JOURNAL OF GEOPHYSICAL RESEARCH: EARTH SURFACE, VOL. 119, 12–27, doi:10.1002/2012JF002711, 2014
Mapping Quaternary alluvial fans in the southwestern United States based on multiparameter surface roughness of lidar topographic data Netra R. Regmi,1 Eric V. McDonald,1 and Steven N. Bacon 1 Received 11 January 2013; revised 18 November 2013; accepted 26 November 2013; published 14 January 2014.
[1] Quaternary alluvial fans have diverse surface morphologies related to both
depositional and weathering processes. Numerous studies have demonstrated that the surface expression and morphometry of alluvial fans can be used as an indicator of their relative age of deposition, but only recently has there been an effort to utilize high-resolution topographic data to differentiate alluvial fans by surface age with automated and quantifiable routines. We developed a quantitative model for mapping the relative age of alluvial fan surfaces based on multiparameter surface roughness values computed from 1 m resolution lidar topographic data. Roughness is defined as a function of observational scale and integration of slope, curvature, and aspect topographic parameters. Alluvial fan roughness values were computed across multiple observation scales (3 × 3 m to 150 × 150 m) based on the standard deviation (SD) of slope, curvature (tangential), and aspect topographic parameters. Plots of roughness value versus size of observation scale suggest that the SD of each parameter over a 7 × 7 m observation window best identified the signature of surface roughness elements. Roughness maps derived from slope, curvature, and aspect at this scale were integrated using fuzzy logic. The integrated roughness map was then classified into five relative morphostratigraphic surface age categories (active wash to ~400 ka) and statistically compared with a similar fivefold surface age map of alluvial fans developed using traditional field surveys and aerial photographic interpretation. The model correctly predicted the distribution and relative surface age of ~61% of alluvial fan landforms based on traditional mapping techniques. Citation: Regmi, N. R., E. V. McDonald, and S. N. Bacon (2014), Mapping Quaternary alluvial fans in the southwestern United States based on multiparameter surface roughness of lidar topographic data, J. Geophys. Res. Earth Surf., 119, 12–27, doi:10.1002/2012JF002711.
1.
ecosystem processes in arid environments [Sweeney et al., 2011]. A key quality of alluvial surfaces is that they can be stratigraphically subdivided by their local relief or height above the active channel, degree of dissection, drainage pattern, soil characteristics, and development of desert pavement [Christenson and Purcell, 1985; McFadden et al., 1989; Bull, 1991; McDonald et al., 2003; Bacon et al., 2010a]. [3] Many qualitative and quantitative techniques have been used to differentiate or subdivide sequences of alluvial fan surfaces. The most common techniques include (1) mapping characteristics of a fan surface in the field by describing surface clast size, rock varnish accumulation, desert pavement development, stratigraphic relationships, and evaluation of surface morphology [Colman and Pierce, 1986; Wells et al., 1987; McFadden et al., 1989; Bull, 1991; Ritter et al., 1993; Birkeland, 1999]; (2) using soil stratigraphy and the relative degree of soil development [McFadden et al., 1989; Bull, 1991; McDonald et al., 2003; Bacon et al., 2010a]; (3) mapping fan surfaces based on the difference of the surface brightness manifested in aerial or satellite images [Christenson and Purcell, 1985; Bull, 1991]; (4) analysis of remotely sensed
Introduction
[2] Alluvial fans have long been recognized as an important record of Quaternary (1.8 Myr to present) climate and tectonic activity across arid to semiarid deserts of North America [Gilbert, 1877; Davis, 1905; Blackwelder, 1931; Denny, 1965; Bull, 1977, 1984, 1991, 2008; Wallace, 1977; Wells et al., 1987; Lubetkin and Clark, 1988; Whipple and Dunne, 1992; Ritter et al., 1993; Bierman et al., 1995; McDonald et al., 2003; Matmon et al., 2005; Nichols et al., 2006; Bacon et al., 2010a]. Mapping the spatial distribution of alluvial fans of different ages is a critical part of deciphering Quaternary geologic history, as well as elucidating key
1
Division of Earth and Ecosystem Sciences, Desert Research Institute, Reno, Nevada, USA. Corresponding author: N. R. Regmi, Division of Earth and Ecosystem Sciences, Desert Research Institute, 2215 Raggio Pkwy, Reno, NV 89512, USA. (
[email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9003/14/10.1002/2012JF002711
12
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS N
0
5
10 km
Jsv
Area Shown
Tv
Qa Muggins Mountains
Study Area
Yuma
Figure 1. Location map of the study area and surrounding terrain bounded by the Colorado and Gila Rivers in southwestern Arizona. Rectangle on map shows the location of the study area north of Muggins Mountains. The study area consists of Quaternary alluvium (Qa) derived from upland areas consisting of Jurassic sandstone and conglomerate (Jsv) sedimentary rocks and Tertiary dacitic and rhyolitic (Tv) volcanic rocks [Richard et al., 2000].
Kierein-Young, 1997; Frankel and Dolan, 2007]. Use of digital topographic data to identify fan characteristics is time efficient and can be cost effective when applied over a large area; however, its relative accuracy compared to traditional mapping methods remains uncertain. Surface morphology is a time- and process-dependent feature widely used to distinguish alluvial fan types because (1) fan surfaces initially tend to become smoother with increasing age due to the formation of desert pavement and the degradation of bar-andswale topography and (2) subsequently, landforms become more dissected due to tectonics and climate change induced increased erosion and channelization of the fan surface with time [e.g., Wells et al., 1987; Bull, 1991; Ritter et al., 1993; McDonald, 1994; Frankel and Dolan, 2007]. [6] The overall focus of this paper is twofold. First, we evaluate the potential application of multiparameter surface roughness values to automatically map alluvial fan stratigraphy using high-resolution lidar (light detection and ranging) topographic data. Second, we compare model-based maps computed from multiparameter surface roughness values with alluvial fan stratigraphy mapped using traditional field and image analysis techniques. We present a way to quantify roughness by analyzing three geometries (slope, curvature, and aspect) of surface irregularities within different scales of observation. This approach differs from other studies [e.g., Frankel and Dolan, 2007] where only a single geometric measure, slope, was used to characterize the surface roughness of alluvial fans. A number of other approaches to quantifying landscape roughness [e.g., McKean and Roering, 2004; Booth et al., 2009; Hurst et al., 2013] also exist in the literature; however, these approaches have yet to be tested
multispectral images [Alwash et al., 1986; White, 1993; Farr and Chadwick, 1996; Beratan and Anderson, 1998], multichannel thermal infrared images [Gillespie et al., 1984], hyperspectral images [Crouvi et al., 2006], and radar images [Kierein-Young, 1997]; (5) analysis of digital elevation models [Frankel and Dolan, 2007]; and (6) application of cosmogenic age dating techniques to determine the ages of the alluvial deposits and the rates of arid-region alluvial processes [Nichols et al., 2002, 2006; Matmon et al., 2006]. [4] Each of the above approaches has important benefits and limitations. Traditional field mapping techniques provide the highest level of accuracy; however, field-based techniques can be labor intensive, time consuming, and difficult for mapping regional areas. Mapping based mostly on aerial or spaceborne imagery can be subjective with the accuracy of the map depending on the expert’s prior knowledge, map scale, and the quality and resolution of images that show contrasts between different alluvial fan surfaces. Remote sensing techniques also have limitations. The spectral and spatial resolutions of multispectral sensors are not sufficient to explain the surface variability of alluvial deposits. The range of reflectance of alluvium is influenced by soil geomorphic surface processes including varnish and pavement development, degree of dissection and weathering, and lithology of source materials [McDonald, 1994]. Alluvial deposits of similar age may contain sediment of different compositions, which can influence rates of varnish development and weathering, thereby affecting the accuracy of interpreting remotely sensed data. [5] One technique being increasingly applied to differentiate alluvial fan surfaces is to quantify the expression of alluvial surface roughness using digital topographic data [e.g., 13
2.
The Study Area
[7] The study area is located in the Sonoran Desert of southwestern Arizona approximately 40 km northeast of Yuma, Arizona (Figure 1). The studied area (hereafter simply “Yuma”) covers ~60 km2 area of extensive alluvial fans that are just north of the Muggins Mountains. The area has an arid climate with a mean annual precipitation of 93 mm based on precipitation data recorded between 1958 and 2012 [Western Regional Climate Center, 2012]. The study area is dominated by low-gradient and broad alluvial fans that cover most of the lowland area between intervening mountain highlands. The principal sources of fan deposits in and around the study area are moderate to low relief mountains composed mostly of Cretaceous and Tertiary granitic and volcanic rocks and lesser amounts of sedimentary rocks [Richard et al., 2000].
Geologic age from Lashlee et al. [2002], McAuliffe and McDonald [2006], Nichols et al. [2006], and Bacon et al. [2010a].
Ballena topography, about 50% of surface is preserved with convex slopes; eroded surface composed mostly of pebbles to cobbles with petracalcic coatings Very low (on channel margins) None (surface destroyed) to strong (surface preserved) Very high (>5 m) Older than late Pleistocene (>140 ka) Dissected alluvial fan Qf1
Late Pleistocene (140 to 70 ka) Alluvial fan Qf2
Late Pleistocene to early Holocene (15 to 8 ka) Alluvial fan/terrace Qf3
Late Holocene (3.2 to 2.9 ka) Alluvial fan/terrace Qf4
on alluvial fan landforms. The specific goal of this study is to assess the ability of lidar elevation data (1 m horizontal resolution) to separate different aged alluvial fan surfaces in a manner comparable to the subdivision of alluvial fans based on traditional mapping techniques. To achieve this goal, the following objectives were met: (1) prepare a geomorphic map of alluvial fan stratigraphy based on traditional field data and image analysis, (2) define and quantify the degree of roughness of alluvial fans at multiple scales using lidar elevation data, (3) determine a scale most appropriate to characterize the roughness of alluvial fan surfaces, and (4) directly compare the alluvial fan stratigraphy derived from traditional techniques with the alluvial fan stratigraphy derived from modeled surface roughness in order to evaluate the relative accuracy of a multiparameter roughness approach.
2.1. Surface Morphology of Alluvial Fans in Yuma [8] The ages of alluvial fans vary greatly, ranging from active wash (Map unit: Qf5) to ~400 ka (Qf1) (Table 1 and Figure 2). The younger Holocene alluvial fan surfaces have well-developed bar-and-swale microtopography with variable relief (1–2 m) that is predominantly controlled by extremely gravelly soils with a range of mixtures of boulders to cobbles and pebbles. The microtopography lacks well-developed desert pavement. In contrast, Pleistocene alluvial fan surfaces exhibit smooth surface morphologies and well-developed varnished desert pavements. The oldest Pleistocene fan surfaces are incised by a network of channels that grade to Holocene age alluvial surfaces [Lashlee et al., 2002; Nichols et al., 2006; Bacon et al., 2010a]. The fans in Yuma have a range of surface morphologies at local or microtopographic scales (10 m planimetric observation length), the morphology of these fans is reflected by the following surface attributes: (1) depth of channel incision, (2) density of active channels, (3) pattern of drainage networks, and (4) topographic characteristics spanning several channel networks on the same geomorphic surface. The channels developed on older alluvial fans have dendritic patterns and significantly greater depths of incision compared to the channels on younger alluvial fans that have mostly distributary channel patterns (Table 1). The density of active channels on older fans is significantly lower than
3.2. Surface Roughness [13] Surface morphology of alluvial fans can be defined by the frequency (number of occurrence) and magnitude (size) of topographic irregularities at a given scale of observation. We present a way to quantify surface roughness by analyzing multiple topographic geometries of slope, curvature (tangent), and aspect in different scales of observation. We used the standard deviation (SD) of slope, curvature, and aspect to quantify 16
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS y x
C1
C2
C3
C4
C5
C6
C7
C8
C9
that the SD of slope alone does not completely define roughness. Although the SD of slope provides information on the variation in the magnitude (i.e., relief) of roughness elements in the vertical dimension, it does not sufficiently describe the variation in curvature and orientation of roughness elements with respect to the horizontal dimension. In this regard, we propose that the integration of the SDs of slope, curvature, and aspect better characterizes surface roughness at a given scale of observation. 3.2.1. Multiscale Surface Roughness [15] Alluvial fan surfaces have roughness elements that are reflected with different wavelengths in topographic data. The patterns of surface roughness are considered to be primarily a function of both magnitude (i.e., relief or amplitude) and frequency (number of occurrence) of topographic irregularities over an observational area (window size). For example, Figure 4 shows a schematic diagram of how surface roughness depends on the size of observation window or scale and the frequency and magnitude of microtopographic versus macrotopographic relief features. When microtopographic and macrotopographic relief features are compared over the same observation area (Figure 4a), significantly different frequencies and magnitudes of features are observed. Shortwavelength (3°) determined by overlaying a slope map on aerial imagery. The surface roughness of the excluded area was then determined from the interpolation of roughness from surrounding areas. 3.3. Combination of Roughness Maps Based on Fuzzy Logic Approach [20] All roughness maps were first standardized to a common measurement scale and then combined using fuzzy operators [Zadeh, 1965]. Data standardization is needed because the DEM-derived slope-, curvature-, and aspect-based roughness values are independent from each other and are measured in different units. Slope values were calculated in degrees with respect to vertical direction, aspect values were calculated in degrees with respect to horizontal direction, and curvature values were calculated in 1/m. In addition, standardizing the data to a common scale allows comparisons among the data. All the roughness maps obtained at each scale of observation were standardized from 0 to 1 using the following linear function: rsi ¼ ðri rmin Þ=ðrmax rmin Þ;
where dz/dx and dz/dy are the rates of change of the surface elevation in x and y directions, respectively, L is the width of the cell, and Ci is the elevation of the cell at ith location (Figure 5a). The atan2 is the arctangent function whose value ranges from π to π. [18] Maps showing the SDs of slope, curvature, and aspect were developed using moving windows of sizes ranging from 3 × 3 m to 150 × 150 m (3 cell × 3 cell to 150 cell × 150 cell) from maps of slope, curvature, and aspect. The largest window size was selected based on the average wavelength of the
(8)
where rmin is the minimum roughness value of a roughness map, rmax is the maximum roughness value of a roughness map, and rsi is the output standardized value computed for a roughness value (ri) of ith grid cell. [21] Five fuzzy operators [An et al., 1991; Bonham-Carter, 1994; Chung and Fabbri, 2001; Regmi et al., 2010] can be employed to combine standardized values of two or more input maps. These operators (1) fuzzy OR, (2) fuzzy AND, 18
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS Table 2. Comparison of Observed Versus Predicted Maps Based on Standard Deviation of Slope, Curvature, Aspect, and Combination of All Parameters Predicted Versus Observed Alluvial Fan Unit
Combined Accuracy (%)
Slope-Based Accuracy (%)
Curvature-Based Accuracy (%)
Aspect-Based Accuracy (%)
53 10 0 0 1 34 68 29 5 7 2 15 50 27 13 0 1 9 22 13 11 6 13 46 65 61
30 25 20 5 1 38 36 23 8 4 17 28 38 30 18 2 3 8 27 19 14 8 11 30 58 43
41 10 7 2 1 30 49 39 17 5 10 28 36 31 20 1 4 9 26 21 18 10 9 25 53 47
64 14 0 0 2 33 68 24 5 19 1 14 45 18 22 0 2 22 26 18 2 2 10 51 40 53
Qf1-Qf1 Qf1-Qf2 Qf1-Qf3 Qf1-Qf4 Qf1-Qf5 Qf2-Qf1 Qf2-Qf2 Qf2-Qf3 Qf2-Qf4 Qf2-Qf5 Qf3-Qf1 Qf3-Qf2 Qf3-Qf3 Qf3-Qf4 Qf3-Qf5 Qf4-Qf1 Qf4-Qf2 Qf4-Qf3 Qf4-Qf4 Qf4-Qf5 Qf5-Qf1 Qf5-Qf2 Qf5-Qf3 Qf5-Qf4 Qf5-Qf5 Overall Accuracy (%)
Bold numbers represent the percentage of areas predicted correctly for each pair of predicted versus observed alluvial fan units. The agreements (accuracy) between the pairs of predicted and observed fan units were computed in percent by taking the ratio of area matched between the pair to the area of the observed unit in the pair. The overall accuracy was determined in percent by taking the ratio of total correctly predicted area to the total area of the observed map.
operator combines outputs obtained from fuzzy algebraic sum and fuzzy algebraic product based on a gamma value. The value of gamma ranges from 0 to 1. In the fuzzy gamma operation, when gamma is 1, the combination is the same as the fuzzy algebraic sum, and when gamma is 0, the combination equals the fuzzy algebraic product. Therefore, the appropriate choice of gamma produces output values that ensure a flexible compromise between effects of the values obtained from the fuzzy algebraic sum and the fuzzy algebraic product. In all fuzzy operations, the output values range from 0 to 1, where 0 represents the smoothest surface and 1 represents the roughest surface. Further details about fuzzy logic and fuzzy operators are discussed in BonhamCarter [1994] and Regmi et al. [2010]. [23] The roughness values computed from slope and curvature can be expected to be higher around convex and concave areas of the landscape and lower in flat and planar areas, suggesting that these parameters are correlated in some cases. We used the fuzzy OR operator to combine the standardized roughness values derived from slope and curvature so that the effect of dependency of one parameter on the other is reduced. The output map was then combined with aspect-based standardized roughness map using fuzzy algebraic sum, fuzzy algebraic product, and fuzzy gamma operations. Eleven combined roughness maps were prepared with values of gamma ranging from 0 to 1.
(3) fuzzy algebraic sum, (4) fuzzy algebraic product, and (5) fuzzy gamma can be expressed mathematically as rcs ¼ max ðr1s ; r2s ; r3s ::::ÞðFuzzy ORÞ;
(9)
rcs ¼ min ðr1s ; r2s ; r3s ::::ÞðFuzzy ANDÞ;
(10)
n
rcs ¼ 1 ∏ ð1 ris Þ ðFuzzy algebraic sumÞ;
(11)
i¼1 n
rcs ¼ ∏ ris ðFuzzy algebraic productÞ;
(12)
i¼1
rcs ¼ ðFuzzy algebraic sumÞγ
· ðFuzzy
algebraic productÞ1γ ðFuzzy gammaÞ
(13)
where ris is the standardized value for the ith map (i = 1, 2, …, n) at a particular location (grid cell) and rcs is the combined output value. [22] Fuzzy OR and fuzzy AND operators are appropriate if one of the input maps best characterizes the roughness of a particular location. The fuzzy OR operator returns the maximum standardized value of the input maps occurring at that location, and fuzzy AND operator returns the minimum standardized value of the input maps occurring at that location. Use of these operators reduces effect of the dependency of one parameter on the other. If the combination of two or more input maps best characterizes the roughness of that location, the fuzzy algebraic sum, fuzzy algebraic product, and fuzzy gamma operators are appropriate. The fuzzy algebraic sum and fuzzy algebraic product consider all standardized values of the input maps occurring at that location and combine them based on the expressions shown above. The fuzzy gamma
3.4. Classification of Roughness and Comparison With Observed Geomorphic Map [24] The individual and combined roughness maps were smoothed using a 20 × 100 m moving window (mean filter). 19
Roughness (SD of slope in degree)
Roughness values at maximum frequency (Max. Freq.) and maximum frequency × magnitude (Max. Freq. × Mag.) were obtained visually from Figure 9 by looking at where the curves for frequency and product of frequency and magnitude are at their maximum and then projecting to the x axis to find the range of SD values.
Slope-based
(a)
5
3.0
4 2.5
3 2
2.0
Qf1 Qf2 Qf3 Qf4 Qf5
1
1.5
Qf1: Oldest Qf5: Youngest
1.0 0.5 0
50
100
150
Roughness (SD of curvature in 1/m)
Window length (m) Curvature-based 0.30
(b) 5
0.25
4 0.20
3 1&2
0.15 0.10 0.05 0
50
100
150
Roughness (SD of aspect in degree)
Window length (m) Aspect-based 5 4
90 80
3 2
70
1
(c)
60 50 40 30 0
50
100
150
Window length (m)
Figure 6. Plots showing mean surface roughness of fan units of different ages (Qf1–Qf5; oldest to youngest) versus window length. (a) Slope-derived roughness. (b) Curvature-derived roughness. (c) Aspect-derived roughness. Window lengths range from 3 × 3 m to 150 × 150 m. Microtopographic relief features are represented by the roughness values forming steepest parts of the curves (e.g., Figure 4b). Visual inspection indicates the steepest parts of the curves occur at window length smaller than 7 m (shaded area). Therefore, the right margin of the shaded area represents the most appropriate window size for computing surface roughness. Each figure shows that the surface roughness of all alluvial fan units can be observed best at 7 × 7 m observation window size. Note that as the size of the window length increases, the rate of change in surface roughness values for each map unit decreases and each curve tends to flatten when the area over which roughness values are calculated begins to incorporate other and potentially different alluvial surfaces. The relationship of roughness with fan age is apparent with the overall mean roughness decreasing with alluvial fan age.
a
4812856 20418391 3949654 80 70 60 70 60 20 18 22 22 68 55 44 0.98 0.82 0.79 Qf3 Qf2 Qf1
0.81 0.62 0.56
0.5 0.5 0.5
0.6 0.6 0.6
0.12 0.11 0.10
0.08 0.06 0.06
0.08 0.08 0.08
0.09 0.09 0.09
15 1.48 Qf4
1.05
0.6
2.0
0.16
0.1
0.08
0.09
77
80
90
3317755
Boulders, plant mounds, plant scars, channels, barand-swale, vegetation Channel networks, plant mounds, plant scars, barand-swale Pavement, degraded bar-and-swale, erosional rills Pavement, erosional rills Pavement (only ridges), erosional rills 21918203 90 80 17 77 0.3 0.09 0.16 0.25 2.5 0.8 2.23 Qf5
1.38
At max. At max. SD. Freq.a Freq. × Mag.a Mean At Max. At max. Freq.a “Freq. × Mag.”a SD. Mean Alluvial Fan Unit
SD.
At max. Freq.a
At max. Freq. × Mag.a
Mean
Curvature-Based (1/m) Slope-Based (°)
Roughness
Table 3. Statistics of Surface Roughness Values Obtained for Different Aged Alluvial Fan Units
Aspect-Based (°)
No. of Measurements
Microtopographic Features
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
20
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
Roughness (SD of slope in degree)
Slope-based
and different fan units. The eight maps of smoothed surface roughness were combined at each location (grid cell) by using the expressions
5
(a) 4
r max ¼ max ðrdir1 ; rdir2 ::::::::::::; rdir8 Þ;
(14)
3
r min ¼ min ðrdir1 ; rdir2 ::::::::::::; rdir8 Þ;
(15)
2
where r max and r min are the maximum and minimum of the mean roughness values at each location obtained by the smoothing of data along eight directions ðrdir1 ; rdir2 ::::::::::::; rdir8 Þ . The youngest fan unit (Qf5) having the highest roughness
1 0 Qf1
Qf2
Qf3
Qf4
Qf5
Slope-based Normalized cumulative frequency
Alluvial fan unit Roughness (SD of curvature in 1/m)
Curvature-based 0.6
(b) 0.5 0.4 0.3 0.2 0.1 0
0.8
(a)
3
0.6
4
0.4
Qf1 Qf2 Qf3 Qf4 Qf5
5 Qf1: Oldest Qf5: Youngest
0.2
0.0 2
4
6
8
Roughness (SD of slope in degree) Qf1
Qf2
Qf3
Qf4
Qf5
Curvature-based Normalized cumulative frequency
Aspect-based Roughness (SD of aspect in degree)
1 2
0
Alluvial fan unit 100
(c) 80
60 40 20
0
1.0
Qf1
Qf2
Qf3
Qf4
1.0
0.8
1 2 3
0.6
4
(b)
0.4
5 0.2
0.0 0.0
0.5
1.0
Roughness (SD of curvature in 1/m)
Qf5
Aspect-based Normalized cumulative frequency
Alluvial fan unit
Figure 7. Box and whisker plots showing statistics of surface roughness within a 7 × 7 m observation window for the Qf1–Qf5 map units based on the topographic parameters of (a) slope, (b) curvature, and (c) aspect. The horizontal line inside each box represents the median value. Lower and upper limits of the box represent the 25th and 75th percentiles. Whiskers show the 10th and 90th percentiles, and the black dots represent the 5th and 95th percentiles. The moving window was applied in eight directions with an aspect interval of 45° to produce eight surface roughness maps. We used a rectangular moving window rather than a square or a circular window because the shapes of alluvial fans in the study area are relatively narrow and elongated in the downstream direction. The rectangular shape captured a larger area of a fan unit by decreasing the edge effects of the surface roughness values associated with adjacent
1.0
(c)
1 0.8
2
0.6
3 0.4
4 0.2
5
0.0 0
50
100
150
Roughness (SD of aspect in degree)
Figure 8. Frequency distributions of surface roughness in a 7 × 7 m moving window on the Qf1, Qf2, Qf3, Qf4, and Qf5 map units (oldest to youngest) based on the topographic parameters of (a) slope, (b) curvature, and (c) aspect. 21
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
Figure 9. Relationships of surface roughness with their normalized frequency distributions compared to the normalized product of roughness magnitude and their frequency distribution for the Qf1–Qf5 map units based on the topographic parameters of (a and b) slope, (c and d) curvature, and (e and f) aspect. Roughness values which significantly contribute to the overall roughness of each alluvial fan surface can be determined from these plots. For example, the shaded areas represent roughness values having high-frequency and high-“frequency × magnitude” product which control the overall roughness of Qf5 alluvial fan surfaces. Highest-frequency and highest-“frequency × magnitude” roughness values visually observed from the figure for each alluvial fan surface are provided in Table 3. preserved or mostly intact and planar landform surfaces as crucial criteria for accurately differentiating alluvial fans based on surface roughness. [27] Plots of roughness versus window length indicate that all three parameters of slope, curvature, and aspect are good predictors of alluvial fan surface roughness (Figure 6). In these plots, fans of different ages have distinctive roughness curves that collectively show trends of decreasing surface roughness with increasing age. In addition, the roughness curves have steep slopes up to a point where the window length reaches 7 m. Beyond this point, the slope of each roughness curve rapidly drops and eventually becomes flat (Figure 6). The characteristics of each curve imply that the 7 m window length scales to the dominant wavelength of the microtopographic roughness elements and that the roughness values observed at larger window lengths are the effect of both microtopographic and macrotopographic roughness elements. Box and whisker plots (Figure 7) and frequency distribution curves (Figures 8 and 9) of roughness computed within a 7 × 7 m window also show that alluvial fan surfaces of different ages have distinctively different frequencies and magnitudes of surface roughness values derived from the three parameters of slope, curvature, and aspect. [28] Among the eleven maps of combined roughness developed using the fuzzy gamma operation, the roughness map developed with a gamma value of 0.6 most closely predicted the observed alluvial fan map. The overall prediction accuracy of the combined roughness map is ~ 61%, while the prediction accuracies of slope-, curvature-, and aspect-based roughness maps are ~ 43%, ~47%, and ~53%, respectively (Figure 10 and Table 2). Comparisons based
compared to surrounding older units was classified from the r max map, whereas older units (Qf4, Qf3, Qf2, and Qf1) that are mostly surrounded by the Qf5 unit were classified using r min map. [25] All classified roughness maps were statistically compared with the observed geomorphic map. The agreements between the pairs of predicted and observed fan units were determined in percent by taking the ratio of area matched between the pair to the area of the observed unit in the pair. The overall goodness of agreement between the predicted and observed maps was also determined in percent by taking the ratio of total correctly predicted area to the total area of the observed map (Table 2).
4.
Results
[26] Five prominent alluvial fan units (Qf1 to Qf5) were differentiated from the expert-based geomorphic mapping component of the study. The Qf2 and Qf5 units comprised the largest areas, whereas the Qf3 and Qf4 units comprised the least (Figure 2b). For each window size and for each variable included in this study, ~6,000,000 individual surface roughness values were derived from the lidar topographic data (Table 3). Roughness values from slopes steeper than 3° were excluded from the analysis. The excluded area consists mostly of colluvial sideslopes and channel walls formed along incised channels across Qf1 and Qf5 units and comprises ~12% of the study area. Anomalously high surface roughness values from >3° slopes were excluded so that the topographic elements of these slopes would not be included in the surface roughness analysis. We regard fully 22
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
Figure 10. Roughness maps of alluvial fan surfaces based on (a) slope, (b) curvature, (c) aspect, and (d) a normalized combination of all parameters. The roughness values in (Figure 10d) the combined map are dimensionless because the map was developed by standardizing the roughness values of each topographic parameter from 0 to 1 and then combining them using fuzzy operators. Note the roughness values associated with developed areas (i.e., roads) are significantly different than their surroundings, suggesting that the model is not suitable for mapping alluvial fans in disturbed areas. between the observed and predicted areas of the Qf3 and Qf4 units can be attributed to: (1) similarities in slope and curvature characteristics of the Qf3 and Qf2 surfaces and (2) similarities in aspect characteristics of the Qf4 and Qf5 surfaces (Figure 6).
on prediction accuracies indicate that the combined roughness values best discriminate the surface characteristics of the observed alluvial fan units. The oldest Qf1 and Qf2 units and youngest Qf5 unit had the best match percentage (Figure 11 and Table 2). The reason for the inaccurate match
Figure 11. Base layers used to compare the multiparameter approach of delineating alluvial fans to fans mapped by field and image analysis techniques. (a) Combined roughness map created from the application of a 20 × 100 m moving window (mean filter) in eight directions with interval of 45° azimuths. (b) Predicted age-based geomorphic map developed from the classification of the combined roughness map. (c) Observed age-based geomorphic map developed by using traditional field and image analysis techniques. (d) Map showing areas predicted as true and false from the combination of maps in Figures 11b and 11c (see Table 2 for details). 23
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
occurring and have high products of frequency and magnitude, contribute most to the overall surface roughness of the Qf5 unit. Results show little variation in slope-, curvature-, and aspect-derived roughness values that have the highest frequencies and highest products of frequency and roughness magnitude on individual fan units (Table 3). Visual inspection of roughness values which have high frequency and high products of frequency and magnitude was performed by overlaying the roughness maps on aerial imagery. By doing so, it was apparent that the roughness values coincided with bar-and-swale features, plant mounds, and plant scars on the Qf5, Qf4, and Qf3 units. In contrast, roughness values on the Qf2 and Qf1 units were associated primarily with shallow, incipient channels forming surface undulations that likely developed by long-term sheet wash erosional processes (Table 3).
[29] If we consider slope-, curvature-, and aspect-based roughness observed in a 7 × 7 m moving window as a proxy for the magnitude (size) of surface roughness elements, then the magnitudes and frequencies (number of occurrence) of these elements on different aged surfaces are well characterized by power functions with rollovers (Figure 9). These power function curves (Figures 9a, 9c, and 9e) show that small roughness values occur more frequently on older alluvial fan surfaces and large roughness values occur more frequently on younger alluvial fan surfaces and thereby imply that low-magnitude topographic features dominate older fan surfaces, whereas high-magnitude topographic features dominate younger fan surfaces. Although our algorithms can detect distinctive surface roughness, the question remains as to what types of topographic features are contributing to the detected roughness of each alluvial fan unit. To answer this question, we considered that the overall roughness of an alluvial fan surface is a function of the frequency and magnitude of the topographic features; therefore, topographic features having high frequency and high magnitude dictate the overall roughness of an alluvial unit. Because of the lack of data on frequencies and magnitudes of topographic features on each alluvial fan surfaces, we used frequency and magnitude of modeled roughness values as their surrogates. The frequency-magnitude relationships (Figures 8 and 9) of the data were then evaluated to determine the values of roughness which contribute most to the overall roughness of each alluvial fan surface. The resulting roughness values were then overlaid on aerial imagery to determine the topographic features representing these values. [30] Relations between frequency and magnitude have been used to explain processes in fluvial [e.g., Wolman and Miller, 1960] and hillslope [e.g., Guthrie and Evans, 2007] geomorphology. In fluvial geomorpholgy, the geomorphic work performed by a river has been computed as a product of the frequency and magnitude of flow, whereas in hillslope geomorphology, the work performed by landslides has been computed as the product of landslide frequency and magnitude (area). Although geomorphic forces and their rates of occurrence can be significantly different in fluvial and hillslope systems, we consider that the concept of geomorphic work is also applicable to characterizing surface roughness on alluvial fans, because the magnitudes of the topographic parameters of slope, curvature, and aspect are a reflection of both primary depositional and subsequent erosional and surface weathering processes. For example, smooth fan surfaces are the result of long-term geomorphic work by soil geomorphic processes, whereas rough fan surfaces reflect recent alluvial deposition that has not been significantly affected by these processes. We consider that roughness values which have high frequency and high products of frequency and magnitude contribute most to the overall surface roughness. Such values of roughness for alluvial fan surfaces of different ages (Table 3) were determined from the plots of roughness values in x axis against roughness frequency and frequency-magnitude product in y axis (Figure 9) by looking at where the curves for frequency and frequency-magnitude product are at their maximum and then projecting to the x axis to find the range of roughness values. For example, plots indicate that the geometric irregularities having SD of slope of 0.8°–2.5°, SD of curvature of 0.09– 0.3, and SD of aspect of 80°–90° (shaded areas in Figure 9), which are frequently
5.
Discussion
[31] The results of our analysis show that SDs of slope, curvature, and aspect can be used as predictors of surface roughness to differentiate alluvial fan surfaces (Figure 6); however, there are variations among the distributions of the roughness values determined from slope-, curvatureand aspect-based curves with respect to the observation scale and alluvial fan age. For example, the slope-derived mean roughness values at small observation window lengths (3 m–11 m) are similar for the Qf1 and Qf2 units, but the curvature- and aspect-derived roughness values within the same window lengths are different (Figure 6). Furthermore, the frequency distributions of aspect-derived roughness are not similar to the frequency distributions of slope- and curvature-derived roughness values (Figure 8). But why do these roughness magnitude and frequency curves vary? [32] A possible explanation to this question is that fan surfaces consist of features having diverse geometries and no single parameter capture the signature of all types of topographic geometries. For example, the SD of slope captures morphologic variation of a surface only in the vertical dimension (relief) and aspect captures the variation only in the horizontal dimension (azimuth), whereas curvature (tangent) captures the variation in the pole direction to the surface. The differences in the roughness curves, therefore, reflect the three-dimensional geometry of a typical alluvial fan surface. The roughness values for the Qf5 unit shown by all curves (Figure 6) suggest that the surface geometry of this unit has the highest magnitude of roughness in both the vertical and horizontal dimensions compared to the roughness magnitudes of Qf1–Qf3 surface geometries. The surface roughness of this young alluvial fan unit is a reflection of well-developed bar-and-swale microtopographic relief related to an extensive network of braided distributary channels. Comparison of the curves of slope- and curvature-derived roughness (Figure 6a) between the Qf5 and Qf4 units suggests that these units significantly differ in relief and curvature. In contrast, the aspect-derived roughness values (Figure 6c) indicate that Qf5 and Qf4 units have topographic features of almost similar aspect, which are probably related to similar channel characteristics. We observed in the field that both Qf5 and Qf4 units have distributary patterns of highly sinuous channels; however, Qf4 surfaces are more subdued (less microtopography) than Qf5 surfaces. Taken together, the 24
REGMI ET AL.: MAPPING ALLUVIAL FAN SURFACE ROUGHNESS
[35] The method of integrating the surface geometries of slope, curvature, and aspect used in this study, a fuzzy logic approach, is simple and reproducible. This is the first study to employ high-resolution digital topographic data to successfully predict and then test the surface characteristics of a suite of variable-age alluvial fan surfaces using multiparameter surface geometries. The results of this analysis suggest that the combined use of slope-, curvature-, and aspect-based topographic parameters predicted surface roughness of alluvial fans more accurately than a single topographic parameter (Table 2). The multiparameter approach resulted in a ~61% prediction accuracy for differentiating alluvial fan surfaces with respect to age when compared to an observed data set prepared by traditional geomorphic mapping techniques (Figure 11 and Table 2). [36] We suspect that 39% failure rate of the model is related principally to both the exclusion of slopes >3° and the contrasting scales between map unit boundaries. The failure rate may also be related to lack of accounting for surface roughness variability on each map unit owing to particle size compositions and provenance of surface deposits, along with not excluding areas with anthropogenic surface disturbance in the form of roads and developed areas. [37] The main objective of this study was to identify and then separate alluvial fans by surface age using modeled surface roughness. To characterize surface roughness and relate it to a time-dependent landform evolution model, we used preserved and intact surfaces with slopes
