RESEARCHUncertainty Analysis of Predicted Disturbance fromOff-Road Vehicular Traffic in Complex Landscapesat Fort HoodSHOUFAN FANGSTEPHEN WENTEGEORGE Z. GERTNER*GUANGXING WANGW503 Turner Hall1102 South GoodwinDepartment of Natural Resources and Environmental

SciencesUniversity of IllinoisUrbana, Illinois 61801, USA

ALAN ANDERSONUSACERLP.O. Box 9005Champaign, Illinois 61820-1305, USA

ABSTRACT / The US Army Engineering Research Develop-ment Center (ERDC) uses a modified form of the Revised Uni-versal Soil Loss Equation (RUSLE) to estimate spatially explicitrates of soil erosion by water across military training facilities.

One modification involves the RUSLE support practice factor(P factor), which is used to account for the effect of distur-bance by human activities on erosion rates. Since disturbancefrom off-road military vehicular traffic moving through complexlandscapes varies spatially, a spatially explicit nonlinear re-gression model (disturbance model) is used to predict the dis-tribution of P factor values across a training facility. This re-search analyzes the uncertainty in this model’s disturbancepredictions for the Fort Hood training facility in order to deter-mine both the spatial distribution of prediction uncertainty andthe contribution of different error sources to that uncertainty.This analysis shows that a three-category vegetation mapused by the disturbance model was the greatest source ofprediction uncertainty, especially for the map categories shruband tree. In areas mapped as grass, modeling error (uncer-tainty associated with the model parameter estimates) was thelargest uncertainty source. These results indicate that the useof a high-quality vegetation map that is periodically updated toreflect current vegetation distributions, would produce thegreatest reductions in disturbance prediction uncertainty.

Soil loss in the United States was estimated using theUniversal Soil Loss Equation (USLE) (Wischmeier andSmith 1978) before the modified version was developedand is currently predicted using the Revised USLE(RUSLE) (Renard and others 1994, 1997) for the pur-pose of agricultural, rangeland and environmentalmanagement. Both USLE and RUSLE are related torainfall erosivity factor (R), soil erodibility factor (K),slope length factor (L), slope steepness factor (S),cover management factor (C), and support practicefactor (P). These equations consist of empirical modelsets derived from an extensive database, and theirmodel parameters contain uncertainty when usingthese equations for a specific area.

The RUSLE P factor is used to reflect the effect of avariety of human activities (disturbance) on soil erosionby water. On agriculture land, the P factor is used to

describe the impact of tillage on soil erosion (Hill andothers 1944, Van Doren and others 1950, Wischmeierand Smith 1978, Meyer and Harmon 1985, Renard andothers 1997). On nonagricultural land, P factor esti-mates have been made for logging practices in forestecosystems (Moehring and Rawls 1970), military ma-neuvers at military installations (Goran and others1983, Braunack 1986, Shaw and Diersing 1990), andtracked vehicles and construction activities at construc-tion sites (McKyes and others 1980, Thurow and others1995). These activities disturb ecosystems and changethe structure of soil, microtopographical attributes, andvegetation cover (Wilshire and Nakata 1976, Braunack1986, Wilson 1988, Shaw and Diersing 1990). Thesechanges typically result in an increase of soil erosionrates (Thurow 1991, Thurow and others 1995).

In complex landscapes, disturbance is concentratedat specific locations dependent on the purposes of thedisturbing activities, distribution of natural resourcesand road systems, as well as topographical attributes.Military installations are usually complex landscapes, inwhich the disturbance source is mainly tracked vehicles.Based on studies of environment impact of training

KEY WORDS: Support practice factor; Disturbance; Off-road vehicletraffic; Uncertainty analysis; Error budget; RUSLE

*Author to whom correspondence should be addressed; email:gertner@uiuc.edu

DOI: 10.1007/s00267-002-2565-2

Environmental Management Vol. 30, No. 2, pp. 199–208 © 2002 Springer-Verlag New York Inc.

activities, Guertin and others (1998) developed a re-gression model in 1995, hereafter referred to as thedistribution model, to predict the spatial distributionand intensity of military training activity impacts atmilitary installations. This model has been widely usedin military installations and incorporated into differentmodels. A land repair cost model was developed forseveral installations, which incorporated the distribu-tion model (CAA 1996). This cost model, including useof the distribution model, was subsequently extendedto estimate carrying capacity of military lands for theArmy’s Integrated Training Area Management pro-gram (Anderson and others 1996, 2001, AEC 1999,Anderson and Sydelko 1999). The distribution modelhas also been integrated into the Ecological DynamicsSimulation model and the Corp of Engineer’s LandManagement System (Childress and others 1999, Priceand others 1999, MacAllister and others 2000). Meyerand Guertin (2000) used this model at several installa-tions to predict training intensities for alternative train-ing scenarios. Anderson (1999) demonstrated that sev-eral of these models are sensitive to changes in thedistribution of land-use patterns.

As is the general case with models, uncertainty inboth the information sources (data) and modeling pro-cess will propagate to the model predictions (Dettingerand Wilson 1981, Cox 1977, Gertner 1987, Iman and

Helton 1988, Gertner and others 1995). Quantificationof the contribution of individual uncertainty sourcesserves as the basis for reducing prediction uncertaintyand, therefore, improving the quality of model predic-tions (Gertner and others 1999, Fang 2000). The ob-jectives of this study are to define the uncertaintysources for off-road vehicular traffic disturbance pre-dictions, determine each source’s contribution to pre-diction uncertainty across a complex landscape, andsuggest efficient ways to reduce uncertainty of the mod-el’s predictions.

Methods

The study area, Fort Hood, is a US Army trainingfacility comprised of 172,000 ha of grass, shrub, andforest ecosystems located on the border of Bell andCoryell counties in central Texas USA (Figure 1). To-pographically the facility is relatively flat with slopesaveraging 2.7 degrees, (although they range from 0 to58 degrees) (Figure 2b). The dominant vegetation typeat the east and northeast is oak–juniper woodlands. Thewest and south parts are savannah type, dominated bygrasses with scattered motts of live oak. In the centerthere is a mixture of the savannah-type and oak–juniperwoodlands (Tazik and others 1992). Figure 2c showsthe spatial distribution of vegetation in Fort Hood. This

Figure 1. Location of FortHood in Texas, USA.

200 S. Fang and others

facility has been divided into four regions (Figure 2d).The south region and the south part of the west regionare similar in both topographical features and vegeta-tion. The north part of west region is similar to the eastand central regions in topographical features and veg-etation. Due to topographical features and the pur-poses of military training and facility management,training is not evenly allocated in each region. In FortHood, there is a well distributed road system with nopoint on the facility more than 8.5 km from the nearestroad (Figure 2a).

Training Use Distribution Model

The model used to predict the spatial and temporaldistribution of disturbance probability/intensity in thisresearch area is modified from the distribution modelpublished by Guertin and others (1998). The originalmodel considered the vehicle tracks as disturbance andobserved disturbance as a binary (presence/absence)variable from subplots with plots. One modificationincluded adding the number of battalions training atthe facility in a given year, to represent the change ofactivity intensity over time. The other modification re-interpreted the disturbance observations as a continu-ous variable ranging from 0 to 1, indicating the propor-tion of subplots disturbed within a plot. Thismodification avoids the questionable assumption ofsubplot observation being independent within plots.The general form of the model employed has the form:

y �e�b0��

i � 1

8

bi � xi�

1 � e�b0� �i�1

8

bi �xj�

(1)

where y is disturbance and bi and xj are parameters andindependent variables of the model, respectively, aslisted in Table 1. Among the eight independent vari-ables are five dummy variables representing specifictraining areas (x4 to x6) and vegetation categories (x7

and x8). Model parameters were estimated using non-linear regression in SAS.

The observations used in parameterization of thedisturbance prediction model (equation 1) are col-lected from 100-m transects (plots) located randomlyacross the study area. During annual surveys, the pres-ence or absence of vehicle tracks is visually assessed atthe midpoint of each meter (subplots) along thesetransects. Disturbance in a transect (plot), say, plot j, iscalculated based on the number of its subplots in whichvehicle tracks are observed:

yj �1

100 �k � 1

100

VTjk (2)

where VTjk is the vehicle track indicator for subplot kwithin plot j and has a value of 0 and 1 to indicateabsence and presence of vehicle tracks, respectively.Distance to roads (DR) of the plots is calculated fromglobal positioning system (GPS)-measured coordinatesof the plots and roads. Average plot slope (SL) is cal-culated from measurements at both ends and the mid-point of each transect. Vegetation (VG) is visually as-sessed at each subplot (Tazik and others 1992). Theplot vegetation type is assigned as the type that coversthe largest proportion of subplots. The number of bat-talions training at Fort Hood in a given year (NB) istaken from facility records. The region code (RG) ofthe plots is copied from a facility map. Disturbancepredictions are extrapolated across the facility using 50-� 50-m resolution geographic information system(GIS) maps of the independent variables DR, SL, RG,and VG.

Uncertainty Sources and Estimation

The model’s uncertainty sources are the model pa-rameter estimates, dependent variables and the inde-pendent variables used to extrapolate disturbance overspace and time. Uncertainty from these sources fallsinto four general categories—modeling, mapping, de-cision, and measurement errors. The uncertainty of themodel parameter estimates is referred to as modelingerror and is measured as the variance of parameterestimates.

Table 1. Independent variables of model used inprediction of spatial and temporal distribution ofdisturbance and estimates of model parameters

Variables Meaning

x1 (NB) Number of battalionsx2 (DR) The shortest distance to roadsx3 (SL) Slope steepness (cotangent of slope angle)x4 (RG) West regiona

x5 (RG) East regiona

x6 (RG) Central regiona

x7 (VG) Vegetation type: Treea

x8 (VG) Vegetation type: Shruba

Parametersb Mean Standard error

b0 �3.49115 0.2776b1 0.14583 0.0115b2 �0.52617 0.0653b3 �0.07093 0.0273b4 1.65672 0.1583b5 0.99172 0.1722b6 �0.41735 0.1872b7 �2.46693 0.4774b8 �1.58176 0.1930

aIndicating a dummy variable. bIn parameter estimation, R 2 is 0.464.

Analysis of Disturbance in Complex Landscapes 201

Mapping error refers to the error in the maps (DR,SL, RG, and VG) used to spatially extrapolate distur-bance across the training facility. The magnitude ofmapping errors is estimated by comparing the map-derived values at each of the plots to the field measure-ments used in calibrating the model. The DR map wascreated by converting a digitized (vector) road map toa 50-m resolution raster map and calculating the aver-age distance of a series of buffer strips on either side ofthe nearest roads using the GRASS GIS (USACERL1993) program r.buffer. Error in the DR map was esti-mated by comparing the distances from plot locationsto the nearest roads measured using the original vectorroads map and GPS. The square of the difference of thedistances was taken in order to calculate the variance ofthe DR map. The standard deviation of horizontal mea-surement error for the particular GPS unit used was 20cm. The GPS values were considered as true values. TheSL map was created using a 30- � 30-m resolutiondigital elevation model (USGS 1993) and the r.slope-.aspect program in GRASS. Error in the SL map wasestimated by calculating the variance of the SL mapestimates from the average slope measured at the sam-ple plots. The VG map was created from an unsuper-vised classification of 1989 remotely sensed SPOT sat-ellite images. Field observations of vegetation made in1998 were used to assess the uncertainty of each of thethree vegetative cover categories (grass, shrub, andtree—modeled as dummy variables x7 and x8 in equa-tion 1). Error in the VG map is due to both error in theremotely sensed image classification method, as well astemporal changes in vegetation between 1989 and1998. The RG map categories (dummy variables x4 – x6

in equation 1) were excluded from the uncertaintyanalysis since there is no variation caused by sampling,measuring, data processing, or modeling in the RGdata.

Decision error is uncertainty contributed from inac-curate management decisions or projections. When fa-cility managers use the distribution model, the inde-pendent variable NB, the number of battalions to betraining at this facility in future years, is projected. Thisprojection of training load is estimated by expert opin-ion to have a 10% variance or decision error associatedwith it.

Measurement error is the uncertainty contributed bythe dependent variable, disturbance, due to sampling,measuring, and data processing. It is estimated using anunbiased estimator of variance and data from a 1998validation study in which two observers independentlyassessed disturbance.

Partitioning Propagated Uncertainty

The uncertainty of all sources propagates into pre-dicted disturbance through the distribution model(equation 1). The uncertainty contribution of dummyvariables x7 and x8 (from the VG map) are consideredjointly as the contribution of categorical variable VGand is defined as the prediction error caused by mis-classification. Therefore, at each pixel, variance contri-bution of vegetation misclassification, var[f( � , V)], is:

var� f � � , V�� � �i � 1

k

� f � � , Vi�

� f � � , Vj��2 � Pe�Vi�Vj� (3)

where f( � , V) is the model prediction, Vj is theclassified vegetation type at a pixel, and Pe(Vi�Vj) is theerror rate of vegetation type Vj being classified as an-other vegetation type, Vi. For other independent vari-ables and model parameters, Taylor expansion (seeAppendix) is used in computing their variance contri-bution.

No correlation was found between vegetation mis-classification and other model components. The totalvariation of prediction at each pixel is the summationof variances from measurement error of disturbance,vegetation misclassification, and other model compo-nents:

var� f �X, B�� � �i � 1

3

var� f � � , xi��

� �i � 0

8

var� f � � , bi�� � var� f � � , V�� � e2 (4)

where x and b are model components defined inTable 1, var[f( � , w)] is the variance of the predictioncaused by model component w (see equation 3 andAppendix), and e

2 is the measurement error of dis-turbance.

A variance map is created to describe the spatialdistribution of total variance of prediction. A transectacross the study area is selected to show the uncertaintyanalysis results along the pixels of this transect.

Results

Figure 2 depicts the disturbance intensity/proba-bility map (Figure 2e) produced by the calibrateddistribution model (assuming an NB value of 22 bat-talions) and its relationship to the DR (Figure 2a), SL(Figure 2b), VG (Figure 2c), and RG (Figure 2d)maps. The distribution model predicts that distur-

202 S. Fang and others

bance: increases with the number of battalions train-ing at the facility (b1 in Table 1); decreases withdistance to roads (b2); decreases with slope (b3); ishighest in the west region (b4), lower in the east (b5)and southern regions (no dummy variable), and low-est in the central region (b6); is highest in grass (nodummy variable), followed by shrub (b8) and lowestin tree (b7). High disturbance intensity/probability(0.6) occurs mainly in grassy areas of the west andeast training areas. Low disturbance intensity/prob-ability (�0.3) generally occurs in the central andsouth training areas and in the roadless portions ofthe east training area.

Figure 3h depicts the total uncertainty (rangesfrom 0.00 to 0.195 variance units) of the disturbanceprediction (Figure 2e) and its major contributingsources of uncertainty. The magnification factors re-quired to display the uncertainty sources on the samescale as the total uncertainty map indicates the rela-tive contribution of the various sources, with lowermagnification factors indicating the larger contribu-tors to total uncertainty. The uncertainty contribu-tion from modeling error is depicted in Figure 3d.The standard errors of model parameters used toestimate this uncertainty are listed in Table 1. Theuncertainty contribution from mapping error is thelargest source of prediction uncertainty and is de-picted in Figure 3e. It is broken out into the uncer-tainty contributions of the DR map (Figure 3a), SLmap (Figure 3b) and the VG map (Figure 3c). Thesquare of the difference between the GIS estimatedand measured DR changes with increasing DR values.The relationship between the square of the differ-ence and the GIS estimated DR is quadratic:

SE�DR� � 0.017541 � 0.075471 � DR � 0.011214 � �DR�2

F2,174 � 36.07 and R2 � 0.293 (5)

where DR is the GIS estimated value of the distanceto roads. The variance of SL at different pixels isconstant since the difference between GIS estimatedand measured values have no trend corresponding tothe change of their estimated values. The estimatedvariance of GIS-estimated SL is 9.3. A confusion ma-trix (Table 2) is used to compare measured andmapped vegetation types of plots and shows the errorrates of grass, shrub, and tree vegetation types are15.6%, 59.1%, and 75.0%, respectively. The uncer-tainty contribution from decision error is depicted inFigure 3f. The uncertainty contribution from mea-surement error is depicted in Figure 3d. Measure-ment error of disturbance is very small at 0.000824variance units.

Discussion

Since the vegetation map uncertainty (Figure 3c) isthe dominant source of mapping contributed uncer-tainty, and mapping uncertainty (Figure 3e) is the dom-inant source of total prediction uncertainty (Figure3h), the spatial distribution of predicted disturbanceuncertainty is largely determined by the vegetation map(Figure 2c) as well as the predicted disturbance map(Figure 2e). The central, northeast, and southwestparts of the study area have little predicted disturbanceand therefore have relatively low uncertainty (�0.04)associated with those predictions. The west region andthe parts of the east region with roads have morepredicted disturbance and, therefore, have relativelyhigher prediction uncertainty (Figure 3) for those ar-eas that fall within the vegetation map categories (treeand shrub) that produced the greatest amount of un-certainty. With the vegetation map, pixels in urban andbare ground areas were also classified as grass. Due todata availability, this classification error was not ana-lyzed in this study. The uncertainty contribution of thevegetation map would have been larger if this error wasconsidered.

The contribution of various uncertainty sources ateach pixel is made more understandable by looking ata selected transect across the west region that has highpredicted disturbance and the largest range of predic-tion variance (insets of Figures 4–7). The amount andproportion of variance contributed by grouped uncer-tainty sources across this transect are shown in Figures4 and 5. Mapping and modeling processes contributemore than 65% of the total variance for any pixel acrossthis transect. On the other hand, measurement error ofdisturbance contributes less than 8% of the uncertaintyfor any pixel on this transect. When total variance of apixel is larger than 0.03, mapping contributes 50%–95% prediction uncertainty. Otherwise, modeling andmapping contribute about 50% and 15% predictionuncertainty, respectively.

The variance contribution of mapping processesacross the transect (Figure 6) shows that DR caused

Table 2. Confusion matrix for vegetation classification.

Vegetation class

Mapped

Grass (%) Shrub (%) Tree (%)

ObservedGrass 84.3 40.9 25.0Shrub 11.4 40.9 50.0Tree 4.2 18.2 25.0

Total error ratea 15.6 59.1 75.0

aSum of the percentages of the nonmapped vegetation classes.

Analysis of Disturbance in Complex Landscapes 203

Figure 2. The modified Training Use Distribution Model uses maps of distance to roads (DR, unit: km) (a), slope (SL, percent)(b), three vegetation classes (VG) (c), and training regions (RG) (d) in conjunction with the number of battalions training ina given year to predict disturbance in percent (e) due to off-road vehicular traffic across the Fort Hood training area.

Figure 3. The total variance (that is, uncertainty) of predicted disturbance (h) is the sum of the variance contributed by modelingerror (d), mapping error (e), decision error (f), and measurement error (g). Similarly, uncertainty contribution of mapping error isthe sum of contributions of distance to roads (DR) mapping error (a), slope (SL) mapping error (b), and vegetation (VG) mappingerror (c). The legend is specified for each map using a magnification factor (the number in the upper right-hand corner of each map).

204 S. Fang and others

almost no variance and SL caused little variance(�0.005) for any given pixel. The role of VG dependson the amount of variance caused by mapping pro-cesses. When the latter is larger than 0.01 (vegetationtypes shrub and tree), the former is the major variancecontributor. When the latter is smaller than 0.01 (veg-etation type grass), the former is a minor variancecontributor. Since the variation of VG is from misclas-sification, misclassification in the vegetation map is thesingle largest source of uncertainty in disturbance pre-dictions.

The variance contribution of modeling processacross the transect (Figure 7) shows that parameters b0

and b1 contribute 60%–90% of the uncertainty caused

by modeling process. The three parameters associatedwith the training region map (RG), b4, b5, and b6, to-gether contribute more uncertainty to prediction thanthe parameters associated with the vegetation map(VG), b7 and b8.

Conclusions

The utility of the uncertainty analysis presented isthat facility managers can know the amount andsources of uncertainty in the distribution model for anyregion of the facility that the managers are interestedin. For example, if the transect in the previous analysiswas a proposed utility corridor and this project was

Figure 4. Total variance ofprediction and its compositionacross the selected transect.

Figure 5. Proportion of vari-ances contributed by uncer-tainty sources across the se-lected transect.

Analysis of Disturbance in Complex Landscapes 205

impacted by the amount of disturbance within thiscorridor, managers could use this uncertainty analysisto determine if the distribution model’s disturbancepredictions were of sufficient accuracy for making man-agement decisions. If the uncertainty in the modelpredictions was too high, knowing the vegetation mapwas the greatest source of uncertainty could aid inreducing the model prediction uncertainty. In thiscase, vegetation along the corridor can simply be sur-veyed to reduce disturbance prediction uncertainty inthe region of interest to the point where managementdecisions could be made.

Due to uncertainty from information sources andprocesses, the disturbance predicted by the distributionmodel contains uncertainty. The spatial distribution ofprediction uncertainty is heterogeneous and corre-

sponds to the spatial distribution of components of theprediction model. The majority of the prediction un-certainty is caused by high classification error rates forvegetation types shrub and tree in the vegetation map(VG). When the error rate of vegetation classification islow, as in vegetation type grass, the total amount ofuncertainty is greatly reduced. Under such conditions,vegetation misclassification contributes only a minoramount of uncertainty to the model prediction andmodeling error becomes the dominant source of pre-diction uncertainty. Decision and measurement errorof disturbance contribute only a small amount to pre-diction uncertainty.

Based on the behavior of the model components inuncertainty propagation, reducing the error rate ofvegetation classification is probably the most efficient

Figure 6. Composition of predic-tion variance caused by mappingprocesses across the selectedtransect.

Figure 7. Composition ofprediction variance causedby modeling across theselected transect.

206 S. Fang and others

way to increase the precision of disturbance prediction.Using an updated high-quality vegetation map shouldreduce a large proportion of the variance at the pixelswhose vegetation type is tree or shrub.

Appendix: Variance Transformation Using TaylorExpansion

According to Taylor series, if a function (model) isdifferentiable, it can be expanded into the form of aseries:

f �X� � f �X0� � �i � 1

�

f �i��X0� � �X � X0�i (A1)

where f (i) (X0) is the i th order of differential of themodel, and X0 is the mean value of X.

Considering the first order of differential of themodel, the approximation of the model is:

f �X� � f �X0� � f �X0� � �X � X0� (A2)

Based on this approximation, the variance of themodel can be approximated as:

var� f �X�� � � f �X0��2 � var�X� (A3)

When the model has p independent components,i.e., X � (xl, . . . , xp) equation A3 becomes:

var� f �X�� � �i � 1

p

��f �X0�/� xi�2 � var� xi� (A4)

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