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Ecological Modelling 221 (2010) 2353–2362

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

ombined effect of fire and water scarcity on vegetation patterns in arid lands

adia Ursinoa,∗, M. Cristina Rulli b

Department IMAGE, Università di Padova, via loredan 20, Padova, ItalyPolitecnico di Milano, Italy

r t i c l e i n f o

rticle history:eceived 29 March 2010eceived in revised form 9 June 2010ccepted 16 June 2010

eywords:

a b s t r a c t

In many arid zones around the word, the vegetation spontaneously forms regular patterns to optimizethe use of the scarce water resources. The patterns act as early warning signal that fragile ecosystemsmay suddenly undergo irreversible shifts, thus, interpreting the structural shape of vegetation patterns iscrucial to deciphering the ecosystem history and its expected further development. The sudden and irre-versible shift of delicate ecosystems as a consequence of minor variation of the climatic forcing has beenstudied extensively in the past. The attitude of the ecosystem to recover after a catastrophic event, such

rid landco-hydrologyire modellingreferential infiltrationegetation patterns

as fire, did not receive as much attention so far. Here we modelled fire, as a sudden shift of the ecosystemstate variables and functionality and evaluated post-fire scenarios under the hypothesis that two majorfeedbacks shaped the vegetation patterns: a positive feedback between preferential infiltration and plantgrowth, and a second feedback between infiltration and vegetation burning. A simple model solving a setof partial differential equations for soil moisture, plant biomass, surface water and dead biomass balance

versellency

predicted significantly didegree of soil water repe

. Introduction

Fire controls vegetation spreading and promotes changes of soilharacteristics that are relevant for post-fire vegetation growthRavi and D’Odorico, 2009; White et al., 2006; Van Langevelde et al.,003). Fire may adversely affect the physical, biological, and chem-

cal aspect of ecosystems, depending on the intensity and durationf the heat produced, the degree of biotic destruction and climaticonditions at the time of fire (Neary et al., 1999). Fire severity,lassified as low, medium, or high, describes the change that fireauses in particular ecosystem resources such as vegetation and/oroils. Moderate to severe fire can result in soil surface tempera-ures greater than 500 ◦C and temperatures greater than 400 ◦C at25 mm depth which destroy the vegetation cover and can oxi-

ize and volatilize essential plant elements (DeBano et al., 1998).hese substances then move downward in the soil and condense inhe cooler underlying layers, causing a long lasting water-repellentayer at that depth. Once a water-repellent layer is formed, waterannot infiltrate the soil to that point (DeBano et al., 1998). Per-

olation through the soil can also be reduced this way. Reducednfiltration and percolation in turn can increase overland flow,rosion and sediment yield (Rulli and Rosso, 2007). Thus, intensend/or prolonged rainstorms occurring on burned areas can cause

∗ Corresponding author.E-mail addresses: nadia.ursino@unipd.it, nadia@idra.unipd.it (N. Ursino),

ristina.rulli@polimi.it (M. Cristina Rulli).

304-3800/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2010.06.018

post-fire vegetation patterns depending on the fire severity and on theinduced by the vegetation burning.

© 2010 Elsevier B.V. All rights reserved.

significant increase in runoff, in erosion and sediment yield whichin turn can lead to the so-called fire floods (Rulli and Rosso, 2005).Fire affects processes and pathways controlled by vegetation andsoil. They include cycling of nutrients, biotic, rainfall interception,infiltration, evapotranspiration, soil moisture storage, and overlandflow. Alterations in fire frequency can have significant effects onprimary productivity and carbon and nitrogen cycling in terres-trial ecosystems (Tilman et al., 2000; Reich et al., 2001). In theshort term fire has been found to enhance nitrogen mineraliza-tion (Hobbs et al., 1991) with losses of nitrogen through frequentburning ultimately leading to long-term decreases in nitrogenavailability (Blair, 1997) and cycling (Dijkstra et al., 2006). Also,fire can substantially reduce interception and evapotranspirationby destroying both the vegetation canopy and the organic litter onthe soil surface, thereby exposing the soil to raindrop impact andsubsequent soil detachment (Rulli et al., 2006).

Many ecohydrological models predict regular vegetation pat-terns in arid and semiarid lands as a result of Turing instability(Turing, 1952; HilleRisLambers et al., 2001; Rietkerk et al., 2004;Gilad et al., 2004; Ursino, 2007). Nevertheless, the origin of thesepatterns has been ascribed to a mechanism of preferential infil-tration in the vegetated area (Borgogno et al., 2009; Rietkerk etal., 2004). The bare soil is sealed by a soil crust, whereas the

biomass growth hinders the crust formation on vegetated zones.Thanks to a mechanism of runoff run-on from bare zones towardvegetated ones the vegetation survives despite the scarce waterresources (Valentin et al., 1999). Soil properties (Rietkerk et al.,2002; Fernando and Cortina, 2002; Ursino, 2005), plant physiology

2 gical M

(a2ip(oebtafssdlscmfim(ifitrgwdere

ulgbvmstm

a(a1arsoFaosdlrcriees

e

354 N. Ursino, M. Cristina Rulli / Ecolo

Ursino, 2007), and rainfall seasonal and daily variability (Ursinond Contarini, 2006; Nordbotten et al., 2007; De Michele et al.,008) have an impact on vegetation mosaic. Furthermore, numer-

cal models suggest that the characteristic length of the vegetationatterns depends also on the below ground biomass organizationUrsino, 2009) and on seed dispersal (Thompson et al., 2008). Tour knowledge, the impact of a fire induced sudden shift of thecosystem on its reorganization after fire has never been evaluatedefore. Major interest has been dedicated in the past two decadeso the possible sudden shifts that the ecosystem may undergos a consequence of even minor fluctuations of the hydrologicalorcing. The resilience of the ecosystem to relevant and suddenhifts of its characteristics, as a consequence of catastrophic eventsuch as fire, has not been studied so extensively. Ravi et al. (2009)escribe post-fire resource redistribution in desert grassland high-

ighting the fire feedback on land degradation. In particular, theyhowed that in shrub–grass transition systems with enough grassonnectivity for fires to propagate, fire plays a major role in deter-ining the dominance of grasses. Using a combination of replicated

eld experiments to monitor soil erosion processes, changes inicrotopography and post-fire nutrient redistribution, Ravi et al.

2009) showed that at the early stages of shrub encroachment firesnteract with soil erosion processes resulting in enhanced post-re redistribution of soil resources from the fertile shrub islandso the intercanopy areas. The post-fire enhancement of resourceedistribution was shown to have an impact on the recovery ofrasses following fires. The enhancement of resource redistributionas attributed to an increase in local scale soil erosion processesue to the fire effect. In fact, fires were found to enhance soilrosion in and around burned shrub patches, by inducing waterepellency in the surface soil, and consequently increasing soilrodibility.

According with Ravi et al. (2009) experimental findings, we eval-ate the possibility that fire could alter the shape of the mosaic

andscape primarily by forming a water-repellent soil layer or plug-ing soil pores with fine ashy material locally where vegetationurns, that means by reducing infiltration into the soil where theegetation burns. We considered this to be one of the possibleajor changes that the ecosystem may undergo after fire, since

oil infiltration capacity and the runoff–run-on dynamic interac-ion between vegetated and un-vegetated zones are crucial to the

aintenance of the vegetation mosaic under water scarcity.Regeneration response after fire is also controlled by inter-

ctions between fire severity and species’ regeneration strategyWang and Kemball, 2005). Fire severity has been generally defineds the effects of fire intensity on ecosystem (White and Pickett,985). It describes the biomass loss and influences both the avail-bility of post-fire in situ propagules (buried seeds and spores oregenerating underground parts) and the receptivity of post-fireeedbeds by altering physical, chemical, and biological conditionsf the regeneration substrate (Flinn and Wein, 1977; Keeley, 2009).ire severity is also strictly linked to the potential for water runoffnd erosion (Robichaud et al., 2000; Lewis et al., 2006). The lossf aboveground biomass alters both interception end evepotran-piration and it exposes soil surface to the precipitation splashetachment on the soil surface (Moody and Martin, 2001). Also,

oss of soil organic matter alters the binding capacity of soil andesults in other structural changes that can affect erosional pro-esses (Hubbert et al., 2006). Post-fire increases in soil waterepellency due to hydrophobic soil layers are tied to the fire sever-ty (Robichaud et al., 2000; Lewis et al., 2006), although in some

cosystems, soil hydrophobicity is unrelated to fire severity (Doerrt al., 2006). Soil water repellency increases runoff, erosion andediment transport (Rulli et al., 2006).

Although the importance of fire severity to post-fire plant regen-ration has been well recognized, only a few studies have directly

odelling 221 (2010) 2353–2362

linked vegetation responses to variation in fire severity (Johnson,1992; Shimmel and Granstrom, 1996; Wang and Kemball, 2005).For sprouting species, severe fire can consume underground organsand kill buds on underground organs because of the increased depthand strength of heat penetration. For seed banking species, fires notonly consume seeds or affect seed viability, but also affect germi-nation of surviving seeds. Analysis on forest ecosystem responsesshowed that fire severity is tied to forest recovery and alien plantinvasion (Wang and Kemball, 2005) and belowground changes infauna and flora (Neary et al., 1999). In forests and shrublands proneto crown fires, increased fire severity has been correlated withdecreased resprouting of herbs and shrubs (Flinn and Wein, 1977;Keeley, 2009). Fire severity has also been correlated with ecosystemresponses such as species richness and patterns of seedling recruit-ment (Whelan, 1995), with reduced alien plant invasion (Keeley,2009).

Although we are aware of the importance of simulating repeatedfire events, we focus here on the system recovery after only onefire event, for varying fire severity, by using a simple model. Thisstudy has to be considered as a preliminary step to a more real-istic investigation of the vegetation patterns in arid land underthe risk of multiple fires. Furthermore, although the complexity ofthe soil–vegetation–atmosphere system invites a stochastic anal-ysis (Katul et al., 2007), we simplified the problem and chose adeterministic approach, in order to better clarify the relevance andthe relevant interconnections between fire and water scarcity. Firemay have an impact on nutrient and sediment redistribution, anda positive feedback may arise due to the formation of a fertile ashlayer that could eventually make the vegetation patterns more per-sistent through repeated fire events. (Ravi and D’Odorico, 2009),but we focus here just on its negative feedback with water infil-tration, since our ecosystem survival capacity is mainly limited bywater scarcity. By solving a set of diffusive balance equations forsoil moisture, surface water and vegetation biomass, accountingfor the positive feedback between preferential infiltration and plantgrowth, and the negative feedback between infiltration and vegeta-tion burning, we tried to answer the following question: how couldfire alter the macroscopic overall aspect of vegetation patterns inarid land by altering the soil water repellency?

2. Materials and methods

A set of dimensionless balance equations for soil moisture (w)plant biomass (n), surface water (o) and burned biomass (s) wasused to model the combined effect of fire and water scarcity onregular vegetation patterns in arid land. A simple 1D approach wasadopted, where x is the spatial coordinate and tis time. The relationsbetween dimensionless variables and corresponding dimensionalones are reported in Appendix together with the dimensional val-ues of the parameters that appear in the relations.

∂w

∂t= �o

n + k2k3

n + k2

[1 − s

s + ks

]− ew − f (w, n) + d

∂2w

∂x2

∂n

∂t= f (w, n) − mn + dn

∂2n

∂x2− H(x − xf 1) · H(xf 1 − x) · ı(t − tf ) · n(1 − Kf )

∂o

∂t= a − �o

n + k2k3

n + k2

[1 − s

s + ks

]+ do

∂2o

∂x2

∂s

∂t= H(x − xf 1) · H(xf 1 − x) · ı(t − tf ) · n · Kf − H(x − xf 1) · H(xf 1 − x) · H(t − tf ) · �s

(1)

According to previous related studies (see e.g. Ursino, 2007),the uniform net rainfall a infiltrates preferentially where the plantsgrow, inducing a feedback mechanism that is accounted for by the

term �o(n + k2k3)/(n + k2), where k2 depends on the rate at whichsurface water infiltration increases with biomass density; �ok3 isthe minimum infiltration rate of surface water in the absence ofplants and �o is the maximum infiltration rate (Rietkerk et al., 2002;HilleRisLambers et al., 2001). The water loss due to evaporation

N. Ursino, M. Cristina Rulli / Ecological M

Table 1Model (1) parameter values(HilleRisLambers et al., 2001).

a = 0.104lo = 1k2 = 10k3 = 0.1e = 1

afabaifaswdwottqplfatplimcpaT

Fp

f (w, n) = 5 w0.075+w

m = 2.74d = 1; dn = 0.5; do = 2.5

nd leakage (ew in the first of (1)), is approximated with a linearunction of the soil moisture under stress conditions (Porporato etl., 2001; Feddes et al., 1978). The term mn represents the plantiomass loss due to mortality. The last is due to senescence onlong time scale, whereas fire produces additional biomass loss

nstantaneously. do and d are the surface and subsurface water dif-usion coefficients; dn is the diffusion coefficient of plant dispersal,nd f(w,n) may be interpreted as the plant water uptake within theoil moisture balance equation, and the growth rate of vegetationithin the biomass balance equation. We hypothesized a biomassiffusion-based dispersion behaviour, for the sake of simplicity. Fireas modelled as an irreversible and instantaneous transformation

f a percentage Kf of the living biomass n into burned biomass s overhe sub-domain Xf : xf 1 ≤ x ≤ xf 2. We simulated a fire at t = tf, whenhe vegetation patterns were well established. The severity of fire isuantified by the percentage of biomass loss: Kf. Fire produces theartial destruction of the living biomass in x ∈ Xf =

{xf 1; xf 2

}and

ocally the formation of a soil hydrophobic layer close to the soil sur-ace which degree of imperviousness increases with fire severity,nd decreases with k5 that is the amount of s by which the infil-ration capacity of the soil is reduced up to one half. After fire, soilroperties return to the original values as soon as the hydrophobic

ayer dissolves according to a first order exponential decay where �s the inverse of the mean recovery time of the upper soil layer, that

eans that the water repellency of the upper soil layers, caused by

ombustion of the organic matter, disappears after a time lag com-arable with �−1. In the set (1), H(·) is the Heaviside’s step function,nd ı(·) is the Dirac function. Model parameter values are listed inable 1.

ig. 1. Time sequence of vegetation patterns: before fire (t = 0.9·tf , gray line), shortly aftanels correspond to earlier times. Irreversible (left) versus reversible (right) changes of s

odelling 221 (2010) 2353–2362 2355

3. Results

3.1. Transitory biomass density after fire

In Figs. 1–4 the transitory phase of recovery of the small burnedarea Xf with xf 2 − xf 1 = 1000 is documented by the time sequencesof the biomass density distribution n(x,t) along the transect. Thereversible case (� = 10 · t−1

f), that implies the possibility of soil

property recovery after burning, and the irreversible case (� = 0)are compared.

The numerical solution of the set of equations (1) demonstratedthat the feedback between burned biomass density and water infil-tration, altered by the presence of soil-sealing burned biomass,depending on Kf and ks, may become a more pronounced limitingfactor of infiltration than the presence of a soil crust in between thevegetated areas, influencing the biomass patterns in the transitoryphase shortly after fire and at the steady state long after fire.

Shortly after a severe fire (Kf = 0.8), the burned area appearedstill completely bare with highly vegetated boundaries, supportedby the increased runoff from the bare zone Xf to its vegetatedboundaries (Figs. 1 and 2). For � = 10 · t−1

f(reversible soil prop-

erties shift), Kf = 0.8, and ks = 0.1 (Fig. 1, right panels), shortly afterfire, the absence of preferential infiltration path, due to the factthat fire effect on soil and the presence of the bare soil crust had acomparable impact on infiltration, led to the persistence of peaks ofbiomass density at the boundaries of the burned domain, progres-sively advancing toward its inner part. The inner burned zone inthis case remained bare for a longer time than in the correspondingirreversible scenario (confront right and left panels of Fig. 1).

In case of irreversible soil properties’ shift (� = 0, left panels), thevegetation patterns reappeared after a sufficiently long time fromfire (t = 2tf, in our case study) in all cases, yet shifted with respect tothe original location. Indeed, vegetation regrew in the previouslybare zones where the biomass production was minor and thus, theburned biomass was almost absent. When the simulated fire wasnot too severe and its impact on the soil infiltration capacity was

minor (Kf = 0.2; ks = 0.1), the vegetation patterns were still presentyet shortly after fire, for � = 10 · t−1

f(Fig. 3, right panels), whereas

they shifted and remained in the interband zone for � = 0 (Fig. 3,left panels).

er fire (t = 1.1·tf), later after (t = 1.6·tf) and at steady state after fire (t = 2·tf). Upperoil properties: � = 0 and � = 10 · t−1

frespectively. Kf = 0.8; ks = 0.1.

2356 N. Ursino, M. Cristina Rulli / Ecological Modelling 221 (2010) 2353–2362

F tly aftp es of

(tergbbiattll

r

Fp

ig. 2. Time sequence of vegetation patterns: before fire (t = 0.9·tf , gray line), shoranels correspond to earlier times. Irreversible (left) versus reversible (right) chang

Increasing the degree of soil imperviousness induced by fireFig. 4, Kf = 0.2; ks = 0.01) multiple peaks of biomass characterizedhe early post-fire scenario for � = 10 · t−1

f(left panels) later, veg-

tation patterns characterized by the original characteristic lengtheappeared at t = 2 · tf . For Kf = 0.2 and ks = 0.01 just the centralroups of bands, that regrew where the biomass density was lowerefore fire (and thus the negative feedback induced by the biomassurning was minor), succeeded in colonizing in the neighbour-

ng previously un-vegetated zone. As a consequence, the post-firerrangement of the vegetation was markedly characterized by thewo combined characteristic lengths of the original vegetation pat-

erns: the characteristic length of the mosaic of vegetation and theonger length characterizing the average biomass density (Fig. 4,eft panels), that could be attributed to nonlinearity.

These results are evidenced by the patterns Fourier analysiseported in Section 3.3.

ig. 3. Time sequence of vegetation patterns: before fire (t = 0.9·tf , gray line), shortly aftanels correspond to earlier times. Irreversible (left) versus reversible (right) changes of

er fire (t = 1.1·tf), later after (t = 1.6·tf) and at steady state after fire (t = 2·tf). Uppersoil properties: � = 0 and � = 10 · t−1

frespectively. Kf = 0.8; ks = 0.01.

When the negative feedback between fire and infiltration hada major impact (ks = 0.01) and it resulted in an irreversible reduc-tion of the soil infiltration capacity (� = 0), soil witnessed significantenvironmental shift over time and vegetation patterns bore thesignature of its long lasting and complex evolution. Although, itwas in case of reversible soil properties shift (� = 10 · t−1

f) that

the vegetation patterns displayed multiple scales features expe-cially when the fire severity was minor (Kf = 0.2). This result willbe further explained in the next Subsection. The post-fire vege-tation organization reflected its tendency at colonizing preferablythe unfriendly zones that were bare before fire. Indeed, the pre-

viously bare zone could still be mechanically improved in termsof infiltration capacity by vegetation, suggesting that, whereverthe reproduction process supports this recovery strategy of thevegetation, fire severity plays a crucial role in the landscapeshaping.

er fire (t = 1.1·tf), later after (t = 1.6·tf) and at steady state after fire (t = 2·tf). Uppersoil properties: � = 0 and � = 10 · t−1

frespectively. Kf = 0.2; ks = 0.1.

N. Ursino, M. Cristina Rulli / Ecological Modelling 221 (2010) 2353–2362 2357

F tly aftp es of s

3

to

Fk

ig. 4. Time sequence of vegetation patterns: before fire (t = 0.9·tf , gray line), shoranels correspond to earlier times. Irreversible (left) versus reversible (right) chang

.2. Statistics of pre- and post-fire vegetation patterns

In order to evaluate the statistical and spectral characteristics ofhe biomass distribution at long time after fire (t = 2 · tf ), from nown, we consider a fire event extended over a larger area Xf where

ig. 5. Difference in biomass cover n(x, 2tf ) − n(x, 0.9tf ) before fire and long time aftes = 0.01–Kf = 0.2. Reversible fire impact (� = 10 · t−1

f).

er fire (t = 1.1·tf), later after (t = 1.6·tf) and at steady state after fire (t = 2·tf). Upperoil properties: � = 0 and � = 10 · t−1

frespectively. Kf = 0.2; ks = 0.01.

now x − x = 4000, for different K and k , as in the previous

f 2 f 1 f s

Section 3.1. The patterns of vegetation before and long time afterfire are confronted here in order to evaluate the overall changesin vegetation cover. The difference between the biomass distri-bution before fire n(x, 0.9tf ), and the biomass distribution at long

r fire. Cases: (a) ks = 0.1–Kf = 0.8; (b) ks = 0.01–Kf = 0.8; (c) ks = 0.1–Kf = 0.2 and (d)

2358 N. Ursino, M. Cristina Rulli / Ecological Modelling 221 (2010) 2353–2362

F e aftek

t�keddebbrt

fltaWatr

tttriTikt

ig. 6. Difference in biomass cover n(x, 2tf ) − n(x, 0.9tf ) before fire and long tims = 0.01–Kf = 0.2. Irreversible fire impact (� = 0).

ime after fire n(x,2tf) is plotted in Figs. 5 and 6 for � = 10 · t−1f

and= 0 respectively and: (a) ks = 0.1–Kf = 0.8; (b) ks = 0.01–Kf = 0.8; (c)

s = 0.1–Kf = 0.2 and (d) ks = 0.01–Kf = 0.2. We used the same param-terization for the four scenarios shown in Figs. 5 and 6 and thoseiscussed in the previous subsection (Figs. 1–4) in order to confrontifferent extreme case scenarios. Negative values of such differ-nce indicate a local biomass loss, opposite, positive values muste attributed to colonization of the interband zones that were bareefore fire, or to a local increase of biomass density due to increasedunoff–runon from the bare zones to the vegetated patches. At= 2tf the system can be considered at the steady state.

Figs. 5 and 6 better clarify how fire severity and the negativeeedback between infiltration and burned biomass density mayead to different vegetation patterns (see also Section 3.1). Mul-iple characteristic lengths typify the reversible scenarios (Fig. 5)nd just partially the irreversible ones for ks = 0.1 (Fig. 6.a and c).hereas for � = 0 (irreversible scenarios), the fire events led to the

lmost perfect shift of the vegetation patterns within the zoneshat were bare before fire and thus, to major changes in biomasseorganization. None of the scenarios looks similar to an other.

To evaluate the overall lack of biomass over the burned area,he statistics of the difference n(x, 2tf ) − n(x, 0.9tf ) have been plot-ed in Fig. 7 as a function of the fire severity Kf and ks. The overallemporary loss of biomass cover, to be attributed to the occur-ence of a severe fire (major Kf), long time after fire resulted

n many cases, in an overall biomass gain (Fig. 7, left pannel).his means that what counted more was the negative feedbacknduced by the change of soil properties (particularly for minors). Indeed, we found an increment of average biomass density at= 2 · tf for major fire-induced negative feedbacks between burned

r fire. Cases: (a) ks = 0.1–Kf = 0.8; (b) ks = 0.01–Kf = 0.8; (c) ks = 0.1–Kf = 0.2 and (d)

vegetation–infiltration (minor ks), even for high fire severity Kf (upto Kf = 0.9), in the irreversible case, with a drop of average biomassat (Kf = 1).

In the reversible case (� = 10 · t−1f

, Fig. 7, left pannel, black sym-bols), the average difference n(x, 2tf ) − n(x, 0.9tf ) was lower thanin the reversible case (� = 0, open symbols), evidencing an averagebiomass loss in the case ks = 0.1 for Kf > 0.6. The corresponding stan-dard deviation (Fig. 7, right pannel) increased with Kf up to Kf = 0.9and dropped for Kf = 1, suggesting that, due to the major impact onthe soil repellency, fire produced less regular patterns of vegetationand an overall higher biomass loss.

3.3. Fourier analysis of vegetation patterns

The dominant vegetation pattern wavelength has been inves-tigated both by theoretical modelling (Lejeune and Tlidi, 1999;Ursino, 2005) and by vegetation observation, in field (Hiernauxand Gérard, 1999) and of aerial photographs spectral analysis(Couteron, 2002). These analyses suggested the dominant wave-length being inversely correlated to rainfall, but no mention is doneabout the possible effect of fire disturbances on pattern geometry.

Many authors (Lejeune and Tlidi, 1999; von Hardenberg et al.,2001; Rietkerk et al., 2002; Barbier et al., 2006) observed thesequence of patterns formed under increasing stress. In the fol-lowing the changes in banded pattern dominant wavelength under

increasing fire severity stress is investigated by using Fourier spec-trum analysis.

The bootstrap method has been used to quantify the statisti-cal significance of the computed peaks patterns. From observedtime-series, control datasets are constructed, which share with the

N. Ursino, M. Cristina Rulli / Ecological Modelling 221 (2010) 2353–2362 2359

F fferene

oloecTnqt

FK

ig. 7. average and standard deviation of the difference n(x, 2tf ) − n(x, 0.9tf ) for diffect of fire � = 10 · t−1

f.

riginal series some properties but are constructed under the fol-owing null hypothesis: the variability of the observed time-seriesr the association between two time-series is no different to thatxpected from a purely random process. The construction of ourontrol datasets was performed by classical bootstrap (Efron, 1979),

o test whether the original time-series is inconsistent with theull hypothesis, we have computed the Fourier analysis and relateduantities for each time-series of the control set. Then we comparedhe original values computed from original series with the distri-

ig. 8. Power spectrum of biomass density for fixed ks = 0.1 and 2 values of fire severityf = 0.1/1 and ks = 0.1 (c). Open squares: dominant wavelengths for assigned Kf. Black squa

t Kf and ks . Black symbols: irreversible effect of fire � = 0. Open symbols: reversible

bution of the same quantities under the null hypothesis, extracting,for instance, the 99th or the 95th quantiles of these distributions.

Fourier Spectral analysis shows that in natural scenarios thedominant wavelength is estimated as 62 with a second peak at57.7. The analysis conducted for medium-low fire severity condi-

tions show 2 dominant wavelengths one of them coincident withthe ones of natural condition (62) and a second one, longer thanthe second peak of natural scenario (60). By increasing fire sever-ity a new wavelength longer than the previous is shown (>62). The

: (a) Kf = 0.2 and (b) Kf = 0.8 and dominant wavelengths for different fire severityre: secondary peak for Kf. = 0.

2360 N. Ursino, M. Cristina Rulli / Ecological Modelling 221 (2010) 2353–2362

F everitK ck squ

ecseCib

apcIs

kccIsf

4

vcpct

ig. 9. Power spectrum of biomass density for fixed ks = 0.01 and 2 values of fire sf = 0.1/1 and ks = 0.01 (c). Open squares: dominant wavelengths for assigned Kf. Bla

mergence of a new dominant wavelength or its elongation coin-ides with the loss of bands isotropy and it is dependent from thetress severity. Dominant wavelengths elongation is confirmed andxacerbated by the analysis carried out for the ks = 0.01 scenarios.omparisons among the ks = 0.1 and ks = 0.01 analysis at fixed sever-

ty pointed out that soil (hydrological) properties can strongly affectands wavelength elongation and vegetation restoration.

Fig. 8(a and b) shows the dominant wavelengths and the associ-ted patterns, for fixed ks = 0.1 and fire severity (kf = 0.2 and kf = 0.8),assing from the one at t = 0.9 · tf to the condition at t = 2 · tf . Theorresponding vegetation patterns are reported in Figs. 1 and 3.n Fig. 8(c) the dominant wavelengths and secondary peak (blackquare) in the two conditions for different fire severity are reported.

Fig. 9(a and b) shows the dominant wavelengths for fixeds = 0.01 and fire severity (kf = 0.2 and kf = 0.8), passing from theondition before fire, to the condition long time after fire. Theorresponding vegetation patterns are reported in Figs. 2 and 4.n Fig. 9(c) the dominant wavelengths and secondary peak (blackquare) in the pre and post-fire conditions (t = 0.9 · tf and t = 2 · tf )or different fire severity are reported.

. Discussion

Soil witnesses significant environmental shifts over time and

egetation patterns bear the signature of its long lasting andomplex evolution by displaying multiple scales features. Simplehysically based models could help us evidencing the relevant pro-esses that shape the landscape. They also suggest that attemptingo decipher the vegetation patterns and reconstruct the geneses of

y; (a) Kf = 0.2 and (b): Kf = 0.8 and dominant wavelengths for different fire severityare: secondary peak for Kf. = 0.

regular pattern formation in real ecosystem may be a challengingtask, due to the variety of scenarios that may appear after even onlyone fire event.

Fire and water scarcity have been modelled as joined causesof the shape of vegetation mosaic in arid land for the first time.Two major features involving the soil surface have been accountedfor: the impermeable crust over the non-vegetated soil and the fireinduced hydrophobic layer formation where the sealing of the pre-fire (natural) preferential infiltration paths within the upper layersof the vegetated patterns occur.

The new model discussed here demonstrates that the impact offire, expressed in term of fire severity (modelled as the percentageof biomass loss/gain) on the vegetation patterns, long time after fire,strongly depends from the degree of soil imperviousness inducedby the fire, and may be positively or negatively correlated to the fireseverity at different times after fire. Furthermore, the fire severityand the negative feedback induced by fire on the soil propertiesconcur on the issue of shaping the vegetation patterns at steadystate (long time after fire) and during the transitory recovery phase,leading to completely different vegetation patterns in all cases con-sidered here. Thus, our simple model for water and biomass is basedon the hypothesis that fire alters the biomass density as well as thesoil properties, and it demonstrated the striking effect of fire on thespontaneous vegetation post-fire reorganization and on the related

patterns characteristic lengths.

Nevertheless, the spatial distribution of the biomass densityat short time after fire, in the non-steady conditions, will count,in case of repeated fire events, to be investigated by stochasticmodelling.

gical M

tiaircpcp(mccetttwtwsd

frrbfiEoai(

bmv

hpato

TD(

N. Ursino, M. Cristina Rulli / Ecolo

The results presented in this paper represent an important stepoward the comprehension of the nature, interrelation and tim-ng of those processes that, by altering the soil properties, will beble to change consistently the biomass distribution. This prelim-nary analysis was definitely necessary to interpret more complexesults of stochastic models. Very different patterns of vegetationharacterized the transient recovery regime depending on the fewarameters involved in our analysis, suggesting a crucial inter-onnection between post-fire recovery of vegetation patterns andossible reproductive strategies of the species forming the mosaicgrass and shrubs). Our diffusive model indeed predicted the lateral

igration of vegetation toward zones where the biomass growthould be supported by resource (moisture) availability. This pro-ess could be enhanced by the redistribution of soil resources (Ravit al., 2009), the last due to the increased erosion end sedimentransport caused by fire. However, post-fire recovery is a processhat is strongly conditioned by seed bank survival and advection inhe post-fire scenarios. Seeds are transported by runoff, and thuse may expect a concurrence of preferential infiltration and vege-

ation recovery where infiltration can take place, although, testinghether non-diffusive vegetation growth would support such tran-

ient arrangement of the vegetation could be an interesting furtherevelopment of this research topic.

We restricted our field of investigation to flat plains in order toocus exclusively on the role of fire induced soil property shifts. Theole of topography in fire regime is not taken in account in our cur-ent analysis. Nevertheless, fire behaviour can be strongly affectedy topography (Whelan, 1995). Topographic features can createrebreaks and thereby influence the distribution of fire (Myers andwel, 1990). Steep gradients in elevation, changes in aspect, andther physiographic features have been shown to drive spatial vari-tion in fire regimes by influencing fuel moisture, humidity, andnteraction with the wind, thereby affecting the probability of fireWhelan, 1995; Rowe and Scotter, 1973).

Furthermore, the upslope movement of vegetation patterns haseen observed (Leprun, 1999) and can be predicted by numericalodels (Klausmeier, 1999; Rietkerk et al., 2002; Thiery et al., 1995;

on Hardenberg et al., 2001).The interrelation between reproductive mechanisms and eco-

ydrological feedbacks adds considerable complexity to the

roblem when natural slopes are taken into account (Thompsonnd Katul, 2009), even in the absence of fire, notwithstandinghe characteristic slopes where patterns of vegetation have beenbserved are mild.

able 2imensionless variables, scaling factors and corresponding dimensional variables

capital letters) and corresponding parameter values (Ursino, 2009).

Dimensionless variables,scaling factors andcorresponding dimensionalvariables (capital letters)

Parameter values

x = Dw−1/2L1/2X Dw = 8 m2yr−1

t = LT L = 36 yr−1

w = WsW Ws = 40 mmn = (WsJ)

−1N J = 0.003 kg m−2

o = Ws−1O

s = (WsJ)−1S DN = 4 m2 yr−1

dn = DN DW DO = 400 m2 yr−1

do = DODW g = 5; K1 = 3 mm; M = 100 yr−1

f (w, n) = Ws−1L · F(W, N)

F(W, N) = gW

K1 + W− M

K2 = 0.005 kg m−2

�o = 1; k3 = 0.1k2 = (WsJ)

−1K2 A = 150 mm yr−1

E = 25 yr−1

a = (WsL)−1A Tf = 10 yr−1

e = L−1E

odelling 221 (2010) 2353–2362 2361

Acknowledgements

This study was funded by the University of Padova through theproject: “Dynamic ecological modeling, recovery strategy and manmade restoration”.

Appendix A. Dimensional parameter values

In Table 2 we reported the relation between dimensionlessparameters appearing in model (1) and corresponding dimensionalvariables (indicated with capital letters in the left-hand side col-umn). Dimensional parameter values that have been used in thenumerical simulation are reported in the right-hand side column.

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