as
τ = ρg(NQ)0.6 × S0.7 × W-0.6 = α × S0.7 × W-0.6, (4.7) where α is a new constant. We can further put equation (4.7) back into equation (4.2) and find that the incision rate along the river is now simplified as
i = K (α × S0.7 × W-0.6 − τb). (4.8) If we assume that τb is very small comparing to the shear stress during floods, then
i = Kα × S0.7 × W-0.6 = K′ τ*, (4.9)
where K′ is yet another constant and τ* is a simple variable that is only related to the width and slope of the river channel.
Equation (4.9) indicates that, if all of our simplifications are true, the incision rate along the river is a function of only the width and the slope of the river. Therefore, using profiles of river slope and width, we can calculate a profile of τ* and then use the incision rate we have obtained from the terrace ages to calculate the constant K′, thus getting the incision rate profile for the entire river.
Figure 4.11 shows the results of our calculation. For the long profile of the Hsiukuluan River we have used real-time kinematic (RTK) GPS to measure the slope of the river wherever possible and utilized the 40-m digital elevation model (DEM) of Taiwan for locations that we were unable to reach (Figure 4.11a). It appears that there is only one major slope change along Hsiukuluan canyon. This is where the river flows out of the Paliwan Formation and into the Tuluanshan Formation, where the slope of the river changes from about 3.4 m/km to about 1.9 m/km.
The width of the river channel is more difficult to obtain correctly than the river slope. We used laser range finder as well as the DEM to get the river width profile (Figure 4.11b). It appears that along Hsiukuluan canyon, the river channel is most narrow in its middle part, near the Chimei fault, and becomes wider both upstream and downstream. However, since the river is meandering, laterally aggrading point bars are very well developed, making it very difficult to determine the correct channel width.
This implies that some of the simplifications embedded in the hydrologic equations above, such as rectangular channel cross section [e.g., Lavé and Avouac, 2001], may not be true.
A profile of our calculated τ* is shown as Figure 4.11c. Theoretically, the pattern of the τ* profile should be similar to the pattern of the incision rates we obtained from the terrace ages. However, this is not the case. The τ* profile clearly shows that the
Figure 4.11. Shear stress calculations along Hsiukuluan canyon. (a) Long profile of the Hsiukuluan River. Only one major slope change appears along the canyon, where the river crosses the Chimei fault, the contact between Paliwan Formation and Tuluanshan volcanic rocks. (b) Width of current river channel along Hsiukuluan canyon. The current river channel is narrowest near the Chimei fault. (c) A profile of the calculated τ* along Hsiukuluan canyon (in dark blue). The τ* peaks in the central reach of the valley. This trend is different from the trend of the incision rates obtained from the ages of the river terraces (in red).
incision rate along the river should increase from the Longitudinal Valley fault to somewhere near the Chimei fault. This is opposite of what we have obtained from the uplift of river terraces, which shows that the incision rate is highest near the Longitudinal Valley fault and decreases to the east.
Such discrepancy may have resulted in several ways. For example, the incision of the river may have been controlled by lithologic differences along the river and thus differs from the shear stress patterns. It is more likely that because the Hsiukuluan River across the Coastal Range is highly sinuous, lateral erosion may have consumed much of the energy at the base of the channel, especially at active cut-banks. Therefore the shear stress profile we have calculated will have a different pattern from the pattern of the incision rate, which only considers vertical erosion by the river. Moreover, for a highly meandering river the channel shape is likely to be far from uniform, and many of the hydrologic calculations cannot be simplified as we did above.
4.5.2 Fault-bend fold model
Another way to get a continuous profile of uplift rates is to assume that deformation on the hanging-wall block of the Longitudinal Valley fault is consistent with a fault-bend fold model. Upon casual inspection, it appears that variations in the pattern of the bedding dip angle mimic the pattern of uplift rate along Hsiukuluan canyon (Figure 4.4).
This is consistent with fault-bend folding [e.g., Lavé and Avouac, 2000]. Fault-bend fold models assume that deformation is accommodated by slip along the bedding planes, with no change of bed thickness. At a given point, the local uplift rate (U) relative to a fixed and rigid footwall is simply proportional to the sine of the apparent dip angle of the beds at the direction of fault slip (θ′) with this relationship:
U = d × sin θ′, (4.10) where d is the slip rate along the fault. If the fault eventually turns into a horizontal
décollement, d will simply be the horizontal shortening rate [Lavé and Avouac, 2000].
Along Hsiukuluan canyon, θ′ is close to the true dip (θ) of the beds because most of the bedding attitudes have bedding strike directions similar to the strike direction of the Longitudinal Valley fault (Figure 4.4). Thus, their true dip should be approximately the same as the apparent dip in the direction of fault slip. Nonetheless, several points that are very close to the Chimei fault show anomalous strike directions. Because we have found evidence for drag folding of the beds by the Chimei fault, we decided to discard these dip measurements from our calculations. For the other points we will apply their true dip as θ′.
Since the pattern of bedding dip angle variation is similar to the pattern of the uplift rate, we believe the fault-bend fold model is valid for the Longitudinal Valley fault beneath Hsiukuluan canyon. Continuing with our analysis, we can fit the variation of the sine of bedding dip angles very well with a polynomial function (Figure 4.12a).
Together with the curve of this polynomial function, we can also plot the uplift rates we obtained from the ages of the terraces along Hsiukuluan canyon using different values of d until the two data sets show a good match (Figure 4.12b). The optimal value of d is about 23 mm/yr.
We can also utilize the fault-bend fold model to reconstruct the subsurface geometry of the fault (Figure 4.13). In the model of the fault so constructed, the fault steepens downdip slightly about 1 km below the surface and then becomes gradually shallower farther downdip. At a depth of about 2.5 km the fault dips about 30°. If the dip angle continues to greater depth at this angle, the 23 mm/yr slip rate yields a horizontal shortening rate of about 19.9 mm/yr. If the fault becomes shallower at depth, however, the horizontal shortening rate will increase, to a limit of 23 mm/yr in the case of a flat dip.
Figure 4.12. Fault-bend fold model of the Longitudinal Valley fault along Hsiukuluan canyon. (a) A polynomial function fits the variation of the sine of the bedding dip angles of the Paliwan Formation along Hsiukuluan canyon very well. Bedding dip angle measurements very close to the Chimei fault are not included because they reflect local deformation associated with slip on the Chimei fault. (b) Using different values of slip rate on the Longitudinal Valley fault (d), we can match the polynomial function from (a) with the uplift rates obtained from the river terraces (shown as crosses). The blue line is calculated without footwall subsidence (d = 23 mm/yr). The red line reflects 3 mm/yr of footwall subsidence (d = 29 mm/yr). The circle is the uplift rate obtained from a Hsiukuluan terrace near the river mouth by Hsieh et al. [2003]. The square is the minimum subsidence rate of the Longitudinal Valley footwall obtained from site KKL [W.-S. Chen, unpublished data]. See text for discussion.
Figure 4.13. Reconstruction of the subsurface geometry of the Longitudinal Valley fault near Hsiukuluan canyon from bedrock dip angles. The azimuth of the section is approximately N80°W. This model indicates that the slip rate on the fault is about 23 mm/yr and that all of the deformation is accommodated by the slip along the fault plane, with no internal deformation of the beds.