3 Chapter Spatial Patterns of Erosion in the Taiwan Orogen
3.1
Motivation
The spatial pattern of erosion rates across an active orogen controls the evolution of mountain structure and topography (Koons, 1989; Beaumont et al., 1992; Willett, 1999). Many of the important links between geomorphology, tectonics, and climate that were described in Chapter 1 can be examined more fully using quantitative observations of erosion rates across a range of time-scales from decades to millions of years. The rst aim of the current chapter is to use the suspended sediment discharges for rivers in Taiwan that were presented in Chapter 2 to investigate spatial patterns in erosion across the entire mountain belt. Next, the decadal erosion pattern is compared with Holocene river incision rates and million-year time-scale ssion-track exhumation rates. Finally, topographic, climatic, geomechanical, and seismic databases are used to examine which processes drive erosion of the Taiwan orogen.
3.2
Erosion Rates Estimated from River Loads
3.2.1 Calculating erosion rates
Suspended sediment discharge was estimated for 130 gauging stations across Taiwan, using the bias-reducing monthly average (EMON ) discussed in Chapter 2. The raw sediment discharge data (in Mt yr1 ; Table 2.2; Appendix A) were converted into catchment wide erosion rates
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(mm yr1 ) by dividing by the density of quartz (s = 2.65 103 kg m3 ) and by drainage area. This approach makes the assumption that erosion rates are spatially uniform within each drainage basin. This assumption is valid only for the study of erosion patterns at the scale of an entire mountain belt; it is not valid for the study of erosion at the scale of an individual catchment. In Taiwan, the median drainage area of the catchments under investigation is 240 km 2 , which means that a typical catchment length scale is 15 km. According to this calculation, the areally-averaged suspended sediment erosion rates presented in this study are not representative of erosion rates at length scales shorter than 15 km. Accordingly, all erosion maps presented in this chapter have been smoothed using a circular moving mean with a radius of 15 km. Chemical erosion rates are not considered here. They are probably at least an order of magnitude lower that physical erosion rates (Li, 1976), and are not well constrained.
3.2.2 Temporal and spatial coverage
Temporal uctuations in erosion rate may result from extreme events such as earthquakes and typhoons. To obtain a stable measure of erosion that is independent of the effects of individual earthquakes and typhoons, only observations from stations with records spanning at least eight years were used. This duration was chosen because spectral analysis of the water discharge record showed a four-year periodicity (Figure 3.1); and because eight years is the longest continuous period of time for which adequate spatial coverage is available. Hydrometric stations meeting these criteria cover an area of 24,000 km2 , which is 61% of the total area of Taiwan or 91% of the mountain region (dened as having elevation > 500 m). The analysis presented in this chapter extends until the end of August 1999, to exclude the effects of the September 1999 Mw 7.6 Chi-Chi earthquake. At the time of writing, the onward transport of material produced during the Chi-Chi earthquake is incomplete (see Chapter 4). The erosional response to ChiChi earthquake is dealt with specically in Chapter 4, in which it is shown that extension of the present analysis to the end of 2001 would lead to a 12% increase in estimated decadal-scale annual average suspended sediment discharge from Taiwan.
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Figure 3.1: Periodogram for water discharge in Peinan River (station 2200H011). Spectral power was calculated as the square of the absolute value of the Fourier transform of water discharge using a fast Fourier transform (FFT) with a Hanning smoothing window. Spectral components with period shorter than six months are not shown. In order to construct a map of the spatial pattern of erosion rates, areally-averaged river load data were assigned to drainage basin polygons. Drainage basin polygons were delineated using station locations given by the WRA (19702001) and a 40 m digital elevation model, using the D8 ow-routing algorithm implemented in ARC/INFO. For catchments with several nested gauges, erosion rates were recalculated for multiplygauged parts using data from each upstream station. An alternative approach would have been to calculate the amount of erosion or deposition within each gauged area as the difference in erosion rates between upstream and downstream areas. However, this procedure was found to work poorly because the average erosion rate uncertainty of 37% (calculated in Chapter 2; Table 2.2, Appendix A) places a limit on the precision of the calculation. If erosion rates of similar magnitude are subtracted, the uncertainty of the resulting estimate can become very high indeed. For example, if an erosion rate of 5 2 mm yr 1 is subtracted from an erosion rate of 7 3 mm yr1 , the result is 2 3.5 mm yr1 ; here the uncertainty has risen from 40%
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to 175%. Fortunately addition, which is used to calculate island-wide averages, is not subject to this problem. The catchments used in this study were shown in Figure 2.1 and Figures A.1A.4. Figure 3.2 gives the number of suspended sediment observations per year for each catchment used in this study. There appears to be no spatial bias to the sampling programme and there is no statistically signicant correlation between suspended sediment sampling frequency and erosion rate in each drainage basin (r 2 = 0.02). In the following sections, the spatial pattern of erosion rate is presented.
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Figure 3.2: Number of suspended sediment observations per year in each catchment. The average number of observations per year is 327. Hydrometric stations are shown as black lled circles; rivers are shown as blue lines. Stations within the grey shaded area have less than eight years of data. No data are available for white catchments.
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3.3
Patterns of Erosion
3.3.1 Decadal erosion pattern and sediment delivery to the ocean
The 30-year average suspended-sediment erosion rate of Taiwan is 4 mm yr 1 averaged across the whole of Taiwan, or 6 mm yr1 averaged across the mountain region (dened as having elevation > 500 m). Between 19701999, Taiwan supplied 384 Mt yr 1 of suspended sediment to the ocean. This amount represents 1.9% of the estimated global suspended sediment discharge (Milliman and Syvitski, 1992) and yet is derived from only 0.024% of the Earths subaerial surface. Accounting for the 30% bedload component calculated in Chapter 2 would increase the estimated erosion rate to 5.2 mm yr1 (7.8 mm yr1 in the mountain region) and would increase average annual sediment yield to 500 Mt yr1 , although much bedload is trapped in oodplains before reaching the sea. The spatial pattern of decadal-scale erosion shows that erosion rates were high in the eastern Central Range and south-west Taiwan, but low in the north and west (Figure 3.3). The metamorphic core of the mountain belt is eroding at 6 mm yr 1 . Northern and western Taiwan had lower erosion rates (14 mm yr1 ). The spatial pattern of erosion corresponds to the pattern of sediment delivery to the ocean at coastal stations, indicating that suspended sediment is delivered to the ocean in proportion to mountain erosion. The highest discharging rivers are Peinan, Choshui, and Kaoping. Figure 3.4 shows the spatial pattern of erosion rate uncertainty calculated in Chapter 2. The average erosion rate uncertainty is 37%. Uncertainties were calculated as the 95% condence interval (approximately two standard errors), having removed seasonal variation. The spatial pattern of erosion rate uncertainties shows no obvious trends. Areas of highest uncertainty are in the central and southern parts of the Central Range, in the Hsuehshan Range and the southern part of the thrust belt. The physical processes that drive the decadal erosion rate in Taiwan will be investigated systematically in Section 3.4, but several salient features of Figure 3.3 are worthy of discussion here. In the Western Foothills fold-and-thrust belt, erosion rates were locally found to be up
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to 60 mm yr1 . This area is one of extreme runoff variability. Located in relatively subdued topography, the area receives annual average precipitation of 1.52.0 mm yr 1 , which is below the island-wide average, yet 90% of this precipitation is delivered during typhoon storms. Moreover, the very rapid erosion rates measured in the fold-and-thrust belt occurred around recently-active thrust faults in the south-west. Here, rapid erosion coincides with the loci of slip on active thrust faults. This deformation results in very rapid erosion of weak mudstone lithologies as soon as they are displaced above base level. The combination of focused deformation, high runoff variability, and weak substrate leads to rapid erosion and prevents the construction of high topography and steep relief. The situation is similar to those observed by Burbank and Beck (1991) in the Salt Range, Pakistan and by Burbank et al. (1999) in the Tien Shan, Kyrgyzstan, which were described in Chapter 1.
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Figure 3.3: Erosion rates calculated from uvial suspended sediment observations with 5 km grid resolution, smoothed at catchment scale using a circular moving mean with 30 km diameter. Black arrows indicate mean annual coastal suspended sediment discharge from rivers draining areas greater than 400 km2 . Coastal sediment discharges are reported from hydrometric stations closest to coast. Black circles indicate hydrometric stations used to construct the map; triangles indicate locations of reservoirs used in reservoir ll analysis; no data are available within the grey shaded area.
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Figure 3.4: Uncertainty in the decadal erosion pattern measured as the 95% condence interval calculated as two standard errors around the mean, having removed seasonal variation. The grid is shown at 5 km resolution with a 30 km diameter smoothing mean applied.
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3.3.2 Holocene channel incision rates
To determine whether the decadal pattern of suspended sediment erosion rates has persisted over longer time-scales, longer term measures of erosion are required. River incision rates over Holocene time-scales can be calculated from the ages and heights of strath terraces formed as bedrock channels incise through their substrate. River incision rates provide reach-scale measures of erosion, in contrast to the areally-averaged measure given by suspended sediment yields. Reach-scale and areally-averaged erosion rates can be compared only if it is assumed that the hillslopes above channels are poised at their mechanical threshold for failure. Mean and modal slopes measured from digital elevation data correspond well with geotechnical measurements of the friction angle of bedrock material in Taiwan (see Section 3.4.4). This correspondence suggests that over millennial time-scales, hillslope erosion is likely to keep pace with river incision in Taiwan. Reach-scale river incision rates were obtained from 25 Holocene strath terraces at twelve locations (Table 3.1). Data were collected and processed by Hsieh Meng-Long of the National Taiwan University (Hsieh and Knuepfer, 2001); statistical analysis and interpretation forms part of the present thesis. Bedrock incision rates were obtained by dating organic material deposited on strath terraces formed as rivers incised through their bedrock substrate. Measurements were made from bedrock terraces overlain by less than ve metres of channel deposit. Radiometric ages were calculated from 14 C in wood or plant fragments in the alluvial veneer, and converted to calendar ages (Hsieh pers. comm., 2002; Stuiver and Reimer, 1993). Incision rates were calculated by dividing the elevation of the bedrock terrace above the modern river by the calendar age. Uncertainties were calculated as one standard deviation for age and as 20% for terrace elevation, the latter to account for variations in river stage. Holocene channel incision rates (shown in Figure 3.5) range from 1.5 mm yr 1 in northern Taiwan and 9 mm yr1 in eastern Taiwan, to over 15 mm yr1 around active structures in the Western Foothills thrust belt.
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Table 3.1: Holocene river terrace incision rates.
Locality 1 2 2 2 2 3 3 3 3 3 3 4 5 6 7 8 9 9 10 11 12 12 12 12 12 12 12 River Erjen Erjen Erjen Erjen Erjen Tsengwen Tsengwen Tsengwen Tsengwen Tsengwen Tsengwen Tsengwen Pachang Tsengwen Potzu Tahan Liwu Liwu Hsiukuluan Tsengwen Erjen Erjen Erjen Erjen Erjen Erjen Erjen Lab No NTU2614 NTU2341 NTU1968b NTU2427 NTU2631 NTU2334 NTU2430 NTU2325 NTU2591 Wk6131 NTU2599 NTU2232 NTU2193 NTU2231 NTU3772 NAc NA NA NTU3756 Wk6129 Wk4111 NTU2375 NTU1337 NTU1320a NTU1945b NTU2335 NTU2391 Longitude 120 2349 120 2128 120 2124 120 2124 120 2112 120 2406 120 2439 120 2350 120 2345 120 2340 120 2350 120 2329 120 3220 120 2325 120 2847 121 18 121 2809 121 2841 121 2909 120 2950 120 2249 120 2320 120 2258 120 2238 120 2238 120 2313 120 2258 Latitude 22 5008 22 5203 22 5159 22 5200 22 5254 23 0318 23 0328 23 0318 23 0319 23 0324 23 0406 23 0833 23 2309 23 0832 23 3403 24 55 24 1340 24 1108 23 2816 23 0500 22 5307 22 5331 22 5308 22 5233 22 5233 22 5314 22 5254 age yr BP1 549050 227050 216050 168040 222050 549050 232040 315050 321040 58758 756050 < 250 257070 28045 88030 1160090 248040 240040 383030 963060 5060140 202040 171040 224040 241040 134050 100045
14 C
Calendar age yr BP1 62156306 21562340 20622297 15301611 21412321 62156306 23252348 32773392 33723465 534645 83158371 NA 25092755 289423 736880 1340313668 23762715 23482461 41524274 1056810950 56485935 18971994 15431691 21502326 23502468 11941294 910943
Sample height m 33 15 17 23 12 16 18 30 27 8 59 5 18 5 6.5 22 NA NA 28 56 61 35 36 27 27 19 12
Bedrock height m 31 15 17 17 10 15 18 28 26 7 58 4 18 4 6 1520 30d 15d 27 53 60 34 35 26 26 19 12
Bedrock incision rate Uncertainty mm yr1 mm yr1 50 1.0 67 1.6 79 2.0 < 110 2.4 45 1.1 < 24 0.5 < 78 1.6 84 1.8 76 1.6 < 130 3.5 70 1.4 > 160 NA 69 1.7 121 4.5 76 2.2 13 0.3 120 3.2 63 1.4 < 65 1.4 < 50 1.1 104 2.3 176 3.9 219 5.3 117 2.8 109 2.4 154 3.7 130 2.8
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Note: Localities are numbered clockwise from south-west on Figure 3.5. NTU, National Taiwan University; Wk, University of Waikato; a, Chen (1993); b, Lee et al. (1994); c, Chen and Liu (1991); d, obtained from palaeo-valley ll.
Figure 3.5: Holocene river incision rates in mm yr1 obtained from dated bedrock straths. Values for each locality represent mean incision rate for all terraces measured at that locality. Uncertainties are one standard deviation in radiometric age and 20% in strath elevation.
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3.3.3 Fission-track exhumation rates
Persistence of erosion rates over million-year time-scales was assessed using new and published apatite ssion-track data with a geothermal model to calculate exhumation rates (Figure 3.6). Long-term exhumation rates were calculated by Sean Willett of the University of Washington, USA, from samples collected by himself, Donald Fisher, Chris Fuller, Yeh En-Chao, and Lu Chia-Yu (Willett pers. comm., 2002; Willett et al., 2003). Fission-induced damage tracks in apatite are annealed at million-year time-scales at temperatures over 110 C, so that ssion-track ages normally reect cooling associated with exhumation from depths of 35 km. Published ages from the Central Range (Willett et al., 2003) and unpublished ages (Willett pers. comm., 2002) from the Western Foothills thrust belt, interpreted through a thermal model with onedimensional heat transfer, an initial geothermal gradient of 25 C km1 , a surface temperature of 10 C, and a constant erosion rate, yield the exhumation rates in Figure 3.6 (Willett, pers. comm., 2002). Lacking an independent measure of the duration of exhumation, the rst occurrence of reset ages at the surface was used. This assumption provides a maximum estimate of exhumation rate: if geothermal gradients are higher due to a greater duration of exhumation or conductive focusing of heat into valleys where samples were primarily obtained, the inferred exhumation rates would be lower. Samples whose ssion-track age was reset in the present orogeny ( 5 Myr) were found in the eastern section of the thrust belt and the metamorphic core of the mountain belt. They indicate exhumation rates of 36 mm yr1 in the eastern Central Range and 1.52.5 mm yr1 in the eastern thrust belt and south-central Taiwan. In contrast, unreset apatite ages from the Western Foothills fold-and-thrust belt and southern Taiwan probably reect earlier resetting (>5 Myr) that is not associated with exhumation during the Plio-Pleistocene collision. No rate information can be obtained from unreset samples.
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Figure 3.6: Exhumation rates (mm yr1 ) calculated from apatite ssion-track ages: red, reset; orange, partially reset; blue, unreset. Dashed lines are exhumation rate contours.
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3.3.4 Discussion
In this chapter, erosion rates across a range of time-scales have been presented: modern river sediment loads; Holocene river incision rates; and million-year time-scale thermochronometry. These data permit examination of the spatial patterns of mountain belt erosion across multiple time-scales. Erosion rates in the eastern Central Range were 36 mm yr1 across all time-scales considered here, although some catchments had higher decadal erosion rates. Persistent, rapid erosion has exhumed greenschist-grade metamorphic rocks in eastern Taiwan and created a steep, high mountain belt. Ernst (1983) has estimated that the physical conditions for the formation of the observed greenschist-grade mineral assemblages (quartz + chlorite + carbonate + albite + biotite + epidote + sphene actinolite tremolite) in the eastern part of the Tananao Schist complex are: T 425 75 C, P 4 kbar. This pressure condition indicates that rocks currently
at the surface were formed at a depth of approximately 15 km (assuming that the conning pressure was equal to the lithostatic pressure with a crustal density of 2.8 10 3 kg m3 ). Together with the temperature condition, this depth gives an initial geothermal gradient in the area of approximately 295 C km1 . The depth also indicates that long term exhumation rates have been approximately 3 mm yr1 in this area (assuming that exhumation began 5 Myr ago (Teng, 1990)). This exhumation rate is consistent with the erosion and exhumation rates presented above. By comparison with the long-term exhumation rates, rapid Holocene river incision rates of 512 mm yr1 , and decadal erosion rates averaging 15 mm yr1 in the Western Foothills fold-and-thrust belt are probably a recent feature associated with westward propagation of the thrust belt. Unreset apatite ssion-track ages in the Western Foothills thrust belt support the view that deformation there is recent. One interpretation of the occurrence of unreset apatite ssion-track ages is that exhumation of the Western Foothills did not occur before 300500 kyr (the time required to exhume reset apatite from 35 km depth at a rate of 10 mm yr 1 ). This interpretation implies westward propagation of the thrust belt in the middle-late Pleistocene. An alternative interpretation is that exhumation did occur earlier than 300500 kyr, but at a slower
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rate or with shallow, horizontal rock advection. A denitive conclusion is not possible from ssion-track data alone, because thermochronometers are relatively insensitive to the shallow, largely horizontal rock advection in the thrust belt. Rapid rates of Holocene uvial incision in the Western Foothills correlate with active, blind thrusts and fault-ramp systems in poorly-consolidated Pliocene-Quaternary sediments (Hsieh and Knuepfer, 2002; Hickman et al., 2002), which suggests that high catchment-wide erosion rates have suppressed the topographic expression of these faults. Patterns of Holocene incision rate and decadal suspended-sediment erosion rate are broadly consistent, but decadal rates systematically exceed Holocene incision rates in southwest Taiwan, with maximum values of 60 mm yr1 . Moreover, decadal erosion rates are lower than expected in the north of the Western Foothills fold-and-thrust belt. Explanations include changing climate and land-use, or brevity of the hydrometric record. Palynology indicates substantial climate variation across Taiwan during the Holocene (Liew et al., 1998), but this is unlikely to account for the north-south contrast. Growth of agriculture and urbanization may have affected erosion, although the latter is limited to the coastal plains. The sediment-discharge data show no secular trend, despite a ten-fold increase in economic development between 1970 1999. It is proposed, instead, that the decadal erosion pattern reects the location of recent climatic and seismic perturbations, superimposed on other, persistent controls on erosion. In the next section, these controls are evaluated.
3.4
Controls on Erosion Pattern
Factors commonly thought to control the spatial pattern of erosion rates include precipitation, runoff and runoff variability, relief, bedrock uplift, lithology and seismicity. The aim of this section is to identify the dominant controls on short-term erosion rates in Taiwan using the decadal pattern of suspended sediment erosion together with topographic, climatic, geomechanical, geodetic, and seismic databases. In the following sections, the spatial patterns of precipitation, runoff, slope, stream power, lithology, runoff variability, crustal dilatation rate,
82
and seismic moment are presented, discussed, and compared to the spatial pattern of erosion rate. All spatial datasets (except topographic slope) have been smoothed with a 30 km diameter moving mean, to maintain consistency with the decadal erosion rate data. A multiple regression analysis is then used to determine the best statistical model of erosion, based on these controls.
3.4.1 Precipitation and runoff
Precipitation rates are known from meteorological observations made between 19491990 by the Central Weather Bureau of Taiwan, which are reported by the Water Resources Agency (WRA, 19702001). The annual average precipitation rate is shown in Figure 3.7. Precipitation rates range between 1.56.0 m yr1 , with mean precipitation of 2.5 m yr1 . Precipitation is highest along the backbone of the Central Range, with particularly high rates in several distinct pockets in the northern and southern extremes of Taiwan. Precipitation rates are low on the coastal plain, which generates no orographic precipitation. An average of four typhoons pass over Taiwan each year (Shieh et al., 2001). In eastern and central parts of Taiwan, 80% of total annual precipitation falls during the typhoon season between May and October. This gure is lower in northern Taiwan (60%) and higher in southern Taiwan (90%). There is little correspondence between the annual average rate of precipitation and the decadal pattern of erosion. There appears to be no association between annual average precipitation and erosion within each drainage basin (Figure 3.8), and the correlation coefcient between annual average precipitation and erosion rate for each drainage basin is not statistically signicant (r 2 = 0.001). Runoff is dened as annual average river discharge divided by drainage area and was calculated from the hydrometric record. The relation between precipitation and runoff depends on evapotranspiration losses and percolation into deep groundwater. Comparison of Figure 3.7 with Figure 3.9 indicates a close correspondence between runoff and precipitation (r 2 = 0.56). This correspondence suggests that losses due to evapotranspiration and percolation into and out of deep groundwater appear to be approximately uniform in space over decadal time-scales. The average runoff ratio (runoff/precipitation) is 0.8 in Taiwan. This value is much higher than the
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global average of 0.3 (Ward and Robinson, 1990), and is typical of regions like Taiwan where most precipitation is delivered to a steep, bedrock landscape during extreme storms. Annual average runoff correlates poorly with erosion rate (r 2 = 0.03). This correlation is slightly better than that found between annual average precipitation and erosion rate, but is not statistically signicant. A plot of catchment-wide erosion rates within runoff bins (Figure 3.10) indicates that erosion rate varies inversely with runoff. This is counter-intuitive, because erosion of rivers is driven by the water running within them. Two explanations are possible. The rst possibility, which is discussed more fully in Section 3.4.5, is that erosion depends not on mean runoff but on runoff variability. In turn, runoff variability is inversely correlated with mean runoff (cf. Tucker and Bras, 2000), hence erosion also varies inversely with runoff. An alternative explanation, which is favoured here, is that runoff is highest in areas of steep topography where precipitation is orographically enhanced, yet erosion rates are highest in areas where weak lithology allows only subdued topography to develop and results in no orographic effect (Dadson et al., 2003).
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Figure 3.7: Annual average precipitation in Taiwan measured between 19491990. This gure was compiled from measurements reported by WRA (19702001).
8 7
Erosion Rate (mm yr )
-1
6 5 4 3 2 1 0 1 2 3 4 -1 Precipitation (m yr ) 5
Figure 3.8: Erosion rate and annual average precipitation. Mean erosion rates from 128 drainage basins were binned by precipitation rate (two extreme outliers were removed). Error bars show 95% condence interval.
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Figure 3.9: Annual average runoff in Taiwan between 19701999 estimated from the hydrometric record (see Appendix A; WRA (19702001)).
7 6
Erosion Rate (mm yr )
5 4 3 2 1 0 1 2 3 Runoff (m yr )
-1
-1
4
5
Figure 3.10: and Erosion average annual runoff for each drainage basin. Mean erosion rates from 128 drainage basins were binned by runoff (two extreme outliers were removed). Error bars show 95% condence interval.
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3.4.2 Slope
Local slope is typically thought to correlate strongly with erosion rate (e.g., Montgomery and Brandon, 2002). This view is physically reasonable, since the topographic gradient provides potential energy to drive down-slope erosional processes such as river ow and hillslope masswasting. An alternative view, proposed by Molnar and England (1990), suggests the opposite cause: steep topographic gradients result from prolonged river incision, because erosional unloading drives isostatic uplift and steepens relief further. Both hypotheses predict a strong correlation between topographic slope and erosion rate. This dependence can be examined using high resolution erosion and topography data available for Taiwan. Slope was computed using a 40 m digital elevation model (Figure 3.11). Slopes were calculated over one pixel in the direction of steepest descent, to ensure that river channel gradients were not articially elevated by the effects of steep valley sides. As expected, slopes are steep in the core of the mountain belt and in the northern Hsuehshan Range. Locally, very steep slopes are maintained in areas with high rock mass strength in marble and quartzite lithologies in northern Taiwan. In contrast, many areas of the thrust belt, which is comprised of weak mudstone, contain subdued topography. In spite of the theoretical link predicted between slopes and erosion, no correspondence was found between the spatial patterns of topographic slope and measured erosion rate (Figure 3.11). The correlation between average slope and erosion rate for each watershed is not statistically signicant (r 2 = 0.01; Figure 3.12). The highest erosion rates were found in areas with only moderate slopes. This is probably because the highest erosion rates are in areas with weak substrates, which cannot sustain steep topography. The signicance of these ndings is discussed later in Section 3.4.4.
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Figure 3.11: Slope map computed from 40 m digital elevation model as tangent in direction of steepest descent.
9 8
Erosion Rate (mm yr )
7 6 5 4 3 2 1 0 0 0.05 0.1 0.15 0.2 Basin Slope (tangent) 0.25
Figure 3.12: Erosion and slope for each drainage basin. In total, data from 128 drainage basins are shown (two extreme outliers were removed), binned by slope. The gure shows mean erosion rate within these bins, and its 95% condence interval.
-1
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3.4.3 Stream power
A common assumption is that erosion rates are jointly governed by relief and precipitation (see Chapter 1). In particular stream power, which is calculated from the product of local slope and runoff, has recently been suggested as a proxy measure of erosion (section 1.1.1; Montgomery et al., 2001; Finlayson et al., 2002). First introduced by Bagnold (1956), stream power is a measure of the rate at which a river is able to do work on its bed. Stream power per unit area of bed, (W m 2 ), can be written as:
= w gQS
W
,
(3.1)
where w is the density of water (1,000 kg m3 ), g = acceleration due to gravity (9.8 m s1 ), Q = water discharge (m3 s1 ), S = channel slope, and W is channel width (m) (cf. Eq. 1.2). Unit stream power was computed using a 40 m resolution digital elevation model (DEM) to measure slope in the direction of steepest descent (Figure 3.11). Runoff was estimated from water discharge measurements (Figure 3.9) and annual discharge was calculated for each point in the DEM by integrating runoff upslope. Channel width cannot be resolved using a DEM of this scale. However, measurements from a 5 m resolution satellite image of channel width at 12 gauging stations in central Taiwan (Figure 3.13) conrm that channel width varies as the square root of mean annual ood discharge (e.g., Leopold and Maddock, 1953). This scaling relation (W Q0.5 ) was used to rewrite unit stream power as:
= w gQ0.5 S.
(3.2)
The spatial pattern of unit stream power emphasises areas of high relief and orographic precipitation along the Central Range, where rapid exhumation has persisted longest (Figure 3.14). However, it does not match rst-order features of the decadal erosion pattern, such as high erosion rates at mountain fronts, the order of magnitude increase from north to south, and high erosion rates around active thrusts in the south-west. No signicant correlation was found between erosion rate and stream power within each drainage basin (r 2 = 0.01; Figure 3.15). The spatial pattern of unit stream power was found to be almost identical to the patterns of the alternative measures of total stream power and shear stress described in Section 1.1.3. 89
1000
Channel width (m)
100
10
Houlung Taan Tachia Wu Pachang Choshui 10 100 3 -1 Qmaf (m s ) 1000
1 1
Figure 3.13: River channel width annual ood discharge (downstream) in central Taiwan. Widths were measured as the distance between banks discernible on a 5 m panchromatic IRS satellite image of central Taiwan. Sampling locations are at hydrometric stations from whose river discharge record mean annual ood (Qmaf ) was calculated. It was impossible to tell from the image whether individual sampling sites were in bedrock or alluvial reaches. The solid line is a least-squares t to the data for Choshui River; it has a slope of 0.498 (r 2 = 0.64; s2 = 1.04).
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Figure 3.14: Unit stream power (W m2 ) presented at 1 km grid resolution with 30 km diameter circular moving mean applied.
10
8 Erosion Rate (mm yr )
-1
6
4
2
0
2
4
6
8 10 12 14 16 -2 Unit stream power (W m )
18
20
Figure 3.15: Erosion and unit stream power for each drainage basin. Mean erosion rate from 128 drainage basins was binned by unit stream power (two extreme outliers were removed). Error bars indicate 95% condence interval.
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3.4.4 Lithology
The effect of substrate strength was assessed using 1,114 measurements of uniaxial compressive strength and shear strength at 23 sites across Taiwan (Tables 3.2 and 3.3). Compressive rock strength varies over three orders of magnitude (0.1 253 MPa), broadly increasing with metamorphic grade from west to east, and south to north, with a drop in the alluviated depression between the Central Range and the Coastal Range. This trend is reected in the relief of Taiwan. Shear strength measurements reported in Table 3.3 refer to the weakest plane in the sediment sample, which is the most geomorphically meaningful measure. Many factors other than bulk shear strength are also important, such as joint spacing and degree of chemical weathering, although data on these variables are not available. There is little variation in cohesion values. Measured friction angles were between 2735 degrees; they are lowest in the mudstones of the thrust belt and highest in the slate belt and Tananao Schist. Histograms of slope were calculated from a 40 m DEM for hillslope locations (dened as having drainage area < 5 103 m2 ). These plots show that slopes are steepest in competent schists, meta-sandstones, marbles and gneisses in the Tananao Schist and Hsuehshan Range in northern Taiwan, and lower in the weak Pliocene-Quaternary sediments of the Western Foothills thrust belt (Figure 3.16). In most lithologies, mean and modal slopes are close to the reported friction angle (to within one standard deviation) (Table 3.4), which suggests that hillslopes are at their limit of mechanical stability (Burbank et al., 1996). The discrepancy between the modal slope in the thrust belt (22.5 ) and the friction angle (27 ) is not statistically signicant, but may indicate that hillslopes in the thrust belt have not everywhere reached their threshold of mechanical strength. Across Taiwan, compressive strength correlates with average slope (r 2 = 0.31) and relief (r2 = 0.17). The highest erosion rates are in low-relief terrain with weak substrate. This reinforces the notion that substrate properties modulate the topographic expression of tectonic deformation and erosion. Determining erosion rates from topography is possible only when spatially variable substrate erodibility is taken into account.
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Table 3.2: Compressive rock strength measurements. Number of Uniaxial compressive strength (MPa) samples Min Max Mean SD 1 range 682 0.1 109.2 20.0 13.8 6.233.8 88 5.1 219.9 79.7 34.2 45.5 113.9 57 1.5 253.4 39.2 34.4 4.8 73.6 287 1.2 189.9 45.3 23.1 22.2 68.4
Region WF HS SL TS
Note: SD, standard deviation; WF, Western Foothills; HS, Hsuehshan Range; SL, Slate Belt; TS, Tananao Schist; No data available in Coastal Range or Coastal Plain. Rock strength data compiled by Hongey Chen, Natl. Taiwan Univ.
Table 3.3: Shear strength measurements. Cohesion (MPa) Max Mean 116 11 7 1 11 46 12 Friction angle (deg.) Min Max Mean SD 95 480 270 54 125 580 290 78 350 161 617 311 87
Region WF HS SL TS
Samples Min 309 0 35 0 1 15 0
SD 10 1 11
Note: see Table 3.2 for key.
Table 3.4: Mean and modal slopes for lithological regions in Taiwan. Region Western Foothills Hsuehshan Range Slate Belt Tananao Schist Mean slope degrees 20.6 32.1 31.9 34.4 Modal slope Friction angle degrees degrees 22.5 27.05.4 32.5 29.07.8 32.5 35.0 32.5 31.18.7
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0.20 0.18 0.16 0.14 Proportion of area 0.12 0.10 0.08 0.06 0.04 0.02 0.00 10 20 30 40 Slope, degrees 50 60 CP WF HS SL TS CR
Figure 3.16: Slope histograms for lithological regions in Taiwan. Slope was calculated from a 40 m DEM in the direction of steepest descent. Only measurements for locations with upslope drainage area < 5 103 m2 were used to ensure that hillslopes were being sampled. Bins are 5 degrees wide. See Table 3.2 for key.
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3.4.5 Runoff variability
No signicant correlations were found between erosion and annual average precipitation, runoff, slope or stream power in Taiwan. An alternative view is that the erosion of Taiwan may be driven not by the pattern of average precipitation or runoff, but by the pattern of storm-driven runoff variability. This view makes sense because sediment supply and transport processes such as landsliding and oods are driven by storms. Runoff variability was calculated from the hydrometric record as the standard deviation of daily measurements of specic river runoff (river discharge divided by drainage area). To obtain a measure of runoff variability that can be compared between drainage basins, the standard deviation was normalized by mean runoff, to give the dimensionless runoff coefcient of variation. The runoff coefcient of variation is high along the east coast of Taiwan, where most incoming typhoons make land-fall; it is especially high in the south of Taiwan where typhoon passage is not obstructed by topography (Figure 3.17). Erosion rates in each drainage basin show a statistically signicant correlation with the coefcient of runoff variation (r 2 = 0.27; Figure 3.18).
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Figure 3.17: Runoff coefcient of variation (dimensionless), dened as standard deviation of runoff divided by mean runoff. Runoff was measured as average annual river discharge divided by drainage area (from data supplied by WRA (19702001)).
12
Erosion rate (mm yr-1)
10 8 6 4 1.6 2 0 1.5 3.7 5.2 3.8
10.4
2
2.5
3
3.5
4
Runoff coefficient of variation
Figure 3.18: Erosion and runoff coefcient of variation for each drainage basin. In total, data from 128 drainage basins were used (two extreme outliers were removed), binned by runoff coefcient of variation. The gure shows mean erosion rate within these bins, and its 95% condence interval.
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3.4.6 GPS dilatation rate
In addition to climate-driven runoff variability, the spatial pattern of crustal deformation may also control the pattern of erosion. Indeed, in a ux steady-state landscape, the erosion rate should be equal to the input of material through tectonic processes. Two datasets were used to investigate the links between crustal deformation and erosion: (i) crustal velocities and strain rates measured by repeated Global Positioning System (GPS) surveying of geodetic benchmarks (this section); and (ii) the rate of seismic moment release in M w >5 earthquakes between 1900 1998 (next section). GPS velocities were measured at 131 locations between 19901995 by Yu et al. (1997). From these published measurements, the surface dilatation rate was calculated by John Haines using the method described by Beavan and Haines (2001). Dilatational strain rate was computed as the divergence of a velocity eld interpolated from GPS velocities using bicubic splines in a curvilinear geometry matching the shape of the Taiwan region (Figure 3.19). The rate of shear strain was also computed from GPS measurements; it is not shown here because shear strain is not easily related to uplift of rock. The surface dilatation rate eld provides a measure of crustal shortening and extension (positive dilatation is extension; negative dilatation is contraction). The degree to which shortterm decadal GPS measurements are representative of long-term crustal strain rates is not well known (Segall and Davis, 1997). Many features of the GPS dilatation eld agree with strain rates inferred from seismic moment tensors (Yeh et al., 1991) and geodynamic models (Hu et al., 2001). High rates of contraction were found in the eastern Central Range and in the Western Foothills fold-and-thrust belt. Signicant positive dilatation observed in the north-east Ilan Plain is due to backarc extension associated with the Okinawa Trough (Teng, 1996). However, some features of the GPS dilatation eld are more difcult to interpret. Extension observed along the ridge pole of the southern Central Range may be due to gravity spreading, as suggested by Lu and Malavieille (1994) and Yu et al. (1997). If so, this extension is not likely to have persisted for very long, given the considerable topography in this part of the Central Range. An alternative explanation may be that dilatation observed in this area between
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19901995 is due to a visco-elastic crustal response to a number of M w > 6 earthquakes in the thrust belt in the last fty years. Assuming that local uplift is proportional to crustal contraction, the pattern of crustal deformation can be compared with the observations of erosion rate (the validity of this assumption is discussed in detail in the next section). Areas of rapid crustal shortening correspond with areas of high erosion, particularly in eastern Taiwan and in the south-western part of the fold-and-thrust belt. A plot of dilatation rate and erosion rate for each drainage basin shows a four-fold increase in erosion rate over the range of contraction rates (Figure 3.20). Erosion rates are lowest in areas where the crustal dilatation rate is low, and increase slightly in areas of extension, although the range of variability is large and the correlation is only marginally signicant (r 2 = 0.05).
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Figure 3.19: Crustal dilatation rate from GPS observations calculated using the method of Beavan and Haines (2001) from GPS crustal velocities measured by Yu et al. (1997).
18 16 14 Erosion Rate (mm yr )
-1
12 10 8 6 4 2 0
2
0 -2 -4 -6 -8 -15 -1 GPS Dilatation Rate (10 s )
-10
Figure 3.20: Erosion and crustal dilatation rate for each drainage basin. Mean erosion rate from 128 drainage basins were binned by crustal dilatation rate (two extreme outliers were removed). Error bars show 95% condence intervals.
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3.4.7 Seismic moment
In addition to crustal deformation measured by GPS, the record of historical seismicity 1900 1998 was analysed. Differen...