soils & hydrology

Can the Water Erosion Prediction ProjectModel Be Used to Estimate Best ManagementPractice Effectiveness from Forest Roads?Kristopher R. Brown, Kevin J. McGuire, W. Cully Hession, andW. Michael Aust

The Water Erosion Prediction Project (WEPP) was used to predict event-based sediment yield and runoff forrainfall experiments on six stream-crossing approaches with different intensities of best management practice(BMP) implementation (i.e., different proportions of gravel on the road surface). WEPP was calibrated for threedifferent BMP intensities at each site using a Markov chain Monte Carlo approach to explore parameteruncertainty and prediction performance. WEPP predictions of sediment yield showed clear differences among thedifferent road surface treatments, but prediction intervals (or the range of possible simulation results) were wide,reflecting substantial parameter and prediction uncertainty. The posterior distribution analysis for rill erodibility,interrill erodibility, and critical shear indicated that we cannot recommend parameter ranges specific to differentsurface treatments. Results suggest that the utility of WEPP for estimating BMP effectiveness is limited topredicting relative differences in sediment yield among vastly different surface treatments (e.g., native surfacedversus completely graveled roads). Sediment predictions from models should always include informationregarding the range of possible outcomes, given the many sources of uncertainty.

Keywords: forest roads, best management practice effectiveness, erosion modeling, uncertainty, watershedmanagement

F orest roads at stream crossings are amajor source of sediment delivery tostreams (Lane and Sheridan 2002,

Harris et al. 2008, Anderson and Lockaby2011a). The management of channelizedrunoff from roads has been the focus of re-

cent legislative debates in the United Statesregarding the protection of aquatic ecosys-tems in forests (Boston 2012). For the past40 years, forestry best management practices(BMPs) have been used to manage runoffand sediment delivery from roads, but some

environmental organizations have soughtlegislation to achieve the goal of water qual-ity protection with National Pollution Dis-charge Elimination (NPDES) permits (Bos-ton 2012). Currently, stormwater runoff(and sediment) from forest roads is managedas a nonpoint source pollutant in the UnitedStates. However, the potential shift toNPDES permits prompted the US Environ-mental Protection Agency to request thatstate forestry organizations evaluate the ef-fectiveness of existing BMPs for reducingsediment delivery from major sources (i.e.,roads and stream crossings) and provideguidance for enhanced BMPs (Jackson2014, Loehle et al. 2014, MacDonald andCoe 2014).

Field studies provide valuable informa-tion about the effectiveness of different in-tensities of BMP implementations to reduceerosion and sediment delivery (Appelboomet al. 2002, Turton et al. 2009, Anderson

Received September 1, 2014; accepted January 6, 2015; published online February 12, 2015.

Affiliations: Kristopher R. Brown (krisrb3@vt.edu), Virginia Tech, Forest Resources and Environmental Conservation, Blacksburg, VA. Kevin J. McGuire(kevin.mcguire@vt.edu), Virginia Tech. W. Cully Hession (chession@vt.edu), Virginia Tech. W. Michael Aust (waust@vt.edu), Virginia Tech.

Acknowledgments: Funding and support for this research were provided by the Department of Forest Resources and Environmental Conservation at Virginia Tech andthe Virginia Water Resources Research Center. We thank Dr. Jasper Vrugt for providing access to DREAM_(ZS) software. Paolo Benettin assisted with computerprogramming in Matlab to run DREAM_(ZS) and the WEPP model. We also thank two anonymous reviewers whose comments improved the quality of this article.

This article uses metric units; the applicable conversion factors are: centimeters (cm): 1 cm � 0.39 in.; meters (m): 1 m � 3.3 ft; millimeters (mm): 1 mm �0.039 in.; kilograms (kg): 1 kg � 2.2 lb; grams (g) 1 g � 0.035 oz.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Noncommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Forcommercial reuse, please contact the Journal of Forestry at journal@safnet.org.

RESEARCH ARTICLE

Journal of Forestry • January 2016 17

J. For. 114(1):17–26http://dx.doi.org/10.5849/jof.14-101

Copyright © 2016 The Author(s)

and Lockaby 2011b). “Intensity” is usedthroughout this article in the context ofBMP implementations to describe the levelof effort (e.g., time and money) involved inplanning or practices to reduce soil erosionand sediment delivery. However, field ex-periments and monitoring of BMPs onroads is often an impractical option formanagers because of cost, time, and site-spe-cific road conditions (i.e., different climates,soils, slopes, road types, and traffic charac-teristics). This has led to increased interestin using models for evaluating BMP effec-tiveness. In particular, the Water ErosionPrediction Project (WEPP) model has beenused extensively as a tool for this purpose(Sawyers et al. 2012, Wade et al. 2012, El-liot 2013) and is currently recommendedby many forest management organizations.

WEPP is physically based and was de-signed to incorporate field observations andsite-level information for predicting sedi-ment yield and runoff. Previous studies in-dicate that WEPP can be a useful tool forestimating soil erosion from forest roads,where overland flow is the dominant hydro-logic process (Laflen et al. 2004, Crokeand Nethery 2006, Fu et al. 2010). How-ever, model performance has not been eval-uated for forests roads at stream crossings fora wide range of stream-crossing approachcharacteristics, BMP implementations, andrainfall conditions.

In addition, methodologies for evaluatingsoil erosion model performance have typicallyincluded model calibration and evaluationprocedures without explicitly accounting forsources of model prediction uncertainty (Bra-zier et al. 2000, Beven 2008). Commonly, oneor more objective functions (e.g., sum ofsquared errors and Nash-Sutcliffe efficiency)are used to identify the most acceptable modelbased on prediction performance for runoffand sediment yield. However, it is possible thatmultiple models, with unique combinations ofparameter values, can generate equally accept-able model predictions. In the case of physi-cally based models with many parameters, itcan be very difficult or impossible to identifythe most acceptable model due to complex in-teractions among the model parameters(Beven 2008). Further, it is an uncommon oc-currence for the modeler to know the appro-priate a priori values of all parameters used inmodel calibration because of the spatial andtemporal heterogeneity of site physical charac-teristics, which translates to variability in mea-surements of runoff and sediment yield.Therefore, it appears prudent to embrace the

concept of model equifinality, in which anumber of different models (i.e., unique sets ofparameter values) can produce satisfactory pre-dictions and identify distinct ranges of modelparameter values that are associated with ac-ceptable model runs (Beven 2008, Ascough etal. 2013).

In light of the different types of uncer-tainty (Hession and Storm 2000) associatedwith soil erosion predictions (e.g., measure-ment error, model parameterization, andmodel structure), as well as the challengesassociated with defining sediment criteria tomaintain or improve aquatic habitat (Ice2011), model utility need not be definedsolely by prediction accuracy. However, use-ful models should facilitate the identifica-tion of problem road segments for waterquality protection, or better, allow us to dis-tinguish different treatments that representincreasing intensities of BMP implementa-tion according to their respective soil erosionor sediment delivery rates.

The objectives of the study were to deter-mine the overall prediction performance ofWEPP and its ability to distinguish betweendifferent BMP intensities. This study focusedon two research questions in the Piedmontphysiographic region of southwestern Vir-ginia, USA: How well does WEPP predictevent-based runoff and sediment yield fromforest roads at stream crossings? and Can dis-tinct ranges of parameter values be identifiedin association with acceptable model runs anddifferent road surface treatments?

WEPP was used to predict event-basedsediment yield and runoff from rainfallsimulation experiments on six stream-cross-

ing approaches having different intensitiesof BMP implementation (i.e., different pro-portions of gravel on the road surface abovethe stream crossing). WEPP was calibratedfor each of these stream-crossing approachesfor three different BMP intensities using aMarkov chain Monte Carlo (MCMC) ap-proach to explore parameter identifiability,and prediction performance and uncer-tainty.

Materials and Methods

Study AreaRainfall simulation experiments were

performed on a reopened forest road at theReynolds Homestead Forest Resources Re-search Center (RHFRRC), located in Critz,Virginia (Patrick County), USA (Figure 1)to measure event-based surface runoff andsediment yield associated with successive in-creases in gravel cover on stream-crossing ap-proaches (Brown et al. 2014). Site topographyis characterized by rolling hills, with side slopesgenerally ranging from 8 to 25% and a meanelevation of approximately 335 m above meansea level (Natural Resources Conservation Ser-vice [NRCS] 2013). The mean annual rainfallis 1,250 mm, with a mean snow contributionof 270 mm to the total precipitation. Themean air temperature ranges from a low of�1.8° C in January to a high of 29.7° C in July(Sawyers et al. 2012). The predominant soilseries is Fairview sandy clay loam (fine, kaoli-nitic, mesic typic Kanhapludults). The soilparent material is residuum from mica schistand mica gneiss. There is a severe erosion haz-ard rating for forest roads and trails at RH-

Management and Policy Implications

The complexity of data requirements for many physically based erosion models makes them best suitedfor academicians and state and federal agencies that have the resources to couple field monitoring withevaluations of model performance. Forestry practitioners can reduce sediment delivery from major sources(e.g., roads, trails, and associated stream crossings) through a careful emphasis on preharvest planningand the use of erosion models with readily attainable parameter values (e.g., the Universal Soil LossEquation modified for forestland) to estimate the sediment-reduction efficacy of site-specific BMPimplementations. Future research and extension programs should seek to improve road planningtechnology to reduce forest road length within a given watershed, minimize stream crossings, maintaingentle road gradients, and avoid locations where it is difficult to shed water from the road surface. Inthis way, water quality protection is not overly dependent on postconstruction BMP implementations tocorrect road deficiencies that resulted from poor planning. The field component of this study showedthat completely graveled forest roads at stream crossings can reduce sediment delivery to streams. In lightof potential policy shifts for the forest industry (i.e., NPDES permits for roads), continued research isneeded to document the cost and effectiveness of site-specific BMP implementations to reduce sedimentdelivery.

18 Journal of Forestry • January 2016

FRRC (NRCS 2013), which is due to thecombination of moderate slopes and highlyerodible soils. This underscores the impor-tance of controlling road grade, water, and sur-face cover to reduce erosion and sedimentdelivery.

Field MethodsBefore road reopening, a Sokkia model

SET-520 total station was used to measure thelength of the stream-crossing approach studyplots, as well as the approach slope and meanwidth of the running surface. Length was de-

fined as the distance between the nearest watercontrol structure (i.e., water bar and turnout)and the stream (Figure 2). In late July 2011, sixstream-crossing approaches were reopened bybulldozer blading, creating initial conditionsof approximately 100% bare soil on the ap-proach running surfaces. In October 2011,Kadak used double-ring infiltrometers to esti-mate the infiltration capacities of the reopenedstream-crossing approaches (M. Kadak, un-dergraduate student researcher, unpubl. data,Feb. 11, 2012). The infiltration capacitiesranged from 0.6 to 7.2 mm hour�1. Bulk den-

sity samples (n � 4–7 per site) were obtainedfrom the running surface via the soil extractionmethod (Soil Science Society of America1986).

Rainfall simulation experiments wereconducted for a succession of gravel surfac-ing treatments that represented increasingintensities of BMP implementations on thestream-crossing approaches (Brown et al.2014) (Figure 3). All rainfall experimentswere conducted between February and Au-gust 2012. The unsurfaced approaches weretrafficked with a bulldozer immediately be-fore the first series of rainfall experiments tomimic newly disturbed conditions associ-ated with road reopening. After this treat-ment (“no gravel”), the stream-crossing ap-proaches had 10–19% surface cover, whichconsisted of residual leaf litter and other de-bris. After the no gravel treatment rainfallexperiments, a dump truck was used to tail-gate spread a mixture of size 3, 5, and 7(ranging from 5.1- to 1.9-cm diameter)granite gravel beginning at the lower plotboundary (Figure 2) and continuing uphillfor a distance of 9.8 m (“low gravel” treat-ment). The mean gravel depth was approxi-mately 0.08 m, and the width of gravel ap-plication extended across the width of theroad between the outer edges of the runningsurfaces, which averaged 2.8 m. Gravel wasnot washed before application to the stream-

Figure 1. Location map adapted from Brown et al. (2014) of the RHFRRC in Critz, Virginia(Patrick County), USA, and a schematic diagram showing the road location within thesecond-order watershed that contains three unimproved ford stream crossings. Stream-crossing approaches are labeled 1–6.

Figure 2. (A) Plan view of two idealized stream-crossing approaches with rainfall simulator equipment and monitoring instrumentation(adapted from Brown et al. 2014). Open-top box culverts collected surface runoff at the bottom of the plot, immediately upslope of thestream. Photographs depicting a rainfall experiment on Mar. 12, 2012 (B) and the equipment used to measure surface runoff quantity andquality (C).

Journal of Forestry • January 2016 19

crossing approaches as is typical during for-est road construction and graveling.

The near-stream 9.8-m gravel sectionwas chosen for the low gravel treatment be-cause this length approximated half the dis-tance of the shortest approach used in thisstudy. The low gravel treatment resulted indifferent proportions of cover on the run-ning surface area of the study plots primarilybecause each approach length was different,ranging from 19.2 to 41.3 m. For example,the low gravel treatment resulted in 60%surface cover for the shortest approach and40% surface cover for the longest approachused in this study. After the low gravel rain-fall experiments, no additional gravel wasapplied to the initial 9.8-m-long segment,but gravel was applied to the adjacent (up-hill) 9.8-m section of the road approach(“high gravel”). This treatment effectivelydoubled the length of the first gravel appli-cation and resulted in an overall range of50–99% surface cover on the approach run-ning surfaces. The succession of treatmentsat each site (no gravel, low gravel, and highgravel) facilitated the evaluation of a widerange of surface cover on the stream-crossingapproaches (10–99% cover) in reducingsediment delivery to streams during simu-lated rainfall events (Figure 4). Three to fourrainfall experiments were completed in suc-cession within a given treatment at each site

(n � 6), which resulted in a total of 58 rain-fall experiments.

Overall, sediment yield was reduced ateach stream-crossing approach as a result ofthe combined effect of decreased soil erod-ibility from successive rainfall events withina given treatment and increased gravel sur-face cover between treatments (Brown et al.2014). Brown et al. (2014) found that sedi-ment yield per unit rainfall (g m�2 mm�1)was commonly greatest during the firstrainfall experiment within the no graveltreatment, whereas subsequent no graveltreatment experiments (e.g., no gravel exper-iments 2, 3, and 4) were similar. The authorsconcluded that the supply of loose sedimentwas approaching depletion after the first nogravel treatment rainfall experiment and thatthe treatment effect of gravel application wasevidenced by further declines in sediment yieldwith increasing gravel cover. Renewed sedi-ment sources associated with the application ofthe gravel treatments included truck traffic onthe stream-crossing approaches and dust asso-ciated with the unwashed gravel. Conse-quently, sediment yields were also greatest forthe first rainfall experiments within the lowgravel and high gravel treatments, whereassubsequent experiments within each treatmentwere similar.

Applied rain event characteristics (amount,duration, and intensity), total runoff, and

total sediment yield were quantified for eachrainfall experiment. These data were used toevaluate WEPP model predictions of event-based runoff and sediment yield.

WEPP Model SetupThe WEPP model (version 2012.8) was

used to build unique hillslope profiles for eachrainfall experiment (N � 58). Each hillslopeprofile contained site-specific details related toslope, soil type, vegetation management, andapplied rain event characteristics (amount, in-tensity, and duration). Data regarding stream-crossing approach length, slope, running sur-face width, road vertical shape (concave,convex, linear, or S-shaped), and aspect wereused to create six slope files corresponding tothe six stream approaches used in this study.Significant changes in road grade (e.g., astream approach with a 12% slope at the top ofthe approach, which transitions to a 4% slopenear the stream) were included in theslope profiles as breakpoints by using the slopeprofile editor.

Unique breakpoint climate files werecreated for each rainfall experiment so thatWEPP could be run in single-storm mode.Breakpoint climate files contained cumula-tive rainfall amounts in 1-minute intervals(i.e., breakpoints) for the duration of eachrainfall experiment. We selected the “skid-clay loam” soil file because the parametervalues were representative of a low-volumeforest road with a clay loam soil texture. Weselected the “insloped road-unrutted bare”vegetation management file because it wasrepresentative of road surface conditions af-ter road reopening by bulldozer blading.These files for soil and vegetation manage-ment were used at each of the study sites.

The initial plant file, which is part of theinitial conditions database in the vegetationmanagement file, was “insloped road-bare.”This file was used without alteration for each ofthe stream-crossing approaches. However, itwas necessary to create unique vegetation man-agement files for each rainfall experiment toreflect changes in antecedent rainfall, as well assurface cover. Specifically, cumulative rainfallamounts since bulldozer trafficking were cal-culated for each rainfall experiment, and thesevalues were used for the parameter, “cumula-tive rainfall since last tillage.” Field estimates ofsurface cover on the running surface compo-nent of the stream-crossing approaches weremade before each rainfall experiment. Thesesurface-cover estimates were used as the pa-rameter values for initial rill and interrill cover.Rill width type was set to “permanent” because

Figure 3. Measurements of event-based rainfall, surface runoff, and sediment yield wereused to evaluate the performance of the Water Erosion Prediction Project (WEPP) model toestimate the sediment-reduction efficacy of increasing gravel cover at road-stream cross-ings. (Photo credit: Kristopher Brown.)

20 Journal of Forestry • January 2016

tillage was not recurring. The mean of the soilbulk density measurements for each stream-crossing approach was used as a constant pa-rameter value in the vegetation managementfiles.

Forest cover adjacent to the stream-crossing approaches consisted of maturehardwood forests. Therefore, the parameter,“days since last harvest”, was set to 3,650 (10years), which reduced the effect of this pa-rameter on soil erosion predictions. The pa-rameter, “days since last tillage” was calcu-lated as the cumulative number of days sincethe stream-crossing approaches were traf-ficked with a bulldozer (i.e., before the firstseries of no gravel treatment rainfall experi-ments). The remaining model parametersassociated with the initial conditions sectionfor insloped road-unrutted bare were notchanged, with the exception of initial ridgeroughness and initial rill width.

We defined ranges of values for modelcalibration parameters that are integral toWEPP predictions of runoff and sedimentyield from forest roads. Specifically, we de-fined ranges of values for effective hydraulicconductivity, initial ridge roughness, initialrill width, rill erodibility, interrill erodibil-ity, and critical shear (Table 1). Field obser-vations of antecedent soil water content

expressed relative to saturation (i.e., deter-mined from field conditions at each stream-crossing approach) were used for the param-eter, initial saturation, in the soil input files.The ranges for model parameters were cho-sen to reflect site conditions of the stream-crossing approaches used in this study andwere based on our own field observations,when possible. In other cases, ranges formodel parameter values were based on fieldexperiments by Foltz et al. (2008) or WEPP’stechnical documentation (National Soil Ero-sion Research Laboratory [NSERL] 1995).

Uncertainty AnalysesA MCMC algorithm, DREAM_(ZS)

(ter Braak and Vrugt 2008, Vrugt et al.2008, Laloy and Vrugt 2012), was used toefficiently select parameter ranges for WEPPthat minimize the discrepancy betweenmodel predictions and observations basedon a simple least-squares objective function.In this case, WEPP was used to simulate to-tal runoff and total sediment yield from asingle event for 58 different rainfall experi-ments. The use of ordinary Monte Carlo-based random sampling was not feasible be-cause of the number of potential parametersets that had to be generated to explore the

complex parameter space of the WEPPmodel. DREAM_(ZS) is adaptive and effi-cient for finding “acceptable” parameter setsin complex inverse modeling problems(Vrugt et al. 2009). The resulting posteriorparameter distributions from WEPP cali-bration using DREAM_(ZS) were used toexplore the uncertainty associated withmodel parameters and model predictions, aswell as parameter identifiability/sensitivity,and overall prediction performance.

The main advantage of using DREAM_(ZS) to derive posterior distributions ofmodel parameters is that the sampling pro-cedure learns from experience (i.e., modelperformance in predicting runoff and sedi-ment yield) and provides denser sampling inthe model parameter ranges that are associ-ated with acceptable model runs. Conse-quently, fewer model runs (and less com-puter processing time) are necessary toadequately sample the model parameterspace. DREAM_(ZS) was used to generate10,000 unique sets of model parameter val-ues for each rainfall experiment. The num-ber of model runs was selected based onanalysis of chain convergence for each of themodel parameters.

During model calibration, the range ofparameter values for effective hydraulic con-ductivity was 0.1 to 10 mm hour�1 (Table 1),based on previous field estimates of hydraulicconductivity at the stream-crossing approaches(Brown et al. 2014). WEPP model runs wereperformed with hydraulic conductivity heldconstant, meaning that WEPP did not inter-nally adjust hydraulic conductivity duringevent simulations. The range for initial ridgeroughness was 0–0.08 m, with the lower val-ues representing road conditions immediatelyafter bulldozer trafficking and the higher val-

Figure 4. Photographs depicting rainfall experiments for a succession of gravel surfacing treatments at site 5. (A) No gravel. (B) Low gravel.The yellow lines approximate the upper boundary of the first gravel application. The lower boundary of gravel application was theopen-top box culvert (Figure 2C), immediately uphill of the stream. (C) High gravel. The yellow lines indicate the additional coverageafforded by the second gravel application. Surface cover for the rainfall experiments at site 5 was 14, 47, and 63% for the no gravel, lowgravel, and high gravel treatments, respectively.

Table 1. Description of model parameters and the ranges of values used in thegeneration of unique sets of parameters by way of MCMC sampling of the modelparameter ranges.

Parameter Description Units Minimum Maximum WEPP file

RRINIT Initial ridge roughness m 0 0.08 ManagementWIDTH Initial rill width m 0 0.2 ManagementKi Interrill erodibility kg s m�4 2 � 106 11 � 106 SoilKr Rill erodibility s m�1 0.0001 0.01 SoilSHCRIT Critical shear N m�2 0.4 2.6 SoilAVKE Effective hydraulic conductivity mm hour�1 0.1 10 Soil

Journal of Forestry • January 2016 21

ues associated with maximum gravel cover onthe stream approaches.

No distinct rills (concentrated overlandflows) were observed during the field rainfallexperiments. However, we used a parameterrange of 0–0.2 m for rill width to reflect thelikelihood that erosion by concentrated run-off had at least a small effect on observedsediment yields. The parameter range for rillerodibility (0.0001–0.01 s m�1) was set toreflect the wide range of values reported inthe peer-reviewed literature (e.g., Foltz et al.2008). The range of parameter values usedfor interrill erodibility (2 � 106 to 11 � 106

kg s m�4) was based on the range of valuesreported in the WEPP technical documen-tation (NSERL 1995). The range of param-eter values used for baseline critical shear was0.4 to 2.6 N m�2 (Foltz et al. 2008).

Evaluation of Model PredictionsOf the 10,000 model runs for each rain-

fall experiment, the last 25% were chosen forestimating the posterior distributions of pa-rameters (Figure 5). Posterior distributionswere estimated from the last samples in theMarkov chains when convergence of the indi-vidual chains was consistently below thethreshold of 1.2 for the Gelman and Rubinstatistic (Gelman and Rubin 1996). It has beensuggested that the last 25% of the samples ineach chain are an appropriate characterizationof the posterior distribution (Vrugt et al.2009). In all simulations for this study, conver-gence was reached within 1,500 samples; thus,

the last 25% was a conservative estimate. Toaccount for variability in applied rainfallamounts and intensities, model performancewas based on the comparison of observed andpredicted runoff coefficients (runoff depth/rainfall depth) and sediment yield per unitrainfall (mg m�2 mm�1).

The 95% confidence intervals of modelpredictions resulting from the posterior pa-rameter distributions were used to evaluatemodel performance in comparison to event-based runoff and sediment yield for a succes-sion of applied rainfall events, as well as asuccession of gravel treatments that repre-sented increasing intensities of BMP imple-mentation. Posterior distributions of themodel parameter values were expressed asempirical cumulative distribution function(ECDF) plots to identify regions of themodel parameter space (i.e., specific rangesof values for each of the model parameters)that were associated with acceptable modelruns. For a continuous variable, the gradientof an ECDF plot is equal to the probabilitydensity at that point. This means that thesteepest slopes on the ECDF plot indicatethe highest relative frequencies on a histo-gram of the posterior distribution (Figure5). Therefore, we can use ECDF plots toidentify the best range of model parametervalues (as indicated by the steepest slopes onthe ECDF plots) to be used for differentroad surface treatments (e.g., no gravel, lowgravel, and high gravel).

Results and Discussion

Model Performance in PredictingEvent-Based Surface Runoff

For many of the rainfall experiments,WEPP predictions matched the observedrunoff coefficient (Figure 6). This meansthat for a given rainfall experiment, therewas at least one parameter set that resulted ina prediction that matched observed runoff.WEPP also predicted higher runoff coeffi-cients for the no gravel treatment, which issimilar to findings from the field rainfall ex-periments (Brown et al. 2014). However,the ranges of predicted runoff coefficientswere often very wide (Figure 6), reflectingthe substantial uncertainty associated withmodel parameter values related to runoffgeneration (e.g., effective hydraulic conduc-tivity). Variability in runoff is also influ-enced by the water content of the road onthe day of the event and the duration andintensity of the event. Initial water content,rainfall duration, and intensity were fixed(i.e., held at the field-measured values) foreach rainfall event. However, initial watercontent of the road surface is an importantfactor controlling runoff for a given event(Flanagan et al. 2012).

Model Performance in PredictingEvent-Based Sediment Yield

WEPP performed well in predicting re-ductions in sediment yield for successiverainfall events within a given treatment and

Figure 5. Idealized schematic diagram depicting the relationship between the probability density function and cumulative distributionfunction of the model parameter values (e.g., effective hydraulic conductivity) before and after MCMC sampling of the parameter ranges.The dashed gray lines represent the cumulative distribution function of a uniform distribution. The solid gray lines indicate the cumulativedistribution function of the actual range of parameter values, before and after MCMC sampling.

22 Journal of Forestry • January 2016

reductions in sediment yield associated withincreasing gravel surface cover on thestream-crossing approaches (Figure 7).However, the prediction intervals were oftenwide, reflecting the substantial uncertaintyassociated with model parameters related tosediment yield. For example, observed sedi-ment yield at site 3 (Figure 7C) decreasedwith successive rainfall events for the nogravel treatment (event numbers 1, 2, and3) as a result of decreased soil erodibility.WEPP predictions also reflect the effect ofdecreased soil erodibility as a function ofsuccessive rainfall events within a giventreatment.

WEPP predictions of sediment yieldclearly show differences (i.e., sediment re-ductions) among the different road surfacetreatments that represent increasing intensi-ties of BMP implementation. This capabil-ity is important for evaluating the effective-ness of different BMP implementations toreduce sediment delivery for a wide range ofroad conditions (i.e., climate, soil, topogra-phy, surface cover, and traffic). However,such wide prediction intervals for runoff andsediment yield underscore the importance ofexplicitly accounting for the uncertainty as-sociated with model parameterization by

utilizing a range of erosion predictions (Hes-sion et al. 1996), as opposed to a single ero-sion prediction, to aid forestland managersin prescribing site-specific BMP implemen-tations to reduce sediment delivery to waterbodies. The complexity of data require-ments for many physically based erosionmodels make them best suited for academi-cians and state and federal agencies that havethe resources to couple field monitoringwith evaluations of model performance.Forestry practitioners can reduce sedimentdelivery from major sources (e.g., roads,trails, and associated stream crossings)through a careful emphasis on preharvestplanning and the use of erosion models withreadily attainable parameter values (e.g., theUniversal Soil Loss Equation modified forforestland) to estimate the sediment-reduc-tion efficacy of site-specific BMP implemen-tations (Dissmeyer and Foster 1984).

Therefore, despite the ability of WEPPto predict relative differences in event-basedsediment yield among different types ofBMP, such wide prediction intervals suggestlimited applicability for scenarios that de-mand a high level of prediction accuracy,such as total maximum daily load develop-ment. This issue is not specific to the WEPP

model. Because of the inherent variability inmeasuring soil erosion rates, it follows thatmodel predictions are also highly variable(Brooks et al. 2006). Therefore, it is recom-mended that prediction intervals be used toshow the substantial variability in sedimentyield predictions that can result from mea-surement error and parameter uncertainty,among other sources (i.e., model structure).Commonly, evaluations of model perfor-mance have compared an optimal model runwith observations of runoff and sedimentyield (Croke and Nethery 2006, Sawyers etal. 2012, Wade et al. 2012, Brown et al.2013). Our study findings show that al-though a single optimal model run may beuseful for comparing relative differencesamong treatments, it is less meaningful if alarge subset of model runs (with uniquecombinations of values for model parametersets) can yield equally acceptable model pre-dictions as defined by an objective functionsuch as the least squares of the model resid-uals.

It is possible that in this research, thesubstantial uncertainty associated withWEPP predictions of event-based runoffand sediment yield is partly a function of therelatively small quantities of runoff and sed-iment yield observed during the field rainfallexperiments (Brown et al. 2014). The rain-fall simulator used in this study has a de-signed rainfall application rate of 50.8 mmhour�1 (Dillaha et al. 1988). At 50.8 mmhour�1, the Rain Jet 78C nozzles provideabout 40% of the kinetic energy of naturalrainfall (Renard 1989). In addition, afterroad reopening by bulldozer blading, trafficwas limited to light-vehicle use to completethe rainfall experiments (i.e., one to twopasses per week), as well as two passes by adump truck to spread gravel on the ap-proaches. As a result, in a few cases we areattempting to predict runoff depth as low as0.3 mm and sediment yield as low as 0.04kg. A runoff prediction of 1 mm in compar-ison to an observed runoff depth of 0.3 mmrepresents an overprediction by 233%. Pre-diction accuracies would probably improvein the case of much greater observations ofrunoff and sediment yield (i.e., for very largestorm events or for annual runoff amountsand rates of sediment delivery). For exam-ple, another study suggested that WEPPpredictions of erosion could be assumed tobe within �50% of observations for erosionpredictions over longer timescales, such as inannual sediment budget analyses (Brooks etal. 2006).

Figure 6. Predicted (bars) versus observed (stars) runoff coefficients for the six stream-crossing approaches used in this study (sites 1–6 are shown as A–F) and by treatment type(none � no gravel, low gravel, and high gravel). Bars represent the 95% confidenceintervals for the model predictions for each rainfall experiment. Simulation number specifiesthe order in which rainfall experiments were conducted within each treatment.

Journal of Forestry • January 2016 23

Model Parameter IdentifiabilityThe posterior parameter distributions

for interrill erodibility, rill erodibility, andcritical shear did not differ substantiallyfrom their prior distribution (i.e., a uniformdistribution) (Figure 8). This is indicated bythe relatively constant slope steepness of theECDF plots over the full range of modelparameter values for interrill erodibility, rillerodibility, and critical shear. Consequently,there are no discernible differences amongthe road surface treatments. Therefore, forthese parameters, we cannot recommend pa-rameter ranges that are specific to the roadsurface treatments used in this study. Thisfinding indicates that these parameters areinsensitive to changes in soil erodibility as-sociated with successive rainfall events, aswell as surface cover associated with the dif-ferent gravel surface treatments. Parameteridentifiability may improve with furtherfield experimentation to better define or nar-row the initial ranges for model parametersthat are integral to WEPP predictions ofrunoff and sediment yield. In the case of in-terrill erodibility, we used a wide range of

potential values (2–11 � 106 kg s m�4)(NSERL 1995), which was higher than thatoften observed on roads (see Foltz et al.2009, 2011), because we had limited a prioriknowledge of erodibility parameter rangesfor soils at RHFRRC.

Despite limited parameter identifiabil-ity for interrill erodibility, rill erodibility,and critical shear, WEPP predictions showeddecreases in sediment yield associated withsuccessive rainfall events and increasedgravel surface cover (Figure 7). WEPP pre-dictions showed decreases in sediment yieldbecause we manually changed the model pa-rameter values for initial rill and interrillcover (corresponding to the succession ofgravel treatments) and the cumulative rain-fall amount since last disturbance for eachrainfall experiment. For initial ridge rough-ness, better model runs for the high graveltreatment were associated with lower values,whereas better model runs for the no graveltreatment were associated with higher values(initial range � 0–0.08 m). For initial rillwidth, better model runs were associatedwith lower values (initial range � 0–0.2 m)

for all treatments, and this finding wasmost pronounced for the no gravel treat-ment, followed by low gravel, and then highgravel. For effective hydraulic conductivity,better model runs for the low gravel andhigh gravel treatment were associated withlower values (initial range � 0.1–10 mmhour�1).

Overall, despite using a MCMC algo-rithm to search the model parameter ranges,we found that it was difficult to identify pa-rameter ranges that were associated with ac-ceptable model runs, especially for interrillerodibility, rill erodibility, and critical shear.Brazier et al. (2000) also found that param-eter identifiability was difficult for interrillerodibility. For physically based modelssuch as WEPP that have many detailedmathematical equations and model parame-ters, there are complex interactions amongmodel parameters that confound parameteridentifiability (Beven 2008). Therefore, inthis case, it is possible for predictions tomatch observed runoff and sediment, but itis difficult to know whether the model pa-rameters adequately represent runoff anderosion processes that were observed in thefield.

ConclusionsSediment delivery from forest roads at

stream crossings can be a major threat towater quality and aquatic habitat. Modelsare needed to evaluate the effectiveness offorestry BMPs to reduce sediment deliveryover large spatial scales and to guide site-specific BMP implementations to protectwater quality. In this study, WEPP modelperformance was evaluated for the predic-tion of event-based runoff and sedimentyield at forest stream-crossing approachesand for different gravel surfacing treatmentsthat represented increasing intensities ofBMP implementation. WEPP was evaluatedbased on prediction performance for runoffand sediment yield, as well as its ability todistinguish between the different BMPtreatments. The posterior parameter distri-butions that resulted from MCMC sam-pling were evaluated to determine whetherwe could recommend parameter ranges thatare specific to the different road surfacetreatments used in this study.

WEPP was able to match observed run-off and sediment yield for many of the rain-fall experiments. WEPP predicted reduc-tions in sediment yield that were observed inthe field resulting from decreased soil erod-ibility associated with successive rainfall

Figure 7. Predicted (bars) versus observed (stars) sediment yields for the six stream-crossingapproaches used in this study (sites 1–6 are shown as A–F) and by treatment type (none �no gravel, low gravel, and high gravel). Bars represent the 95% confidence intervals ofpredicted sediment yield for each rainfall experiment. For instances in which the predictionlimit exceeded the y-axis limit (30 g m�2 mm�1), the value is labeled at the top of thefigures. Simulation number specifies the order in which rainfall experiments were con-ducted within each treatment.

24 Journal of Forestry • January 2016

events, as well as the treatment effect of in-creasing gravel cover on the stream-crossingapproaches. However, 95% confidence in-tervals representing the range of predictedrunoff and sediment yield for the best modelruns were often very wide for each rainfallexperiment. This result reflects the substan-tial uncertainty in model parameter valuesand model predictions. Based on analysisof the posterior distributions of model pa-rameters, we could not recommend rangesof parameter values that were specific to thedifferent road surface treatments for inter-rill erodibility, rill erodibility, or criticalshear.

Overall, these results suggest that thereis limited utility in estimating soil erosion orsediment delivery based on a single, opti-mized model run (i.e., one set of model pa-rameters that result in an acceptable predic-tion for runoff and sediment yield). Rather,predictions should be made with a range ofpotential values for model parameters re-lated to runoff generation and sedimentyield to reflect the uncertainty associatedwith model parameterization. In this way, arange of erosion predictions associated withdifferent intensities of BMP implementa-

tions can be compared to aid in watershedmanagement efforts to protect water quality,while explicitly accounting for the uncer-tainty associated with model predictions.These results also suggest that watershedmanagement decisions should not be basedon model predictions of sediment yieldalone but rather on a combined effort thatincludes field monitoring to determineBMP effectiveness in reducing sediment de-livery, improve a priori estimates of modelparameters, and evaluate the performance ofmodels to estimate BMP efficacy.

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