LandslidesDOI 10.1007/s10346-018-0950-zReceived: 20 July 2017Accepted: 10 December 2017© This is a U.S. Government work andnot under copyright protection in the US;foreign copyright protection mayapply 2018

Matthew A. Thomas I Benjamin B. Mirus I Brian D. Collins I Ning Lu I Jonathan W. Godt

Variability in soil-water retention propertiesand implications for physics-based simulationof landslide early warning criteria

Abstract Rainfall-induced shallow landsliding is a persistenthazard to human life and property. Despite the observed con-nection between infiltration through the unsaturated zone andshallow landslide initiation, there is considerable uncertainty inhow estimates of unsaturated soil-water retention propertiesaffect slope stability assessment. This source of uncertainty iscritical to evaluating the utility of physics-based hydrologicmodeling as a tool for landslide early warning. We employ anumerical model of variably saturated groundwater flow pa-rameterized with an ensemble of texture-, laboratory-, andfield-based estimates of soil-water retention properties for anextensively monitored landslide-prone site in the San FranciscoBay Area, CA, USA. Simulations of soil-water content, pore-water pressure, and the resultant factor of safety show consid-erable variability across and within these different parameterestimation techniques. In particular, we demonstrate that withthe same permeability structure imposed across all simulations,the variability in soil-water retention properties strongly influ-ences predictions of positive pore-water pressure coincidentwith widespread shallow landsliding. We also find that theensemble of soil-water retention properties imposes an order-of-magnitude and nearly two-fold variability in seasonal andevent-scale landslide susceptibility, respectively. Despite thereduced factor of safety uncertainty during wet conditions,parameters that control the dry end of the soil-water retentionfunction markedly impact the ability of a hydrologic model tocapture soil-water content dynamics observed in the field.These results suggest that variability in soil-water retentionproperties should be considered for objective physics-basedsimulation of landslide early warning criteria.

Keywords Hillslope hydrology . Unsaturated zone . Shallowlandslides . Numerical modeling . Early warning

IntroductionShallow landslides remain a highly relevant societal hazardbecause of the threat to human life and infrastructure associ-ated with their potential mobilization as debris flows (Sidleand Ochiai 2006). The majority of shallow landslides areinduced by precipitation (Lu and Godt 2013), so understand-ing the associated near-surface hydrologic response is para-mount to assessing the potential for landslides that maymobilize into debris flows. The primary focus of hydrological-ly driven landslide investigations is the temporal variation insubsurface fluid pressure that can eventually cause instability.Conceptual models for pore-water pressure dynamics relevantto shallow slope failures (i.e., where the length to depth ratiois > 10; Casadei et al. 2003) necessarily involve the transmis-sion of groundwater through the unsaturated zone. Thegoverning equation for one-dimensional (1D) subsurface flow

through the unsaturated zone, commonly known as theRichards equation (Richards 1931), is given by:

∂ψ∂t

∂θ∂ψ

¼ ∂∂z

K ψð Þ ∂ψ∂z

þ 1� �� �

ð1Þ

where ψ is the pressure head [L], θ is the soil-water content [−], zis the vertical spatial coordinate [L], K is the hydraulic conductiv-ity [LT−1], and t is the time [T]. Pore-water pressure (uw) isexpressed as (see Freeze and Cherry 1979):

uw ¼ pwgψ ð2Þ

where pw is the density of water (998 kg m−3) and g is theacceleration due to gravity (9.81 ms−2).

Nonlinear functions that describe θ(ψ) and K(ψ) are requiredto solve Eq. 1. Numerical simulations of variably saturated flowrelated to slope instability problems (e.g., Ebel et al. 2010; Thomasand Loague 2014; McGuire et al. 2016) have used the closed-formexpressions of van Genuchten (1980) and Mualem (1976), whichare respectively given as:

θ ψð Þ ¼ θr þ θs−θr1þ αψj jnð Þm ð3Þ

K ψð Þ ¼ Ksθ−θrθs−θr

� �ℓ

1− 1−θ−θrθs−θr

� � 1m

!m" #2ð4Þ

where θs is the saturated soil-water content [−], θr is the residualsoil-water content [−], α is the inverse of the air-entry ψ [L−1], n isthe pore-size distribution index [−], ℓ is the pore-connectivityparameter [−], Ks is the saturated hydraulic conductivity [LT−1],and m ¼ 1− 1

n [−]. The parameters α, n, m, and ℓ (typically ℓ = 0.5;Mualem 1976) are empirical fitting coefficients that are not mea-sured directly. Herein, we refer to soil-water retention propertiesas the parameter set including θs, θr, α, n, and m.

Texture-, laboratory-, and field-based methods are three typ-ical approaches used to approximate soil-water retention prop-erties and to facilitate the quantification of Eqs. 3 and 4.Texture-based methods are relatively easy to use, often requir-ing only an estimate of particle size distribution to queryagainst a library of historical drainage experiments for repackedsoil cores (e.g., Schaap et al. 2001). Texture-based parameter

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estimates, however, do not represent the actual soils from thearea of interest and generally describe only an average dryingbehavior. Wetting experiments conducted in the laboratory per-mit an investigator to closely manipulate and measure variablessuch as column inflow/outflow (e.g., Wayllace and Lu 2012), butthe soil sample is typically small and usually repacked, therebylimiting the scale of heterogeneity and expression of anisotropytrue to the field. Parameters derived from in situ field measure-ments of θ and ψ record the impacts of site-specific heteroge-neity and anisotropy in response to natural climatic forcings(e.g., Ebel et al. 2010), but the sensor arrays can be costly toinstall, require a considerable effort to maintain, and may in-troduce point-specific bias. Prior simulations for a gently slop-ing rangeland catchment suggest that these three differentmethods for estimating soil-water retention properties can im-pact simulated runoff response (Mirus 2015), so here, we exam-ine this possibility further within the context of hillslopehydrology and landslide initiation potential.

Early warning systems for widespread shallow landsliding havetypically relied on historical rainfall and landslide records todevelop empirical thresholds for hazard or warning levels (Baumand Godt 2010). However, the automatic monitoring of subsurfacehydrologic state variables critical to the assessment of shallowslope failure (i.e., θ and uw) is becoming more common (e.g.,Torres et al. 1998; Baum et al. 2005; Collins et al. 2012; Smithet al. 2014). Scientists have identified the value of pairing suchdata with physics-based models, advocating the development ofrainfall thresholds with deterministic simulations of variably sat-urated flow (e.g., Godt and McKenna 2008; De Vita et al. 2013; Papaet al. 2013; Salciarini et al. 2013). Numerical simulation of near-surface hydrologic response for the shallow landslide initiationproblem is a promising approach to better inform or advanceearly warning capabilities beyond thresholds based on rainfallduration and intensity (Capparelli and Versace 2011). The realiza-tion of that goal, however, requires improved quantitative under-standing of how alternative methods to parameterize simulationsof variably saturated flow impact slope stability calculations.

While valuable contributions focusing on the major role playedby boundary conditions and initial conditions on the simulatedbehavior of shallow slope covers have been made (e.g., Greco et al.2014; Bogaard and Greco 2016; Napolitano et al. 2016), the impactof measurement-based variability in soil-water retention proper-ties (i.e., θs, θr, α, n, and m) on slope stability assessment is lessstudied. Herein, we investigate the sensitivity of soil-water reten-tion properties on slope stability assessment using texture-, labo-ratory-, and field-based parameter estimates from a landslide-prone site in the East Bay Hills of the San Francisco Bay region,CA, USA. (Collins et al. 2012). Rather than exhaustively character-izing the full spectrum of heterogeneity that is possible for ourstudy area, the objective is to quantify the effect of the (presentlyknown) measurement-based uncertainty in soil-water retentionproperties on simulated variables that could be used for landslideearly warning criteria. Specifically, we conduct numerical simula-tions of variably saturated flow with texture-, laboratory-, andfield-based parameter estimates for the θ(ψ) and K(ψ) functionsto examine their impact on θ, uw, and the attendant factor of safety(FS). We hypothesize that modeled event-scale and seasonal shal-low landslide susceptibility will be influenced by the selection of aparameter estimation method as well as variability within each

method for characterizing a soil of interest. We also expect thatneglecting this source of variability for the unsaturated zone willdegrade the ability of a forward simulation protocol to capturepositive uw coincident with widespread shallow landsliding. Thevalue of the work presented here lies in its ability to (1) improveunderstanding of how approaches to parameterize and simulatevariably saturated flow influence slope stability assessment and (2)generate insight relevant to a hypothetical physics-based earlywarning system for widespread shallow landsliding.

Study AreaOur simulations use information from a shallow landslide moni-toring station operated by the U.S. Geological Survey in the SanFrancisco Bay region, CA, USA (Fig. 1a; Collins et al. 2012). Ourstudy area, termed BBALT1,^ is located in a steep (greater than 30°)first-order drainage in the East Bay Hills of Alameda County (Fig.1b, c). The site consists of an approximately 1000 m2 grasslandhollow with shallow (≈ 1 m in depth) silty sand to silty clay soils(Lu et al. 2013) overlying sandstone bedrock of the Orinda Forma-tion (Dibblee and Minch 2005). The topographic hollow is typicalof many that experience landslides in the East Bay region duringwinter rainstorms.

The BALT1 monitoring station was established in 2009 with asuite of telemetered instrumentation for better understanding theeffects of hydrology on shallow landsliding. Two sensor arrays (anupslope and downslope; Fig. 1d) are installed along the axis of thehollow. Each array includes two Decagon EC-5 volumetric soil-water content sensors (0.25 and 0.7 m depth for the upslope; 0.3and 1.4 m depth for the downslope) and one Stevens GreenspanPS7000 positive uw sensor (0.75 and 1.3 m depth for the upslopeand downslope, respectively). The PS7000 sensors are installednear the soil-weathered bedrock interface where shallow landslidesare expected to initiate. An Onset Hobo U30 tipping bucket raingauge is located midslope, just off the hollow axis. We use thesetelemetered (10-min) data to evaluate simulated θ and uwdynamics.

In addition to the telemetered data, the western nose of theBALT1 hollow is also instrumented with three arrays of collocatedEC-5 sensors and Decagon MPS-1 soil suction sensors. Thesearrays are connected to a separate data logger and are nottelemetered. The three arrays are oriented in a line parallel tothe slope and spaced 0.4 m apart. Each array includes four pairsof soil-water content and soil suction sensors spaced 0.2 m in thevertical. We use these non-telemetered (15-min) data to establishfield-based soil-water retention parameter estimates.

Although much of the BALT1 hydrologic dataset reflectsdrought conditions, several time frames were sufficiently wetto cause widespread landsliding in the East Bay region. Rainfallin March 2011 triggered 31 shallow landslides within a 5-kmradius of the site where positive uw as high as 1.8 kPa at 0.75-m depth was recorded (Collins et al. 2012). Water year (WY)2016–2017 (measured from 1 October to 30 September) alsohosted a wet winter season. Cumulative rainfall in January andFebruary 2017 (Fig. 2) was 130 and 150% of normal, respectively.Positive uw in excess of 2.5 kPa at 0.75-m depth occurred duringfour rainstorms over this 2-month period, with thousands ofresultant landslides in the East Bay region, including at least 90slope failures in the greater BALT1 catchment (Corbett, personalcommunication). The widespread landsliding wreaked havoc on

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roads and other infrastructure (e.g., water and electrical trans-mission lines) and severely damaged several homes in the SanFrancisco Bay region.

The BALT1 hollow did not experience slope failure in WY 2016–2017, but the monitoring station did capture the hydrologic re-sponse for the same rainfall events that generated the widespreadregional slope instability. The WY 2016–2017 data provide a richresource for evaluating hydrologic simulations designed to quan-tify the effects of unsaturated zone hydrology on shallow landslideinitiation.

Methods

Simulation frameworkWe conducted numerical simulations of 1D, transient, and variablysaturated flow for a two-layer system to quantify the impact of soil-water retention properties on hydrologic conditions and FS calculationsrelevant to shallow landslide potential. The single vertical dimensionfacilitated our understanding of parameter variability and infiltrationisolated from the effects of lateral saturated flow and spatially variablebedrock thickness. The numerical model we used to solve Eq. 1 (with anadditional sink term to account for evapotranspiration and root-wateruptake) is HYDRUS-1D (Šimůnek et al. 2009), which employs aGalerkin-type linear finite-element scheme and Picard iterative solutionscheme to approximate the spatial and temporal derivatives. The suite ofHYDRUS 1, 2, and 3D codes have been applied successfully to a varietyof recent investigations focusing on shallow landslides (e.g., Lanni et al.2013; Bordoni et al. 2015; McGuire et al. 2016; Mirus et al. 2017).

Our boundary-value problems (BVPs; Fig. 3) correspond to theupslope and downslope sensor arrays at our field site (Fig. 1d); eachdomain consists of a two-layer (i.e., soil and weathered bedrock)system, totaling 5 m in depth. The finite-element mesh for each BVP

includes 1001 nodes with a uniform spacing of 5 × 10−3 m. We selectedthe 5-mdepth tominimize the impact of the lower boundary conditionon the area of interest (i.e., the soil-weathered bedrock interface).Although we characterized the soil-water retention properties fromtexture, laboratory, and field measurements, we have no water reten-tion information for the weathered bedrock and therefore made nodistinction between the θr, θs, α, and n values for the two layers.

Soil-water retention propertiesThe three data sources we used to estimate soil-water retentionproperties are (1) soil texture, (2) laboratory experiments, and (3) insitu field monitoring. Six sets of parameter estimates for each type ofdata represent a possible range of variability within the soil at BALT1.We estimated the texture-based soil-water retention properties usingexisting particle size distribution data from six samples collected atBALT1 (Lu et al. 2013) and hierarchical pedotransfer functions (Schaapet al. 2001). We selected the Schaap et al. (2001) method because it isone of the most commonly employed approaches to relate soil textureinformation to the closed-form expressions of Van Genuchten (1980)and Mualem (1976). We assigned the laboratory-based soil-waterretention properties from existing parameter sets, as reported by Luet al. (2013). These wetting condition values were derived from exper-iments using a transient release and imbibitionsmethod (seeWayllaceand Lu 2012) for six intact soil core samples collected at BALT1. Finally,we derived the field-based θr, α, and n values by conducting anonlinear least squares fitting of the non-telemetered data from thewestern nose of BALT1 using the collocated soil-water content and soilsuction data. We optimized and evaluated curve-fitting for the wettingdata with the Levenberg-Marquardt (Marquardt 1963) approach. Thesix best fit parameter sets (Supplementary Figure S1), each represen-tative of an average wetting curve, were insensitive to our initialestimates and exhibit coefficients of determination (R2) ranging from

Fig. 1 a Location of the BALT1 shallow landslide monitoring station in the San Francisco (SF) Bay region of CA, USA. Coordinates in degrees and meters correspond toWGS84 and NAD83 (Zone 10) projections, respectively. b Topographic map of the 1.5 km2 BALT1 catchment (darker shading with white border). c East-looking photographof the BALT1 area and location of a nearby slope failure (white circle). d Southeast-looking photograph of the 1000 m2 BALT1 hollow paired with a schematic cross sectionof the BALT1 subsurface monitoring network. Rain gauge, data acquisition, and telemetry equipment shown housed in the lower right corner of photograph. Depthslabeled in schematic indicate location of soil and weathered bedrock interface

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0.63 to 0.87. Due to the limited operational range of the MPS-1 sensors(i.e., − 10 to − 500 kPa), we selected the field-based θs value as themaximum θ coincident with positive uw in WY 2016–2017 (Fig. 2). Weused the telemeteredmonitoring network at BALT1, located within theaxis of the hollow, to evaluate the performance of the texture-, labo-ratory-, and field-based soil-water retention properties. In this way,the field-based soil-water retention properties are not unfairlyBtrained^ to the telemetered observations of soil-water content.

To capture the Ks needed for our simulations, we made 18 fieldmeasurements within the BALT1 hollow with a Decagon DualHeadinfiltrometer and Soilmoisture 2800 Guelph Permeameter. These dataindicate the soil Ks and the weathered bedrock Ks at our site may bereasonably approximated as 1 × 10−5 and 1 × 10−7 ms−1, respectively. Theorder-of-magnitude estimates are corroborated by the upper and lowerbounds of permeameter experiments conducted throughout the EastBay region (Godt and Coe, personal communication). We appliedidentical soil Ks (1 × 10−5 ms−1) and weathered bedrock Ks (1 ×10−7 ms−1) values across all simulation scenarios to focus our effortsexclusively on soil-water retention properties.

We constructed a seventh parameter set for each of the threeparameter estimation methods (i.e., texture, laboratory, and field) fromthemean of the six sets of soil-water retention properties, resulting in 21total parameter sets (Fig. 4; Table 1). The ensemble of soil-waterretention parameter sets exhibit considerable variability in θ(ψ) andK(ψ) curve shape (Fig. 4). High α values for the texture-based param-eter estimates (Table 1) produce the sharpest changes in θ and K forψbetween− 1 and 0m. The laboratory-based parameter estimates, with awider range of θs and θr values, but the lowest α values, produce θ(ψ)and K(ψ) curves with the shallowest slopes forψ between − 1 and 0 m.The intermediate range of θr, α, and n values for the field-basedparameter estimates produces θ(ψ) and K(ψ) curves with a steepnessintermediate to those of the texture- and laboratory-based curves.

Boundary and initial conditionsThe upper boundary condition for the numerical simulations is a time-dependent flux accounting for rainfall and evapotranspiration (ET)from 1 November 2016 to 31 March 2017 at 10-min intervals. As we haveno site-specificmeasurements to constrain ETat our study area, we useddaily temperature records from the Oakland International Airport (≈15 km to the west) and a formulation by Hargreaves (1994) to estimatedaily potential ET. To meet the resolution of our rainfall data, wecalculated 10-min variation in potential ET using the Fayer (2000)approach. This formulation assumes that potential ET from 00:00 to06:00 and 18:00 to 24:00 represents 1 % of the total daily potential ETand that a sinusoidal shape, with a peak at 12:00, follows for theremainder of the day (Šimůnek et al. 2009). We accounted for root-

Fig. 3 Schematic of the upslope and downslope boundary-value problems (BVPs).Upper boundary conditions shown with rainfall (R) and evapotranspiration (ET)prescribed as a function of time (t). Lower boundary conditions shown as a drainreflecting the pressure head- (ψ) dependent hydraulic conductivity (K). Example ofpiecewise linear initial soil-water conditions (dashed black line) based on fieldobservations of soil-water content (black circles) and the depth to the regionalwater table (≈ 100 m)

Fig. 2 Observed rainfall, soil-water content, and positive pore-water pressures for the BALT1 site from 1 November 2016 to 31 March 2017

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water uptake in the upper 0.15 m of each BVP (based on field observa-tions of grass-rooting depths) with a plant water uptake stress responsefunction (Skaggs et al. 2006). HYDRUS 1-D estimates actual ET based oncalculated ψ and root-water uptake.

The lower boundary for the simulations is a unit-gradient (freedrainage) condition. This boundary type is appropriate for situationswhere the regional water table is thought to be well below the simulationdomain (Šimůnek et al. 2009). The best estimate for the depth to theregional water table for the semiarid hillslope conditions endemic to oursite is 100 m, which is based on geotechnical exploration conductedalong the Caldecott Tunnel, approximately 15 km north of our studyarea (California Department of Transportation 2009).

Initial conditions for the transient simulations (Fig. 3) corre-spond to a simple piecewise linear interpolation of the 10-min θdata and the approximate depth of the regional water table.

Soil-water content, suction stress, and slope stability calculationsWe evaluated our numerical simulations with hourly θ observationsusing a root mean square error (RMSE) calculation to illustrate thevariability in simulated response, with respect to the available groundtruth. The intention of these calculations is not to screen and rankindividual soil-water retention parameter sets. After assessing the θresults, we calculated suction stress at the soil-weathered bedrock

interface for the upslope and downslope BVPs (0.75- and 1.5-m depth,respectively) with the Lu and Likos (2004) approach:

σs ¼ −θ−θrθs−θr

ua−uwð Þ ð5Þ

where σs is the suction stress [ML−1 T−2] and ua is the atmosphericpressure [ML−1 T−2].

We calculated the FS time series (< 1 corresponding to slopefailure) over the 5-month simulation period with the infinite slopeequation (see Lu and Godt 2008):

FS tð Þ ¼ c0 þ γd cos2β−σs tð Þ½ � tanϕ0

γd sinβ cosβð6Þ

where c′ is the effective cohesion [ML−1 T−2], γ is the unit weight[ML−2 T−2], d is the vertical depth from the surface to the failure plane[L], β is the slope angle [°], and ϕ′ is the effective friction angle [°]. Wesourced c′ (7 kNm−2) andϕ′ (33°) from existing strength testing data forthe overlying (0.2- to 0.6-m depth) soil at BALT1 (Lu et al. 2013). Ratherthan adopt a complex strength parametrization scheme, we used themean of the available estimates. Our personal field observations ofnearby shallow landslides indicate that the weathered bedrock typically

Fig. 4 The seven texture-, laboratory-, and field-based θ(ψ) and K(ψ) curves we employed for the soil and weathered bedrock. Thick dashed line indicates the meanparameter value of the other six individual parameter sets (Table 1). Black arrows and identifiers indicate curves described further in BDiscussion^

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does not fail and there is not a distinctly weak horizon at the base of thesoil, but rather a somewhat gradual transition from soil to highlyweathered bedrock. Our estimates for β (34°) and d (0.75 and 1.5 mfor the upslope and downslope BVPs, respectively) came from Chenet al. (2017) and field observations. The γ for each parameter set wascalculated assuming full saturation, which we view as the most conser-vative option for our calculations (see Lu and Godt 2013):

γ ¼ γwGs þ eSð Þ1þ e

� �ð7Þ

where γw is the unit weight of water [ML−2 T−2] (here assumed9.8 kN m−3; Freeze and Cherry 1979), Gs is the specific gravity [−](here assumed 2.65; Freeze and Cherry 1979), e is the void ratio [−],and S is the saturation [−] (here assumed 1).

Assumptions linked to the infinite slope equation (see BeVille et al.2010), such as the underestimation of resisting forces because multi-dimensional effects are not considered, are commensurate with thedegree of complexity we used to simulate near-surface hydrologicresponse. Importantly, we chiefly focus on the change in FS throughtime relative to each set of parameter estimates, rather than the absoluteFS magnitudes.

A positive uw sensor is located at soil-weathered bedrock inter-face for the upslope (but not the downslope) location (Fig. 1d).

Therefore, in addition to calculating the 5-month FS time seriesbased on hydrologic simulation, we used the positive uw recordedby the upslope sensor in four January and February 2017 rain-storms to calculate Bobserved^ FS values. The PS7000 sensorsinstalled at BALT1 can only measure positive pore-water pressures.Therefore, Bobserved^ FS values can only be calculated for thetransient windows when positive pore-water pressures persist. Forthose infrequent and narrow time windows, we focused on themaximum positive pore-water pressure (i.e., the values most rele-vant to slope failure initiation) to calculate an Bobserved^ FS.

Data availability All data are available through the U.S. Geolog-ical Survey ScienceBase Catalogue (see Thomas et al. 2017).

Results

Soil-water content, measured and modeled valuesOur hydrologicmodel results (Table 2, Figs. 5 and 6, and SupplementaryFigures S2 to S5) indicate that laboratory- and field-based parameterestimates are associated with the lowest RMSE values. The averageparameter sets (which dampen end-member θr, θs, α, and n valueswithin each method) typically result in RMSE values between the bestand worst cases for each parameter estimation technique. No single

Table 1 Soil-water retention parameter sets we used for the upslope and downslope simulation scenarios

Parameter set θr [−] θs [−] α [m−1] n [−] m [−]

T-1 0.04 0.38 4.03 1.68 0.41

T-2 0.05 0.39 1.54 1.44 0.30

T-3 0.05 0.38 3.38 3.98 0.75

T-4 0.04 0.39 3.42 1.42 0.30

T-5 0.05 0.39 1.85 1.42 0.30

T-6 0.04 0.38 3.91 1.78 0.44

T-AVG 0.05 0.39 3.02 1.95 0.41

L-1 0.10 0.33 1.27 1.52 0.34

L-2 0.15 0.41 1.47 1.90 0.47

L-3 0.07 0.40 5.09 1.70 0.41

L-4 0.13 0.30 0.49 1.75 0.43

L-5 0.15 0.40 1.27 1.46 0.32

L-6 0.19 0.46 1.66 2.20 0.55

L-AVG 0.13 0.38 1.88 1.76 0.42

F-1 0.16 0.43 1.82 2.37 0.58

F-2 0.15 0.43 2.63 2.44 0.59

F-3 0.15 0.43 1.48 2.34 0.57

F-4 0.19 0.43 3.03 2.16 0.54

F-5 0.21 0.43 1.83 2.22 0.55

F-6 0.15 0.43 2.08 2.2 0.55

F-AVG 0.17 0.43 2.15 2.29 0.56

Entries that are italicized are the average amounts per parameter set

T, texture; L, laboratory; F, field; AVG, average

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parameter set exhibits the lowest RMSE for all locations. The mostnoticeable shortcomings of the simulations in shallow (≤ 0.3 m depth)locations include a tendency to over predict late-season θ (e.g., upslopeL-5; Fig. 5a) ormisrepresent the averageθ regime for the 5-month period(e.g., upslope T-3; Fig. 5a). In deeper (≥ 0.7-m depth) locations, simula-tions commonly over predict θ (e.g., downslope L-6; Fig. 6b) or under-estimate the total change in late-season θ for a given rainfall event (e.g.,upslope L-4; Fig. 5b). Despite complex θ dynamics, RMSE values as lowas 0.01 (e.g., downslope F-5; Fig. 6a) reflect the ability of select realiza-tions to capture the timing andmagnitude of observed fluctuations in θat specific locations throughout the 5-month period.

Factor of Safety, observation- and simulation-based valuesAlthough we do not incorporate uncertainty in soil strength parametersfor our slope stability calculations, the modeled FS values (Figs. 7 and 8,Supplementary Figures S6 and S7) are consistent with observationsmade at BALT1 in that slope failure that does not occur within the 5-month simulation period. The timing of upslope-modeled FS minimaalign closely with (but generally over predict) the FS valueswe calculated

with the maximum observed uw across four January and February 2017rainstorms (Fig. 7a). Upslope-modeled FS values are clearly more sen-sitive, on daily timescales, to the effects of rainfall (e.g., L-4; Fig. 7). Thiscontrast in simulated hydrologic response is an attenuation effect tied tothe 0.75 m difference in depth to the soil-weathered bedrock interfacebetween the upslope and downslope BVPs (Fig. 3).

Composite variability in our modeled upslope FS values (Fig. 8a),defined here as the area between the minimum and maximum FS timeseries results we calculated based on our hydrologic simulations usingtexture-, laboratory-, and field-based soil-water retention properties,shows a sharp decline in FS as the wet period begins in December2016 and a series of fluctuations from January to February 2017. Thecomposite downslope results (Fig. 8b) exhibit a comparativelymuted FSresponse during the wettest portion of the simulation period. Both theupslope and downslope results show that the widest range in modeledFS values occurs for the laboratory-based parameter estimates, followedby the texture- and field-based parameter estimates. The variability in FScalculations is a reflection of the variability in soil-water retentionproperties (e.g., θr and θs) obtained from each method (Table 1; Fig. 4).

Table 2 Summary of the relative performance among soil-water retention parameter sets we used for the upslope and downslope simulation scenarios

BVP Location Depth [m] Lowest RMSE; soil-water content [−] Highest RMSE; soil-water content [−]

Upslope Shallow 0.25 F T

Downslope Shallow 0.3 L/F T

Upslope Deep 0.7 L L

Downslope Deep 1.4 L T

BVP, boundary-value problem; RMSE. root mean square error; T, texture; L, laboratory; F, field

Fig. 5 The best, worst, and soil-water retention parameter average cases of measured and modeled soil-water content (beginning 1 November 2016) for the upslope ashallow and b deep observation locations. Identifiers T, L, and F refer to texture, laboratory, and field, respectively. Root mean square error (RMSE) shown in the upper left

Landslides

Our simulations indicate event-scale and seasonal shallowlandslide susceptibility is markedly influenced by variability

in the parameterization of soil-water retention properties. Themean difference in minimum and maximum dry- (November)

Fig. 6 The best, worst, and soil-water retention parameter average cases of measured and modeled soil-water content (beginning 1 November 2016) for the downslope ashallow and b deep observation locations. Identifiers T, L, and F refer to texture, laboratory, and field, respectively. Root mean square error (RMSE) shown in the upper left

Fig. 7 Modeled factor of safety (FS) values (beginning 1 November 2016) calculated for the overall best, worst, and soil-water retention parameter average cases ofmeasured and modeled soil-water content for the a upslope and b downslope soil weathered-bedrock interface. Dashed vertical lines correspond to timing of maximumobserved positive pore-water pressures. White diamonds in (a) indicate FS values calculated with observed positive pore-water pressures

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and wet-period (January to February) modeled FS values for theupslope BVPs are 3.2 and 0.6, respectively (Fig. 8a). The meandifference in minimum and maximum dry- and wet-periodmodeled FS values for the downslope BVPs are 15.6 and 0.4,respectively (Fig. 8b). Differences in θ(ψ) and K(ψ), therefore,result in up to an order-of-magnitude more variability in themodeled FS values for dry seasonal periods than for wet seasonalperiods. Based on the mean upslope FS during four January andFebruary 2017 rainstorms, event-scale slope stability calculationsvary by nearly a factor of 2 (i.e., 1.3 versus 2.4; Fig. 8a).

Discussion

Variability in soil-water retention propertiesAlthough the effect of soil-water retention properties on FS calcula-tions has been explored by previous research (e.g., Collins and

Znidarcic 2004; Ebel et al. 2010; Lu and Godt 2013; Chen et al. 2017;Greco et al. 2017), here we show that parameter variability imposedacross and within different parameter estimation techniques canimpart substantial effects on slope stability calculations. For example,T-3 exhibits the steepest texture-based θ(ψ) and K(ψ) curves (Fig. 4);the corresponding high α and n values, as well as low θr (Table 1),facilitate the most extreme dry out of the soil. This effect can substan-tially offset seasonal simulated θ dynamics from observed values(Figs. 5 and 6) and lead to modeled FS values with little changethroughout the season (Fig. 7). Parameter sets L-6 and F-5 are similarto each other in that they exhibit the highest θr value among theirrespective parameter estimation approaches (Table 1). The higher θrvalues prevent the simulations from drying beyond observations inthe shallow subsurface, but the simulation results do not match manyof the dry-period observations in the deeper subsurface (Figs. 5 and 6),suggesting heterogeneity may be a factor.

Fig. 8 Composite variability of modeled factor of safety (FS) values (beginning 1 November 2016) at the a upslope and b downslope soil-weathered bedrock interface.Shaded areas encompass the highest and lowest FS values estimated for the texture-, laboratory-, and field-based soil-water retention parameter sets. White diamonds in(a) indicate mean FS values calculated with observed positive pore-water pressures. Note: the maximum FS value for the laboratory-based parameters in (b), which isoutside the y-axis scale window, is 17

Landslides

The Ks is known to strongly affect the FS at the base of shallow soilcovers (e.g., Greco et al. 2017). However, the importance of soil-waterretention properties (i.e., θs, θr, α, n, andm) on θ(ψ) and K(ψ) is rarelyconsidered. We show that highly variable FS estimates are possiblewithout altering the simulated Ks values. An increasing trend in com-posite FS variability from field-, to texture-, and to laboratory-basedparameter estimates is consistent for the upslope and downslope BVPs(Fig. 8). Despite the large degree of FS variability during the drier parts ofthe simulation period, the range of FS values narrows markedly as thesystem wets up. In the wetter regime, the θ(ψ) and K(ψ) relations fordifferent parameterizations tend to converge (Fig. 4). This result isencouraging given that, in practice, FS estimates are more importantduring wet seasonal periods when hillslopes are more likely to fail andfor which model calibration should be prioritized. However, our resultssuggest thatmodel performance during wet periods is still influenced bydry-end soil-water retention properties such as θr.

Although we used three methods for estimating soil-water retentionproperties, we recognize that different data availability and methodolo-gies could result in different parameter sets. For example, texture-basedsoil-water retention properties could be estimated with site-specificpedotransfer functions. Laboratory experiments could be conductedon larger or repacked soil cores. More or different soil probes couldbe used to estimate field-based soil-water retention properties withinverse modeling at larger scales or to better constrain variations in θs.

Implications for landslide early warningThe BALT1 monitoring network recorded positive uw during four rain-storms between 1 January and 28 February 2017 (Fig. 2). The upslope anddownslope locations experienced positive uw for days and hours, re-spectively. Although the BALT1 hollow did not fail, widespread shallowlandsliding did occur in the East Bay region during these 2017 storms,including one shallow landslide within 20 m of our instrumentation(Fig. 1c). We draw a connection between the observed hydrologicresponse (local positive uw) and coincident geomorphic response (wide-spread shallow slope failure) to discuss the significance of our work for aphysics-based landslide early warning system.

A target-style interpretation (Fig. 9) illustrates how our hydro-logic simulation results relate to three metrics we view as relevantto landslide early warning design. The outermost ring (Metric 1)indicates the RMSE representing the lag between observed andmodeled uw peaks. The middle ring (Metric 2) is the percentage ofobserved positive uw occurrences captured by each simulation.The innermost ring (Metric 3) indicates the RMSE representingthe lag between the onsets of observed and modeled positive uw.Each successive ring represents a more complex expectation ofmodel capability for landslide forecasting. Any model should beable to predict a rise in uw (i.e., Metric 1, ring 1; Fig. 9), but not allwill predict the occurrence of positive uw. For those models that dopredict positive uw (i.e., Metric 2, ring 2; Fig. 9), only a few willsuccessfully approximate the timing of positive uw onset (i.e.,Metric 3, ring 3; Fig. 9).

We find that the upslope and downslope BVPs exhibit mean uw peaklag times of 1.6 and 3.6 days, respectively (Table 3; Fig. 9). Forty-threepercent of the positive uw occurrences are captured by the upslopeBVPs, but none are captured by the downslope BVPs. For the upslopecases where positive uw is reported, the onset lag time ranges from 0.5 to2.8 days, with a mean lag time of 1.8 days. Note that we cannot calculatean onset lag time for the downslope BVPs because no positive uw eventsare simulated.

The consistent lag between observed and simulated uw could beproblematic for early warning. Forward numerical simulation basedon a 3-day rainfall forecast would be unable to predict conditionsrelevant to widespread landsliding if these lags persist. However, thesystematic nature of the lag between observation and simulation sug-gests that the problem may be corrected through adjustments to themodel setup. For example, unsaturated zone preferential flow (e.g.,Gerke 2006; Germann and Hensel 2006; Nimmo 2012) may accountfor the simulated lag, but was not considered in these simulations. Thiscomplexity would affect the flow in our domain and, to a lesser extent,the pressure head-dependent drain. Similarly, the Ks values we selectedfor our simulations are based on field measurements, rather than whatmight best fit the observations as part of an inverse modeling approach(e.g., Godt and McKenna 2008). Our 1D simulations also neglect thepotential for lateral flow within perched saturation, which can influencethe timing of positive uw occurrences (e.g., Mirus et al. 2007). Finally, weassumed identical soil-water retention properties (but different Ks

values) for our two-layer conceptualization, although we suspect unsat-urated bedrock properties have less of a potential impact (compared tounsaturated preferential flow and lateral saturated flow in the soil) onslope instability in our study area. We recognize that these types ofmodel complexity could further enhancemetric performance, but likelyat the expense of greater data demands and computational burden; thistrade-off is an important topic that warrants further research. Ratherthan identify a best-case total parameterization, we focus on howuncertainty in characterizing soil-water retention properties influencesimulations of vertical infiltration and positive uw response.

The upslope BVPs are much more successful than the downslopeBVPs at predicting the occurrence of positive uw (Fig. 9). This disparitysuggests that a physics-based landslide early warning systemmay not beable to capture positive uw lasting only a few hours as measured at thedownslope sensors. However, there may also be a process or heteroge-neitymissing in our downslope simulation design. Given that ourmodelapproach includes many simplifications and is parameterized with thebest available field characterization data, the ability of our simplisticBVPs to predict the occurrence of positive uw at one location at the endof a 5-month simulation period within 12 h is encouraging. Our work,however, highlights that caution should be exercised in the potential useof physics-based numerical models of variably saturated flow to furtherthe development of landslide early warning systems.

Our metrics indicate that variability in soil-water retentionproperties can appreciably impact the ability of a forward simula-tion to predict the occurrence of positive uw. Whereas, we focus onmeasurement- (i.e., texture, laboratory, and field) based variabilityfor our site, it seems reasonable to assume parameter uncertaintywould expand with additional consideration of soil type withinlarger realms (i.e., hollow, catchment, or regional scales). Addi-tionally, without monitoring data to evaluate model performance,the uncertainty in soil-water retention properties and the impacton simulated uw would remain unknown. Simoni et al. (2008)treated cohesion and friction angle using a probability distributionto account for uncertainty in soil strength parameters within acoupled hydrology and slope stability modeling study, but thenalso used a texture-based pedotransfer function to parameterizesoil-hydraulic properties across entire soil units. Our results sug-gest that a physics-based early warning system for widespreadshallow landsliding would also benefit from a stochastic treatmentof soil-water retention parameters (e.g., Gomes et al. 2017). Giventhe number of potential simulation scenarios, we expect that these

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kinds of simulations may be initially limited to representative 1Dcolumns (as used here) or a series of quasi-distributed 1D columns(Baum et al. 2010) corresponding to the region-of-interest.

ConclusionWe used an ensemble of texture-, laboratory-, and field-based soil-water retention properties for a monitored landslide-prone hill-slope to examine simulated soil-water content (θ), pore-waterpressure (uw), and the resultant factor of safety (FS) time seriesfor conditions relevant to widespread shallow landslide initiation.Specifically, we evaluated the impact of variability in parameter

estimation methods on seasonal- and event-scale shallow landslidesusceptibility, with a particular focus on positive uw development.

Our results indicate that differences in soil-water retention propertiescan impart a noticeable effect on simulatedθ anduwdynamics, and thusalso on FS calculations. The ensemble of simulation scenarios fordifferent parameter sets generates an order-of-magnitudemore variabil-ity in the modeled FS values for dry seasonal periods than for wetseasonal periods. Slope stability estimates based on four observedrainstorms vary by nearly a factor of 2 across different estimationmethods. Despite the reduced FS uncertainty during wet conditions,dry-end soil-water retention properties strongly influence the ability of a

Fig. 9 Pore-water pressure (uw) metrics for the a upslope soil-weathered bedrock interface and b near the downslope soil-weathered bedrock interface. Outer ring is theroot mean square error (RMSE) representing the lag (days) between observed and modeled uw peaks. Middle ring is the percentage of observed positive uw occurrencescaptured by the simulation. Inner ring is the RMSE representing the lag (days) between the onset of observed and modeled positive uw. A solid line from the outermostedge to the center would represent perfect model performance across all three metrics. Example, Fig. 9a: the simulation using the laboratory-based parameter set, L-1,reported peak uw lagged behind observations by approximately 1 day (Metric 1, ring 1), captured 100% of the positive uw occurrences (Metric 2, ring 2), and reported theonset of positive uw lagged behind observations by approximately 1 day (Metric 3, ring 3)

Table 3 Summary of pore-water pressure metrics relevant to landslide early warning design

BVP Outer ring1; RMSE [lag, days] Middle ring1 [%] Inner ring1; RMSE [lag, days]Min. Max. Mean Min. Max. Mean Min. Max. Mean

Upslope 1.4 2.3 1.6 0 100 43 0.5 2.8 1.8

Downslope 2 5.7 3.6 0 0 0 n/a n/a n/a

1 see Fig. 9

BVP, boundary-value problem; RMSE, root mean square error; Min, minimum; Max, maximum; n/a, not applicable

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hydrologic model to match observed point measurements of θ. Ourfindings motivate work to better understand how evapotranspirationand shifts in climate (e.g., shorter or longer dry seasons) may impactantecedent conditions and the seasonal window for shallow landslidehazard.

The pore-water pressure metrics we formulated and compiledin this study indicate that a numerical model parameterized withhigh-frequency rainfall information can mimic the timing forevent-scale peaks in subsurface fluid pressure reasonably well.Confidently predicting the occurrence and onset of positive uw ismore difficult. The problem of lagged simulation results that arelikely due to our simplified modeling constraints provides oneexample of a future research challenge. Despite the simplicity ofour conceptual model, we demonstrate that neglecting variabilityin soil-water retention properties could be problematic for land-slide early warning. Thus, our results encourage the probabilistictreatment of soil-water retention parameters for early warning ofwidespread shallow landsliding.

AcknowledgementsThe East Bay Municipal Utility District facilitated access to theBALT1 site. Jonathan Stock, Kevin Schmidt, Mark Reid, and SkyeCorbett provided invaluable field assistance. The authors appreci-ate the constructive comments provided by William Schulz, An-derson Ward, and two anonymous reviewers on earlier versions ofthis work.

Funding This study was supported in part by a National ScienceFoundation grant (CMMI-1561764) awarded to Ning Lu.

Compliance with ethical standards

Disclaimer Any use of trade, firm, or product names is for de-scriptive purposes only and does not imply endorsement by theU.S. Government.

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Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10346-018-0950-z) contains supplementary material, which is available toauthorized users.

M. A. Thomas : B. B. Mirus : J. W. GodtLandslide Hazards Program, Geologic Hazards Science Center,U.S. Geological Survey,Golden, CO 80401, USA

M. A. Thomas ())Denver Federal Center,U.S. Geological Survey,Box 25046MS 966, Denver, CO 80225, USAEmail: matthewthomas@usgs.gov

B. D. CollinsLandslide Hazards Program,U.S. Geological Survey,Menlo Park, CA 94025, USA

N. LuColorado School of Mines,Golden, CO 80401, USA

Landslides