Coupled hydrologic and vegetation dynamics in wetland ecosystems

Transcription

1 WATER RESOURCES RESEARCH, VOL. 44,, doi: /2007wr006528, 2008 Coupled hydrologic and vegetation dynamics in wetland ecosystems Chitsomanus P. Muneepeerakul, 1 Fernando Miralles-Wilhelm, 2 Stefania Tamea, 1 Andrea Rinaldo, 3,4 and Ignacio Rodriguez-Iturbe 1 Received 14 September 2007; revised 10 April 2008; accepted 2 May 2008; published 31 July [1] The stochastic nature of long-term dynamics of soil moisture, water table, and vegetation in wetland ecosystems driven by precipitation are investigated through this modeling study. A simple model is presented here to couple the hydrologic and vegetation dynamics via transpiration and ecosystem carrying capacity. The simulation results portray possible competition outcomes between plant species having different survival strategies in response to the fluctuating soil moisture and water tables under different rainfall conditions. Long-range correlations in the dynamics were detected in several of the key variables of wetland ecosystems, as the result of their dependence on the long- memory structure of the water table. The statistical structure of the modeled water table fluctuations is found to be similar to that obtained from a real case study, validating the ability of the model in capturing water table dynamics and suggesting its potential toward the quantification of the long-term dynamics of wetland vegetation. Citation: Muneepeerakul, C. P., F. Miralles-Wilhelm, S. Tamea, A. Rinaldo, and I. Rodriguez-Iturbe (2008), Coupled hydrologic and vegetation dynamics in wetland ecosystems, Water Resour. Res., 44,, doi: /2007wr Introduction [2] All together, wetlands constitute 6 7% of the Earth s land surface [Jackson et al., 1991; Lehner and Doll, 2004], where they provide ecological services as producers, stores, sinks, pathways and buffers of energy, water and nutrients from a local to a global scale [Jackson et al., 1991; van der Valk, 2006]. In spite of the abundant evidence confirming the value of wetlands, they are seriously threatened by human exploitation and further challenged by climate change [Davis and Ogden, 1994; Jackson et al., 1991; van der Valk, 2006]. In the attempt to protect wetlands and the ecological, cultural and social services they provide, understanding of the underlying mechanisms and processes of wetlands is crucial. The rapidly growing field of research about these ecosystems is addressing the necessary questions for the conservation management of wetlands. [3] Wetlands cover diverse types of landscapes and occur in a wide range of climates from semiarid to humid [Jackson et al., 1991; Davis and Ogden, 1994; Semeniuk and Semeniuk, 1995]. In these ecosystems, hydrologic forces interact with chemical and biological processes, creating continually changing conditions and a diverse biological community. Despite the presence of wetlands on a variety of hydromorphologic settings, wetlands share two characteristics that are unique to and distinguish them 1 Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey, USA. 2 Department of Civil and Environmental Engineering, Florida International University, Miami, Florida, USA. 3 Dipartimento IMAGE, Università di Padova, Padova, Italy. 4 Facultè ENAC, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. Copyright 2008 by the American Geophysical Union /08/2007WR from terrestrial and aquatic ecosystems: (1) hypoxic/anoxic soil resulting from a high level of soil moisture, and (2) macrophytes that influence the environmental processes in wetlands [van der Valk, 2006]. The anoxic stress causes direct adverse effects on photosynthesis of macrophytes: the increase in stomatal closure as soil becomes more anoxic reduces plant transpiration, similar to the case of plants under drought stress [Mitsch and Gosselink, 2000]. Moreover, in these environments with reduced redox potentials, nutrient availability declines because of the reduced mineralization rate [Mitsch and Gosselink, 2000; van der Valk, 2006]. In a wetland, the severity of anoxic conditions increases along the following order of prevalent hydroperiods: seasonal waterlog, intermittent, seasonal and permanent inundation. These hydroperiods are the result of hydrologic balance within the region and are prescribed by the fluctuations of water table levels. Subsequently, the survival and competition of plants in wetland ecosystems are found to be particularly sensitive to water table fluctuations [Ursino et al., 2004; Marani et al., 2006; van der Valk, 2006; Ridolfi et al., 2006]. For example, it has been observed that in the Everglades ecosystem, muhly grass, saw grass, and spikerush replace each other according to the flood regimes imposed by the water management of the region [Armentano et al., 2006]. [4] The delicate balance in species composition determines the vulnerability of wetland ecosystems to biotic feedbacks and to sudden changes in environmental conditions. Wetlands are highly fluctuating environments and in order to survive and reproduce successfully, wetland plants require specialized morphology and/or metabolism [Vartapetian, 2006]. An example of morphological adaptations to cope with anoxic stress is the development of aerenchyma, the continuum air spaces, which provides long-range oxygen transport from aboveground to oxygen- 1of15

2 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS ate the root zone [Vartapetian, 2006]. Besides maintaining high plant transpiration rate, the presence of this locally oxygenated zone enables microorganisms participating in decomposition and mineralization to function properly. Thus the overall effect of anoxic conditions on photosynthesis of wetland plants is reduced. Flood resistance abilities in adult plants have been reported to be one of the most important factors (among seed dispersal, seed establishment, etc.) in determining plant survival and competition outcomes [van der Valk, 2005]. This important feature will be captured in our work in the modeling of plant species characteristics. Nevertheless, these specialized metabolisms and morphologies often come at the price of a reduction in growth rate, leading to a limited plant tolerance to anoxic stress. Depending on how much a species and its competitors have adapted, the success of a particular strategy is then determined by characteristics of the species, strategies of other species in the ecosystem, and whether the environmental conditions favor that particular species. [5] Hydrology is a key component in the study of dynamics of vegetation species in wetlands. Unlike semiarid ecosystems, wetlands have shallow water tables which interact with the vegetation roots and pose a challenge in capturing the intertwined dynamics of the groundwater and soil moisture as well as the vegetation response to these hydrologic conditions. In many wetlands, the water balance in the unsaturated and the saturated zone is largely controlled by precipitation. However, the basic role of rainfall and its stochastic nature on long-term hydrologic and vegetation dynamics of wetlands is not yet well understood. Precipitation stochasticity, in terms of the frequency and intensity of rainfall, has an important effect on the timing and distribution of water in the soil column. The accurate description of the ecosystem response to stochastic rainfall is also necessary because of the threat of climate change, whose effects on precipitation regime are predicted and supported by observations [Rosenzweig et al., 2007]. As a result of climate change, it is reasonable to expect that the short-term and long-term hydrologic and vegetation processes occurring in wetlands will be altered in response to the rainfall variability. In the investigation that follows, we will focus on quantifying the characteristics of this response through a mechanistic modeling approach. [6] This paper explicitly addresses how the stochastic character of precipitation controls the interplay between hydrologic and vegetation dynamics in natural wetlands. To explore this issue, we develop a simple stochastic model linking the dynamics of plant growth, soil moisture, and water table fluctuations (section 2). Hydrology is linked to vegetation growth through evapotranspiration. The analysis is focused on those environments where the role of precipitation on fluctuations of soil moisture, water table, and species composition is crucial. This is the case of an isolated palusplain wetlands whose landform is flat without standing water [Semeniuk and Semeniuk, 1995]. Through the analysis of a large number of simulations where different stochastic rainfall patterns are explored, we provide a probabilistic interpretation of the general nature of the results (section 3). In addition, the simulation results of the dynamics of the key ecosystem variables are further analyzed through their study in the time and frequency domains (section 4). Finally, the statistical structure of the modeled water table levels is found to be similar to that obtained from a real wetland suggesting the potential of this modeling approach toward the quantification of the longterm dynamics of wetland vegetation (section 5). 2. Model Description [7] The dynamics of wetland ecosystems are modeled here through the intertwined behaviors of three major components: (1) the soil moisture dynamics in the unsaturated zone, (2) the fluctuations of the water table, and (3) the dynamics of the vegetation biomass. Driven by a stochastic rainfall forcing, one can write the water balance of the soil column on the basis of a simple bucket model of the soil water content coupled with the dynamics of the water table. The modeling of the unsaturated and saturated zones at the daily timescale is based on the following simplifications: [8] 1. The ecosystem is assumed to have flat topography with an isolated horizontal water table, such that it is not affected by other water bodies in neighboring systems. [9] 2. Extended periods of multiple days with standing aboveground water are not considered in the model. Thus wetlands which are permanently or semipermanently inundated are not appropriately modeled by this approach. [10] 3. Hydraulic conductivity is simplified to be negligible below field capacity and infinite above it, so that, the infiltrating water front leaves the soil behind the front at field capacity, which is then the maximum level of relative soil moisture for the unsaturated zone. No intermediate levels of soil moisture are allowed between field capacity and saturation. This is a reasonable assumption when modeling the daily dynamics of shallow water tables in most types of soil, except for clay [Brady and Weil, 2002]. [11] 4. Noncooperative root functioning above and below the water table is assumed. [12] 5. The presence of capillary fringes is not considered. [13] The last two assumptions allow for the decoupling of the dynamics of unsaturated and saturated zones, such that the evapotranspiration from above and below the water table can be considered separately. After accounting for rainfall interception, infiltrating water is partitioned into the soil moisture of the unsaturated zone, s, and that reaching the water table located at a depth y, where y is held at the minimum of zero at the soil surface and measured positive downward. [14] It is important to note that, in reality, the frequent rise of the water table to the soil surface, similar to what is obtained in the following simulations, is often accompanied by the presence of standing water. The specification of an isolated water table having minimum y at zero implies the presence of instantaneous runoff generated by Dunne s mechanism. The instantaneous runoff is possible with negative topographic gradients further away from the considered area. An obvious example of this type of system is an isolated palusmont (mountaintop wetlands) whose instantaneous runoff is driven topographically because of the lower elevated neighboring area. A different type of system is a slightly higher elevated wetland inserted in a middle of a larger similar wetland area having steady state horizontal ground water flow. Also, the baseline dynamics of those wetlands whose water balance is mainly controlled by rainfall and evapotranspiration may be qualitatively described by this simplified system. 2of15

3 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Table 1. Lists of Variables and Their Definitions Symbols Definition of Variables Units s average relative soil moisture y water table depth cm y* water table depth immediately cm following infiltration I infiltration cm a mean infiltration depth cm (effective rainfall depth) l 0 infiltration arrival rate d 1 Re recharge cm WSC water storage capacity of the cm unsaturated zone n soil porosity s fc soil moisture level at field capacity B plant biomass per unit land area g m 2 D canopy interception depth cm T p potential evapotranspiration rate cm/d per unit leaf area T uns evapotranspiration per unit leaf area cm/d from the unsaturated zone T s evapotranspiration rate per unit leaf cm/d area from the saturated zone R proportion of roots above the water table r plant water stress [15] An explicit scheme is used with the following sequential processes, with each time step equal to 1/10 day: (1) infiltration is modeled as an instantaneous water input at the beginning of every time step; (2) the average relative soil moisture throughout the unsaturated zone, s, and that reaching the water table located at depth, y, are then updated; (3) evapotranspiration rates are calculated for both the saturated and the unsaturated zones; (4) both s and y are updated explicitly again after the loss of water through evapotranspiration; (5) at the end of the time step, the biomass of species i is calculated on the basis of its evapotranspiration rate and the ecosystem carrying capacity for each particular species, K i. It is worth noticing that a more complete and realistic model of the infiltration: water table interaction could be developed to obtain analytical solutions for the probability density functions of the water table and soil moisture at different depths. Nevertheless it would be unfeasible in such an analytical approach to incorporate biomass dynamics whose inclusion is the goal of this paper and which then leads to a simpler scheme for the infiltration and water table dynamics as used in this paper. [16] All results are interpreted at the daily timescale which is the one embedded in the modeling of the rainfall input, infiltration and the resulting soil moisture. Moreover, the control of soil moisture on the hourly fluctuations of photosynthesis and transpiration allows for the upscaling of plant assimilation and the water balance to the daily dynamics, which is equivalent to the integrated hourly response regardless of the hourly-level details influenced by atmospheric processes [Daly et al., 2004a, 2004b].The different components of the model are described in detail in the following subsections with the list of variables provided in Table Soil Moisture Dynamics in the Unsaturated Zone [17] The unsaturated zone is defined as the soil column above the water table up to the soil surface; the soil moisture dynamics within this zone is modeled by a bucket type of model, i.e., with an average soil moisture value over the unsaturated soil column. Infiltration, I(t), arises from the excess rainfall after interception, occurring stochastically in time. Water is lost from this zone through leakage, i.e., as groundwater recharge, Re(t), and evapotranspiration. The term evapotranspiration is used here for the completeness of the water balance. However, in the following simulations, soil evaporation will be assumed to be negligible and hence evapotranspiration is determined entirely by transpiration. This assumption is reasonable and the practice is common in the modeling of water losses from land that is fully covered by canopy where much less water is lost from evaporation compared to that from transpiration [Schaap and Bouten, 1997; Bauer-Gottwein et al., 2007]. The assumption of full vegetation coverage is also supported by the total biomass obtained from the simulations, which is always close to the maximum ecosystem carrying capacity. In case one wanted to explicitly consider the evaporation component, this can be accomplished by suitably modifying the arrival rate of the rainfall events in the rainfall simulator as pointed out in the next section. [18] In each time step, evapotranspiration per unit leaf area from the unsaturated zone, T uns, is determined from the existing water table depth and the existing soil moisture. Infiltration and recharge are modeled as point processes, occurring instantaneously at the beginning of each time step. The time varying water storage capacity of the unsaturated zone, WSC, is given by WSCðs; yþ ¼nyðtÞ½s fc sðtþš; ð1þ where n and s fc denote the porosity and field capacity of the soil, respectively. The governing equations for the soil moisture dynamics are then stþ ð DtÞ ¼ sðtþþ IðtÞ T unsa L f L BDt nyðtþ stþ ð DtÞ ¼ s fc T unsa L f L BDt ny*ðtþ if IðtÞ WSCðs; yþ if IðtÞ > WSCðs; yþ; where I(t), [L], denotes the infiltration input within a time interval Dt; T uns,[lt 1 ], is the transpiration rate per unit leaf area from the unsaturated zone occurring continuously over Dt; A L,[L 2 M 1 ], denotes leaf area per unit aboveground biomass; f L,[ ], stands for aboveground biomass per unit plant biomass, and B, [M], is the plant biomass. [19] In cases where I(t) > WSC(s, y), the unsaturated soil column is left at field capacity by the infiltrating water front. The term y*(t) in equation (2) is the water table depth immediately following infiltration: ð2þ Re y*ðtþ ¼yðtÞ nð1 s fc Þ ; ð3þ which will be addressed in section 2.2. We now briefly describe the modeling of infiltration, and evapotranspiration from the unsaturated zone Infiltration, I(t) [20] The rainfall input is treated as an external random forcing which is statistically homogeneous in time. The 3of15

4 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS temporal structure within each rain event is not considered. The rainfall process is modeled as a marked Poisson process with rate l, [T 1 ], and the marks representing the depth of rainfall events are assumed to be an exponential random variable with mean a,[l]. Although continuous modeling is performed, the model is interpreted at the daily timescale. The interception depth, D, [L], is assumed to be the same over the entire area being considered. The fraction of the rainfall that is not intercepted by vegetation canopy is assumed to reach the soil as infiltration, I, [L]. The marked Poisson rainfall process is thus transformed into a censored marked Poisson infiltration, with new rate l 0 ¼ le D=a and effective rainfall depth which is still exponentially distributed with mean a [Rodriguez-Iturbe et al., 1999]. The average daily infiltration is then the product, al 0,[LT 1 ]. Although soil evaporation has not been modeled explicitly, it can be accounted for through its incorporation in the D factor [Guswa, 2008] of equation (4) Evapotranspiration From the Unsaturated Zone, T uns [21] Evapotranspiration from the unsaturated zone, T uns, has a potential maximum rate, T p, and is given by ð4þ T uns ðs; yþ ¼T p RyðtÞ ð ÞrðsðtÞÞ; ð5þ where R(y) is the proportion of roots above the water table (e.g., the evapotranspiration from the unsaturated zone is reduced when the water table rises and more roots become waterlogged). The factor r(s) represents the plant water stress and is given by 8 9 < 1 if s s* = s s rðsþ ¼ w if s s* s w s < s* : w ; ; ð6þ 0 if s < s w where s* and s w represent the levels of soil moisture associated with the soil matrix potentials at which stomatal closure begins and is fully completed, respectively [Rodriguez-Iturbe and Porporato, 2004]. Both T uns and T p are the evapotranspiration rates per unit leaf area [LT 1 ] Dynamics of the Water Table [22] The saturated zone is defined as the zone where the water fills all the soil pores, i.e., s = 1, with the water table being its top boundary. The dynamics of the saturated zone is controlled by recharge and evapotranspiration depending on the extent of submerged roots. Recharge, Re, decreases the water table depth, y, while evapotranspiration from the saturated zone, T s, increases it according to T s A L f L BDt Reðs; yþ ¼n1 ð s fc Þ½yðt þ DtÞ yðtþš: ð7þ The modeling of recharge and evapotranspiration is now described in the following Recharge, Re(s, y) [23] At any time the unsaturated zone has a finite amount of water storing capacity, WSC(t), [L], which can be viewed as the threshold above which recharge, Re, [L], occurs. The amount of water reaching the water table is then Reðs; yþ ¼ IðtÞ WSCðs; yþ if IðtÞ WSCðs; yþ 0 otherwise Evapotranspiration From the Saturated Zone, T s [24] Evapotranspiration from the saturated zone, T s, is measured as evapotranspiration rate per unit leaf area with a maximum rate, ct p. The factor c 1 accounts for the reduction from the potential rate due to anoxic stress. T s is also directly proportional to the fraction of roots under the water table, 1 R(y). Thus, ð8þ T s ðyþ ¼cT p ½1 RðyÞŠ: ð9þ The anoxic coefficient, c is a parameter reflecting the plant intrinsic adaptation to the lumped adverse effects of anoxic conditions, e.g., reduced photosynthesis activity from increased stomatal closure, toxicity of reduced minerals, and possible reduction of leaf nitrogen, etc Biomass Dynamics [25] The dynamics of biomass of each species is described through an equation of the Lotka-Volterra type [Lotka, 1925, 1956; Volterra, 1926, 1931] modified for plant growth dynamics. Thus, db i dt ¼ B i r i 1 ða iib i þ P j6¼i a ijb j Þ K i ðyþ b i : ð10þ [26] B i,[ml 2 ], denotes plant biomass of species i per unit area; r i, [T 1 ], denotes the intrinsic growth rate of species i; a ij is the impact coefficient of species j on species i; K i (y), [ML 2 ], is the ecosystem carrying capacity limited by environmental factors (e.g., light, nutrient, water and air in the soil), and b i,[t 1 ], denotes the decay rate per unit biomass resulting from senescence and root respiration. The intrinsic growth rate of a species depends on the water use efficiency and the evapotranspiration rate of the plants and is given by r i ¼ w i A Li f Li ðt uns þ T s Þ; ð11þ where w i, [ML 3 ], stands for the intrinsic water use efficiency of species i; A Li,[L 2 M 1 ], denotes leaf area per unit aboveground biomass, and f Li, [ ], is the ratio of aboveground biomass to total biomass. The biomass decay rate, b i, can be expressed as b i ¼ R ri ð1 f Li Þþq i : ð12þ R ri,[t 1 ], being the root respiration coefficient and q i the senescence rate, [T 1 ]. [27] The parameter w i in equation (11) is determined by the ratio of the maximum assimilation rate, A mi,[mt 1 L 2 ] and T pi given by w i ¼ A m Y g ; ð13þ T p i 4of15

5 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 1. The ecosystem carrying capacities of two species as a function of the water table depth, y. The two curves follow equation (14) with parameters given in Table 2. These relationships are used for all the three cases in the analysis. The thin line represents the flood resistant species (FR), and the thick line represents the less flood resistant species (LFR). where Y gi denotes the growth yield of the species i defined as the fraction of carbon assimilation that remains after paying aboveground growth respiration costs. Although A mi depends on nitrogen in rubisco which could be reduced under anoxic conditions as nitrogen mineralization in the ecosystem decreases, wetland plants seem to be able to maintain adequate levels of nitrogen in their leaves through constant nitrogen uptake despite temporal anoxic conditions [Mitsch and Gosselink, 2000]. The possible reduction in A mi from the decline of nitrogen in rubisco will be thus assumed as negligible. In this regard, the control of nutrients on the dynamics of vegetation is then modeled solely at the ecosystem level through the ecosystem carrying capacity as described in the following. [28] Light, nutrients and water are common limiting factors in many plant ecosystems. In the case of wetlands the critical resource is quite frequently the amount of oxygen and subsequent nutrient availability in the soil column. The nitrogen cycle, in particular, is controlled by the degree of wetness [Porporato et al., 2003]: microbial mineralization declines under either too high or too low levels of soil moisture. When the water table rises, the amount of oxygen and nutrient availability may decrease while toxicity from reduced minerals accumulates to the level that causes reduction in the metabolism of plants, impacting growth and maintenance up to the point of plant death. The reduction in ecosystem carrying capacity can also happen in the case of the significant depletion of groundwater. Because of this, the carrying capacity of species i, K i is modeled as a function of water table depth (a rearranged form of the equation proposed by Ridolfi et al. [2006]) y y ci K i ðyþ ¼K* i e y pi y ci y pi y y pi y ci ; ð14þ where y ci is the water table depth below which the carrying capacity of species i becomes zero because of flooding stress (e.g., a parameter of negative value to define the curves shown in Figure 1 to be discussed later), y pi stands for the water table depth at which K i = K* i, the maximum carrying capacity of species i, taking into account a limitation on light only. The carrying capacity decreases as y deviates from y p : the ecosystem is oxygen controlled when y < y p while it is water controlled when y > y p. This decrease of the carrying capacity from its maximum value implicitly incorporates the side effects resulting from anoxic and drought stresses. These side effects are mainly the reduction of available nitrogen owing to the reduced mineralization rate as the saturation in the soil column deviates from the optimum values. In addition, the production of toxic chemicals and loss of nitrogen through denitrification under anoxic conditions further justify the more rapid decrease in the carrying capacity in the oxygenlimited zone than that in the water-limited zone. [29] In the scope of wetlands where standing water is not captured, we will consider only the water table depth y >0 where y is measured positive downward. The parameter y ci is assigned negative values, indicating the ability of the ecosystem to support nonzero biomass of species i when the soil is completely waterlogged. [30] The maximum total evapotranspiration per unit land area of species i, T mi, is defined as the total evapotranspiration at potential rate when the species biomass is at the maximum ecosystem carrying capacity, K* i, i.e., T mi ¼ðT p A L f L K*Þ i : ð15þ In the simulations presented later in this paper, an important difference is made between flood resistant species and those which are less resistant to floods. The simplifications that standing water and soil evaporation are considered minimal lead to a choice of total precipitation less than potential evapotranspiration. Actually, potential evapotranspiration is not frequently achieved in the model. Thus when al 0 > T mi, we could expect that flooding conditions will prevail and will lead to the dominance of flood resistant species. For this reason we will use climatic condition such that al 0 T mi, where stochasticity of rainfall plays a crucial role in the multiple feedbacks of the dynamics as well as in the type of vegetation developing in the ecosystem Survival and Competition Strategies [31] In the simulations of this paper, we will consider competition between two species which are different in their flood and drought resistances. The more flood resistant species (FR) has shallow roots, as it tends to keep root biomass away from the saturated zone, but has relatively high evapotranspiration under waterlogged condition. The less flood resistant (LFR) species has a reduced evapotranspiration under waterlogged conditions but it develops deeper roots to uptake groundwater when drought conditions arise. Generally, the flood resistance ability requires physiological adaptation which results in a lower growth rate. This trade-off can be parameterized through the ecosystem maximum carrying capacity (K* i ), the intrinsic water use efficiency (w i ) and the potential evapotranspiration per unit land area when its biomass is at the ecosystem maximum carrying capacity, T mi. Keeping T mi the same allows us to single out the influence of stochasticity of precipitation on the dynamics of species composition. The actual evapotranspiration rate depends on how plants 5of15

6 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Table 2. Descriptions of Plant Parameters in All Simulations a Symbols Parameters Species 1 (FR) Species 2 (LFR) a ij impact coefficient of species j on species i a 11 = a 12 =1 a 22 = a 21 =1 A mi maximum assimilation rate (g d 1 m 2 ) Y gi growth yield of the species i T mi maximum total evapotranspiration per unit land area of species i when its biomass is at K i *(cm/d) A Li leaf area per unit aboveground biomass (m 2 /g) f Li ratio of aboveground biomass per unit biomass R ri root respiration coefficient (d 1 ) q i senescence rate (d 1 ) MR i mean root depth (cm) c i reduction factor for transpiration under anoxic conditions s wi soil moisture level at which stomatal closure is fully completed s* i soil moisture level at which stomatal closure begins K* i maximum ecosystem carrying capacity of species i (g/m 2 ) (0.9) y ci critical water table depth (cm) y pi water table depth where K i = K* i (cm) a Plant parameter values are taken from the range of values derived from Larcher [2001] and Lambers et al. [1998]. actually experience anoxic and water stresses under the hydrologic dynamics created by a particular climate. In our analysis, the trade-off is reflected in the different values of K* i and w i which are assumed for FR species and LFR species while the value of T mi is assumed the same in both species (see Table 2). [32] The rest of this subsection presents more specific (but necessary) aspects of the modeling. Survival and competition strategies of the two competing wetland plant species in this modeling study are parameterized as follows. The dependence of the ecosystem carrying capacity on the water table depth y is shown in Figure 1 for both types of species. The critical water table depths, y ci, are set negative for both species in order to have nonzero ecosystem carrying capacity when the water table is at the soil surface; this allows plants to grow even when the soil is completely waterlogged. Although the two carrying capacity functions are not very different since both species can live in the same ecosystem, there are several characteristics distinguishing their flood resistance abilities: (1) the values of the ecosystem carrying capacity associated with shallow water table levels are smaller for the LFR species than for the FR species; (2) as the water table becomes deeper, K LFR becomes larger relative to K FR and both of them increase until the water table depth is at a value where the carrying capacity functions reach their maximum values, K* FR = 2250 gm 2 for y = 80 cm and K* LFR = 2500 gm 2 for y = 100 cm; and (3) when y > 180 cm, K FR (y > 180) < K FR (y =0) and the FR species becomes more disadvantaged under the drought condition than it does when the soil is completely waterlogged while the LFR species is better off in the condition of deep water table. [33] In order to avoid the complete and permanent disappearance of a plant once its biomass approaches zero, a minimum level of biomass, minb, is maintained throughout the simulation. Here, minb is the state-dependent threshold set at 0.1 K i (y) for each species; it reflects that seed implantation and species recovery is less likely to occur under the increasingly flooded or drought conditions. In this modeling study, in order to simplify the recovery of a plant species, plants can transpire even though their biomass is reduced to minb such that the recovery takes place from a positive intrinsic growth rate when there exists some unoccupied carrying capacity. This specification allows for some resilience to environmental fluctuations, eliminating the tendency of catastrophic shifts to cause irreversible species death and permits the recovery of species from seeds or residual biomass. When a species is not completely wiped out (i.e., biomass remains at least at the minimum level, minb), alternative stable vegetated states are possible, which are often observed in riparian environments for successional vegetation [Ridolfi et al., 2006]. By having minb and the positive growth rate, the model can capture the recovery nature of wetland plants from a pool of diverse species [van der Valk, 2005]. A criterion of significant existence needs to be fixed above the minimum level of biomass, in order to clearly identify when a species is healthily settled and not only fluctuating around the imposed minimum. In this paper we use 500 g/m 2 as the threshold for well-established vegetation. [34] Roots are assumed to be exponentially distributed with a mean root depth MR i assigned according to the species strategies. The same initial conditions, soil and species parameters are used in all simulations, each of which is run for a total of 240,000 days. The length of simulation time is approximately in the order of magnitude of the timescale where long-term dynamics of wet-dry cycles in wet prairies is observed to be unchanged [van der Valk, 2005]. The stochasticity of infiltration is modeled through a censored marked Poisson process as already discussed in section 2.1 of this paper. In the following analysis, we select three climatic conditions, which, although apparently not very different among themselves, nevertheless yield quite different dynamics of species composition: (1) intermediate climate where al 0 = 0.40 cm/d, a = 1.4 cm, and l 0 = d 1 ; (2) wetter climate where al 0 = 0.44 cm/d, a = 1.5 cm, and l 0 = d 1 ; and (3) drier climate where al 0 = 0.36 cm/d, a = 1.5 cm, and l 0 = d 1. [35] The simulation results consist of three possible outcomes of species composition, namely species coexistence, dominance of the flood resistant species and dominance of 6of15

7 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 2. Transitions to different dominance states in vegetation composition and the corresponding hydrologic and plant dynamics under the intermediate long-term climate (al 0 = 0.40 cm/d): (a) recharge, (b) average relative soil moisture in the unsaturated zone, (c) water table depth measured downward from the soil surface, (d) biomass, and (e) evapotranspiration rate. Soil is a loamy sand with n = 0.42 and s fc = The plant parameters are given in Table 2. In Figures 2d and 2e, solid thin lines represent biomass and evapotranspiration dynamics, respectively, of the FR species, while thick lines represent those of the LFR species. Gray lines represent total biomass and total evapotranspiration rate, respectively. the less flood resistant species. The amount of time the ecosystem spends in each type of composition is measured on the basis of the following criteria: (1) the two species coexist when both B FR and B LFR 500 g/m 2, (2) the flood resistant species dominates when only B FR 500 g/m 2, and (3)the less flood resistant species dominates when only B LFR 500 g/m 2. The amount of time in a particular state provides a probabilistic interpretation of the model results. The statistics of the different dynamic variables obtained from the 240,000-day time series were compared with those resulting from 50 simulations, each of 30,000 days, and they were found to be statistically the same. 3. Coupled Hydrologic and Vegetation Dynamics [36] In all cases, the initial water table is at a depth of 50 cm from the ground surface while the initial relative soil moisture is at Each species has an initial biomass of 40% of its corresponding maximum carrying capacity. Figures 2 and 3 show the typical hydrologic and vegetation dynamics resulting from the model simulation for the case of the intermediate climate with a mean infiltration of 0.4 cm/d. Because of stochasticity, this long-term climate can be considered as a series of many short-term climates whose various characteristics create the continuously changing hydrologic regimes, which then lead to changes in species composition. [37] We find that in order to understand the temporal hydrologic and biotic dynamics of the ecosystem, it is helpful to compare infiltration, I, to water storing capacity, WSC, and recharge, Re, throughout the transitions the ecosystem undergoes between stages characterized by either the dominance of one of the two species or the coexistence of both. In the model, the randomly fluctuating I is considered an externally uncontrolled factor and there are no feedbacks between biomass and precipitation. As WSC buffers against the rise of the water table, its evolution is thus dictated by its existing condition and the nature of the incoming precipitation. The intricate water balance driven by climate fluctuations involving feedbacks between the water table and the evapotranspiration rate creates continually changing stresses of moisture deficiency and anoxic character which are dealt with differently by different plant species. The response reflected in evapotranspiration rate and growth induces the change in species composition: low 7of15

8 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 3. Transitions to the same dominant states in vegetation composition and the corresponding hydrologic and plant dynamics under the intermediate long-term climate (al 0 = 0.40 cm/d): (a) recharge, (b) average relative soil moisture in the unsaturated zone, (c) water table depth measured downward from the soil surface, (d) biomass, and (e) evapotranspiration rate. In Figures 3d and 3e, solid thin lines represent biomass and evapotranspiration dynamics of the FR species, while thick lines represent those of the LFR species. Gray lines represent total biomass and total evapotranspiration rate, respectively. All parameters are the same as in Figure 2. WSC induces the FR dominance while high WSC induces the LFR dominance. [38] Figure 2 exemplifies the case where species composition switches successively from the dominance of a species to coexistence to dominance by the other species. At the beginning, the hydrologic conditions are characterized by high WSC, and species composition is one of the LFR dominance. Later on after a period of high infiltration, WSC is continually reduced with an increasing fraction of infiltration becoming recharge, and species composition evolves from the state of the LFR dominance to the state of coexistence. When the two species coexist, WSC, although increasing because of the transpiration from the two species, still remains relatively low. The continuation of wet climate over the condition of low WSC enhances the waterlogged condition, leaving the soil moisture in the unsaturated zone at field capacity for most of the time. At this stage, almost all of I becomes Re, raising the water table and thus lowering WSC further. The shallower water table level favors the growth of the FR species which tends to become dominant after some transient period of coexistence. In this particular example, the larger biomass of the FR species lasts only for about 4 years since the occurrence of a lengthy period of below average precipitation leads to the strong dominance of the LFR species. The hydrologic conditions show then an increase in the water table depth and the soil moisture level as the evapotranspiration surpasses infiltration, WSC increases, and Re decreases. [39] Figure 3 shows the case where species composition alternates between coexistence and dominance by a single species without changing to the other type of dominance. At the start, the ecosystem is under the period of relatively high infiltration but the rising water table has not yet reached very shallow levels and the LFR species is still controlling most of the ecosystem biomass. Under the occurrence of very wet conditions, the water table rapidly becomes shallower, leading to the growth of the FR species which then coexists with the LFR species. The return to a less humid climate leads to a drop in the water table and the renewed dominance of the LFR species. [40] The simulation shows that when a period of climate unfavorable for the dominating species persists long enough, the species composition changes from the state of dominance by that species to one of coexistence. The climate following the coexistence stage dictates either how long the two species can coexist or if a species will 8of15

9 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 4. Hydrologic and vegetation dynamics in the case of the intermediate climate (al 0 = 0.40 cm/d): (a) biomass, (b) average relative soil moisture in the unsaturated zone, and (c) water table depth. All parameters are the same as in Figure 2. become dominant. As has been observed in wetlands [van der Valk, 2006], the dynamics of species composition depends on the magnitude of water level fluctuations resulting from the undergoing climatic regimes: the increasing degree of fluctuations dictates the level of change in species composition ranging from fluctuations in species biomass to the alternation in dominant species (microsuccession) whose timescale varies from a few years to decades. [41] The typical hydrologic and biotic results from the intermediate climate are shown in Figure 4. The results obtained under the wet climate of al 0 = (1.5 cm)(0.293 d 1 ) = 0.44 cm/d are shown in Figure 5, while those of the dry climate having al 0 = (1.5 cm) (0.24 d 1 ) = 0.36 cm/d are shown in Figure 6. Over the 240,000 days, the ecosystem under the intermediate climate spends 44% of the time in coexistence with 26% and 30% of the time being dominated by the FR and LFR species, respectively. The wetter climate leads to 70% of the time in FR dominance, 25% of the time in coexistence, and 5% of the time in LFR dominance. For the case of the drier climate, the proportions of time are 1%,7%, and 92% for FR dominance, coexistence, and LFR dominance, respectively. [42] The general characteristics of long-term dynamics of the ecosystem are controlled by the nature of a long-term climate which also dictates the interruption or persistence of a species existence over shorter timescales. Neither the FR nor LFR species are significantly dominant under the intermediate climate. Thus, the intermediate climate allows the most diverse types of transitions by having frequent interruptions on the dominance states as well as enough enhancement for changes toward alternative dominance states to become fully developed. In contrast, in the wetter or drier climates, most of the time there are only alternations between coexistence and the dominance state favorable to that particular climate. Thus, for example, under the wetter climate, the alternation between species coexistence and FR dominance is the most common while the alternation between coexistence and LFR dominance is rare. [43] The change in climate toward a different precipitation regime can cause a permanent change in the long-term and subsequent short-term characters of the hydrologic and biotic dynamics. As we can see from the simulation results, when the climate becomes increasingly wet, we can expect more frequent recharge events, less WSC, high soil moisture levels, and a shallow water table with a small number of events when the water table reaches deeper levels. This leads to a persistent dominance of the FR species. Table 3 shows the mean values of hydrologic and biotic variables obtained from the three long-term climates. In this example, 9of15

10 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 5. Hydrologic and vegetation dynamics in the case of the wet climate (al 0 = 0.44 cm/d): (a) biomass, (b) average relative soil moisture in the unsaturated zone, and (c) water table depth. All parameters, except those for the climate, are the same as in Figure 2. the average total biomass obtained under the dry long-term climate is the highest among the three cases because of the impact of the dominating LFR species whose ecosystem maximum carrying capacity is higher. In the intermediate climate, the average values of biomass of both species are about the same magnitude as well as their contribution to the total evapotranspiration. [44] Deviations from the simplifications specified in section 2 should not change the results obtained from this simple model qualitatively. Although the small presence of standing water may prolong the wet cycle, this persistence is likely to be offset by high surface water evaporation rate, which in this case, should be considered separately from transpiration. When hydraulic conductivity is finite, water is lost through instantaneous runoff in the situation where the rate of water input is larger than the infiltration rate. Moreover, transpiration rate also increases as the water table rises more slowly. In this regard, the effect of finite hydraulic conductivity only requires the use of wetter climates to obtain the similar results presented here, similarly to that of evaporation. [45] It is important to study the dynamics of the evapotranspiration rate as the result of the interplay of the major ecosystem variables, namely biomass, water table position, and soil moisture. As clearly observed in Figures 2e and 3e, in addition to roughly following the biomass signal, the evapotranspiration rate fluctuates with the fluctuations of water table and soil moisture. The water table dynamics become increasingly important to the evapotranspiration rate when the average depth of the water table is shallow as in the cases of the intermediate and wetter climates. The dynamics of soil moisture plays a more important role in the drier climate as the soil moisture fluctuates more frequently in the plant water stress range, leading to a decrease in evapotranspiration rate along with the decrease in soil moisture. [46] Different types of feedbacks are possible depending on the position of the water table. A decrease in water table depth because of large values of recharge in the wetter climate leads to a positive feedback causing the already shallow water table to become shallower owing to the reduced evapotranspiration rate under the high anoxic stress. When the water table is at a moderate depth, it tends to become deeper because of the increase in the evapotranspiration rate as plants experience less anoxic stress, but are still free of water stress. Conversely, when the water table is deeper, most of the infiltration results in an increase of the soil moisture in the unsaturated zone and the increase or 10 of 15

11 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 6. Hydrologic and vegetation dynamics in the case of the dry climate (al 0 = 0.36 cm/d): (a) biomass, (b) average relative soil moisture in the unsaturated zone, and (c) water table depth. All parameters, except those for the climate, are the same as in Figure 2. decrease in the evapotranspiration rate tends to follow the fluctuations in soil moisture without much interaction with the water table. [47] The average total evapotranspiration rates from the three climates are quite similar as shown in Table 3. The similarity comes from the same total potential evapotranspiration rate that the two species have. The slight difference in their actual evapotranspiration rate comes from the different survival strategies the two species use in response to changes in hydrologic conditions. Although the ecosystem experiences both water and anoxic stresses under the three climates considered, the impact from anoxic stress is more pronounced; thus, the drier climate results in a higher average evapotranspiration rate. In fact, even the average water table depth obtained under the drier climate (1.5 m) is not deep enough for the plants to experience more than mild water stress while they are free from the high anoxic stress. 4. Spectra and Correlation Analysis [48] The results obtained from the simulations with Dt = 0.1 day have been averaged over a day span, and the obtained daily time series are analyzed in the time and frequency domains, as described in the following Autocorrelation and Cross Correlation [49] While the Poisson precipitation process is memoryless, the memory of each key ecosystem variable is quite long and is dictated by the underlying deterministic mechanisms which control its response to the fluctuations of climate. For example, the direct impact of rainfall events on soil moisture explains why the autocorrelation of the water table (Figure 7a) decays more slowly than that of the average relative soil moisture (Figure 7b). While every infiltration event contributes to the fluctuation of soil moisture, the water table rises only when the infiltration is Table 3. Mean Values of Biotic and Hydrologic Variables Obtained From Simulations Under the Three Different Climates Ecosystem Variable Dry Climate Intermediate Climate Wet Climate B FR (g/m 2 ) B LFR (g/m 2 ) B tot (g/m 2 ) T tot, FR (cm/d) T tot, LFR (cm/d) T tot (cm/d) y (cm) s of 15

12 MUNEEPEERAKUL ET AL.: WETLAND VEGETATION DYNAMICS Figure 7. Autocorrelation functions of the (right) water table depth and (left) average relative soil moisture in the unsaturated zone. The thin, medium, and thick lines belong to the drier (al 0 = 0.36 cm/d), intermediate (al 0 = 0.40 cm/d), and wet (al 0 = 0.44 cm/d) climates, respectively. larger than the existing water storage capacity, WSC. That the autocorrelation functions of biomass and evapotranspiration of each species also exhibit long memory can be explained by their strong dependence on the water table through the relationships explicitly discussed in section 2. This observation confirms, once again, the importance of the water table in controlling the dynamics of species composition in wetlands. [50] In addition, the autocorrelation function of the water table decays more rapidly as the climate becomes wetter as shown in Figure 7. In drier climates, the memory of the water table dynamics is particularly long because of the high buffering effect of the water storage capacity, WSC. The condition of high WSC is maintained in the absence of anoxic stress by the feedbacks between the evapotranspiration rate and the water table discussed before. In wetter climates, although the memory of shallow water table is also extended by the reduced evapotranspiration rate under high anoxic stress, it is somewhat shorter because of the frequent rise of the water table to the ground surface. [51] The responses of the two plant species to changes in the water table position, y, are reflected on the cross correlation functions between the biomass of each species and y as shown in Figure 8. The biomass of the flood resistant species, B FR, shows a strong negative cross correlation with y contrary to the positive character of the function in the case of the less flood resistant species, B LFR. The increase in the water table depth y, will be followed by the increase in B LFR at the expense of B FR. [52] The delayed response of the biomass of each species to water table fluctuations could be detected from the peaks at nonzero lags of their cross correlation functions as shown in Figure 8. This inertia of the biomass response to water table fluctuations has been mentioned in section 3 when discussing the transitions among species composition. As equation (10) suggests, the delay in the response of biomass of each species can be explained by the logistic growth dynamics. Thus, the influences of soil moisture and water table dynamics do not operate directly on the biomass itself; instead, they operate on the rate of change in biomass through the intrinsic growth rate and on the logistic term Figure 8. Cross-correlation functions with the water table depth of the (a) biomass of the FR species and (b) biomass of the LFR species in the case of the intermediate climate (al 0 = 0.40 cm/d). 12 of 15