We developed a new approach for mapping landslide hazards by combining probabilities of landslide impacts derived from a data-driven statistical approach and a physically based model of shallow landsliding. Our statistical approach integrates the influence of seven site attributes (SAs) on observed landslides using a frequency ratio (FR) method. Influential attributes and resulting susceptibility maps depend on the observations of landslides considered: all types of landslides, debris avalanches only, or source areas of debris avalanches. These observational datasets reflect the detection of different landslide processes or components, which relate to different landslide-inducing factors. For each landslide dataset, a stability index (SI) is calculated as a multiplicative result of the frequency ratios for all attributes and is mapped across our study domain in the North Cascades National Park Complex (NOCA), Washington, USA. A continuous function is developed to relate local SI values to landslide probability based on a ratio of landslide and non-landslide grid cells. The empirical model probability derived from the debris avalanche source area dataset is combined probabilistically with a previously developed physically based probabilistic model. A two-dimensional binning method employs empirical and physically based probabilities as indices and calculates a joint probability of landsliding at the intersections of probability bins. A ratio of the joint probability and the physically based model bin probability is used as a weight to adjust the original physically based probability at each grid cell given empirical evidence. The resulting integrated probability of landslide initiation hazard includes mechanisms not captured by the infinite-slope stability model alone. Improvements in distinguishing potentially unstable areas with the proposed integrated model are statistically quantified. We provide multiple landslide hazard maps that land managers can use for planning and decision-making, as well as for educating the public about hazards from landslides in this remote high-relief terrain.
Most mountain ranges are susceptible to landsliding due to their steep geomorphology, loose-soil development, geology, and high precipitation (e.g., Coe, 2016). Landslides disrupt aquatic habitats (May et al., 2009; Pollock, 1998), damage infrastructure such as roads, utilities, and dams (Ghirotti, 2012; Baum et al., 2008), and harm people (Wartman et al., 2016; Taylor and Brabb, 1986). Landslide hazards are expected to increase globally with growing climatic extremes (Coe, 2016; Haeberli et al., 2017; Crozier, 2010).
Maps of landslide hazards, quantified as a probability of landslide initiation or impact, can be obtained using empirical methods that statistically relate the location of existing landslides to other environmental variables and physically based models based on geotechnical slope stability equations driven by hydro-climatic inputs (Bordoni et al., 2015; Mancini et al., 2010; Sidle and Ochiai, 2006; El-Ramly et al., 2002). While detailed quantitative and categorical climatic, geologic, ecologic, and pedologic information can be used in statistical models, physically based models are limited to geotechnical stability analyses driven by soil pore water pressure, and they often neglect geological factors such as bedrock, faulting, and complexities of microclimatic conditions. To date, data-driven empirical research on landslide hazard mapping (Corominas et al., 2014; Lee et al., 2007; Chung and Fabbri, 2002) has been typically conducted independently from hydroclimate-driven modeling of landslides that largely focus on hydrologic controls on landsliding (Wooten et al., 2016; Cevasco et al., 2014). There is a need for unifying these two lines of research to provide regional-scale landslide prediction for resource management and hazard mitigation strategies. In this paper we develop a statistical approach to combine the probability of landslide initiation obtained from an observation-based statistical mapping method and a physically based model. The proposed approach is illustrated in the North Cascades region of the state of Washington, USA.
Data-driven statistical landslide susceptibility approaches assess the inherent or quasi-static stability of hillslopes derived from statistical associations (e.g., correlations) between site attributes (SAs) (e.g., soil, geology, and topography) and an inventory of past landslides that includes landslide type and locations (e.g., Dai and Lee, 2002; Gupta and Joshi, 1990; Pachauri and Pant, 1992; Kirschbaum et al., 2012). These models focus on prevailing conditions that predispose hillslopes to failure (Hungr et al., 2014), typically providing general indices of relative landslide susceptibility or spatial probabilities applicable to the study location and cannot represent causal factors or triggering conditions that change in time (Van Westen et al., 2006; Sidle and Ochiai, 2006). The outcome of such analyses depends on the completeness of observations, hindering the use of such techniques over large areas where complete inventories are typically lacking. Since empirical models are based on observations of past landslides, the preconditioning relationships are assumed to prevail into the future until an updated study is completed (Lepore et al., 2012).
Physically based models require considerable data on the spatial-temporal characteristics of the landscape and triggering hydro-meteorologic events. These models are also usually restricted to a specific type of landslide and can be limited in representing local geologic, soil, and hydrologic conditions that may be difficult to observe and map in the field and parameterize in model theory. Data-driven statistical methods could be used to condition physically based model results to incorporate the influence of environmental and geologic factors that are not represented in process theory. Linking these empirically based and physically based models may improve the spatial-temporal patterns of landslide hazard at medium-to-large scales where landslide inventories exist to provide support tools for authorities addressing risk management. Additional descriptions of the advantages and disadvantages of data-driven and physically based models and landslide hazards assessments can be found in reviews by Ercanoglu and Sonmez (2019), Reichenbach et al. (2018), Hungr (2018), and Aleotti and Chowdhury (1999).
This paper describes research designed to address the following questions: (1) How can we quantify the relative contributions of local topography, geology, and ecology on landslide frequency and derive spatial probabilities of landsliding using a statistical model? (2) How would probabilities of landslide initiation derived from empirical observations compare with those derived from a physically based model? (3) How can we combine empirical and physically based models for landslide susceptibility to improve the prediction of landslide hazards?
The empirical approach for landslide susceptibility we used is based on a modification of the frequency ratio (FR) statistical concept which has been found to perform as well as more rigorous statistical approaches such as logistic regression (Hong et al., 2017; Wu et al., 2017; Bellugi et al., 2015; Lepore et al., 2012; Kirschbaum et al., 2012; Lee and Pradhan, 2007; Lee et al., 2007). As for the mechanistic model, we used the results of Strauch et al. (2018), who developed a Monte Carlo solution to the infinite-slope stability equation coupled with a steady-state topographic flow-routing approach to map the annual probability of shallow landsliding. The uncertainty of soil depth in Strauch et al. (2018) was constrained by a soil development model, and subsurface flow recharge was obtained from a regional macro-scale hydrologic model that produced historical hydrologic simulations (Hamlet et al., 2013).
Building on the advantages from the empirical and process models, we combined the two models to develop a map of landslide hazards. The integrated map can be developed to identify landslide hazards that may originate from the initiation of landslides, and it can be used to inform models of transport and deposition (i.e., runout) about landslide material (Fig. 1). The focus of the study was to determine if an empirical-based model of landslide hazards could be used to improve an existing physically based model for shallow landslide probability. The organization of this paper is as follows. Our methodology is discussed in Sect. 2, including the empirical method, model application, data compilation, and model integration approach. Section 3 details our results of the empirical application and integrated hazard model as well as various hazard maps developed. We end with some overall concluding thoughts in Sect. 4.
Primary landslide features of the Goodell Creek landslide
(October 2003) showing source, transport, and deposition areas illustrated over an aerial image. Base of the landslide is about 1 km across. Location in the North Cascades National Park Complex is about 4 km north of Newhalem, Washington. Source: © Google Earth, 48
We characterized the susceptibility of hillslopes to landslides using an empirically based frequency ratio approach (Lee et al., 2007; Kirschbaum et al., 2012). We used the term landslides broadly, covering all types of mapped landslides in our landslide inventory, with their source, transport and depositional zones (Fig. 1). The FR approach is related the density ratio of historical landslides within selected surface attributes, SAs. We considered seven SAs in our analysis: slope, elevation, aspect, curvature, land use–land cover (land cover), lithology, and rating on a topographic wetness index.
Slope, curvature, and lithology directly affect the forces and geotechnical properties in surface sediments. Land cover provides a surrogate for root cohesion, and a topographic wetness index has been used as a surrogate for soil pore water pressure (Borga et al., 2002). Elevation can represent the effects of climate, weathering, vegetation, ground motion, and glacial processes, if any, as well as coincide with variability in slope, soil depth, and land use (Sidle and Ochiai, 2006). Aspect provides an indication of solar insolation, vegetation type and cover density, snow and ice loading, and soil moisture levels via evapotranspiration (Beaty, 1956; Gokceoglu et al., 2005).
Each SA is indexed by attribute type,
The term in the numerator of Eq. (1) gives an empirical probability of a
landsliding impact within SA FR FR FR
FR in Eq. (1) is developed for a population of spatially distributed
locations that has the same attribute of a given SA
In order to develop a continuous relationship between SI
We included all SAs to develop empirical models relating SI to landslide probability, similar to Kirschbaum et al. (2012) and Lepore et al. (2012). We repeated the analysis described above three times: first, considering all landslide types and including their source, transport, and depositional zones, as is commonly done in multi-factor analyses (Sidle and Ochiai, 2006; Ayalew et al., 2004; Carrara et al., 1995); second, focusing on debris avalanches, with all three of their zones (Fig. 1); and third, considering only the source (initiation) areas of debris avalanches. These source areas were identified as the upper 20 % by elevation within mapped debris avalanche polygons, which appeared to align with inspections of aerial imagery of selected debris avalanches. This tiered approach can be used to quantify the relative contributions of different landslide features to overall landslide hazards in a region as well as inform the variability in hazard identification given a landslide dataset.
Here we develop a method to combine the empirical probability for landslide
initiation based on SI,
In combining probabilities, we focus on the landslide initiation areas, as the physically based model we used would only be applicable for landslide initiation. Empirical
If we treat the empirical probability as an index, the probability of
landslide initiation within a bin
Modeled probabilities may be improved when information contained in
empirical probabilities is introduced. The probability of landslide
initiation in areas shared by any two select bins (e.g., co-bins) of
empirically derived,
Illustration of the proposed landslide probability conditioned on estimated spatially distributed SI-based empirical and modeled probabilities as binned indices
We propose that the ratio of
A hypothetical example shown in Table 1 demonstrates calculating the
relative frequencies, the resulting calculated weight, and the adjusted
Hypothetical example of calculating relative frequency, weight, and
An example calculation of
Our study area is within the geographical limits of the North Cascades National
Park Complex (NOCA) managed by the U.S. National Park Service (Fig. 3). NOCA
has experienced damaging and disruptive landslides that have impacted
infrastructure and disrupted public use of the park. NOCA is approximately
2757 km
Four landslide types mapped within the North Cascades National Park Complex (NOCA) in Washington, USA. The number and their total area of each type is given in parentheses. Insert provides an example of mapping over an aerial image (© Google Earth) taken at 48
The orographic uplift of Pacific Ocean air masses generates a spatial
precipitation gradient with an average of 4575 mm of precipitation falling
annually on the highest elevations west of the crest, while lowlands east of
the crest receive a mean annual precipitation of 708 mm (Mustoe and Leopold,
2014; Roe, 2005). Air temperatures vary highly depending on the season and
elevation with the warmest month typically being August and the coldest month being
January; corresponding average daily temperatures are about 25 and 4
NOCA is dominated by forest vegetation, particularly coniferous tree species, up to about 2000 m (Strauch et al., 2018; Agee and Kertis, 1987). A patchwork of shrubs, herbaceous vegetation, and barren land is found above this elevation, which is common in alpine environments and in the paths of frequent snow avalanches. Above 2400 m there is mostly bare rock, snow, and ice. The underlying geology is composed of a primarily old Mesozoic crystalline and metamorphic rock originating far to the south (Haugerud and Tabor, 2009).
Landslide (LS) inventory data are the most requisite information needed for
an empirical statistical analysis (Lepore et al., 2012). Landslides were
mapped in the 2768 km
The landform mapping study identified six different types of mass wasting:
rock fall/topple, debris avalanche, debris torrent, slump/creep, sackung,
and snow avalanche-impacted landforms (SAILs) of which four are described in
Table 2 (Riedel et al., 2012). The single sackung mapped in NOCA represents
a gravitational spreading or slope deformation, sometimes found near ridge
tops. All landslide types were included in the analysis except for the rare
sackung and SAILs, which are created by a snow avalanche impacting
unconsolidated sediments rather than slope instability. The idea is to
capture more spatial variability and geologic controls on observed
landslides by using all the data we obtained that was available from the
inventory for the four common landslide types. There are 1618 landslides
mapped in NOCA: falls/topples (68 %), debris avalanches (17 %), debris
torrents (10 %), slumps/creeps (4 %), and one sackung (
Landslides mapped as part of a comprehensive landform mapping study used in hazard analysis (Riedel et al., 2012).
We constrained our analysis to soil-mantled landscapes by excluding high-elevation areas covered by glaciers, permanent snowfields, and exposed
bedrock, as well as wetlands and other water surfaces, based on landform
mapping and maps of lithology and land cover. We also exclude slopes less
than 17
The seven site attributes investigated using the frequency ratio
approach as they relate to mapped landslide activity vary across the NOCA
study area. Slope, total curvature (Laplacian of elevation), and aspect
attributes were derived using ArcGIS from a 30 m DEM acquired from the National Elevation Dataset (NED) (USGS, 2014a). A
resolution of 30 m was chosen for comparability with other studies and
landslide size (e.g., Strauch et al., 2018; Lepore et al., 2012). Elevation
ranges from 107 to 2794 m with 85 % of the park between 500 and 2000 m.
Subcategories for elevation were based on 200 m increments with lumping at
the ends (e.g.,
The DEM also provides the information needed to derive a distributed wetness index (Beven and Kirkby, 1979; O'Loughlin, 1986), calculated as the natural log of the ratio of the specific catchment area [L] to the sine of the local slope. This index has been used for quantifying the contribution of pore water pressure to destabilizing forces in landslide modeling (e.g., Borga et al., 2002; Gokceoglu et al., 2005). The wetness index was divided into five subcategories based on 20 % quantiles: low, low-medium, medium, medium-high, and high wetness. The land cover was acquired from the 2014 National Land Cover Database (NLCD), which is based on 2011 Landsat satellite imagery (Jin et al., 2013; USGS, 2014b). We categorized this into forest, shrubland, herbaceous, water, wetland, snow/ice, barren, and developed (e.g., roads, campgrounds). Based on this classification, forest, shrubs, and herbaceous vegetation represent 54 %, 15 %, and 10 % of the park, respectively. Barren land and snow or ice together cover 17 %, typically at the high elevations. Water and wetlands cover about 2.5 %, while the developed area is less than 0.5 %.
Lithology provides a description of the rock and deposits that indicates composition, strength, and age, which can influence the hillslope strength and water redistribution. Washington State Department of Natural Resources (WADNR) provides lithology in its surface geology maps that display rocks and deposits as geologic map units (WADNR, 2014). This source of information was chosen because it is available for all of Washington, facilitating future applications. There are 48 lithology map unit types within NOCA. These were aggregated into seven subcategories, based on similarities in origin and generally increasing strength, called (1) unconsolidated sediment, (2) ultramafic, (3) weak metamorphic foliated, (4) sedimentary rock, (5) hard metamorphic, (6) intrusive igneous, and (7) volcanic/extrusive igneous (Table 3). Water and ice were not classified. Both land cover and lithology were rasterized to the same DEM grid resolution using ArcGIS based on the dominant type of attribute in each grid cell. Among the seven types of lithology, hard metamorphic is most common (41 % of NOCA), while ultramafic, sedimentary rock, and volcanic/extrusive igneous combined make up less than 5 %.
Classification from the Washington Department of Natural Resources of surface geology from generally weaker (1) to stronger (6) material along with aerial percentages within NOCA in parentheses.
The results of the FR analyses for each site attribute are presented in
Fig. 4. We discuss the role of SA starting with debris avalanche source
areas as they are hypothesized to represent the initiation processes of
shallow landslides that transform into debris avalanches. The SAs that
impact shallow landslide initiation could arguably play common controls on
the initiation of other types of slope failures. The frequency analysis
shows a clear and growing control of local slopes greater than 35
Frequency ratio (FR) values for different bins of seven site attributes (SA) separated by red lines, based on
The source area of debris avalanches is only about 17 % of the mapped
debris avalanche area and 10 % of the whole landslide inventory, which
predominantly maps transport and depositional areas. A small debris
avalanche source area in steep terrain can lead to large landslide impacts
in lower elevations, as the eroded material travels downhill and deposits in
gentler gradients (Fig. 1). Thus, the runout zones of debris avalanches and
other mapped landslide types cover more area at gentler slopes typical of
lower elevations. This process is captured in Fig. 4a and b where the FR analyses exhibit higher landslide hazards at gentler slopes (
In the study area, local slopes generally increase on average with
elevation, particularly above 1400 m (Strauch et al., 2018). The control of
steeper slopes on debris avalanche initiation is supported by the results
for elevation, where source areas are associated with mid-to-high elevation
(1400 to 1800 m) and entire debris avalanches and all landslides types,
including deposition zones, have growing frequency in lower elevations
(
Developed areas that include impervious surfaces, constructed materials, and lawns have the highest land cover association with all mapped landslide areas, as well as with debris avalanches, yet they have no association with debris avalanche source areas, which are typically higher on mountains and rarely developed. Although dirt roads have been found to disrupt drainage and increase erosion (Croke and Hairsine, 2006; Montgomery, 1994; Swanson and Dyrness, 1975), the lack of association with landslide initiation suggests that developed areas may be positioned on the landscape in areas likely to be impacted by landslide runout or deposition. In general, forest and barren land cover show the least landslide activity compared to other land cover (Fig. 4). The forest association likely indicates the positive contribution of root cohesion to hillslope stability, whereas the barren land cover type results may indicate the effect of mapping completeness or hillslope processes. The results of the barren areas appear counter to the findings of the physically based landslide model applied at the same location, which found a high probability of landslide initiation in barren areas often below retreating glaciers (Strauch et al., 2018). Barren areas include bedrock, glacial debris, and other accumulations of earthen material with vegetation generally accounting for less than 15 % of total cover; thus, there may be a variety of stability conditions within this single-cover class.
The sources of debris avalanches are linked to eastern and southeastern
aspects (Fig. 4c); 20 % and 15 % of source cells by area occur on these
aspects, respectively. Except for western aspects that show the weakest
association debris avalanches, other aspects show landsliding frequency
close to the average frequency in the whole study domain. Vegetation type
and cover that relate to root strength and moisture regime can be related to
aspect. Eastern and southern exposures have lower forest cover fractions compared
to other aspects at mid-to-lower elevations (
Vegetation cover fraction in NOCA on each aspect, taken as the fraction of vegetation type within each 200 m elevation band. Aspects
categorized here as
When all landslides are considered, northern slopes exhibit a growing
landslide association, while landslide frequency declines in southeastern
slopes compared to the other landslide datasets (Fig. 4a and b). North-facing
slopes have been documented to retain more soil moisture than south-facing
aspects in northern latitudes (Geroy et al., 2011), which can be broadly
responsible for more initiation, transport, and deposition impacts of all mass
wasting types. Hillslope asymmetry (i.e., steeper slopes depending on
aspect) was not found during the inspection of the average slope on the four primary
aspects. North–south asymmetry has been found to demonstrate a reversal based
on elevation and a 49
Comparisons among all landslides, whole debris avalanches, and debris
avalanche source areas clearly show that unconsolidated sediments, largely
derived from transport and depositional processes, have a stronger association
with landslides than other lithologies followed by sedimentary rock (Fig. 4). This strong association is expected given the inclusion of mass wasting
landforms in the classification of unconsolidated sediment. The high
ultramafic-rock association when considering all landslide types is driven
by a single topple/fall occurring in this scarce lithology (
The association of landslides on concave/converging vs. convex/diverging topography is relatively consistent among the datasets and generally consistent with the literature due to enhanced wetness where vegetative support may be weak in deeper soils (see Hales et al., 2009; Fig. 4). A high-wetness index is associated with landslides for all landslide types as well as entire debris avalanches (Fig. 4a and b). This result is intuitive as this index is an indicator of increased soil saturation and surface runoff. In contrast, source areas were correlated with a low-wetness index (Fig. 4c). This counterintuitive finding, however, aligns with previously discussed results that source areas are associated with the loss of root strength, steep slopes, and higher elevations, resulting in relatively small specific catchment areas. By definition, a wetness index is negatively correlated with the slope and positively correlated with the specific contributing area. Thus, source areas will have a low-wetness index when they are from steep slopes with small contributing areas (i.e., located higher up on hillslopes).
A susceptibility index is calculated for each grid cell within the
study area domain by Eq. (3). Cumulative distributions for SI, plotted
as a fraction of area of the study domain as well as only in the areas where
landslide impact was mapped, show higher SI values for a given fraction of
the respective domains where a given SI is exceeded (Fig. 6a, d, and g).
Additional support beyond the graphics that these distributions are not
equal is provided by the Kolmogorov–Smirnov test, which rejects the null
hypothesis of equal distributions at
Cumulative distributions
The probabilities of a landslide impact,
The probability of landslide impacts estimated from SI,
Maps of the probability of a landslide impact derived from an empirical model based on
Maps of
We developed a map of annual probability of shallow landslide initiation by
combining the empirical SI-based probability (Fig. 7c) and the
physically based annual probability of landslide initiation from Strauch et
al. (2018),
Approximately 30 % of the analyzed cells had weights
Anomaly maps displaying the difference between
Other cells declined in probability, particularly on gentler slopes, north-to-west-facing aspects, and at low (
To investigate the spatial distribution of
We anticipated that the additional consideration of the empirical model
represented by the weighting term improves the performance of the purely
physically based model. Thus, to assess the potential performance of the
models, we statistically evaluated the models using curves of the receiver operating
characteristics (ROCs) (Fawcett, 2006). This approach examines cells
within mapped landslides and cells outside landslides for a study area and
compares this to randomly distributed landslides over the same landscape.
Confusion matrices are generated from observed and modeled landslides based
on varying the probability of a landslide threshold used to generate curves of the ROCs (Mancini et al., 2010; El-Ramly et al., 2002; Anagnostopoulos et
al., 2015) (Fig. 10b). A better-performing model curves towards the upper-left corner, and a curve along the
Both the physically based model,
Empirically based probability hazard maps were developed from a
statistically based susceptibility index, which integrated the influence of
site attributes on observed landslides based on a frequency ratio approach.
The resulting susceptibility depends on the observations of the landslides
considered: all types of landslides, debris avalanches only, or source areas
of debris avalanches. Thus, the objectives of a hazard identification study
dictate the necessary inventory of landslide features. The empirically based
probability model based on source areas was used to adjust a previously
developed physically based probabilistic model through a calculated
weighting term developed from a joint spatial probability. The frequency
analysis, hazard map development, and integrated-probability model
identified several key findings when applied to a national park.
The frequency analysis shows a clear and growing control of local slopes greater than 35 The debris avalanche source areas are associated with mid-to-high elevation (1400 to 1800 m), while all landslide types and whole debris avalanches have a growing impact in lower elevations ( The slope is a key attribute for the initiation of landslides, while lithology is mainly tied to transport and depositional processes. The transition from subalpine to alpine herbaceous vegetation with lower root cohesion correlates with a higher frequency of debris avalanche initiation. The east and west aspects are positive and negative landslide-influencing factors, respectively, likely due to differences in the moisture regime and forest cover and associated root cohesion. The empirical statistical modeling used to adjust a physically based model of landslide initiation improved the predictability of observed landslides by accounting for additional factors that influence the landscape's susceptibility to failure not represented in the physically based model. Empirical adjustments generally lowered the probability of failure of the physically based model, especially for
As the occurrence of landslide runout is conditioned on the failure of
source areas, future studies could combine the probabilistic initiation
methodology we propose in this paper with a landslide runout model to
improve the prediction of hazards from entire landslides. The applicability of
our approach to characterize shallow landslide hazards is limited by the
quality of the site-specific data on soils and vegetation, the extent of
hydrologic modeling, as well as the accuracy and completeness of the
landslide inventory. Accurate data for environmental variables such as
the geology, soils, and vegetation would be as important as comprehensive
landslide data, as the empirical approach relates landslide hazards to the
environmental variables. Although the approach is applicable elsewhere, our
results from the empirical analyses are specific to the region in which they
were developed and may differ in another location with a different geology and
landslide inventories. Additionally, the probabilities are likely to change
as local conditions change from disturbances such as fires or as the climate
continues to change. Advancements in surface terrain delineation and in
distributed hydrologic modeling specifically contribute to the broad
applicability of this approach. We provide multiple landslide hazard maps
for the national park that land managers can use for planning and decision-making, as well as educating the public about hazards from landslides so they can minimize risks from these geohazards.
The data used in this analysis are available on HydroShare at
RS and EI designed the research, developed the models, performed the simulations, and created the figures. JR provided landslide and geology data as well as insights into the approach and model demonstration. RS prepared the paper with contributions from all co-authors.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Advances in computational modelling of natural hazards and geohazards”. It is a result of the Geoprocesses, geohazards – CSDMS 2018, Boulder, USA, 22–24 May 2018.
We thank Stephen Dorsch of the North Cascades National Park Complex for providing electronic copies of landslide data and reports. Dan Miller and Christina Bandaragoda provided helpful suggestions on preliminary results.
This research has been supported by the US National Science Foundation (grant nos. CBET-1336725 and ICER-1663859, PREEVENTS) and by a Department of the Interior USGS Northwest Climate Adaptation Science Center graduate fellowship awarded to Ronda Strauch (grant no. GS240B-B).
This paper was edited by Albert J. Kettner and reviewed by two anonymous referees.