Badland landscape response to individual geomorphic events

Landscapes form by the erosion and deposition of sediment, driven by tectonic and climatic forcing. The principal geomorphic processes of badland – landsliding, debris flow and runoff erosion – are similar to those in full scale mountain topography, but operate faster. Here, we show that in the badlands of SW Taiwan, individual rainfall events cause quantifiable landscape change, distinct for the type of rainfall. Typhoon rain reduced hillslope gradients, while lower-intensity precipitation either steepened or flattened the landscape, depending on its initial topography. The steep topography observed in our first survey is inconsistent with the effects of any of the rainfall events. We suggest that it is due to the 2016 Mw 6.4 Meinong earthquake. The observed pattern in the badlands was mirrored in the response of the Taiwan mountain topography to typhoon Morakot in 2009, confirming that badlands offer special opportunities to quantify natural landscape dynamics on observational time scales.

The survey error of UAV-SfM-derived DEMs can be divided into three types: 221 The first source of uncertainty (Type-A) is due to survey errors associated with the position of ground 222 control points during field work. We used e-GPS (see method) to measure the spatial coordinates and 223 elevation of 11 control points within the study area. Errors in the e-GPS measurements can be caused 224 by atmospheric interference, instrument system error and human operation. To have a means to check 225 for survey quality, we defined the 9 th ground control point as the origin of coordinate system, and 226 used a total station (LEICA TS02) to measure the positions of eight other ground control points using 227 the 9 th point as the base location. The remaining two ground control points did not have a direct line 228 of sight to the base location. This procedure allows to obtain a control point location error estimate, 229 assuming that the accuracy of the total station is higher than that of the e-GPS. The second source of uncertainty (Type-B) is due to errors in locating ground control points in the 233 drone images. Each ground control point is captured by multiple images from the same survey, and 234 therefore position of the ground control point in the image is subject to errors of projection and image 235 deformation. The Acute3D software provides quality reports for the UAV surveys. These are 236 summarized in Supplementary Table 2. The RMS deviation varies between 0.6 cm to 3.6 cm in the 237 horizontal direction and 0.2 cm to 0.6 cm in the vertical.

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The third source of uncertainty (Type-C) is due to the position uncertainty of checkpoints. The image 239 processing produces image distortion and affects the authenticity of the DSMs. Therefore, to quantify 240 the degree of image distortion, the Acute3D software establishes evenly distributed checkpoints on 241 orthophotos and calculates the position uncertainty of these checkpoints (see Supplementary Figure  242 6). The position uncertainty of checkpoints is shown in Supplementary Table 2. The mean error varies 243 from 2.0 cm to 13.0 cm in the horizontal direction and 0.7 cm to 5.6 cm in the vertical. Overall, the 244 errors in the vertical direction is the level of millimeters to centimeters, with few locally larger or 245 smaller errors. As such, the mean errors give a good representation of the overall errors. In addition, 246 errors show circular symmetry, indicating that they capture random rather than systematic errors. 247 In summary, the main source of error results from Type-C, image distortion in areas without control 248 points.

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We use the elevation data for two main purposes, the detection of erosion or deposition, and the 250 calculation of local slope and its change. 251 In the first application, each pixel is looked at individually. As long as the same pixel refers to the 252 same area in subsequent surveys, the vertical uncertainty is relevant only for change detection of 253 elevation. Image distortion may introduce an effect of the horizontal error, which scales linearly with 254 slope. That is, if a pixel in the later survey contains area that was attributed to different pixels in the 255 earlier survey, the shift in the coordinate system may lead to an apparent change in elevation that is 256 proportional to the local slope times the horizontal error. 257 In the second application, slope is calculated as the ratio of elevation differences of adjacent pixels 258 and pixel size. Assuming normally distributed errors, the relative error in slope can be evaluated as 259 the square root of the sum of the squares of the relative horizontal and vertical errors. For slope 260 changes, individual pixels are compared and similar considerations apply as given above for the errors 261 in elevation changes. 262 From the brief overview, it is clear that both horizontal and vertical errors can contribute to the errors 263 in the quantities of interest. Given that the relative errors may be substantial (up to >40% of the pixel 264 size for the horizontal error and similar mean vertical relative errors for locations), the concerns of 265 the reviewers are reasonable. We want to make a few points to justify our approach for analyzing the 266 data. 267 First, we note that both horizontal and vertical errors can be expected to be highly spatially correlated. 268 For example, if a given pixel has an error due to distortion, in the horizontal or vertical, we expect 269 adjacent pixels to have an error of similar magnitude and direction. This spatial dependence of the 270 uncertainty patterns can be expected to strongly decrease the uncertainties relevant for the analysis, 271 especially for the calculation of slope, which utitlizes data from adjacent pixels. Unfortunately, the 272 degree of spatial dependence cannot be quantified with the available data. 273 Second, due to the high-resolution topography, each dataset consists of a large number of data points.

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Over the entire survey area, we have analyzed more than 1 million individual data points. Due to the 275 law of large numbers, according to which the uncertainty of individual statistics scales with the 276 inverse of the square root of the total number of data points, the central statistics that we use for our 277 interpretation are very robust. 278 Third, the reliability of the height change involves data from multiple periods, and therefore we use 279 LOD (Wheaton et al., 2003) to filter out the data with excessive height differences. 280 Fourth, the availability of large numbers of data points allows the rigorous comparison of distributions, 281 which also allows observing differences for the entire ensembles of data, rather than individual data 282 points or central statistics.

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In light of the discussion of uncertainties above, we approached the data analysis with three broad 284 strategies. 285 First, we considered central statistics, mainly the median, and changes therein, since, given the large 286 number of data points available in the surveys, these bear small uncertainties. 287 Second, we used the Kolmogorov-Smirnov test (KS test) to assess differences in the distributions of 288 the data. The test shows that all of period significantly different from all other periods at the 5% 289 significance level (see Fig. 4 and Supplementary Table 3). 290 Third, we used binning approaches to assess central tendencies in the data. This method is 291 advantageous, as it retains the diminishing errors due to the law of large numbers, but allows to assess 292 trends with potential forcing variables. We note here that the correspondence of trends for example 293 of gradient change for the different survey episodes and the changes due to typhoon Morakot is a 294 strong indication that we do not observe a statistical fluke.

Ks-test for badland data set 316
Observed Simulated