Abstract

Flash floods cause more fatalities than any other weather-related natural hazard and cause significant damage to property and infrastructure. It is important to understand the underlying processes that lead to these infrequent but high-consequence events. Accurately determining the locations of flash flood events can be difficult, which impedes comprehensive research of the phenomena. While some flash floods can be detected by automated means (e.g., streamflow gauges), flash floods (and other severe weather events) are generally based on human observations and may not reflect the actual distribution of event locations. The Storm Data–Storm Events Database, which is produced from National Weather Service reports, was used to locate reported flash floods within the forecast area of the Binghamton, New York, Weather Forecast Office between 2007 and 2013. The distribution of those reports was analyzed as a function of environmental variables associated with flood generation including slope, impervious area, soil saturated hydraulic conductivity ksat, representative rainfall intensity, and representative rainfall depth, as well as human population. A spatial conditional autoregressive model was used to test the hypothesis that flash flood reports are made more frequently in areas with higher populations, even when other flood-generating processes are considered. Slope, soil saturated hydraulic conductivity, and impervious area are significant predictors of flash flood reports. When population is added as a predictor, the model is similarly robust, but impervious area and ksat are no longer significant predictors. These results may challenge the assumption that flash flood reports are strongly biased by population.

1. Introduction

A working definition of the term “flood” can be elusive. For example, a flood could refer to a situation in which a river’s discharge exceeds its bank-full capacity. However, it is often implicitly assumed or explicitly defined that a flood is an event that causes damage to people. An example of this dual meaning of the term is in the 1994 definition developed by the U.S. executive office of the president: a flood is a “temporary condition of . . . inundation of normally dry land . . . and/or the unusual accumulation of waters . . . with undesirable effects to life and property” (Bedient et al. 2013, p. 690). Flash floods are defined by the National Weather Service (NWS) as “a rapid and extreme flow of high water into a normally dry area, or a rapid water level rise in a stream or creek above a predetermined flood level, beginning within six hours of the causative event” (NWS 2012, p. 3). This type of flooding is the most damaging type of extreme weather, causing, on average, $8.2 billion in property damage, and about 89 fatalities each year in the United States (NWS 2014). The NWS has been tasked with predicting and recording flash floods in the United States, as well as communicating flash flood risk to the public (U.S. Department of Commerce 1970; U.S. Secretary of Commerce 1938). In this study we attempt to reconcile the human-centered concept of flash flood with a more physically based definition typically used by hydrologists.

The prediction of flash floods in space and time involves methodology based primarily on natural variables including atmospheric (e.g., rainfall depth) and landscape conditions (e.g., soil moisture; see, e.g., Georgakakos 2006; Ntelekos et al. 2006). The available record of flash floods, however, is more subjective. Most flash floods are much more localized than the typical watershed with a U.S. Geological Survey (USGS) gauge (Fig. 1), making it difficult to amass direct hydrological measurements. Currently our best information about the timing and location of flash floods relies on reports compiled in the Storm Data publication produced by the National Centers for Environmental Information [NCEI, formerly the National Climatic Data Center (NCDC)]. Data reported in this publication include the location, date, and time of occurrence of flash floods. Information about property damage, injuries, and fatalities is included when it is available. A narrative can be included, which contains information of varying kind and detail. Some narratives are very specific about the storm that caused the flooding, the location, and/or the aftermath of the event. Other narratives are quite brief and uninformative. While flash flood reports have been recorded since 1994, location information prior to 2007 is problematic. For example, a flash flood location might be listed as “countywide” with no more specific information to pinpoint where flooding occurred. Beginning in 2005, latitude and longitude coordinates were available, often corresponding to a town or other geopolitical feature. However, the latitude and longitude locations prior to 2007 had potentially large unexplained errors (NCEI 2016). Starting in 2007, geographic extent polygons were recorded by the NWS in the Performance Management StormDat program, which is a precursor to the NCEI Storm Events Database and Storm Data publication (NWS 2015). Reports only occasionally include the kind of information that would be most useful for hydrological analysis, such as the exact location or areal extent of inundation, and the reported events are rarely located at USGS stream gauges. Sources of flash flood reports include emergency managers, state officials, trained observers, private citizens, and media. While the NWS and NCEI do not guarantee the accuracy of data, this database remains the most comprehensive source of flash flood reports.

Fig. 1.

Comparison between drainage areas of flash floods and gauged watersheds in the northeastern United States. (a) Spatial extent of a typical flash flood watershed (striped) and a typical gauged watershed (light gray): Newtown Creek at Elmira, New York (station 01530500). Streams, flood location, and gauge location are shown for reference. (b) Histogram of USGS (2011) gauged watershed areas (light bars) and the watershed areas of a sample of flash floods in the same region (dark bars).

Fig. 1.

Comparison between drainage areas of flash floods and gauged watersheds in the northeastern United States. (a) Spatial extent of a typical flash flood watershed (striped) and a typical gauged watershed (light gray): Newtown Creek at Elmira, New York (station 01530500). Streams, flood location, and gauge location are shown for reference. (b) Histogram of USGS (2011) gauged watershed areas (light bars) and the watershed areas of a sample of flash floods in the same region (dark bars).

The objective of this study was to examine the role of population in flash flood reporting. We hypothesize that flood reports are made more frequently in areas with higher population, even when other flood-generation processes are considered. This paper will investigate the difference between a model based only on physical processes and a model that also includes population to help determine if there is a significant population bias in flash flood reporting.

2. Methods

The study area was composed of 24 counties in New York and Pennsylvania (Fig. 2) that fall within the forecast area of the Weather Forecast Office (WFO) at Binghamton, New York. There are potential differences between forecast offices in local conventions or reporting style (e.g., number of database records per flood event), so we limited our study to an area covered by a single forecast office to avoid any such discrepancies. We chose the temporal scope of this study as 2007–13 because the most detailed location data were available beginning in October 2007, when NWS began using polygons to describe the geographical extent of flash floods.

Fig. 2.

(left) Study area (black outline) with geographic extents of flash flood reports for the 2007–13 study period (gray polygons). (right) State boundaries, shown for reference. Political boundaries were obtained from 2012 Topologically Integrated Geographic Encoding and Referencing (TIGER)/Line Shapefiles prepared by the U.S. Census Bureau (2012). Projection: universal transverse Mercator (UTM) NAD83 zone 18.

Fig. 2.

(left) Study area (black outline) with geographic extents of flash flood reports for the 2007–13 study period (gray polygons). (right) State boundaries, shown for reference. Political boundaries were obtained from 2012 Topologically Integrated Geographic Encoding and Referencing (TIGER)/Line Shapefiles prepared by the U.S. Census Bureau (2012). Projection: universal transverse Mercator (UTM) NAD83 zone 18.

Flash flood reports, including polygons representing the geographical extent of flooding, were obtained from the NWS Performance Management website (NWS 2015). There were 323 flash flood events recorded for the forecast area between 1 October 2007 and 31 December 2013. We aggregated the flash flood reports using the U.S. Census political boundaries at the minor civil division (MCD) level from the 2010 census (U.S. Census Bureau 2012). These geopolitical units are described by the U.S. Census Bureau as “the primary subcounty governmental or administrative units; they have legal boundaries and names as well as governmental functions or administrative purposes specified by State law” (U.S. Census Bureau 1994, p. 8-1). There were 559 MCDs (e.g., towns, cities, villages) in the study area. The areas of the MCDs ranged from 0.5 to 411 km2 with a median area of 81 km2. Their populations ranged from 98 to 145 170 people, with a median of about 2000 people (Fig. 3). MCDs were only included if they were entirely within the WFO Binghamton warning area. Reports occurred in 386 of the MCDs; that is, about 69% of MCDs had at least one flash flood report in the study period.

Fig. 3.

Population from the 2010 census for MCD political units in the study area. Darker shades represent higher population. MCD polygons were obtained from 2012 TIGER/Line Shapefiles prepared by the U.S. Census Bureau (2012). Projection: UTM NAD83 zone 18. See Table 1 for summary statistics.

Fig. 3.

Population from the 2010 census for MCD political units in the study area. Darker shades represent higher population. MCD polygons were obtained from 2012 TIGER/Line Shapefiles prepared by the U.S. Census Bureau (2012). Projection: UTM NAD83 zone 18. See Table 1 for summary statistics.

We tested the influences of selected environmental variables potentially relevant to flash flood generation (Fig. 4). To represent the physical processes underlying flash floods, we chose landscape variables of slope, percent impervious area, and soil saturated hydraulic conductivity (ksat). Basins with high average topographic slope are at particular risk for flash floods because high slopes increase the kinetic energy of surface runoff (e.g., Schmittner and Giresse 1996; Smith 2003). Average slope (percent change with elevation) was derived from the USGS National Elevation Dataset 10-m digital elevation models (Gesch 2007; Gesch et al. 2002). Landscapes with a large fraction of developed impervious area are also susceptible to high runoff (e.g., Hollis 1975; Leopold 1991; Rose and Peters 2001) that can lead to flooding. Average impervious area (percent) was determined from the 2011 National Land Cover Database (Xian et al. 2011).

Fig. 4.

Landscape and precipitation variables (averaged over each MCD). (a) Impervious area (%). (b) Topographic slope (%). (c) Rainfall intensity (mm h−1) represented by 5-yr, 5-min storm. (d) Saturated hydraulic conductivity (ksat; mm h−1). Rainfall depth is not shown because it was not a significant predictor in any model. Data sources are described in the text. All maps are in UTM NAD83 zone 18 projection.

Fig. 4.

Landscape and precipitation variables (averaged over each MCD). (a) Impervious area (%). (b) Topographic slope (%). (c) Rainfall intensity (mm h−1) represented by 5-yr, 5-min storm. (d) Saturated hydraulic conductivity (ksat; mm h−1). Rainfall depth is not shown because it was not a significant predictor in any model. Data sources are described in the text. All maps are in UTM NAD83 zone 18 projection.

Flash floods can result from either infiltration excess (Horton 1940) or saturation excess (Dunne and Black 1970) processes. Soil saturated hydraulic conductivity affects both of these processes. Soil saturated hydraulic conductivity ksat is a measure of how quickly water can move through the soil. This depends largely on soil texture; coarser soils tend to have higher ksat since water can pass more quickly through the soil pores. When the actual soil surface infiltration rate is unavailable, ksat can be used as a proxy to estimate this rate (e.g., Walter et al. 2003). The average saturated hydraulic conductivity (mm h−1) in the surface layer was derived from the State Soil Geographic Database (STATSGO), from the Natural Resources Conservation Service (NRCS 2010). The surface-layer depth varies with soil type; in the study region it is typically around 10–20 cm.

It was not clear how to represent precipitation characteristics in our analysis, but we determined storm duration and return period from radar-derived rain data for a set of 180 flash flood events over the northeastern United States (covering the states of Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, and Vermont) that occurred between 2003 and 2007 [see Jessup and Colucci (2012) for further description of these events]. We found that the median return period for storms causing these flash floods was the 5-yr storm. Thus, a representative rainfall depth for each MCD was defined by the areal average 24-h 5-yr storm rainfall depth (mm). Representative rainfall intensity for an MCD was defined by the 5-min 5-yr rainfall depth, converted to a rate in millimeters per hour. Other storm recurrence intervals (the 1-yr storm and 10-yr storm) were tested, but the model outcomes were similar with all recurrence intervals (data not shown). The values for each storm duration and return period were obtained from Northeast Regional Climate Center (NRCC) data (NRCC 2013).

Storm-specific factors such as rainfall intensity and total storm rainfall depth are important ingredients in producing flash floods (e.g., Maddox et al. 1979; Doswell et al. 1996). In addition, time- and space-variant antecedent soil moisture conditions have been shown through modeling and statistical analysis to be higher when flash floods occur (Jessup and DeGaetano 2008; Javelle et al. 2010; Nikolopoulos et al. 2011). While these dynamic variables are clearly important in determining where and when a given flash flood event will occur, in this study we focused on the relatively static variables as indicators of general landscape susceptibility. Other factors that have been associated with flood risk (e.g., vegetative cover) were not included, since their role is less well defined in the literature.

We modeled the number of flash flood reports Y in a given MCD as a function of slope S, impervious area I, soil saturated hydraulic conductivity K, representative rainfall depth D, and representative rainfall intensity R (Fig. 4; Table 1). We refer to this model as model 1 environment only (EO). The second model, referred to as model 2 with population (WP), included the effect of population P of each MCD, derived from the 2010 census, in addition to the environmental predictors from model 1 EO. For model 1 EO and model 2 WP, we used a Bayesian spatial Poisson model within the CARBayes package (Lee 2013) in R (R Core Team 2013). Random spatial effects are added by a conditional autoregressive (CAR) method to account for spatial structure that might not be totally explained by the model covariates. Using a Bayesian approach allows us to make inferences about the regression parameters while including the random spatial effects. The basic structure of these spatial models is

 
formula
 
formula

where is the set of responses (count of flood reports), λ is the expected mean of , β is the vector of regression parameters, is the matrix of predictor variables (, , , , , and ), and ψ is a set of random spatial effects based on assigned neighborhood weights. Thus, we assume that the count variable follows the Poisson probability distribution, that there is a linear relationship between the predictor variables and the natural log of the expected values of Y, and that there is spatial information, modeled by ψ, which is not accounted for by the predictors. We assigned a sphere of influence (SOI) graph weighting scheme with binary weights. All neighbors are weighted equally and nonneighbors have no influence (Bivand et al. 2008).

Table 1.

Summary statistics for response variable and predictor variables , , , , , and .

Summary statistics for response variable  and predictor variables , , , , , and .
Summary statistics for response variable  and predictor variables , , , , , and .

We used a Gaussian prior distribution for spatial regression parameters ψ suggested by Leroux et al. [2000, as described in Lee (2013)]. The prior distribution includes a spatial autocorrelation parameter ρ, which indicates the degree of spatial influence: where ρ = 0 there is no spatial autocorrelation and as ρ approaches 1 the amount of spatial autocorrelation increases. We also tested a nonspatial Bayesian Poisson regression model based on all of the predictor variables including population, referred to as model 3 nonspatial (NS).

The deviance information criterion (DIC) is a measure of the fit of Bayesian hierarchical models, based on the mean deviance of the responses and the number of effective model parameters (Spiegelhalter et al. 2002). The DIC was used to compare the spatial models, model 1 EO and model 2 WP, with a lower DIC implying better fit. This criterion is preferred to other methods such as Akaike information criterion (AIC) or F test because the number of effective parameters is being estimated. The root-mean-square error (RMSE) was also calculated to compare the spatial models with the nonspatial model 3 NS, with lower RMSE implying better model fit.

3. Results

Predicted flood report counts for each MCD were derived from the three models (Fig. 5). In model 1 EO, slope, impervious area, and ksat were significant at the 5% level, but the precipitation variables were not (Table 2, Fig. 5b). Slope and impervious area were positively correlated with flood reports, meaning an increase in either of these factors correlates with an increase in expected count of flash flood reports. The ksat was negatively correlated with flood reports, meaning that where soils have overall higher infiltration rates there tend to be fewer flood reports.

Table 2.

CAR–Poisson model outputs: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population. The nonspatial model is shown for comparison.

CAR–Poisson model outputs: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population. The nonspatial model is shown for comparison.
CAR–Poisson model outputs: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population. The nonspatial model is shown for comparison.
Fig. 5.

Flash flood report counts by MCD. Darker, bluer tones represent higher flood report counts. (a) Actual flash flood report counts. (b) Predicted counts from model 1 EO, based on only environmental variables. (c) Predicted counts from model 2 WP, based on environmental variables plus population. (d) Predicted counts from nonspatial regression including environmental variables and population. All maps are in UTM NAD83 zone 18 projection.

Fig. 5.

Flash flood report counts by MCD. Darker, bluer tones represent higher flood report counts. (a) Actual flash flood report counts. (b) Predicted counts from model 1 EO, based on only environmental variables. (c) Predicted counts from model 2 WP, based on environmental variables plus population. (d) Predicted counts from nonspatial regression including environmental variables and population. All maps are in UTM NAD83 zone 18 projection.

When population is included as a predictor, model fit only improves slightly (Fig. 6). In model 2 WP, slope is the only environmental variable that is still significant and population is also a significant predictor of flash flood reports (Table 2, Fig. 5c). The parameter estimates (β) indicate the increase in log ratio of the response () for a unit increase in the predictor variable. For example, in model 2 WP, an increase of 1% slope increases flood report count by about 0.06 and an increase of 1000 people increases expected flood reports by about 0.02 reports. The spatial correlation parameter ρ is significant for both models, meaning the properties of neighboring MCDs had significant effect on the expected count. In model 3 NS, all of the predictors except representative rainfall depth were significant (Table 2, Fig. 5d).

Fig. 6.

Graph of actual vs predicted flash flood report counts. Predicted counts shown are the mean predicted count for MCDs with the same actual count. Diamonds represent model 1 EO. Squares show model 2 WP. Triangles show model 3 NS. Overall, the spatial model with population is the best fit (Table 2).

Fig. 6.

Graph of actual vs predicted flash flood report counts. Predicted counts shown are the mean predicted count for MCDs with the same actual count. Diamonds represent model 1 EO. Squares show model 2 WP. Triangles show model 3 NS. Overall, the spatial model with population is the best fit (Table 2).

4. Discussion and conclusions

If flash flood reports are a reflection of “actual” (hydrologically defined) flash floods, we would expect to see reports concentrated in MCDs with high slope, high imperviousness, low saturated hydraulic conductivity, high rainfall depth, and high rainfall intensity. With these environmental variables as model predictors we found approximately this pattern. The representative rainfall variables were the exception, where neither depth nor intensity of a “representative” (5 yr) storm was significantly correlated with flood report count.

Rainfall values did not vary much over the study area, which could diminish the significance of their contribution to variation in flash flood report counts relative to other variables. A recent study by NWS reported flash flood report totals at a county level that do not correlate with rainfall patterns across the region, which corroborates our findings (NWS 2016). The depth and intensity of any given storm would be a better indicator of the influence of precipitation. Gathering these data for all 323 reported flash flood events was not within the scope of this study. However, these data were obtained for a small sample of reported flash flood events (N = 12) distributed across the study area [this sample was derived from the above-mentioned dataset compiled by Jessup and Colucci (2012)]. The storms associated with these flash floods ranged from less than the 1-yr storm to greater than the 100-yr storm. Thus, it is not obvious how to characterize a representative rainfall regime or threshold that would be a good predictor of where flash floods will be reported. Of course, we expect more rain or more intense rain will increase flood risks, but these results suggest other factors, such as antecedent soil moisture, may play comparable roles resulting in conditions in which a relatively wide range of storm sizes could generate a flash flood. Another potential explanation for the lack of association between rainfall variables and flash flood reports could be human adaptation to the rainfall characteristics of an area. For example, storm water systems are designed to manage runoff from a storm with a certain probability in the area. Where these systems are well designed it would take a particularly rare storm event to cause a flash flood. Conversely, where they are poorly designed (e.g., undersized culverts) the flash flood risk may be enhanced. We cannot completely rule out human interactions with the natural environment with respect to flash flood reporting.

Including population as a predictor had only a small influence on the model fit (Fig. 6), but it changed the level of significance of the environmental variables impervious area and ksat, while slope remained a significant predictor. This change in significance implies collinearity among the predictors, meaning places with higher populations also tend to have higher impervious area and higher ksat. As discussed later, the relationships between population, impervious area, and the hydrologic processes involved in flooding are not straightforward. One possible explanation for the relationship between population and ksat is that people tend to settle in valleys and near rivers, where soils tend to be coarser textured and thus have higher ksat.

While most of the environmental variables were significant in the model without population (model 1 EO), only slope remained significant when population was added (model 2 WP). This corroborates the finding of Schmittner and Giresse (1996) as well as the assertion of Smith (2003) that slope is the most important landscape variable in predicting runoff in extreme events.

The effect of impervious surfaces deserves particular attention. While increases in population generally lead to increases in impervious surfaces (e.g., roads and roofs), this is not a direct relationship. For example, MCDs in the study area with population of about 20 000 people had mean impervious areas ranging from about 2% to about 30%. Changes in land use and infrastructure can vary for reasons other than just population increase. The effects of these changes are also not necessarily obvious or intuitive. One study of the effects of roadside ditches on peak flows found that for less frequent storms (i.e., higher return period) the effect of increased development (in the form of increased drainage) is not as important as it is in more frequent storms (Buchanan et al. 2013). Another study showed that increased imperviousness was associated with lower peak flows (which would likely lead to less flash floods), possibly because of a related increase in human-designed storm water storage (e.g., Homa et al. 2013). Thus, the increase in flash floods in populated areas cannot be simply explained by the associated increase in impervious area.

We tested the influence of particularly large events by omitting flood reports from the two tropical storm (TS) systems that caused catastrophic flooding in the area in 2011. Together these events produced 70 flood reports, about 22% of the total number of flood reports in the study period. Excluding these events did not disproportionately affect the results of the models (Table 3). These additional spatial models were labeled model 4 EO no TS (corresponding to model 1 EO) and model 5 WP no TS (corresponding to model 2 WP). Omitting the 2011 tropical storm events produced better model fit by the DIC and RMSE comparisons, but the parameter estimates were very similar to the models with the complete dataset. Slope, impervious area, and ksat were significant predictors in model 4 EO no TS, and when population was added (model 5 WP no TS) impervious area ksat, and population were significant predictors. This suggests that the environmental variables that are most relevant to flash flood reporting could be slightly different in the most severe storm events.

Table 3.

CAR–Poisson model outputs as in Table 2, but excluding events from two tropical storms in 2011: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population.

CAR–Poisson model outputs as in Table 2, but excluding events from two tropical storms in 2011: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population.
CAR–Poisson model outputs as in Table 2, but excluding events from two tropical storms in 2011: posterior median regression parameters (β). Lower DIC indicates significant improvement in the model with the inclusion of population.

We were unable, with these data, to conclude the role that human behavior might have on flash flood reports. For example, one might expect that higher populations increase the number of flood reports simply because more people are present to observe the flood and make a report. Alternatively, if we accept “undesirable effects to life and property” as part of the definition of a flood, then we might conclude the increase in flood reports results from an increased concentration of human capital, that is, flash floods are reported when property is damaged or people are injured or killed. Distinguishing between these two explanations with currently available information is difficult because damage reports in the NOAA NCEI databases often are not precise. Damages, when reported, are estimates, and the full extent of damages might not be determined until well after the report has been recorded. While damage reports are somewhat unreliable, reports of injuries and fatalities are likely to be more accurate. An expanded study could use the model described here to predict the most dangerous floods (i.e., those that cause injury or death) based on the concentration of people in a given area. This would require a much larger sample size, however. Only 2 of the 323 events in this study had associated fatalities or injuries. Regardless, the fact that adding population as a predictor in our model did not substantially improve our predictions suggests that the presence alone of people is probably not significantly biasing the flash flood reporting. Rather, the effects of population are most probably related to the factors discussed above, including storm water systems and impervious surfaces. These interactions are complex and not always intuitive.

It is not possible with the currently available data to determine, for a given MCD with zero flood reports, whether that zero value results from a true lack of flash floods or merely a lack of reports. However, in the subset of this dataset with zero flood reports, places with higher susceptibility based on higher slopes tend to have lower population. Some of these high-slope, low-population places might have experienced unreported floods. For this reason, the records in the database cannot be relied on as identifying negative controls, that is, locations where floods did not happen.

As previously mentioned, the latitude and longitude point locations available from the publicly accessible version of the Storm Events Database are not as complete a representation of the locations of flash flood reports as the polygon data available from the NWS Performance Management Website (which requires a special login). However, we repeated our analysis using those point data from the Storm Events Database (NCEI 2015) as inputs and found the counts of flood reports were generally lower but the overall pattern and relationships were similar.

We conclude that the NWS Storm Data–Storm Events Database can be useful in identifying the locations of flash flood events. There are significant relationships between these locations and population and topographic slope. The correlation with population seems to be in part connected with the effects of impervious area but these interactions are not straightforward. The model developed here could be useful to future research because it accounts for spatial autocorrelation and the influence of population and environmental variables (including identifying variables that do not have significant impact on the number of flash flood reports). Future work could include analyses of the influence of socioeconomic factors like income and property values, infrastructure issues such as local variations in surface drainage and storm water system suitability, and time-of-day questions such as increased populations of downtown areas during working hours.

Acknowledgments

The authors thank the three anonymous reviewers for their valuable suggestions. We also thank Natalie Morse, Allison Truhlar, and Erin Menzies of the Cornell University Soil and Water Lab for their insights. This project was funded by the National Science Foundation Division of Earth Sciences (Award 0911076).

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