Land use and topography bend and break ... - Wiley Online Library

Limnology and Oceanography Letters 00, 2017, 00–00 C 2017 The Author. Limnology and Oceanography Letters published by Wiley Periodicals, Inc. V

on behalf of Association for the Sciences of Limnology and Oceanography doi: 10.1002/lol2.10038

LETTER Land use and topography bend and break fractal rules of water body size-distributions Meredith K. Steele ,1* James B. Heffernan,2 1 Department of Crop and Soil Environmental Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia; 2Nicholas School of the Environment, Duke University, Durham, North Carolina

Scientific Significance Statement The areal extent and size-distribution of inland water bodies have profound effects on regional and global biogeochemistry. Theoretical models assuming fractal landscapes predict the distribution of inland water bodies as a power-law with specific ranges of slopes. Observed regional size-distributions often deviate from these predictions, but the reason is unknown. This study provides empirical evidence that climate, topography, and agricultural land cover alter the areal extent and sizedistributions of water bodies, such that the resulting hydroscapes no longer conform to theoretical predictions derived from simple landscape models.

Abstract The size-distributions of inland water bodies (WB) within different regions often poorly conform to geophysically based theoretical models (power-law: y 5 axb); however, the causes of these deviations remain unknown. Therefore, we compared WB abundance and size-distribution parameters (slope [b] and model fit [r2]) in 164 regions in the United States with varying topography, climate, and agricultural intensity. We found all three factors influenced WB size-distributions and their fit to expected models. WB size-distributions in steeper terrain had more small WB and better fit power-law models, while regions with flatter terrain and greater precipitation had poorer fits. Extensive agriculture increased the proportion of small WB, causing distributions in some regions to fall outside theoretically predicted limits (bCDF < 21). Regional variation of WB sizedistributions can help develop and test integrated theory that accounts for geophysical and anthropogenic drivers of WB sizes, which is essential for scaling biogeochemical processes in aquatic systems. are biogeochemically very active per unit area compared to large lakes (Stallard 1998; Dean and Gorham 1998; Bastviken et al. 2004; Harrison et al. 2008; Downing 2010; Goodman et al. 2011; Holgerson and Raymond 2016), the mis-estimation of water body size-distribution (WBSD) can bias estimates of biogeochemical processes, such as carbon emission and sequestration (Hanson et al. 2007). Understanding the causes and consequences of variation in WBSD is thus central to our macroscale understanding of aquatic ecosystems and the landscapes in which they occur (Heffernan et al. 2014; Soranno et al. 2014). Natural WB, including lakes, ponds, and wetlands, occur in diverse geologic settings resulting from different processes (e.g., tectonic, glacial scour, and fluvial) that create depressions intercepting the groundwater table. The relative proportion of large and small WB within a region, and globally, can be theoretically estimated from the fractal topography of

The abundance, size, and character of naturally occurring and constructed water bodies (WB) influence ecological and biogeochemical characteristics of inland landscapes (e.g., Herbert et al. 2010; Aufdenkampe et al. 2011; Van Meter and Basu 2015; Holgerson and Raymond 2016). Because small WB

*Correspondence: [email protected] Data Availability Statement: Data are available in the VTechData repository at https://data.lib.vt.edu/collections/tb09j565c. Additional Supporting Information may be found in the online version of this article. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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Steele and Heffernan

Water Body Size-Distributions Bend and Break

Small impoundments contribute to historical shifts in regional surface water extent (Christensen et al. 2016; Julian et al. 2015). Cumulatively, impoundments follow power-law distributions (Downing et al. 2006); however, unlike natural features, artificial impoundments are constructed for specific purposes at particular scales and are unlikely to follow purely fractal predictions. Small impoundments occur throughout agricultural landscapes (Downing et al. 2006; Cereghino et al. 2007; Huang et al. 2012), while large dams are generally associated with domestic water sources for population centers and energy production (Graf 1999). Such land-use associations and other geographic patterns, like the correlation between precipitation and the density of small impoundments (Downing et al. 2006), implies that land use effects on WBSD vary regionally and may cause regional WBSD to diverge from strictly geophysical predictions. Even if impoundments are power-law distributed, their size-distribution could influence landscape-scale WB characteristics if impoundments are common relative to natural WB. While substantial research has explored the regional factors affecting WB chemistry and ecology (Heiskary et al. 1987; Soranno et al. 1999; Crawford et al. 2014), empirical tests of the drivers of WB abundance and distributions are limited, and the drivers of deviations from theoretical predictions remains unclear. Here we use deviations from a simple geophysical null hypothesis to assess how regional factors, specifically topography, climate, and agricultural land use, influence broad-scale patterns in WBSD. We evaluated the how WBSD (using the slope and fit of power-law scaling models) and WB area varied across 164 regions from the conterminous United States. This synthetic analysis of WBSD across diverse regions is important for scaling of ecological and biogeochemical processes in aquatic systems, and developing an integrated theory of WBSD that incorporates both geophysical and anthropogenic drivers.

the land surface and described mathematically by power-law distributions (y 5 axb) (Klinkenberg and Goodchild 1992; Goodchild 1988; Downing et al. 2006). The mathematical predictions of the number and size of “pits” in the landscape that intersect the water table or otherwise fill with water provides a simple and useful null model of the distribution of WB (Goodchild 1988). Based on fractal theory, WB size-distributions should exhibit power-law scaling with cumulative distribution function (bCDF) slopes between 20.5 and 21.0, or 21.5 to 22.0 based on the probability distribution function (bPDF) (Seekell et al. 2013). Global estimates of bCDF and bPDF vary, but closely follow power-law models within a specific WB size range (> 1 km2) (Downing et al. 2006; Lehner et al. 2011; Messager et al. 2016). Some regional WBSD conform to this simple prediction; however, some regions either conform poorly or exceed theoretical limits entirely (Downing et al. 2006; Seekell and Pace 2011; Mcdonald et al. 2012; Muster et al. 2013). For example, McDonald et al. (2012) documented regions with bCDF that were substantially lower than the minimum slope predicted by fractal theory (bCDF < 21.0). Extrapolated indefinitely, such distributions would require the entire land’s surface be covered by infinite small WB. Currently, there is no explanation for observations where bCDF < 21.0. Fractal based size-distribution theory was recently extended to explain the poor fits of regional WBSD, based on topography. Seekell et al. (2013) argued that mountainous regions restrict WB formation and cause deviations from the expected fractal distribution, but tested this prediction using only two regions, one with mountainous terrain and one flat terrain (Seekell et al. 2013). Alternatively, percolation theory, which predict a slightly lower minimum bCDF 5 21.05, found that WB > 8.5 km2 conform well to power-law models at the global scale; however, WB < 8.5 km2 do not, potentially because they are more susceptible to dynamical change or landscapes at smaller scales are not topographically selfsimilar (Cael and Seekell 2016). Neither prediction has been examined in a wide variety of geophysical or land use settings at the regional scale. Though WB size-abundance theory is meant to be predictive of undisturbed hydroscapes, it is frequently applied to, and tested using, regions with intense agricultural development, a pervasive modifier of the modern Earth surface (Ramankutty 1999; Hooke 2000; Donchyts et al. 2016). Developed land use manipulate the abundance and characteristics of surface water features through construction, drainage, and infilling (Steele and Heffernan 2014; Steele et al. 2014; Christensen et al. 2016; Julian et al. 2015; Van Meter and Basu 2015). These alterations can affect regional-scale surface water extent, but the direction and magnitude of change vary among regions. For example, rice cultivation has dramatically increased the extent of open water wetlands in some regions (Ellis and Ramankutty 2008), whereas row crop agriculture dramatically reduced the regional surface water area in the central United States (Dahl and Allord 1996; Wright and Wimberly 2013).

Materials and methods Our study initially identified 100 landscapes of mixed land use, located throughout the continental United States and distributed among ecological regions. These 100 landscapes were defined by the Metropolitan Statistical Area (MSA) (Fig. 1). MSAs are one or more counties that encompass an urban center and the surrounding rural lands. In most cases, MSAs include minimally developed, agricultural, and urban areas. To identify regions within each MSA dominated by each land use, for every census block within the MSAs, we calculated in ArcGIS (v10) the percent agricultural, undeveloped, and urban land covers using the 2006 National Land Cover Data (NLCD). Then, for each MSA, we aggregated the census blocks into subregions based on the majority land cover present in the census block. Most, but not all, MSAs had both an intensely developed agricultural subregion (>40% Agriculture) and a less intensely developed subregion (>40% Undeveloped). Sub-regions less than 100 km2 in area were removed from this initial data set. In 2

Fig. 1. Geographical distribution of the 164 regions used in this study. (A) Regions are based on Metropolitan Statistical Areas (MSA), which includes one or more counties. Each MSA contains areas dominated by agricultural land cover, undeveloped land cover (all nonurban and nonagricultural land cover categories), or both. In the map, the black outline represents the MSA boundary and the colored area within represents our defined study regions. (B) The geographic distribution of the slope of the water body size-distribution (Beta). The more negative the slope, the greater the proportion of small water bodies to large water bodies. (C) The geographic distribution of the fit of the power-law model to the size-distribution (BS_r2).



Table 1. Summary of the size, topographic, climatic, land

created by the USDA/NRCS. From these data, we derived a wetness index as the ratio of MAP and the mean subregional topographic slope. We used the NHD feature point data to locate WB with large dams (> 2 m) compiled from the National Inventory of Dams. The number of large impoundments identified in each location was not correlated with the percentage of agricultural land in the region, and we evaluated sizedistributions without these large dams, as they were primarily drinking water reservoirs for the nearby urban centers. To characterize the size-distribution of WB we followed the methods of Downing et al. (2006) and Seekell and Pace (2011). Fitting a linear regression model to the cumulative distribution (log-number of WB with size > area vs. log-area) provided two parameters for comparison: the slope (the exponent of the power-law distribution 5 bCDF) and fit (r2). On a log-abundance log-size plot, the ideal power-law distribution has a negative, linear slope that quantifies the relative proportion of WB sizes. Deviations from the power-law distribution therefore manifest as a low r2 in a linear regression model (Seekell and Pace 2011). Since the smallest WB are more likely to be over or under predicted, we also evaluated the fit of the distribution in the lower tail by calculating the linear regression for all WB while limiting the regression to size range 0.0001–0.01 km2. The choice of 0.01 km2 as the upper limit included the smallest third of WB for the majority of lake districts. We recognize alternative techniques are available which provide additional insight into the nature of WBSD (Clauset et al. 2009); however, this method of fitting the power-law is widely used and reported by limnologists and therefore provides the best comparison with previous studies. The calculated WBSD equations (with parameter error estimates) for the 164 regions can be found in the data file (see Data Availability Statement for access). We evaluated topography, precipitation, agricultural land cover, and their interactions as predictors of WBSD parameters. We first used a Pearson’s correlation analysis to assess the relationships and interactions among site characteristics and hydrographic characteristics. To ensure that measures of the fit of power-law distributions were not statistical artefacts, we evaluated correlations between WBSD parameters and the number and size range of WB as well as the area of each region. To isolate the effects of geophysical characteristics, we used a subset of regions with < 20% agricultural land cover. Within this subset, we evaluated the relationship between precipitation and topography and the fit of the WBSD across the full size range (r2) and for smaller WB (lower tail r2). As a second test of topographic effects on WBSD, we selected high-relief (slope > 8%) and low-relief (slope < 2%) regions from within the low-agricultural subset. We binned the WB size data within these topographic groups, and compared the fit of the power-law distribution for these binned data. Finally, to evaluate the influence of agriculture and its

cover, and hydrographic properties of the 164 sites included in this study. Sum

Max

Min

Median

2

Area (km ) Mean elevation (m)

844,517 —

48,293 2395

113 2

3154 289

Standard deviation

—

1019

1.1

74

elevation (m) Mean slope (degree)

—

18.1

0.03

3.0

Precipitation (mm)

—

1656

76

984

Agricultural cover (%) Row crop cover (%)

— —

88 85

0 0

31 10

Pasture cover (%) Water bodies (#) Water bodies (km2)

—

56

0

9

913,418 29,574

66,385 5871

36 0.232

2910 50.6

this study, we included only sub-regions dominated by agricultural and less intensely developed regions of the MSA (those with < 10% urban land cover) in this study; results of the hydrographic analysis of the urban sub-regions are available elsewhere (Steele and Heffernan 2014; Steele et al. 2014). To employ a continuous rather than categorical statistical approach, we characterized land use in each subregion as the exact percent agricultural land cover. Surface water data layers obtained from the high resolution National Hydrography Dataset (NHD) included all WB (lakes/ponds, reservoirs, swamps/marshes). It is important to note that the NHD data does not distinguish between naturally occurring WB and those artificially created by impoundments or modified by other human activities. Therefore, the size-distributions reflect both a mix of natural conditions and human modifications. The maximum resolution of the NHD high-resolution data is 1 : 5000, but varied by state. Completeness of these data was determined by visual comparisons of the layers and satellite images in randomly chosen sub-locations at each site. Ninety-two locations of the original 100 MSAs were found to have acceptable coverage for WB as small as 0.0001 km2. This procedure resulted in 164 subregions that were used in the final analysis of WB size-abundance distributions. We characterized the topography of each subregion by calculating the mean and standard deviation (SD) of both the elevation and slope of the land using a 30 m digital elevation model (DEM) from the 3DEP seamless DEMs (USGS 2012). Local slope was derived using the “slope” tool in the Spatial Analysis Toolbox, which calculates the slope of each 30 3 30 m pixel based on the maximum rate of change in values from one cell to its neighbors (Burrough et al. 2015). We calculated the mean and SD of all the slope pixels to characterize the subregion slope. We also calculated mean annual precipitation over each study region, using the 1981– 2010 Mean Annual Precipitation (MAP) published in 2012 4



Fig. 2. A graphical representation of the Pearson’s correlation (Supporting Information Table 1) analysis between site area, geophysical (Topographic slope), climatic (Precipitation), and land use (total agriculture (% Ag), pasture agriculture (% Pasture), and row crop agriculture (% Row Crop) characteristics and the water body abundance (total number of water bodies [#WB], total WB area [Area of WB], WB areal density [WB km2/km2] and numeric density [WB #/km2]) and the size-distribution power-law parameters (Slope 5 Beta) and fit (the r2 and r2 of the lower tail [Truncated r2]). Solid lines represent a significant (p < 0.05) positive relationship between the variables. While dashed lines represent a significant (p < 0.05) negative relationship. To be visually clearer, only relationships between regional variables (in gray) and hydrographic characteristics (in white) are shown. Interrelationships between hydrographic characteristics are not shown, but can be found in Supporting Information Appendix 1.

and climatic variables were not correlated with one another (Fig. 2). The proportion of agricultural land cover ranged from 0% to 88%, with a median of 31.2% (Table 1). Though many of the variables were inter-correlated, several dominant patterns emerged between WB extent and sizedistribution fit to the power-law model, and the regional topography, precipitation, and agricultural intensity.

interactions with geophysical characteristics, we subdivided all study regions into smaller ranges of agricultural land use, and evaluated geophysical drivers as predictors of hydrographic characteristics within each range of agricultural extent. All statistical analyses were performed in SigmaPlot v12.5.

Results

Topography and precipitation Across all regions, WB number and area increased with precipitation (Fig. 2); however, greater precipitation also correlated with fewer small WB relative to large ones (less negative bCDF) and a poorer fit to the power-law model (r2 and truncated r2; Fig. 2). Conversely, as the terrain became

The 164 study regions covered a wide range of climatic, topographic, and hydrographic conditions (Fig. 1A). Study regions varied in terms of geographic size (Table 1), which increased slightly with steeper slope and less precipitation (Fig. 2; Supporting Information Appendix 1). Topographic 5



Fig. 3. Relationships between topographic and climatic variables and the fit (r2) of the power-law model to the water body (WB) size-distribution when < 20% agricultural land cover. (A) There is no significant relationship between precipitation and the fit of the power-law model to the entire WB size range. (B) However, precipitation is negatively correlated with fit of the power-law model for the small WB. (C) The fit of the power-law model to the entire WB size range improves as topography becomes steeper. (D) The fit of the power-law model to small WB size range also improves as topography becomes steeper. Topography is quantified by the mean slope of the land and climate by mean annual precipitation. The fit of the power-law model for the smallest WB is measured by the lower tail r2, where the regression is truncated to < 0.01 km2.

Absent agricultural land use, the geographic distribution of WBSD reflected relief (Fig. 1B,C). The highest r2 (and the most negative bCDF) values were observed in both the eastern and western mountain regions and in the southern midsection. Several very flat locations (ex. Florida, eastern coastal locations) had very high r2 for the total WBSD, but a much lower r2 of the lower tail. The high r2 for complete size range is likely the result of very large WB increasing the size range and fit. Topography influenced the shape of WBSD. When data from regions with 60%, bCDF ranged from 21.46 to 20.55 (mean bCDF 5 20.86), and the relationship between bCDF and topographic slope was much steeper than in areas with minimal agriculture. For areas with agriculture between 4% and 45%, we observed similarly wide ranges of bCDF, but weaker relationships of bCDF to topographic slope. In sum, as the percent agriculture increased in a region, the WBSD shifted toward a larger proportion of small WB compared to regions with less agriculture, and this effect was greatest in regions with the moderate slopes. The interactive effects of land use, climate, and topography best predicted WB extent (Fig. 5B). In regions with minimal (60% agricultural land cover, there was no significant relationship between the wetness index and WB extent.

Fig. 4. The log abundance (nA > A) vs. log size (A) plots for distributions in flat and mountainous land. Regions with standard deviation (SD) of the slope 5 0–2%: Charleston, SC; Gainsville, Fl; Gulf Port MS; Hinesville AL; Houston TX; Miami, FL; Orlando, FL; Tallahassee, FL; Toledo, OH; Wilmington, SC; Baton Rouge, LA. Regions with SD of the slope 5 8–18%: Billings, MT; Blacksburg, VA; Boise, ID; Charleston, WV; Chico, CA; Denver, CO; Eugene, OR; Flagstaff, AZ; Grand Junction, CO; Idaho Falls, ID; Kingsport, TN; Los Angeles, CA; Madera, CA; Missoula, MT; Phoenix, AZ; Portland, OR; Sacramento, CA; Salt Lake, UT; San Luis Obispo, CA; Seattle, WA; Williamsport, VA; Yuma, AZ. Each point on the regression represents the median of the nA > A among the regions in the size category. In flat terrain, the size-distribution displays a general curvature and overall poorer fit to of the power-law model. In contrast, landscapes with variable terrain (i.e., mountainous) and steeper slopes, the size-abundance relationship better fits the power-law model.

Discussion Implications for WB size-distribution theory Theoretically, bCDF should be less than 20.5, but no less than 21.0 based on D-dimension limits in fractal theory (Goodchild 1988; Seekell et al. 2013) or no less than 21.05 based on percolation theory (Cael and Seekell 2016). Here, regions with bCDF < 21.0 also had agricultural land cover was greater than 20% of the total landscape. WBSD that fall outside of the theoretical limits most likely result from draining and impoundment associated with agricultural activities. Our findings also relate to recent theoretical models that relate topographic variability to WBSD. We observed opposite patterns from Seekell et al. (2013), who predicted WBSD would best conform to power-law models when the majority of land is near the mean elevation (i.e., flat) and poorly conforms the more land that is further from the mean elevation (i.e., mountainous). WB size-distributions in terrain with

2

(r 5 0.972) to the power-law model compared to regions with steeper slopes (8–18% slope) which fit very well across the entire size range (r2 5 0.997; Fig. 4). Regions with moderate slopes exhibited power-law fits that were intermediate to these extremes (data not shown). Agriculture Agricultural intensity affected WBSD and WB extent. Total agricultural land cover and row crops tended to decrease WB area and model fit (Fig. 2). Pasture agriculture, however, negatively covaried with bCDF (increasing smaller WB) (Fig. 2). Note, pasture cover positively correlated with precipitation and row crop cover negatively correlated with slope (Fig. 2). Rather than a sampling artifact, this pattern likely reflects that pasture management is more adaptable to (and 7



Fig. 5. The relationship between topography and the slope (b) of the size-distribution (A) and (B) the percent water body area, for six agricultural classes with increasing percentage of agricultural land cover: (1) < 3.9%, (2) 4–9.9%, (3) 10–20%, (4) 20–40%, (5) 40–59.9%, and (6) 60–88%. Regressions shown are significant at p < 0.05. models regardless of the current climate regime. Linking the specific geology of a region to the fit may provide insights into the mechanisms underlying regional WBSD.

steep slopes fit power-law models better than regions with flatter terrain. The two regions used by Seekell et al. (2013) to test their prediction were within the range of relief where we observed tremendous variability (SD of elevation < 200 m) in the fit of the WBSD. Our results are consistent with similar observations in flat land of the Artic where WBSD also poorly fit the lower tail (Muster et al. 2013). While our findings contradict the specific theoretical predictions of Seekell et al. (2013), they support the broader conclusion that power-law models may over-estimate the abundance of small WB (Seekell and Pace 2011; McDonald et al. 2012). Because this deviation is greatest in flat land, it applies to a much greater area than if larger deviations were found in regions of high relief. Our findings support the theory that small WB are unlikely to conform to power-law distributions because small WB are subject to more dynamical change (Cael and Seekell 2016). Independent of agriculture, regional precipitation did not affected the power-law model’s fit across entire range of WB sizes, but negatively correlated with model fit of smallest WB. Precipitation increases erosion and deposition of sediments that are likely to disrupt the self-similarity of topography. Furthermore, depositional landscapes (i.e., glacial till, marine, and riverine sediments) also tend to be flatter. WBSD of flatter landscapes often conform poorly to power-law

Shaping surface water This study confirms and expands previous findings that agriculture can alter the landscape-scale characteristics of aquatic ecosystems, including WBSD. Recent historical regional- and watershed-scale reconstructions clearly link changes in WB extent and WBSD with conversion of lands for agriculture (Christensen et al. 2016; Julian et al. 2015). Deliberate drainage and infilling of wetlands and other WB to increase arable land is likely the most important cause of the large differences in WB extent between agricultural and undeveloped landscapes (Fig. 4B). This study applies a similarly fine spatial grain, but over a broad spatial extent, which allows us to evaluate how the hydrographic effects of agriculture vary with climate and topography. Landscapes with intermediate slopes (5–10%) had the greatest deviations between agricultural and undeveloped lands (Fig. 5), likely due to their suitability for channeling water and creating small impoundments. Previous studies also that found that construction of impoundments correlates with the relief and the availability of water (Downing et al. 2006; Huang et al. 2012). 8



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Our synoptic approach neglects the potential role of historical agriculture and subsequent reforestation, particularly in the eastern half of the United States. In areas with moderate amounts of agricultural land cover, where abandoned agriculture may be relatively common, we observed a wide range of hydrographic characteristics (Fig. 2). This variance may reflect signatures of land use history that persist as hydrographic differences in some contemporary landscapes (Harding et al. 1998; Walter and Merritts 2008).

Conclusion Anthropogenic alteration is a major driver of regionalscale surface water extent and WB size-distributions, on par with the climatic and topographic characteristics. The effect of agricultural land use should be incorporated into theoretical models of surface water distributions, and studies that evaluate geophysical drivers of surface water distributions should account for or avoid potential effects of land use.

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Acknowledgments We thank the anonymous reviewers and the editors for suggestions that greatly improved the manuscript. This research was supported by a grant from the National Science Foundation’s Macrosystems Biology program (NSF EF 1065785). Submitted 23 June 2016 Revised 13 February 2017 Accepted 07 March 2017

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