Geomorphic signatures of deltaic processes and ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH: EARTH SURFACE, VOL. 118, 1838–1849, doi:10.1002/jgrf.20128, 2013

Geomorphic signatures of deltaic processes and vegetation: The Ganges-Brahmaputra-Jamuna case study Paola Passalacqua,1 Stefano Lanzoni,2 Chris Paola,3 and Andrea Rinaldo2,4 Received 11 January 2013; revised 23 July 2013; accepted 9 August 2013; published 12 September 2013.

[1] Deltas are complex ecogeomorphic systems where features such as channels and interchannel islands are present over a wide range of spatial scales. A quantitative description of the morphology of deltas is fundamental to address how they react to changes in climate forcing and human pressure. In particular, it is interesting to ask how the distributary patterns we observe in coastal areas around the world result from processes and external forcing acting on deltas, and how such patterns might be related to deltaic function, vulnerability, and resilience. Using the example of the Ganges-Brahmaputra-Jamuna Delta, we show that the statistics of island size, shape factor, aspect ratio, and nearest-edge distance show distinct spatial patterns. Comparison between regions identified by our statistical analysis and a physiographic zonation of the delta suggests that the planform extracted from satellite imagery carries the signature of processes responsible for delta formation and evolution and of vegetation. The tidal region is characterized by high channel density, small islands, and short nearest-edge distance (shortest straight-line distance to the nearest water). The results suggest that regions of the delta characterized by presence of vegetation and active transport of water and sediment are statistically distinct from less active regions. Further, we perform a weighted connectivity analysis of the channel patterns based on channel width. The analysis suggests that channels connecting the upper portion of the delta to the coast do not play a significant role in the transport of water and sediment. Citation: Passalacqua, P., S. Lanzoni, C. Paola, and A. Rinaldo (2013), Geomorphic signatures of deltaic processes and vegetation: The Ganges-Brahmaputra-Jamuna case study, J. Geophys. Res. Earth Surf., 118, 1838–1849, doi:10.1002/jgrf.20128.

1. Introduction [2] Delta distributary networks span a wide range of spatial and temporal scales: channel widths, for example, range in scale from hundreds to thousands of meters in the main network, down to a few meters for drainage distributors within islands; channel migration and avulsions occur on periods up to thousands of years, while the reworking of channel bed and banks due to flood events can occur within a single year [e.g., Bristow, 1987; Slingerland and Smith, 2004; Ashworth et al., 2007; Syvitski, 2008]. Channels are the conductors and distributors of water and 1 Department of Civil, Architectural and Environmental Engineering and Center for Research in Water Resources, The University of Texas at Austin, Austin, Texas, USA. 2 Dipartimento IMAGE and International Center for Hydrology ‘Dino Tonini’, Università di Padova, Padua, Italy. 3 Department of Earth Sciences and St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota, USA. 4 Faculté ENAC, École Polytechnique Fédérale, Lausanne, Switzerland.

Corresponding author: P. Passalacqua, Department of Civil, Architectural and Environmental Engineering and Center for Research in Water Resources, The University of Texas at Austin, 301 E. Dean Keeton St. STOP C1700, Austin, TX 78712-2100, USA. ([email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9003/13/10.1002/jgrf.20128

sediment through the system. Although the channel network distributes a range of materials (water, sediments, nutrients, organisms), sediment is critical in terms of creating and maintaining the delta structure [Edmonds et al., 2011]. Deltaic sediments are also responsible for roughly 45% of global carbon burial [Hedges and Keil, 1995]. [3] Deltas are threatened by several factors, including anthropogenic disturbance (e.g., upstream sediment trapping due to dam construction, sediment mining, navigation structures, accelerated subsidence due to oil or water extraction), natural subsidence, and eustatic sea level rise [Ericson et al., 2006]. The response of a deltaic system to these forcings can be dramatic and result in loss of human lives, economic resources, and environmental services. Yet, under the right conditions, deltas are resilient, capable of adapting to a changing environment and recovering from damage caused by extreme events, such as storms [Paola et al., 2011]. [4] Looking at delta distributary patterns, it is natural to ask how the system’s morphological organization is the result of the processes acting on the delta, and how the distributary patterns might be related to deltaic function, vulnerability, and resilience. Does the spatial structure of the deltaic network carry information about the dominant processes acting on it? Can we link connectivity of distributary fluvial patterns, remotely acquired and objectively manipulated, to deltaic ecosystem services? Can a quantitative

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Figure 1. Landsat image of the GBJ Delta. Data specifications: Landsat GeoCover TM 1990 Edition Mosaics, tiles N– 45–20 and N–46–20; spatial resolution 28.5 m; spectral TM bands: 7 (mid-infrared), 4 (near-infrared), 2 (visible green), here represented in RGB false color. Source for this data set is the Global Land Cover Facility, www.landcover.org. The physiographic regions active, inactive, tidal are based on a geological map of Bangladesh developed by the Geological Survey of Bangladesh [Alam et al., 1990] and by the USGS [Persits et al., 2001].

reading of the network help us understand and predict the future of these fascinating and critical coastal systems? [5] Among the early quantitative studies of delta networks was that of Smart and Moruzzi [1972], who focused on topology and proposed representing the deltaic network as a directed graph and analyzing various functions of vertex and link number. Among recent efforts, Syvitski [2005] and Syvitski and Saito [2007] illustrated empirically the scaling of the number of distributary channels with respect to river length and delta gradient, and Edmonds et al. [2011] proposed five metrics (fractal dimension, distribution of island size, nearest-edge distance, synthetic distribution of fluxes at the shoreline, and nourishment area) for describing deltas and comparing natural and experimental systems. [6] The recent availability of satellite imagery over much of the Earth (Figure 1 shows an example for the GangesBrahmaputra-Jamuna Delta) [Syvitski, 2005] has greatly improved the quantitative analysis of geomorphic features. Examples of features mapped from satellite imagery include: number and size of distributary channels [Syvitski, 2005; Syvitski and Saito, 2007], container valleys, floodplain depressions, oxbow lakes [Syvitski et al., 2012], floodplain channel network and morphology [Trigg et al., 2012], shoreline erosion/accretion patterns [Aly et al., 2012], and flood area and volume [Rakwatin et al., 2013]. In terms of automatic feature extraction, the detection of roads and river networks has been addressed [e.g., Liu et al., 2001; Dillabaugh

et al., 2002; Soille and Grazzini, 2007; Grazzini et al., 2010] by using mathematical morphology and other approaches employed in the extraction of linear features from images [e.g., Quackenbush, 2004]. However, these techniques usually require manual intervention and post-processing due to the complexity and variability of channel patterns. This is particularly true in coastal areas, where low gradients and the presence of features such as sediment plumes make it challenging to separate channels from other water bodies within the image. Recent efforts have focused on the extraction of the shoreline [Shaw et al., 2008; Geleynse et al., 2012], rather than the entire channel network. [7] In this paper, we propose a statistically based analysis framework for deltaic networks extracted from satellite imagery. Our goal is to identify key metrics and attributes of the network (e.g., island geometry, channel width), analyze their statistical behavior, and explore their potential linkages to processes acting on the delta. In particular, we are interested in understanding whether the spatial structure of the deltaic network carries any signature of the processes responsible for delta formation and evolution and whether a statistical analysis of deltaic network metrics may highlight scaling breaks and characteristic scales of delta forming processes, vegetation type, and anthropogenic modifications. Linkages between network statistics and processes have been previously explored in alluvial rivers [Rodriguez-Iturbe and Rinaldo, 1997] and tidal channel networks [Fagherazzi et al., 1999; Marani et al., 2003]. We apply our analysis framework to the Ganges-BrahmaputraJamuna (GBJ) Delta, one of the largest and most densely populated deltas in the world. [8] The paper is organized as follows: section 2 describes the proposed analysis framework; in section 3, we describe the GBJ Delta; the application of the analysis method is presented in section 4; we discuss the analysis results in section 5; and we present conclusions in section 6.

2. Background: Statistical Analysis to Identify and Interpret Delta-Forming Processes [9] Our approach is based on the analysis of satellite imagery. We acknowledge the importance of the third dimension (topography and bathymetry), as well as of the fourth dimension (time). But at present, planform data are far more readily available than high-resolution topography, and so we wish to determine how much information can be obtained from planform alone. Also, the generally low relief of deltas means that suitably accurate elevation data, e.g., submeter resolution lidar data sets, are typically available only for areas of small extent, rather than the scale of a deltaic system such as the GBJ Delta. [10] Likewise, we focus on a time snapshot of the GBJ Delta. We acknowledge that channels are hydrodynamic and the information extracted from satellite imagery changes due to several factors including tides and seasonal changes in vegetation cover. While ignoring temporal information prevents us from capturing short-term dynamical changes in the system, we focus on the statistics of the network structure, particularly of island geometry. Apart from extreme floods, variations due to temporal fluctuations in water level would not significantly change the statistical distribution of island geometry over the delta.

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[11] The first analysis step consists of extracting the channel network and validating it. We then define key metrics and descriptors, taking into account the intrinsic distributary nature of deltaic networks and building on the previous work discussed above. Finally, we analyze the various quantities statistically. 2.1. Channel Network Extraction From Satellite Imagery [12] In order to extract the channel network from satellite imagery, we use a relatively simple approach: taking advantage of tools available in ArcGIS (as well as ENVI and other software packages), satellite imagery can be exploited through unsupervised and supervised classifications. With an unsupervised classification, classes are identified based on the spectral signature of the image such that each pixel within the image can be assigned to a class, e.g., deep water, vegetation cover, and soil. With a supervised classification, classes can be clustered in two groups, water and land, such that water pixels can be isolated from the rest of the image. The channel network obtained from the unsupervised and supervised classifications is thus a wet map of the submerged pixels (map of the water surface). An additional product of the binary classification of water and land pixels is the map of interchannel islands, here defined as channel-bounded land masses. [13] The binary classification into water and land pixels can result in detection of spurious features and isolated water bodies that are not necessarily part of the deltaic channel network, requiring further manual intervention. Once the water pixels are identified, if desired, channel pixels can be separated from ocean pixels using shoreline extraction techniques [Shaw et al., 2008; Geleynse et al., 2012]. 2.2. Metrics and Deltaic Channel Network Descriptors [14] Once the channel network is extracted from the satellite image, key metrics representative of the deltaic network can be identified and computed. A variety of metrics is available for the analysis of river networks [Rodriguez-Iturbe and Rinaldo, 1997], some of which have been successfully extended to tidal networks [Fagherazzi et al., 1999; Rinaldo et al., 1999a, 1999b; Marani et al., 2003], and submarine tributary channel networks [Straub et al., 2007]. However, these metrics are not readily applicable to distributary networks since attributes such as upstream length and elongation cannot be uniquely computed. In addition, while the total planform fraction occupied by water (wet fraction) is vanishingly small in most tributary networks, this is not the case for most deltas. Metrics specific to distributary systems are thus needed [Edmonds et al., 2011]. 2.2.1. Island Area, Shape Factor, and Aspect Ratio [15] In many deltas, including the GBJ Delta, the channel network includes confluences and bifurcations, such that nearly the whole deltaic landmass comprises islands bounded by channels. Islands are among the best descriptors of a deltaic network, since they reflect the morphology of the channels and the relationship among neighboring channels. In process terms, we believe there is a difference between islands whose length scale is comparable to or less than the width of the bounding channels, and islands whose length scale is much greater than that of the bounding channels. The former might be called ‘true’ islands and

bars, strongly worked by channel processes, while the latter are simply channel-bounded land masses. We lump them together here for simplicity but consider this a point worth further study. [16] Metrics of interest here include island area, shape factor, and aspect ratio. The island area reflects channel connectivity: areas of the delta characterized by small islands, for example, represent highly connected parts of the network. The island shape factor ˇ , here defined as the ratio pof the wetted perimeter P to the square root of the area A, quantifies the shape of the island and the degree of drainage within the island. The wetted perimeter used to evaluate ˇ , in fact, includes also the overall length of the channels dissecting the island. As such, the shape factor ˇ is a measure of relative boundary roughness [Wolinsky et al., 2010]. The island aspect ratio is given by the ratio of the principal axes (ratio of the major axis to the minor axis of the ellipse with the same normalized second central moments), and quantifies the degree of elongation of the islands. If = 1, the shape is equant, if >> 1 the shape is elongated. 2.2.2. Nearest-Edge Distance [17] The nearest-edge distance L is defined as the shortest straight-line distance from any land pixel to the nearest water (channelized or unchannelized) [Edmonds et al., 2011]. As such, the statistical analysis of nearest-edge distance quantifies spatial variations in distributary channel density. Areas of the delta with relatively short nearest-edge distance, for example, indicate the availability of nearby sources of water. 2.2.3. Channel Width [18] Channel width can be computed along each extracted channel within the deltaic network as the local shortest distance between the channel edges. Assuming the width has a consistent scaling to landscape-forming discharge [e.g., Leopold et al., 1993], the analysis of mean channel width for channel reach gives information about the water distribution along the system. [19] In fluvial basins the landscape forming discharge Q (and, hence, the cross section geometry) is usually found to be proportional to the total contributing area A, provided the basin dimension does not exceed a scale characteristic of the heterogeneity of meaningful spatial patterns of intense rainfall. This proportionality commonly holds for several orders of magnitude. In tidal channels it is the tidal prism that determines the cross section geometry, relating the total water volume entering the channel watershed during a characteristic tidal cycle (i.e., spring tide) to the size of a given cross section [Rinaldo et al., 1999b; D’Alpaos et al., 2010]. Consequently, the width of fluvially dominated channels stays constant over length scales of hundreds to thousands of widths [Rodriguez-Iturbe and Rinaldo, 1997], while tidally dominated channels show strong variations in space [Leopold et al., 1993; Marani et al., 2003]. In systems like the GBJ Delta, the scenario is much more complex, owing to the different nature of dominant landscape forming processes likely active in the various delta regions (e.g., fluvial discharge, tidal currents, wind waves, storm surges). These differences should however be revealed by an analysis of the channel width of the type pursued in Rinaldo et al. [1999b]. Indeed, the power law exponents that relate channel width, flow depth, and mean velocity to the formative discharge are different for terrestrial rivers and tidal estuaries [Myrick and Leopold, 1963; Sassi et al., 2012].

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[20] Looking at the deltaic network as a graph, the network can be seen as composed of nodes (apex, junctions, bifurcations, outlets) and links connecting the nodes. Thinking of water and sediment as a form of information transmitted between nodes, an estimate of mean channel width per channel link quantifies link strength and allows more substantive analysis of network connectivity. If the channel carries a significant amount of water (and hence has a relatively large width), that connection should be present regardless of flow variations during the year. Conversely, relatively narrow channels are less likely to transport water during drought and low discharge periods. We can thus think about channel width as a measure of the strength of connectivity among network nodes. Our use of the term “strength” is analogous to the “weight” used in mathematical representations of networks as an adjacency matrix when a connection between two nodes is not represented in binary fashion (1 if two nodes are connected, 0 otherwise) but with a real number that represents how strong that connection is [Newman, 2010]. The strength of links within a network thus provides important information in network analysis: in the case of deltas, water and sediment can be transferred between two nodes as long as a connection (link) exists; however, changes in external forcing (e.g., discharge, wind, tides) and disturbances acting on the system (e.g., deposition) can easily lead to the removal of weak network links, resulting in lack of information transfer among network nodes. While here we focus on water and sediment as information, and channel width as a measure of connectivity strength, it is interesting to think about similar weights to quantify connectivity strength in terms of, for example, dissolved nutrients, or organisms. While we only have channel width estimations available from satellite imagery, we note that the link strength distribution could change depending on the quantity analyzed. 2.2.4. Oxbow Density [21] Channel avulsions and cutoffs result in abandoned channels and oxbow lakes. The presence and spatial density of these features may indicate the age of a given area within the delta and/or the frequency of channel migration through time. At present, without independent age control on the oxbows, we cannot separate these effects, but we consider it worth mapping oxbow density nonetheless, for example, to investigate the possibility that oxbow density may be related to vegetation and land-use patterns. 2.3. Statistical Analysis [22] The metrics just described should vary among deltas and could also vary within the same system, especially if it is large relative to the characteristic channel size. While statistical descriptors such as the mean and the variance may help to summarize the salient characteristics of a system, they are not sufficient to describe variables that vary over a wide range of scales [Newman, 2005]. Analysis of the probability density function (PDF) or the cumulative distribution function (CDF) is helpful in this respect, particularly in identifying statistical changes in the behavior of the system and corresponding scales of change. [23] In network theory, it is quite common to analyze the distribution of network metrics and the possible presence of power law behavior [e.g., Newman, 2005; Clauset et al., 2009]. Power laws suggest that certain network properties

Figure 2. Map of the GBJ Delta. The map shows a zonation of the delta into four main geomorphic regions: active, tidally active, mature, moribund. The Sundarbans (mangrove forest) is located within the tidally active area. Map source: National Encyclopedia of Bangladesh (www.banglapedia.org). are scale free, i.e., the statistical characteristics of the system do not change across the range of scales over which the power law applies. Lack of power law behavior, or breaks or thresholds in the power law, highlight characteristic scales of processes acting within the system. Here the presence or absence of scale-free behavior in deltaic networks is relevant as it could suggest ranges of scales over which processes give rise to (internally) statistically similar morphology, such as channels and islands.

3. Study Area [24] The GBJ Delta, located in Bangladesh and eastern India, includes the Ganges, Brahmaputra, Jamuna, Padma, and Meghna Rivers [e.g., Coleman, 1969]. With an area of 100, 000 km2 , the GBJ Delta is one of the largest in the world. The rivers discharge nearly 1.7 105 m3 /s to the Bay of Bengal and transport about 106 tons/day of suspended sediment during flood events [Coleman, 1969] for a total of about 109 tons/year [Goodbred and Kuehl, 2000a]. Channel width ranges from the scale of meters within islands, to the scale of kilometers in the main channels (Figure 1). Along the western coast of the Delta lie the Sundarbans, a tidal halophytic mangrove forest (location shown in Figure 1 with a white dotted boundary). The Sundarbans and most of the delta experience significant tidal influence as the system is subject to a macrotidal regime with a semidiurnal amplitude of 4.7 m [Goodbred and Kuehl, 2000a]. The extent of the tidally influenced region is shown in Figure 1 (white solid boundary). In the same figure, the northern portion of the delta is divided into active (yellow dotted boundary) and

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(a)

(b)

(c)

(d)

Figure 3. Example of channel extraction from satellite imagery. Several oxbow lakes are present in the upper portion of the GBJ Delta. (a) The majority of the oxbows (about 80 out of 120) are connected to channels. An unsupervised classification followed by a supervised classification performed in ArcGIS, allows the extraction of the channel network. Disrupted channels, spurious water pixels, and isolated water sources are present in the (b) extracted network. By inspection of Google Earth imagery, (c) oxbows connected to nearby channels and spurious pixels can be identified. By manual intervention, (d) spurious pixels are removed and links between oxbows and nearby channels traced where Google Earth imagery shows a connection between the oxbow and the channel.

through a comparison with Google Earth imagery. Links between oxbows and nearby channels were manually added where Google Earth imagery showed a connection between the oxbow and the channel (Figures 3c and 3d). Repeating these operations on the whole delta converts the wet map to the channel network shown in Figure 4. [26] The extracted channel network shows how channel morphology and channel density vary spatially within the GBJ Delta. Channel density is particularly high near the coast and within the mangrove forest (Figure 1). The northwestern region is characterized by a large number of oxbow lakes. Through analysis of Google Earth imagery, we found that 65% of the oxbow lakes (80 out of 120) in the northwestern portion of the delta are connected to channels. These are likely relict fluvial channels whose lower reaches have been tidally reworked, as suggested by Fagherazzi [2008]. The number of oxbow lakes present in the northeastern portion of the delta is much smaller (about 10). 4.2. Island Size and Geometry Analysis [27] The map of interchannel islands of the GBJ Delta (Figure 5) shows that islands of large area are located within the upper portion of the delta, while smaller islands are mainly located close to the coast, particularly within the mangrove forest, and along the Ganges and Padma Rivers, and the main branches of the Meghna River. The observed CDF of island area (Figure 6) indicates a relatively well identified regime where power law behavior (and log-log linear distribution) with exponent ˛ = 1.9 for island area 88°E

inactive (red dotted boundary) regions. The physiographic zonation of the GBJ Delta into three regions (tidal - near the coast, including the Sundarbans, active - corresponding to the area occupied by the major rivers, and inactive - the upper western portion of the delta) is based on a geological map of Bangladesh developed by the Geological Survey of Bangladesh [Alam et al., 1990] and the report and digital data released by the U.S. Geological Survey [Persits et al., 2001]. The U.S. Geological Survey digital data covers only the Bangladesh portion of the GBJ Delta; we have extended the region boundaries to the West Bengal (India) portion based on an additional physiographic map of the whole delta distributed by the National Encyclopedia of Bangladesh (Figure 2).

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4. Analysis of the GBJ Delta Network

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4.1. Channel Network Extraction From Satellite Imagery and Network Analysis [25] For the present study, we use Orthorectified Landsat Thematic Mapper Mosaics available at the resolution of 28.5 m (source: Global Land Cover Facility, www. landcover.org), shown in Figures 1 and 3a. The images have three spectral TM bands (7 mid-infrared, 4 near-infrared, and 2 visible green), represented in RGB false color in Figure 1. By applying unsupervised and supervised classification techniques, as described in section 2, we obtained a noisy wet map, as shown in Figure 3b. The wet map requires manual intervention due to the presence of disrupted channels, spurious water pixels, and isolated water bodies. These spurious features were identified and removed

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Figure 4. Channel network of the GBJ Delta extracted from the satellite image in Figure 1. The channel network map shows how channel morphology and channel density largely vary among different portions of the delta. Drainage density is particularly large within the tidally dominated region of the delta. The northwestern portion of the delta (inactive) is characterized by a large number of oxbow lakes. The number of oxbow lakes present in the northeastern portion of the delta is instead much smaller (about 10). The gray boundaries represent the zonation shown in Figure 1.

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89°

90°

Table 1. Estimated Power Law Parameters and p-Values

91°

log(A)

A ˇ L

3.39 24° N

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N 0

xO min

˛O

ntail

p

1.96 107 ˙ 4.2 106 13.7 ˙ 2.3 2.7 ˙ 0.6 1.054 103 ˙ 72.2

1.9 ˙ 0.05 5.2 ˙ 0.6 3.7 ˙ 0.36 2.96 ˙ 0.1

353 ˙ 50 138 ˙ 206 461 ˙ 138 403 ˙ 48

0.78 0.64 0.01 0.43

Metric 9.73

25 Km

100

Figure 5. Channel network of the GBJ Delta and islands (colormap based on the logarithm of island area). Islands of larger area are located within the northern portion of the delta, while smaller islands are located near the coast and along the main rivers (Ganges, Padma, Meghna). A > Amin = 1.96 107 m2 holds. The goodness of fit between the data and the model is given by the p value which quantifies whether the difference between the data and the hypothesized model can be attributed to statistical fluctuations (resulting in a p-value close to 1), or if the difference is due to a lack of fit of the model to the data (resulting in a small p-value) [Clauset et al., 2009]. The p-value of the fitted power law of island area is 0.78, implying that a power law distribution is not rejected at a conservative significance level (e.g., p > ˛ = 0.1 with 10% representing an already conservative significance level). The analysis was performed with the approach and tools made available by

Clauset et al. [2009]. Table 1 shows the estimated power law model parameters (lower bound xO min , exponent ˛O , and number of data points in the tail ntail ), their estimated uncertainty, and the p-value. The total number of islands in the delta (at the resolution of our satellite image) is 1291, of which 938 have area A < Amin and are thus located outside the power law regime. These sub-power law islands are numerous, but quite small, covering only 7% of the exposed land area. The map of the logarithm of island area normalized by Amin (Figure 7) shows that smaller islands outside the power law regime are predominantly located within the mangrove forest and along the Ganges and Padma Rivers, and the main branches of the Meghna River. This result suggests that these portions of the GBJ Delta behave differently than the rest of the system. The superimposed physiographic boundaries indicate that the smallest islands are mainly located within the tidal region, particularly within the mangrove forest. The break in the power law emerging from the observed CDF of island area (Figure 6) can then be interpreted as a distinction between the part of the delta near the coast and the upper part, particularly the inactive region. [28] Islands vary not only in size, but also in shape (Figure 5). This can be quantified by looking at the statistical distribution of the shape factor ˇ . It is worth noting 88°E

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log(A/Amin) 2.44 -3.90 24° N

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Pr(A ≥ a)

10-1

α = 1.9

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109

a [m2]

Figure 6. Empirical distribution of island area and fitted power law distribution. The power law model has exponent ˛ = 1.9 and lower bound (to the power law behavior) Amin = 1.96 107 m2 . The p-value for the fitted power law model is 0.78.

Figure 7. Channel network of the GBJ Delta and map of logarithm of island area normalized by Amin = 1.96 107 m2 . The islands outside the power law regime shown in Figure 6 are mainly located near the coast and along the main rivers (Ganges, Padma, Meghna). The superimposed physiographic boundaries (white) show that larger islands are mainly located within the inactive portion of the delta.

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α = 3.7

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α = 5.2 Pr(γ ≥ g)

Pr(β ≥ b)

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Figure 8. Empirical distribution of island shape factor (defined as ˇ = P/A0.5 , where P is perimeter and A is area) and fitted power law distribution. The power law model has ˛ = 5.2 and lower bound (to the power law behavior) ˇmin = 13.7. The p-value for the fitted power law model is 0.63.

Figure 10. Empirical distribution of island aspect ratio and fitted power law distribution. The fitted power law model has ˛ = 3.7 and lower bound (to the power law behavior) min = 2.7. The p-value for the fitted power law model is 0.01.

that the perimeter P is larger not only for islands of larger size, but also for islands with a significant number of intraisland channels. A small but highly channelized island will thus be characterized by a large shape factor. We note that the extraction of the channel network depends on the image resolution; thus, the metrics here analyzed are resolutiondependent. Part of these intraisland channels, characteristic of the islands within the mangrove forest, could in fact be through going, resulting in islands of even smaller size. The

resolution-dependency of this analysis is unavoidable and the mangrove forest too thick for assessing the continuity of the intraisland channels from Google Earth imagery, as we did for assessing the connectivity of the oxbow lakes. [29] The observed CDF of island shape factor ˇ (Figure 8) shows that a power law distribution with exponent ˛ = 5.2 holds for ˇ > ˇmin = 13.7 (Table 1). The exponent is quite large compared to the common range 2–3 [Clauset et al., 2009]. The p-value of the fitted power law model is 0.63, implying that the model is not rejected at a conservative significance level. The map of the logarithm of

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Figure 9. Channel network of the GBJ Delta and map of logarithm of island shape factor normalized by ˇmin = 13.7. Islands with small shape factor are mainly located near the coast and along the main rivers (Ganges, Padma, Meghna). The superimposed physiographic boundaries show that islands with large shape factor (rougher) are located within the inactive portion of the delta.

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Figure 11. Channel network of the GBJ Delta and map of island aspect ratio normalized by min = 2.7. The majority of the elongated islands is located near the coast and along the main rivers (Ganges, Padma, Meghna), but the distribution of aspect ratio within the delta is heterogeneous.

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log(L/Lmin) 1.10 -1.57 24° N

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Figure 12. Channel network of the GBJ Delta and map of the logarithm of nearest-edge distance L. The nearest-edge distance is calculated as the shortest straight-line distance from the nearest source of water (channelized or unchannelized) from any land pixel within the delta. The smallest values of nearest-edge distance are located near the coast, in particular within the mangrove forest.

Figure 14. Channel network of the GBJ Delta and map of the logarithm of nearest-edge distance normalized by Lmin = 1.054 103 m. The superimposed physiographic boundaries show that islands with short nearest-edge distance are mainly located within the tidal portion of the delta, particularly within the mangrove forest.

island shape factor normalized by ˇmin (Figure 9) shows that islands outside the power law regime are located near the coast and along the Ganges and Padma Rivers, and the main branches of the Meghna River, containing 1153 (out of a total of 1291) relatively small islands. The superimposed physiographic boundaries indicate that these regions roughly coincide with the tidal portion, particularly the mangrove forest, and the active portion of the delta. Islands within these regions thus tend to have smaller ˇ values, resulting in

less rough shapes than the northwestern inactive portion of the delta. [30] The observed CDF of island aspect ratio (Figure 10) indicates a relatively well identified regime where a power law distribution with exponent ˛ = 3.7 above threshold equal to min = 2.7 (Table 1) may hold. The pvalue is 0.01; the power law model fit is thus not as robust as for other metrics analyzed here (the model would not be rejected only at significance level 1% or lower). The map of the logarithm of the island aspect ratio normalized by min (Figure 11) shows that although the majority of the elongated islands are located near the coast and along the Ganges and Padma Rivers, and the main branches of the Meghna River (except for 6 islands, out of 461), the spatial distribution of the island aspect ratio is more heterogeneous than island area and island shape factor. In particular, the mangrove forest appears to include both round and more elongated islands. This is also supported by the fact that a sharp break is not observed in the CDF of island aspect ratio (Figure 10).

100

α = 2.96

10-1

10-2

10-3

10-4 1 10

102

103

104

105

Figure 13. Empirical distribution of nearest edge distance (maximum value per island) and fitted power law distribution. The power law model has ˛ = 2.96 and lower bound (to the power law behavior) Lmin = 1.054 103 m. The p-value for the fitted power law model is 0.42.

4.3. Nearest-Edge Distance [31] The map of nearest-edge distance L (Figure 12) shows that islands with the smallest values of L are located near the coast, particularly within the Sundarbans, suggesting that the mangrove forest has the highest channel density, smallest island area, and smallest nearest-edge distance. The observed CDF of nearest-edge distance (maximum value of L per island) (Figure 13) shows reasonable power law behavior with exponent ˛ = 2.96 above threshold Lmin = 1.054 103 m (Table 1). The p-value of the model is 0.42, implying that the power law fit is not rejected at a conservative significance level. The map of the logarithm of

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89°

90°

91°

the relationships proposed by Wilkerson and Parker [2011] for sand-bed rivers in equilibrium. Assuming a width to depth ratio of 20, we estimate the bankfull Shields stress as * 0.045, which is close to typical values of the critical Shields stress *c , supporting the idea that sand transport in the small channels is weak.

log(A) 10.57 4.40 24° N

23°

22°

N 0

25 Km

100

Figure 15. Channel network of the GBJ Delta with channels of width 57 m and islands (colormap based on the logarithm of island area). The effect of eliminating the smallest channels of the network is that the upstream portion of the delta behaves as a single large island. This is because the channels connecting the coastline and the upstream portion of the delta are predominantly narrow. nearest-edge distance normalized by Lmin (Figure 14) shows that the 888 islands outside the power law regime (out of 1291 total), are mostly located near the coast and along the Ganges and Padma Rivers, and the main branches of the Meghna River, confirming that these regions of the delta exhibit the smallest values of L. The superimposed physiographic boundaries indicate that these regions coincide with the tidal portion, particularly the mangrove forest, and part of the active portion of the delta. 4.4. Width Analysis [32] To investigate the relation between network structure and link strength in the GBJ Delta, we analyzed the behavior of the system as the weakest links (i.e., the narrowest channels) are removed from the network. This is a way of quantifying the sensitivity of network metrics to the least important (and, in our case, least certain) links. Choosing 57 m (twice the pixel resolution) as the threshold width below which channels are removed, we analyzed the resulting configuration of channels and islands (Figure 15). This map shows that, as the weakest links within the network are removed, the upstream portion of the delta behaves as a single large island. This is because channels connecting the northwestern part of the delta to the coastline are mostly small, i.e., weak network links. Flow through the northwestern part of the delta occurs via weak connections, suggesting lack of significant water and sediment transport. As seen from the superimposed physiographic boundaries, the inactive region of the delta is included in this portion of weak transport. These narrow channels may be active only during relatively large floods. A rough estimate of the bed shear stress * in a 57 m wide channel can be obtained by using

4.5. Oxbow Analysis [33] The extracted channel network (Figure 4) is characterized by the presence of a large number of oxbow lakes concentrated mainly in the northwestern part of the delta. The spatial distribution of the number of oxbows per island normalized by its maximum value (Figure 16) shows that all the oxbow lakes are located far from the coast and are concentrated in the northwestern region, while the northeastern region has few oxbows (< 6 oxbows per island), and no oxbows are present near the coast and along the Ganges and Padma Rivers, and the main branches of the Meghna River. As seen from the superimposed physiographic boundaries, the area where oxbows are present coincides with the inactive region of the delta. The greatest number of oxbow lakes (40) is observed in the only area in the northwestern part of the delta that is disconnected from the main channels, being drained only by the weak links previously discussed. This suggests a connection between the lack of channels able to carry significant amounts of water and sediment, and the presence of abandoned channels and oxbows. These relict landforms presumably formed when this region of the delta was more active. The likelihood of the oxbows to be preserved should increase with distance from a chan88°E

89°

90°

91°

O/Omax 1 0 24° N

23°

22°

N 0

25 Km

100

Figure 16. Channel network of the GBJ Delta and map of number of oxbows per island normalized by its maximum value. All the oxbows are located away from the coast. Based on the superimposed physiographic boundaries, islands in the active part of the delta have a small number of oxbows, while the majority of the oxbows are located in the inactive portion. The island with the largest number of oxbows is the only area in the upper part of the delta that is disconnected from the main channels.

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nel, and thus island area; the majority of the oxbows are in fact located in the largest islands within the delta. A combination of trimming (e.g., filling/opening of small channels) and occupation and stabilization of relatively inactive landforms seems to be one important signature of human effects in the GBJ Delta.

5. Discussion [34] The statistical analysis of metrics and descriptors of the channel network extracted from satellite imagery indicates that island area, shape factor, aspect ratio, and nearestedge distance show power law behavior above a threshold value. The comparison with a physiographic zonation of the GBJ Delta suggests that portions of the delta characterized by active flow and transport differ substantially from the upper, less active, region, and are characterized by high channel density, small and highly drained islands, and short distances to the nearest water. This is observed in particular within the Sundarbans, suggesting a link between vegetation, especially mangroves, channel morphology, and linkages within the network. Such a high channel density is likely due to tidal drainage, as suggested by Fagherazzi [2008]. We consider this a point worth further investigation in the future. [35] The uncertainty in the estimated power law lower bounds does not affect the nature of the above results. This was verified by creating maps of the network metrics for a range of plausible values of Amin , ˇmin , min , and Lmin (Table 1). [36] Extraction of the whole network of the GBJ Delta also allowed us to identify narrow channels connecting the coast to the upstream northwestern part of the delta. The high-density channel network characterizing a relatively narrow belt parallel to the coast is essentially dominated by tides and by the mutual interplay of sediment fluxes and vegetation (mangrove) dynamics. The northwestern portion of the delta is instead characterized by numerous oxbow lakes representing the current, low-activity stage of development fed only by small, muddy, and sinuous ephemeral distributaries of the Ganges. This surface morphology covers extensive subsurface channel sands representing an earlier constructional stage of this area by the main stem Ganges [Goodbred and Kuehl, 2000b]. [37] The weighted analysis of network connectivity, based on the extracted channel width at each network link, highlights that many of the channels that extend from the coast to the upper part of the delta are weak and do not seem to play a significant role in terms of water and sediment delivery, suggesting lack of significant transport in most of the upper portion of the delta. In particular, the highest number of oxbow lakes was found within the only island in the upper part of the delta not connected to the main channels, showing the link between lack of strong connectivity and the presence of abandoned channels and oxbow lakes. [38] While satellite imagery provides a unique, synoptic way of analyzing a large system such as the GBJ Delta, it has the limitation of not capturing features and thus processes acting at scales smaller than the image resolution. This is especially relevant to identifying human modifications, which are likely to be most important for small, relatively

inactive channels. While less important for the overall morphology of the GBJ Delta [Goodbred and Kuehl, 2000a, 2000b; Goodbred et al., 2003], subgrid-scale features may be needed for a complete quantification of human alterations within the system. [39] As noted earlier, the satellite image analyzed here is only a snapshot of the water surface elevation of the GBJ Delta. The channel network obtained from the unsupervised and supervised classifications is a wet map of the submerged pixels (map of the water surface). We inferred the channel-planform pattern from the wet map, but noting that channels are hydrodynamic features evolving through time. Monsoonal flooding, unusual tides, and storms, could substantially modify the wet map. Although the effect of water level fluctuations on the results presented here could be assessed only through analysis of multiple images through time, we believe that the main findings of this study would not be fundamentally altered by water level fluctuations over the delta. We consider this an interesting topic for future analysis once comprehensive image data for various wetting conditions are available. [40] One piece of information excluded from our analysis is the direction that characterizes the delta network links and thus directions of transport through the network. A method based on an analogy with electric circuits was proposed by Feola [2006] and could be used to analyze the behavior of the system as a directed graph. Also, the correlation among surface statistics, as the ones analyzed here, and subsurface statistics related to the stratigraphic record [Goodbred and Kuehl, 2000a, 2000b; Goodbred et al., 2003] could certainly highlight other characteristic scales of the dynamical behavior of the system. Finally, it would be useful to compare the GBJ results to a delta, such as the Po or the Danube, that is smaller and more heavily anthropogenically modified. We believe that comparison could highlight thresholds in terms of total sediment flux or morphology change rate above which human modifications affect natural morphology. While in the GBJ Delta the natural processes are very strong, and anthropogenic disturbance cannot be captured at the resolution of the satellite imagery analyzed here, this style of analysis may also indicate anthropogenic influences in other deltas. [41] While we focus here on the GBJ Delta, the analysis framework we propose is portable to any other deltaic system, given the availability of satellite imagery. It is particularly relevant to large systems, such as the Niger or the Mekong, where direct field observations are hard to make over the entire delta. The metrics proposed here will not always show power law behavior, particularly in smaller systems where network properties may not cover several orders of magnitude. Power laws are one of many possible distributions. A network-scale statistical analysis of island and channel properties, such as the one proposed here, provides a useful quantitative description of delta morphology whether the observed distributions are power law or not.

6. Conclusions [42] In this work we have proposed a statistical analysis framework of delta networks extracted from remotely sensed data. We have identified several descriptors of the channel network and analyzed them statistically. We have applied

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the proposed statistical framework to the deltaic network of the GBJ Delta. The main conclusions of this work are the following: [43] 1. Island area, shape factor, aspect ratio, and nearestedge distance vary spatially in different regions of the GBJ Delta. In particular, the statistical behavior of these metrics distinguishes the coastal region and the portion along the main rivers (Ganges, Padma, Meghna) from the upper region of the delta; [44] 2. A comparison between our statistically based zonation and preexisting qualitative physiographic maps of the GBJ Delta shows good correspondence between the two zonations. In particular, the region near the coast corresponds to the previously mapped tidally influenced portion of the GBJ Delta, while the portion along the main rivers is part of the previously mapped active region. These are statistically different from the northwestern portion of the delta previously classified as inactive and characterized by the presence of numerous oxbow lakes; [45] 3. The tidal region, particularly the mangrove forest, and the portion along the main rivers are characterized by small islands, small shape factor, short nearest-edge distance, and absence of oxbows. Islands within this region tend to have smooth boundaries compared to islands in the inactive portion of the delta. Some (about half) of the islands within the Sundarbans are elongated; [46] 4. Islands within the previously mapped inactive region tend to have large area, large shape factor (resulting in rough boundaries), and long nearest-edge distance. The area is characterized by frequent oxbow lakes, suggesting a link between the lack of strong connectivity to the rest of the delta and the presence of abandoned channels and oxbow lakes; [47] 5. The active region of the delta presents characteristics between the inactive, and tidal-dominated regions. The area along the main rivers (Ganges, Padma, Meghna) behaves like the region near the coast, while the rest of the active region is characterized by medium-sized islands, moderate nearest-edge distance, and moderate shape factor, indicating island shapes that are not as rough as in the inactive region. Oxbow lakes are present but in much smaller number than in the inactive region; [48] 6. While the shape factor has a clear spatial distribution within the delta, this is not the case for the island aspect ratio, whose distribution is much more heterogeneous within the delta and the power law fit less robust; [49] 7. Large islands whose length scale is much greater than that of the bounding channels (channel bounded land masses) tend to have rougher boundaries than true islands with length scale comparable to or less than the width of the bounding channels, suggesting process differences between the two island types; [50] 8. A weighted connectivity analysis based on channel width can identify weak channels within the delta network. In particular, channels connecting the upper portion of the delta to the coast do not seem to play a significant role in the transport of water and sediment. [51] Acknowledgments. P.P. would like to acknowledge support from the National Science Foundation (grants FESD/EAR-1135427, GSS/BCS1063228), and from the University of Texas at Austin. C.P. is grateful for support from the National Science Foundation BanglaPIRE project (OISE 09-68354). We thank A. Feola for sharing her channel centerline extraction

algorithm and, together with K. Caylor and I. Rodriguez-Iturbe, for contributing initial ideas related to this project. We thank A. Clauset and C. R. Shalizi for developing and releasing the methods and tools for the analysis of power law distributions in empirical data (http://tuvalu.santafe. edu/~aaronc/powerlaws/). We are grateful for the comments received from the Editor, Alexander Densmore, the Associate Editor, Andrew Ashton, Matthew Wolinsky, and two anonymous reviewers who have helped improve this paper.

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