interplay between field observations and numerical...

Geomorphology xxx (2013) xxx–xxx

GEOMOR-04327; No of Pages 17

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Geomorphology

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Interplay between field observations and numerical modeling to understandtemporal pulsing of tree root throw processes, Canadian Rockies, Canada

Y.E. Martin a,c,d,⁎, E.A. Johnson b,c, O. Chaikina a

a Department of Geography, University of Calgary, Calgary, AB T2N 1N4, Canadab Department of Biological Sciences, University of Calgary, Calgary, AB T2N 1N4, Canadac Biogeoscience Institute, University of Calgary, Calgary, AB T2N 1N4, Canadad Department of Geoscience, University of Calgary, Calgary, AB T2N 1N4, Canada

⁎ Corresponding author at: Department of GeographUniversity Dr. NW, Calgary, Alberta T2N 1N4, Canada. T403 282 6561.

E-mail addresses: [email protected] (Y.E. Martin)(E.A. Johnson), [email protected] (O. Chaikina).

0169-555X/$ – see front matter © 2013 Elsevier B.V. Alhttp://dx.doi.org/10.1016/j.geomorph.2013.04.017

Please cite this article as: Martin, Y.E., et al., Inroot throw processes, Canadian Rockies, Can

a b s t r a c t
a r t i c l e i n f o
Article history:Received 21 December 2012Received in revised form 12 April 2013Accepted 14 April 2013Available online xxxx

Keywords:Root throwTree population dynamicsPit-mound microtopographySoil bioturbationDiffusion

During the cycle of forest disturbance, regeneration, and maturity, tree mortality leading to topple is a regularoccurrence. When tree topple occurs relatively soon after mortality and if the tree has attained some thresh-old diameter at breast height (dbh) at the time of death, then notable amounts of soil may be upheaved alongwith the root wad. This upheaval may result in sediment transfers and soil production. A combination of fieldevidence and numerical modeling is used herein to gain insights regarding the temporal dynamics of treetopple, associated root throw processes, and pit-mound microtopography. Results from our model of treepopulation dynamics demonstrate temporal patterns in root throw processes in subalpine forests of theCanadian Rockies, a region in which forests are affected largely by wildfire disturbance. As the forest regen-erates after disturbance, the new cohort of trees has to reach a critical dbh before significant root plate up-heaval can occur; in the subalpine forests of the Canadian Rockies, this may take up to ~102 years. Oncetrees begin to reach this critical dbh for root plate upheaval, a period of sporadic root throw arises that iscaused by mortality of trees during competition. In due course, another wildfire will occur on the landscapeand a period of much increased root throw activity then takes place for the next several decades; tree sizesand, therefore, the amount of sediment disturbance will be greater the longer the time period since the pre-vious fire. Results of previous root throw studies covering a number of regional settings are used to guidean exercise in diffusion modeling with the aim of defining a range of reasonable diffusion coefficientsfor pit-mound degradation; the most appropriate values to fit the field data ranged from 0.01 m2 y−1 to0.1 m2 y−1. A similar exercise is then undertaken that is guided by our field observations in subalpine forestsof the Canadian Rockies. For these forests, the most appropriate range of diffusion coefficients is in the range0.001 m2 y−1 to 0.01 m2 y−1. Finally, the model of tree population dynamics is combined with the model ofpit-mound degradation to demonstrate the integration of these combined processes on the appearance ofpit-mound microtopography and soil bioturbation in subalpine forests of the Canadian Rockies. We concludethat the appearance of notable pit-mound microtopography is limited to very specific time periods and is notvisible for much of the time. Most of the hillslope plot is affected by root throw during the 1000-year modelrun time.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Biological processes are one of themost important factors influenc-ing formation and perturbation of surface and near-surface soil layers(e.g., Paton et al., 1995; Wilkinson et al., 2009; Roering et al., 2010).The latter constitute an important element of the Critical Zone,the outer layer of Earth that provides life-sustaining resources

y, University of Calgary, 2500el.: +1 403 220 6197; fax: +1

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terplay between field observada, Geomorphology (2013),

(Wilkinson et al., 2009). The life cycle processes of vertebrates, in-vertebrates, and plants may affect soil formation and characteristicsand result in mixing of soil layers; these processes are collectively re-ferred to as bioturbation (Humphreys and Mitchell, 1983; Paton et al.,1995; Lavelle et al., 1997;Wilkinson et al., 2009).Whereas recognitionof bioturbation goes back at least as far as Darwin (1881), if not fur-ther, this topic has come to the forefront of research only in more re-cent years (Wilkinson et al., 2009). Characteristics such as soilporosity, structure, moisture, pH, organic matter, and nutrients maybe affected by these biological agents. Among the biological agentsthat have received the most attention are earthworms, ants, termites,mammals such as gophers, and trees (Butler, 1995; Paton et al., 1995;Wilkinson et al., 2009).

ations and numerical modeling to understand temporal pulsing of treehttp://dx.doi.org/10.1016/j.geomorph.2013.04.017

http://dx.doi.org/10.1016/j.geomorph.2013.04.017

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2 Y.E. Martin et al. / Geomorphology xxx (2013) xxx–xxx

Soil detachment may occur as a result of tree fall, and the growthof roots and stems may also disturb soils (e.g., Gabet et al., 2003;Gallaway et al., 2009; Hancock et al., 2011) and result in bedrockweathering and soil production (Gabet and Mudd, 2010). In thispaper, we consider pit-moundmicrotopography caused by the upheav-al of a root plate during tree topple, herein referred to as the root throwprocess. In particular, if a tree upheaves significant sediment on its rootsas it topples, then this affects the soil characteristics and also hillslopesediment transfers and landscape microtopography (Stephens, 1956;Henry and Swan, 1974; Schaetzl and Follmer, 1990; Gabet et al., 2003;Gallaway et al., 2009). A pit is left behind where the root plate wasupheaved, and depending on the position of the root plate relative tothe pit, the upheaved sediment may eventually be returned to the pitor may form a mound feature located in proximity to the pit feature(Fig. 1) (Lutz and Griswold, 1939; Stephens, 1956; Beatty and Stone,1986; Schaetzl and Follmer, 1990; Gallaway et al., 2009). Rotationaltree falls, versus hinge falls, are more likely to result in a root plate situ-ated over the pit; and in these cases, sediment is returned to the pit, andmound development does not occur (Beatty and Stone, 1986). Normanet al. (1995) andGallaway (2006) found that a greater proportion of thedisturbed soil makes its way back into newly formed pits on gentlerslopes relative to steeper slopes because of the root plate sediment ei-ther falling entirely or partially back into the pit. Pit-mound longevityis influenced by pit-mound magnitude and rates of degradation.

Sediment upheaval caused by root throw and the eventual returnof sediment to the landscape surface is a sediment transfer processthat may be significant in certain landscapes (Gallaway et al., 2009;Hancock et al., 2011). While pit-mound features remain evident onthe landscape, they may impact depression storage in locations whereoverland flow is important and may impact any sediment transportthat occurs by providing topographic barriers to sediment movement(Martin et al., 2008). Pit-moundmicrotopography also provides specificmicrohabitats for flora and fauna (Denny and Goodlett, 1956; Lyfordand MacLean, 1966; Falinski, 1978; Beatty and Stone, 1986). Duringthe time period when pit-mound features are visible on the landscapeand even after the topographic form has been flattened, the resultantsoil bioturbation impacts soil moisture and infiltration.

Pit-mound microtopography is created when trees fall over (not asnap in the bole). In some situations, trees may die during forestcompetition as a result of processes associated with tree population

Fig. 1. Example of a tree root throw in a subalpine forest, Canadian Rockies. Note that the bphotograph.

Please cite this article as: Martin, Y.E., et al., Interplay between field observroot throw processes, Canadian Rockies, Canada, Geomorphology (2013),

dynamics (Gallaway et al., 2009). Other disturbances, such as windevents or fire disturbance, however, are also responsible for treedeath. If the tree dies while still standing (e.g., natural death duringforest development or wildfire disturbance), then a time lag betweentree death and tree topple (and possible root plate upheaval) mayoccur. If a tree topples soon after death (or the tree topple itself resultsin death), then a root plate is more likely to be upheaved; if more timepasses, then it may instead snap at the base of the bole because of rot(Johnson and Greene, 1991). Disturbance bywinds have the capabilityto kill large numbers of trees simultaneously (e.g., Canham andLoucks, 1984) and are responsible for forming some of the most pro-nounced cases of pit-mound microtopography in temperate foreststhat have been documented in eastern andmidwestern deciduous for-ests (e.g., Lyford and MacLean, 1966).

Assemblages of pit-mound features that have formed in responseto a particular tornado, hurricane, or strong windstorm have beendated in temperate forests of Michigan and Wisconsin (Schaetzl andFollmer, 1990). Given the often large size of trees in these study re-gions, the initial pit-mound topography is expected to be very pro-nounced, which may be a key factor in the notable longevity (up tomany hundreds of years or more). In addition to pit-mound magni-tude, rates of degradation of these features may also factor into lon-gevity. Schaetzl and Follmer (1990) estimated values of pit-moundlongevity that were about 2–5 times longer than earlier published es-timates, with ages often exceeding 1000 years. They emphasized theneed for studies in other temperate forest locations, tropical forests,and alpine and cold coniferous forests. To our best knowledge, a gapstill remains in our understanding of tree throw and pit-mound lon-gevity, formation, and dynamics in these other regions.

Our earlier studies of tree population dynamics demonstrated thattree topple in subalpine forests of the Canadian Rockies is associatedwith temporal pulsing (Gallaway et al., 2009). Because of these tempo-ral patterns of tree topple, pit-mound formation, soil bioturbation, andsediment transport are likewise going to exhibit temporal variability.Root throw processes and associated pit-mound features may occurmore frequently at certain times during forest development and muchless so at other times. An emergent idea guiding the present study isthat what we observe on the landscape may be a function of when welook at the landscape. Although root throw activity and pit-mound fea-tures are observed in subalpine forests of the Canadian Rockies, the

ole associated with the tree topple is located in the middle of the left-hand side of the



3Y.E. Martin et al. / Geomorphology xxx (2013) xxx–xxx

impact of such features on microtopography may appear negligibledepending on the stage of tree population dynamics that is observed.Pit-mound features are not particularly large in subalpine forests ofthe Canadian Rockies; the degradation may be relatively rapid for thisreason, and, therefore, longevity will be shorter. Despite the temporalpulsing of root throw occurrence and the possibly shorter longevityof individual pit-mound features (and often minimal pit-moundmicrotopography), soil bioturbation caused by root throw may still bea significant factor in these forests depending on overall rates of rootplate upheaval. A focus of this paper is to explore possible scenarios ofthe rates of pit-mound degradation for these subalpine forests and tolink these rates of degradation with tree population dynamics to assessthe overall significance of hillslope microtopography and bioturbationcaused by tree throw.

Within our paper, the framework of Schaetzl and Follmer (1990) forestimating the density of pit-mound features is developed into a moreformal numerical modeling framework. Their equation has the form

D ¼ f dU=dt; dE=dtð Þ ð1Þ

where D is density of pit-mound features (whichmay be at any stage inthe degradation process), dU / dt is the rate of pit-mound formationover time (which in reality is expected to vary over time dependingon tree population dynamics), and dE / dt is the rate of pit-mound deg-radation. Datingmethods have provided some information on longevityof pit-mound features (Schaetzl and Follmer, 1990), contributing someidea about the rates of degradation. While pit-mound diffusion is acritical factor in determining pit-mound longevity, the mechanisms ofpit-mound degradation remain a largely unexplored topic. The twoterms in the above equation will vary amongst geographic settingshaving different forest ecology and tree sizes and having differentpit-mound degradation processes and rates; these factors in turn willaffect the persistence (or not) of pit-mound microtopography.

Within this paper, we follow several main lines of analysis:

(i) First, we run our model of tree population dynamics (withoutthe incorporation of pit-mound degradation) to provide in-sights into the temporal pulsing of root throw and pit-mounddevelopment.

(ii) We then tackle the question of the rates of pit-mound degra-dation in a methodical way in an attempt to identify futureresearch requirements and to inform future studies. We under-take a numerical modeling exercise to calibrate the diffusionequation to simulate degradation, and we also explore howthe sizes of pit-mounds may affect their degradation and lon-gevity and, hence, microtopography. We utilize results of ourfield studies of root plates and pit-mound features for ourfield site in Hawk Creek, British Columbia, to inform themodelingexercise.

(iii) We then combine our model of tree population dynamics with anumericalmodel of pit-mounddegradation to explore the tempo-ral variability in the appearance of pit-mound microtopographyon the land surface and to assess the significance of soil bioturba-tion in these forests. Once again,field evidence is invoked to guidethis exercise.

2. Study area and field methods

2.1. Study area

Hawk Creek Watershed, Kootenay National Park, is the locationfor the field component of this study. This location also represents theprototype subalpine forest for the numerical modeling component ofthis paper. HawkCreek is situated in the CanadianRockies, in southeast-ern British Columbia (Fig. 2) and is dominated by folded and faultedsedimentary rocks (limestone and shale). The last glaciation resulted


in major erosion throughout the region. Hawk Creek drains an area ofabout 24 km2 and is a tributary of the Vermilion River. The elevationrange is 1330 to 3086 m, with moderate hillslopes (b30°) dominatingthe lower portion of the basin where most of the field workwas carriedout. Compact, massive debris flow deposits, morainal material, and/orbedrock underlie the soils in the lower portions of the basin. Soils aremost often unconsolidated and unsorted, with cobbles and boulderscontained within a matrix of mainly silty sand (sand often >70%) andlow clay content (b2%) (sandy loam).

Climate in this region is Cordilleran and is influenced in turn byeither cold continental air masses from the north, or warmer airmasses from the west. The average annual amount of rainfall isabout 340 mm, with summer rainfall dominated by convectionalthunderstorms. Winter precipitation occurs mainly as snow and ac-counts for about 50–60% of annual precipitation.

Vegetation consists of subalpine forest species dominated bylodgepole pine (Pinus contorta Loudon var. latifolia Engelm.) andEngelmann spruce (Picea engelmannii Parry ex. Engelm.). Crown firesare the primary forest disturbance, with peak lightning activity occur-ring in July and August (Masters, 1990; Reed et al., 1998). The firereturn interval has been estimated as 60 years for the period 1508–1778, 130 years for 1778–1928, and 2000 years for the recent period1928–1988 (Masters, 1990; Reed et al., 1998). The long return intervalfor 1928–1988 has a large confidence range (Reed et al., 1998) be-cause of the short period of record.

2.2. Field methods

Earlier results of our field-based root throw study can be found inGallaway et al. (2009). In this paper, we present some additional re-sults and analysis for root plate dimensions that did not appear inthis earlier work. We outline the field methods briefly; the reader isreferred to Gallaway et al. (2009) for additional details.

Three plots for root throw (tree topples associated with anupheaved root plate) measurements were delineated in the lowerportion of Hawk Creek drainage basin. The plots had an average areaof approximately 3 ha and were stratified by gradient while keepingother physical characteristics (i.e., elevation, surficial material) as con-sistent as possible. Plots 1, 2, and 3 had average gradients of 3°, 15°,and 28°, respectively. A consistent regional aspect was chosen for allthree plots (SW). Topples caused by a break or snap in the bole werenot included in our field work because no sediment upheaval is asso-ciated with this type of tree fall. Surveys of root plates in all plots wereperformed. Fall direction relative to local contour and the pit wererecorded for each root plate in survey plots 2 and 3; plot 1 had anear-zero gradient and, hence, no downhill slope direction was de-fined. The two areal dimensions for a root plate are defined as widthand height with depth being the other dimension (Fig. 3). Root platewidths (w) were measured parallel to the ground surface, whereasheight (h) measurements were made orthogonal to width. Definingthe depth (d) of the root plate required two measurements. The firstmeasurement involved placing a rod at right angles to the bolewhere the trunk intersected the ground surface (refer to the dashedline in Fig. 3); a measurement was then made from this rod to theplane passing through the outside edge of the roots (refer to the twoshort arrows in Fig. 3). An additional measurement was made fromthe rod to the maximum root plate depth. The difference betweenthe two measurements defines the depth, which can then be used inthe half-ellipsoid model of Denny and Goodlett (1956) and Normanet al. (1995) to calculate root plate volume (see Gallaway et al., 2009).

A meteorological station located in the lower portion of Hawk Creekdrainage basin recorded precipitation, wind speed, and wind directionover the study period. Some additional data were measured for eachtree throw including tree species and bole diameter at breast height(dbh). Forest density was calculated by counts of standing trees withdbh ≥ 10 cm in six sample tracts (each about 150 m2) for each plot.



Fig. 2. Hawk Creek, Kootenay National Park, British Columbia, Canada. Hawk Creek was the location for field work used in this study. This location is an example of the subalpineforest in the Canadian Rockies that is simulated in the numerical modeling exercise.


3. Tree population dynamics as a driver of root throw processes

3.1. Model outline

Whereas the geomorphic and pedological aspects of pit-moundformation and degradation are critical to understanding pit-moundmicrotopography, forest ecology principles of tree population dynam-ics drive the rate of pit-mound formation. Unfortunately, focus has


generally not been placed on understanding the forest population dy-namics that drive root throw, particularly in forests affected by wild-fire disturbance. The types of forest ecology data that are neededwithin such studies are specific in nature and are not generally avail-able within the forest ecology literature; therefore, calibration of ourexisting model of tree population dynamics (see Gallaway et al.,2009) for regional forest settings other than the study area consid-ered herein requires additional, targeted field work. Herein, we utilize



Fig. 3. Root plate dimensions measured in the field. (A) Width and height dimensions.(B) Measurements for depth dimension.


forest ecology data that are available for our study region within ex-ploratory model runs to identify which ecological variables are mostcritical to root throw processes and development of pit-moundmicrotopography; it is these variables that should be the focus ofadditional study in our study region as well as for other forestsettings.

The reader is referred to Gallaway et al. (2009) for full details of themodel of tree population dynamics. A brief outline of core componentsof the model is provided below. The primary forest disturbance inour region is crown fire; crown fires kill all trees and result in the de-velopment of a new forest. In our model, fire occurrence is based onthe Weibull probability density function (Johnson and Van Wagner,1985):

f tð Þ ¼ γ=α t=αð Þγ−1e− t=αð Þγ ð2Þ

where t is time interval between two fires (in years), α is a scale pa-rameter (expected fire return interval in years), and γ is a shape pa-rameter (dimensionless). Based on fire return intervals, our modelcycles through generations of forest. Within the model, trees germi-nate, grow, and are killed, with some proportion of the trees that fallto the ground generating root throws; if trees are below some mini-mum value of dbh or if breakage of the bole occurs, then a root plateis not upheaved and a pit-mound is not formed.

After fire occurrence in the model, the recruitment and mortalityof trees is calculated for two types of cohort. The fire cohort is definedas those trees recruited in the 5- to 10-year period after the crown fire(Johnson et al., 2003). Our recruitment and mortality rates are basedon the graphs provided in Gallaway et al. (2009) (based on Johnsonand Fryer, 1989; Johnson et al., 2003). The fire cohort includes alltrees within the above-mentioned time period after the fire andduring which the canopy trees become established. Subsequently,any new recruits are assigned to the understory cohort, which has adecreased rate of recruitment. Each cohort has separate mortalityrates.

Trees contributing to root throw include trees killed by fire, treesdead standing before fire, or trees recruited after fire. An exponentialmodel, whereby a fraction of the remaining standing dead boles fallsin each year, is used to determine the number of toppling trees (Lyon,


1977; Johnson, 1986, unpublished data; Johnson and Greene, 1991).The fraction of dead trees that topple in a given time interval is

FT ¼ 1− exp −F � dtð Þ ð3Þ

where F is a parameterization based on field studies of fraction deadstanding trees that topple (Lyon, 1977; Johnson, 1986, unpublisheddata; Johnson and Greene, 1991), and dt is the time interval (years)used in model runs.

Dead trees can fall either by uprooting or breakage. Ongoing fieldobservations for our study area indicate that the percentage of treesthat uproot as opposed to breaking ranges from approximately 50%and up to 80% (Johnson and Martin, unpublished data). Within themodel, only trees above a critical value of dbh upheave sediment.Field observations suggest that this critical value is approximately15 cm, with a range of several cm in either direction being reasonable(Johnson and Martin, unpublished data).

For a tree that upheaves a root plate, the mean tree dbh is basedon its age according to our field data. The dbh of a tree is then usedto determine the diameter of the root plate using the relation derivedfrom our field data:

Rdiam ¼ −18:1506þ 6:1004dbhð Þ ð4Þ

where Rdiam is root plate diameter, and dbh is diameter at breast height(both values are in cm). Root plate depth, Rdepth, is defined on the basisof a defined diameter/depth ratio of 5, as found for our field data (seefield data in following section of paper):

Rdepth ¼ Rdiam=5: ð5Þ

3.2. Results of the model

Manyyears of fieldwork in subalpine forests in the Canadian Rockiesby author E. Johnson and collaborators have resulted in field data forsome of the variables required in themodel of tree population dynamics(see Gallaway et al., 2009); however, data for many/most of these vari-ables have not beenmeasured for a full range of forest types. Results of amodel run for tree population dynamics are provided to demonstratethe nature of temporal sequencing of root throws. Input variables forthe model run are given in Table 1, and results are shown in Fig. 4.

The first fire occurs at model run time t = 20 years, and all treesare too small in dbh to result in any post-fire root throws. As forest re-generation occurs after the fire at time 20 years, the trees eventuallyreach a dbh that is large enough for tree toppling (via competition-induced mortality processes) to possibly upheave a root plate (unlessit is assigned as a tree that breaks at the bole according to modelrules); a time somewhat greater than 100 years is required to reachthis situation. During this next phase, root throws are temporally spo-radic (note that according to model rules, trees can only upheave sed-iment until 25 years after tree death).

A fire then occurs at t = 180 years. Although examination of in-termediate model results shows that some tree topples did occur inthis immediate post-fire period, they are not assigned as root throwsin the final results. This is because the random selection componentwithin the model chose these to be trees that fall by breakage andnot root throw. Another fire, however, occurs soon after at t =187 years, and a number of moderate-sized dead standing trees (alltrees were dead for less than 25 years) begin to fall sporadicallyaccording to model rules. After all trees have been dead for25 years, a phase of relative quietude for root throw occurrence be-gins. In due course, the next generation of trees reaches a criticaldbh for root throw, and some small to moderate tree throws occursporadically until the next fire occurs at t = 370 years.



Table 1Input parameters for the model of tree population dynamics.

Number of years of simulation 1000 yearsPlot area 10 m × 10 mAverage fire return interval (scale parameter)(see Eq. (2))

110 years

Shape parameter for fire (see Eq. (2)) 1.0Duration of fire cohort 10 yearsRecruitment values See graph in Gallaway et al. (2009)Mortality values See graph in Gallaway et al. (2009)dbh for trees of certain age See graph in Gallaway et al. (2009)Between-fire falling rates (see equation)

Fire cohort 0.058Understory cohort 0.058

Post-fire falling rates for fire-killed trees 0.025Fraction uprooted versus broken boles 0.5Critical dbh for uprooting of root plate 15 cm# years root plate can be upheaved aftertree death

25 years


After the fire at t = 370 years, a number of reasonably large rootthrows then occur in this post-fire period. The next fire occurs att = 428 years, before any of the new generation of trees, however,reaches the critical dbh for root throw resulting from competition.Following on from this, after the fire at t = 428 years, trees are toosmall for post-fire root throw occurrence. Similarly, another fire oc-curs at 491 years, and leading up to this fire, none of the new treeshave reached the critical dbh for root throw in the post-fire period.Eventually, the new generation of trees reaches a critical dbh and spo-radic root throw occurrence occurs. Once the forest reaches a rela-tively stable population after most competition has occurred, rootthrow occurrence becomes a relatively rare event statistically speak-ing; no root throws occur until after the next fire. The next fire occursat time = 723 years. Once again, the pattern shows a number of rootthrows in the post-fire years followed by a period of quietude untilthe next generation of trees reaches the critical dbh for root throw.

Of particular interest, we found that the model of tree populationdynamics, which is the driver of root throw, is particularly sensitiveto several variables: (i) between-fire and post-fire falling rates;(ii) fraction uprooted vs. broken boles; (iii) critical dbh for root plate

Fig. 4. Root throw results for tree population dynamics model showing dates of tree topplesthe dates of wildfire occurrence in the model run. (A) Ages of trees at death (years). (B) db


upheaval; and (iv) number of years that a root plate can be upheavedafter tree death. Unfortunately, these happen to be variables aboutwhich the least field information is available. As one example,Table 2 shows how changing the critical dbh for root throwoccurrencesignificantly impacts the total number of events. Of particular note isthat intra-fire root throws (resulting from competition) tend to haveoverall lower tree dbh as trees can range in age from moderatelyyoung to much older. Post-fire root plates are often associated withtrees in larger, mature forests and, hence, often have a greater ageand tree dbh. Therefore, changing the critical dbh for root plate up-heaval to higher values reduces the number of intra-fire root plates,while the post-fire root plate numbers stay approximately the same.Given the sensitivity of results to the above-mentioned variables, ad-ditional field observations of these variables must be undertaken inour study area and in other regional forest settings to improve our un-derstanding of tree population dynamics, root throw processes andsoil bioturbation.

4. Pit-mound degradation and diffusion coefficients

4.1. Model outline

Two primary factors affecting pit-mound degradation are (i) ini-tial size of the pit-mound feature, and (ii) rate of pit-mound degrada-tion. In this next modeling exercise, a numerical model of pit-mounddegradation is run for a range of pit-mound magnitudes and for var-ious rates of pit-mound degradation. In doing so, we hope to highlightsome of the factors that might explain the often contrasting pit-mound observations made in different regional settings, and in par-ticular the lack of pronounced pit-mound microtopography in ourstudy region. Herein we do not model pit-mound degradation forflat landscapes, because in these cases most sediment is returned tothe pit (Gallaway et al., 2009). For each model simulation, the chosendimensions of the pit-mounds are used to define a pit-mound pairwith the pit and mound component each having the shape of ahalf-ellipsoid; the pit-mound feature is placed on the chosen hillslopegradient (10°). We should note that these pit-mound sizes do notspecifically account for the return of some proportion of sediment

that result in root plate upheaval (minimum tree dbh of 15 cm). The solid bars indicateh of trees at death (cm).



Table 2Changes in numbers and mean dbh of root throws when critical dbh for root plate oc-currence is modified in model runs.

dbhcritical:13 cm

dbhcritical:15 cm

dbhcritical:17 cm

# intra-fire root plates 40 20 7# post-fire root plates 21 17 22Mean dbh (all root throw events) 22 cm 25 cm 29 cm

Table 3Diffusion coefficients implemented in linear diffusion model.

Diffusion coefficient (m2 y−1)

0.00010.0010.010.1


to the pit. Other factors, such as the proportion of the volume of theroot plate made up by the root itself, are not specifically accountedfor. Given that we are approximating, however, a range of pit-moundmagnitudes to see how size affects pit-mound degradation and longev-ity in a general sense, these issues should not pose a specific problemfor generalized interpretations of root throw activity.

Almost no direct process studies considering rates of pit-mounddeg-radation and patterns on which to base formulation or calibration ofdegradation formulae have been published in the literature. Processesthought to be responsible for pit-mound degradation includewater ero-sion, wind erosion, frost heave, soil creep, soil settling, animal/biologicalactivity, and decomposition of organic matter (Schaetzl and Follmer,1990). Therefore, in the absence of measurements of pit-mound degra-dation or formulae, a diffusion-based equationwas selected to representpit-mounddegradation. For simplicity of comparing results in this initialstudy, a linear diffusion model was chosen, because one can readilyadjust the diffusion coefficient by order-of-magnitude values to investi-gate the response of pit-mound degradation. Themodel simulations arerun in two spatial dimensions. The linear diffusion equation is based on acombination of sediment continuity:

∂h∂t ¼ − ∂qx

∂x þ ∂qy∂y

" #ð6Þ

and a linear sediment transport relation:

qx ¼ −k∂h∂x

� �ð7aÞ

qy ¼ −k∂h∂y

� �ð7bÞ

where h is height (m), t is time (years), x and y are the spatial dimen-sions (m), qx and qy are the two components of the volumetric transportrate (m3 m−1 y−1 or m2 y−1), and k is a linear diffusion coefficient(m2 y−1). Together, these equations combine to form the diffusionequation:

∂h∂t ¼ k

∂2h∂x2

þ ∂2h∂y2

" #: ð8Þ

Previous calibrations of the linear diffusion coefficient for soilcreep processes may encapsulate the range of possible diffusion co-efficient values for pit-mound degradation. Therefore, we defined abroad range of possible linear diffusion coefficients to test in variousruns of the model (see for example, Martin and Church, 1997;Martin, 2000) (Table 3). We should note that the values in thistable cover a wide range of possible diffusion coefficients.

4.2. Results for diffusion analysis based on published literature

Based on field results in some previous studies (Beatty and Stone,1986; Schaetzl and Follmer, 1990; Small, 1997), we gain insight aboutwhich values within this range might be expected to be most repre-sentative of pit-mound degradation in particular regions.


Beatty and Stone (1986) provided information about recent rootthrows in deciduous forests of New York State. Typical diameters ofabout 250–300 cm and depths of about 50–60 cm were found (notethat their diameter-to-depth ratios are similar to values in our fieldsite, despite different tree species). The magnitudes of these pit-mound features are typical of those reported in this and other easternandmidwestern deciduous forests. Beatty and Stone (1986) estimatedan age range for their pit-mound features of several hundreds of years.For comparison, Schaetzl and Follmer (1990) estimated the longevityof pit-mound features inWisconsin andMichigan using 14C dating andfound values ranging from hundreds of years to 1000+ years in sev-eral cases. Therefore, when modeling degradation of pit-mound fea-tures of the sizes mentioned above, appropriate diffusion coefficientsshould result in persistence of pit-mound features after hundreds ofyears or more. If a pit-mound feature was to disappear within yearsor decades, then the choice of diffusion coefficient may be too low.To simulate the above scenario, our model of pit-mound degradationwas run for a pit-mound diameter of 300 cm and a depth of 60 cm. Re-sults are shown for a hillslope gradient of 10° (results do not varysignificantly for slopes of 10°, 20°, and 30°; a slope of 10° was usedin all model runs) and for the full range of possible diffusioncoefficient values (0.0001, 0.001, 0.01 and 0.1 m2 y−1) (Fig. 5). Themodel is run in two spatial dimensions; but to facilitate interpre-tation of graphs, we plot the results in profile form. The diffusion coef-ficient of 0.1 m2 y−1 produces pit-mound degradation that is muchtoo rapid, as the pit-mound feature disappears within 10 years. Onthe other hand, the diffusion coefficient of 0.0001 m2 y−1 is too grad-ual, as pit-mound features remain notably visible for many thou-sands of years. The diffusion coefficient of 0.01 m2 y−1 results inpit-mound disappearance after about 50 to 100 years, which maybe somewhat too rapid but is a reasonable result; the diffusioncoefficient of 0.001 m2 y−1 results in pit mound disappearanceafter about 600+ years, which is also reasonable. Based on these re-sults, pit-mound diffusion coefficients between 0.01 m2 y−1 and0.001 m2 y−1 may be most reasonable for the forest setting ofBeatty and Stone (1986).

In a very different forest setting compared to that described above,Putz (1983) undertook a study of pit-mound features in Panama.Whereas the exact sizes of pit-mound pairs were not provided inthis study, the data showed a wide range of tree dbh values, sug-gesting a wide range of pit-mound sizes. Therefore, we chose an in-termediate pit-mound diameter of 200 cm and a depth of 40 cm.Putz (1983) reported that pit-mound features were no longer visibleafter as little as 5 years post-formation; this finding was attributed tothe effects of very significant rainstorms on soils that are relativelyunprotected by either litter or humus layers. We ran our model forthe full range of diffusion coefficients (Fig. 6). Results show that adiffusion coefficient of 0.1 m2 y−1 is most consistent with the obser-vations of Putz (1983). The other somewhat reasonable value of0.01 m2 y−1 results in leveling of the pit-mound feature in severaldecades, which is somewhat longer than suggested by Putz (1983).

Finally, we follow one additional line of evidence for defining plau-sible diffusion coefficients to represent other regions. Small (1997)completed investigative work and re-identified a particular pit-mound feature originally reported in Denny and Goodlett (1956) sothat he could estimate its degradation during the intervening time pe-riod. Small (1997) estimated that in 1963 the long axis of the mound



Fig. 5. Diffusion modeling results for pit-mound dimensions 300 cm × 60 cm. (A) Diffusion coefficient 0.0001 m2 y−1. (B) Diffusion coefficient 0.001 m2 y−1. (C) Diffusion coef-ficient 0.01 m2 y−1. (D) Diffusion coefficient 0.1 m2 y−1.


was about 4 m. Based on visual clues in the original photograph, he es-timated an original mound height in 1963 as about 100 cm. He thenremeasured its current height to estimate the decrease in height.


Small (1997) estimated its height about 30 years later as ~40 cm, in-dicating a total loss in height of about 60 cm over this period. Usingour model, we assign a diameter of 400 cm and a height of 100 cm



Fig. 6. Diffusion modeling results for pit-mound dimensions 200 cm × 40 cm. (A) Diffusion coefficient 0.0001 m2 y−1. (B) Diffusion coefficient 0.001 m2 y−1. (C) Diffusion coef-ficient 0.01 m2 y−1. (D) Diffusion coefficient 0.1 m2 y−1.


Please cite this article as: Martin, Y.E., et al., Interplay between field observations and numerical modeling to understand temporal pulsing of treeroot throw processes, Canadian Rockies, Canada, Geomorphology (2013), http://dx.doi.org/10.1016/j.geomorph.2013.04.017



to represent the original feature. The diffusion coefficients are thentested in an attempt to simulate the field-based estimates of the low-ering of mound height (Fig. 7). The linear diffusion coefficient of

Fig. 7. Diffusion modeling results for pit-mound dimensions 400 cm × 100 cm. (A) Diffusioficient 0.01 m2 y−1. (D) Diffusion coefficient 0.1 m2 y−1.


0.01 m2 y−1 results in about 10 cm of mound lowering in 30 years,whereas a diffusion coefficient of 0.1 m2 y−1 results in nearly 90 cmof mound lowering in 30 years. Diffusion coefficients of 0.001 m2 y−1

n coefficient 0.0001 m2 y−1. (B) Diffusion coefficient 0.001 m2 y−1. (C) Diffusion coef-



Fig. 8. (A) Histogram showing distribution of root plate horizontal dimensions. (B) His-togram showing distribution of root plate depths.

Table 5


and 0.0001 m2 y−1 result in values of pit-mound lowering that aremuch too low. These results suggest that linear diffusion coefficientsof between 0.01 m2 y−1 and 0.1 m2 y−1 provide the best fit to thefield measurements in this case.

4.3. Results for diffusion analysis in subalpine coniferous forests,Canadian Rockies

Results of the field program in Hawk Creek, Kootenay NationalPark, that are relevant to our numerical modeling exercise for pit-mound degradation in subalpine coniferous forests of the CanadianRockies are now introduced. Basic statistics of the two horizontal di-mensions for root plates, width and height, are shown in Table 4Aand Fig. 8A. The statistics for depth of the root plate are shown inTable 4B and Fig. 8B. The ANOVA results indicate that the diameterand depth of the root plate are significantly different (p b 0.05) forthe different gradient classes; diameters and depths increase withincreasing gradient for the different gradient classes.We also analyzedthe ratio of diameter/depth to identify any differences amongst thethree gradient classes; no significant differences were found amongstthe three gradient classes. Mean values of this ratio were found tobe approximately equal to 5 for each gradient class. As reported inGallaway et al. (2009), a mean fall direction of 29° was found for theboles associated with the root plates. This value falls within therange of commonly recorded wind directions of between 20° and30°. Trees fell uphill relative to local contour lines in about 65% ofthe cases, meaning that trees frequently fall uphill and downhill andeither scenario can be considered realistic within model runs.

Pit-mound degradation for the range of pit-mound sizes found inour study region is now investigated in an attempt to shed somelight on pit-mound persistence and microtopography in our study re-gion. Based on results in the previous section of this paper, initialpit-mound sizes that are representative of our study region are cho-sen (Table 5A). The model is run for a range of diffusion coefficientsbased on findings in the previous sections (Table 5B). The ratio of di-ameter to depth is based on our field data and is assigned a value of 5.

Results of the sensitivity analysis are shown in Figs. 9–11 andTable 6. The pit-mound feature with 50 cm diameter disappears with-in a matter of years (diffusion coefficients of 0.1 and 0.01 m2 y−1) orwithin several decades (0.001 m2 y−1). The microtopographic signa-ture of small pit-mound features in our forests would not be expectedto be long lasting. The mid-range size of pit-mound features in ourstudy area (100 cm diameter) is flattened within several years to adecade for diffusion coefficients of 0.1 and 0.01 m2 y−1, respectively.The lowest diffusion coefficient of 0.001 m2 y−1 results in pit-moundflattening in about 60 to 80 years. The pit-mound diameter of 150 cmrepresents an upper range of more commonly occurring pit-moundsin our study area. Depending on the diffusion coefficient utilized inmodels runs (0.1, 0.0, and 0.001 m2 y−1), these pit-mound featuresdisappear within several years, several decades or up to 150–200 years, respectively. These results suggest that a diffusion coefficientof 0.1 m2 y−1 is too high; a 150 cm diameter pit-mound is unlikely toflatten within only several years. Diffusion coefficients in the range of

Table 4Statistics for root plate dimensions.

Gradientclass

N Mean(cm)

Median(cm)

Minimum(cm)

Maximum(cm)

Standarddeviation

(A) Statistics for root plate width and heightLow 86 105.5 97 40 230 44.5Medium 92 113.6 105.5 36 317 48.4High 78 172.5 178.5 33 312 57.6

(B) Statistics for root plate depthLow 43 27.6 26 7 61 12.5Medium 46 30.3 27.5 9 62 13.7High 39 39.0 38 10 82 16.9


0.001 to 0.01 m2 y−1 would seem to be the most reasonable based onthese results. Depending onwhich of these valuesmight bemost repre-sentative of our study region and the particular size of the pit-moundfeature being explored, pit-mound featureswould be expected to disap-pear within just several years or up to 50 to 150 years.

5. Modeling combined tree population dynamics andpit-mound processes

5.1. Model outline and input values

To better understand temporal patterns in pit-mound develop-ment and persistence as well as the possible imprint of soil bioturba-tion in subalpine forests of the Canadian Rockies, we now integrateour model of tree population dynamics (see Section 3 of this paper)with a model of pit-mound diffusion (see Section 4 of this paper)for a hillslope plot over a timescale of order 103 years. The combinedmodel is run for a hillslope plot having dimensions of 10 m × 10 m

Pit-mound sizes and diffusion coefficients implementedin model runs.

(A) Pit-mound magnitudes

Diameter Depth

50 cm 10 cm100 cm 20 cm150 cm 30 cm

(B) Diffusion coefficients

Diffusion coefficient (m2 y−1)

0.0010.010.1



Fig. 9. Diffusion modeling results for pit-mound dimensions 50 cm × 10 cm. (A) Diffusion coefficient 0.001 m2 y−1. (B) Diffusion coefficient 0.01 m2 y−1. (C) Diffusion coefficient0.1 m2 y−1.


with a slope of 10° and is run through several generations of forestusing the tree population dynamics model. A diffusion coefficientof 0.01 m2 y−1 is selected for model runs based on the results ofdiffusion analysis for other field studies and for our study area.Table 1 (see earlier table) provides a list of input parameters thefor tree population dynamics model. Eqs. (4) and (5) are used to de-fine root plate dimensions. When root plate upheaval does occur, apit-mound feature in the shape of a half-ellipsoid and having theassigned dimensions is placed on the model grid domain as perEqs. (4) and (5).

5.2. Results

Hillslope plots for various times of our 1000-year model run areshown in Fig. 12. Of particular note is that when considering the entireduration of the model run, minimal apparent signature of pit-moundactivity exists at most times. Several limited time periods, however,


can be observed during which the signature of pit-mound activity isvisible. For example Fig. 12A shows the landscape soon after a wildfirehas occurred. Once those pit-mounds have degraded, the landscapeshows no apparent pit-mound features (Fig. 12B) until some sporadicactivity occurs once trees have reached the critical dbh (Fig. 12C, D).Finally, Fig. 12E shows the landscape soon after the wildfire at370 years, with distinct pit-mound features being visible. In duecourse, these features degrade (Fig. 12F). Whereas the results inTable 2 indicate some pit-mound activity occurring on the landscape,Fig. 12 shows thatwhen one observes the landscapewill be paramountin whether or not this activity is visible in the form of pit-moundmicrotopography. This result arises from two factors. The first factoris that pit-mound occurrence on the landscape is subject to temporalpulsing of tree population dynamics as demonstrated throughoutthis paper. Moreover, pit-mound features in the subalpine forestsof the Canadian Rockies are not particularly large relative to thosefound in some other forest types, thus allowing for relatively rapid



Fig. 10. Diffusion modeling results for pit-mound dimensions 100 cm × 20 cm. (A) Diffusion coefficient 0.001 m2 y−1. (B) Diffusion coefficient 0.01 m2 y−1. (C) Diffusion coeffi-cient 0.1 m2 y−1.


pit-mound degradation (possibly on the order of 101 years and usual-ly b102 years); this means that evidence of any pit-mound features isrelatively short-lived on the landscape. Therefore, if evidence of pit-mound microtopography observed in the present day is alone usedto estimate the pit-mound activity of a particular forest, the resultsmay well be biased in different possible ways depending on whenone happens to observe the particular forest.

Fig. 13 illustrates the last time that a pit-mound feature wasformed at each location on the hillslope plot. By the end of the1000-year model run time, almost everywhere on the hillslope plothas been affected by pit-mound activity, despite observations of sub-stantial pit-mound microtopography for only several short time win-dows. This finding suggests the ubiquitous nature of soil bioturbationin subalpine forests in the Canadian Rockies, despite the often mini-mal evidence of pit-mound microtopography that can be foundwhen observing the forest at any one point in time.


6. Discussion and conclusions

This paper has demonstrated the necessity to incorporate a realis-tic simulation of tree population dynamics when considering rootthrow processes, as the former is the driver of the latter. During thedevelopment and calibration of our model of tree population dynam-ics, data required for certain key variables were often scarce or nonex-istent (e.g., between-fire and post-fire falling rates; fraction uprootedvs. broken boles; critical dbh for root plate upheaval; and number ofyears that a root plate can be upheaved after tree death). Unfortunate-ly, these variables have not been the topic of much investigation byforest ecologists; integrative biogeomorphological research under-taken in recent years has highlighted the need for collection of partic-ular types of forest ecology data that have not previously beenmeasured. Based on the findings of the present study, we recommendthat focus be placed on making field observations that improve our



Fig. 11. Diffusion modeling results for pit-mound dimensions 150 cm × 30 cm. (A) Diffusion coefficient 0.001 m2 y−1. (B) Diffusion coefficient 0.01 m2 y−1. (C) Diffusion coeffi-cient 0.1 m2 y−1.


knowledge of particular aspects of tree population dynamics in differ-ent forest settings. Within the root throw literature, some effort hasbeen placed on understanding forests subjected to notable wind-driven blowdowns (Schaetzl et al., 1989). Less effort has been focused,however, on forests for which wildfire is the primary disturbance.

Based on physiology, lodgepole pines commonly found in subal-pine forests of the Canadian Rockies can live longer than 400 years(Pruden et al., 1987). The wildfire regime is such that fire recurrenceis generally much shorter than the potential lifespan of these trees.

Table 6Time for pit-mound feature to become approximately flat.

Pit-mound size k = 0.001 m2 y−1 k = 0.01 m2 y−1 k = 0.1 m2 y−1

50 cm × 10 cm 40 y 4 y b0.5 y100 cm × 20 cm 100 y 10 y 1 y150 cm × 30 cm 200 y 20 y 2 y


Therefore, after competition has reduced the tree density to a relative-ly stable value, root throws remain relatively sporadic, with mostmature trees eventually dying as a result of the next wildfire distur-bance. Improved understanding about tree mortality and topple dur-ing the competition phase and the critical post-wildfire period isnecessary. Tree mortality alone does not presuppose the occurrenceof root throws; the latter requires knowledge about the rates of treefalling and the nature of fall (root plate upheaval vs. breakage atbole). Whether a tree falls by being uprooted vs. breaking at the boledepends on a variety of interconnected forces and resistances (biolog-ical and physical) acting on the tree. Uprooting occurs when appliedforces acting on the tree exceed root anchoring (Schaetzl et al.,1989). The degree to which the soil and roots adhere to one anotheris important in determining if root plate upheaval or bole breakagewill occur. For example, if root anchoring is strong relative to bolestrength, then the bole may snap; conversely, if the root anchoring isweak relative to bole strength, then root plate upheaval may occur(Schaetzl et al., 1989). The critical dbh required for root plate upheaval



Fig. 12. Results for the combined tree population dynamics model and diffusion model. (A) Model run time 200 years. (B) Model run time 250 years. (C) Model run time 300 years.(D) Model run time 350 years. (E) Model run time 380 years. (F) Model run time 400 years.


is related to characteristics of the bole and the root wad, as well as thephysical stresses imposed on the bole during toppling; in many cases,smaller trees will snap. Finally, the number of years that a root platecan be upheaved after tree death will depend on the condition of the

Fig. 13.Model result showing the last time that root throw bioturbation occurred on lo-cations across the hillslope plot. Years shown in legend are model run times. Althoughthe simulated area for the combined model is 10 m × 10 m, the model boundary ex-tends an additional 10 m in each direction to avoid edge effects; for occasional cases,the very outer edges of a pit-mound feature may extend outside of the 10 m × 10 mplot area.


bole and the root wad, which is dependent on factors such as climateand its influence on the rate of decomposition.

Johnson and Greene (1991) investigated standing dead boles insubalpine forests of the Canadian Rockies (lodgepole pine, Engelmannspruce). They found that decomposition of standing dead boles wasslow or did not occur because of the lowmoisture content. This findinghas been documented in other similar forest settings (Mielke, 1950;Hinds et al., 1965; Fahey, 1983). A negative exponential equation,in which a constant proportion of standing dead boles falls in anytime interval, is reasonable to estimate the falling rate of boles in theforest setting in our study (Keen, 1955; Cline et al., 1980; Johnsonand Greene, 1991). This approach assumes that no aging effect occurs;this assumption is reasonable in forests with minimal decompositionof standing dead trees. Studies in more humid environments, wherethe wood has a higher moisture content, may need to adopt an alter-native approach. Some earlier studies have suggested that boles oflarger dbh stand longer before toppling than smaller boles (Lyon,1977; Van Sickle and Bensor, 1978; Cline et al., 1980). Johnson andGreene (1991) found no differences, however, amongst boles of vary-ing dbh in subalpine forests of the Canadian Rockies, a finding thatthey at least partly attributed to the relatively small boles in theirstudy forests compared to many other studies.

If patterns of tree topple are assumed to be quasiregular in timewhen they are not, then consideration of sediment transfer and soilproduction will not reflect the temporal pulsing that actually doesoccur in response to tree population dynamics. Within this paper,we focussed on forests subjected to wildfire disturbance and naturalcompetition that occurs after wildfire as the forest redevelops. Manyearlier studies have, in contrast, focussed on forests experiencinglarge-scale wind events that lead to major blowdowns (such as in




the eastern and midwestern deciduous forests). In addition to majordisturbances, we recommend that future studies also evaluate thesignificance of more local winds that might be notable contributorsto root throw processes between major disturbances.

An understanding of the appearance (or not) of pit-moundmicrotopography on the landscape over time requires an understand-ing of pit-mound formation and pit-mound degradation. For thisexploratory modeling exercise, several assumptions were made re-garding pit-mound formation to maintain tractability of the modelingexercise. These assumptions relate to aspects of pit-mound formationfor which additional, future study is recommended. In our study, anassumption was made that pit and mound features are of the samesize and shape. While not strictly valid (see discussion below),this provides an acceptable first-order approximation for studyingthe temporal dynamics and longevity of pit-mound features as theyrelate to hillslope microtopography. Formation of pit features isexpected to be relatively instantaneous, whereas mound featuresdevelop over time as sediment from the root plate falls to the ground.Whereas some studies have investigated this phenomenon (seeGallaway et al., 2009), further examination is required to improveunderstanding so that it can be incorporated within a numericalmodeling framework. In addition, a notable percentage of sedimentfrom the root plate is often returned to the pit on near-flat or gentleslopes (Gallaway et al., 2009), thus leading to pit infilling and smallermound magnitudes than would otherwise be the case. In our study,we assumed that sediment from the root plate fell to the ground(and not into the pit), thus meaning that the magnitudes of pit andmound features within our model represent a maximum value. Final-ly, some percentage of the root plate is made up of tree roots, thusoverall magnitude of individual mound features may be somewhatsmaller than the associated root plate magnitudes.

Degradation of pit-mound features may occur by a range of pro-cesses, including various creep-type processes (soil deformation,frost heave, biogenic activity including possible faunal activity), surfi-cial water-driven erosion processes (rainsplash or rilling), and de-composition of organic material contained within the mounds. Soiland water-related characteristics that affect operation of these vari-ous processes include soil texture, soil permeability, macro- andmicroclimate, and litter/vegetation coverage (Schaetzl and Follmer,1990). To the present authors' knowledge, rigorous systematic studyof pit-mound degradation processes has not been forthcoming inthe scientific literature. Our diffusion modeling exercise was used todefine a possible range of reasonable diffusion coefficients to drivepit-mound degradation in different regional settings, including ourown study area. In addition, the initial size of the pit-mound featureplays a key role in determining how rapidly these processes act to de-grade a pit-mound feature (Zeide, 1981; Schaetzl and Follmer, 1990).

When considering pit-mound microtopography on the landscape,most earlier studies focussed on regions having notable pit-moundmicrotopography (most often resulting from large wind-relatedblowdowns), with study approaches involving documentation ofpit-mound features and related characteristics as well as estimatesof pit-mound longevity (Schaetzl and Follmer, 1990). Herein, weused a combination of available field evidence (from previous fieldstudies and our own field studies) to guide a numerical modeling ex-ercise combining tree population dynamics with pit-mound diffusion.Modeling results for our study area show that evidence of root throwactivity in the form of pit-mound microtopography is relativelyshort-lived for sporadic root throws resulting from competitionbetween wildfire disturbances. This is because pit-mound featuresare obliterated relatively quickly, probably within decades formost pit-mound features (although evidence of unusually largepit-mound features may be longer-lasting). In post-fire years, a timeperiod of significantly increased root throw activity may occur, butonce again this evidence will be obliterated relatively quickly, proba-bly within decades. A period in which pit-mound features are not


observed on the landscape then occurs, lasting until trees reach a criti-cal dbh for root plate upheaval. At this point, sporadic pit-mound activ-ity and microtopography may be observed until a wildfire disturbanceoccurs once again. Even though evidence of pit-mound activity on thelandscape is restricted to only short time periods, soil bioturbationmay still be a notable factor affecting soil development. Modeling re-sults demonstrated that soil bioturbation may be fairly widespreadacross the landscape over millennial temporal scales.

Acknowledgments

The authors would like to thank the various research assistants fortheir contributions to the field component of this research. PeterKlassen is thanked for his contribution to the final figures for the com-bined model runs. We would also like to thank the anonymous re-viewers whose comments helped to improve the manuscript. Theresearch was supported by the NSERC Discovery Grants of Y. Martinand E. Johnson.

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