The origin and causes for the existence of two distinct steady-state modes of soil moisture probability distribution (pdf) have been attributed to several processes, such as land-atmosphere feedbacks or shifts in climatic conditions within seasons. Here we argue that the interaction between saturated and unsaturated zones in soils with shallow water tables might represent a possible mechanism leading to such bimodality. This conclusion is achieved by analyzing soil water content measurements in vegetated soil columns artificially constructed in a laboratory. We used these observations to develop a stochastic model for the daily soil water balance, which shows how the interplay between the water table and the unsaturated zone is able to induce soil moisture bimodality.
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 Experimental and theoretical analyses in several ecosystems have shown the existence of steady-state soil moisture preferential conditions, resulting in soils persistently being either dry or wet. The causes of this bimodality in the long-term soil moisture probability distribution function (pdf) are not completely understood, and thus remain the subject of debate.
 The aim of this paper is to show how the bimodality in the soil moisture distribution in humid lands might be strongly related to the capillary rise, which represents a key process in soils with shallow water tables. In these ecosystems, the near-surface unsaturated zone becomes relevant in determining water availability for vegetation [Bradley and Gilvear, 2000; Naumburg et al., 2005; Brolsma and Bierkens, 2007], and microbial decomposition and mineralization rates [Linn and Doran, 1984; Skopp et al., 1990]. Therefore, the potential persistence of dry or wet states as well as the shift from one to the other state are important for vegetation and microbial communities, and for the biogeochemical cycling of carbon and nitrogen [Rodriguez-Iturbe et al., 2007].
 Our analysis is based on laboratory measurements of soil water content in the unsaturated zone of biofilters, both with and without a shallow water table. The data are used to fit to humid environments an existent stochastic model developed for arid and semi-arid climates [e.g, Laio et al., 2001]. This model, opportunely modified, takes into account the key interactions between the unsaturated zone, vegetation, and climate, and includes an approximated description of the capillary rise from the saturated to the unsaturated zone. We underline that such a simplified model does not aim at a detailed description of the complex water fluxes occurring in the soil [see, e.g., Ridolfi et al., 2008], but is targeted at showing the mechanism through which the capillary rise might generate two distinct modes in the long term (e.g., steady-state) soil moisture pdf.
 The experimental setup is described in detail by Y. Zinger et al. (The effect of various intermittent dry-wet cycles on nitrogen removal capacity in biofilter systems, paper presented at the 13th International Rainwater Catchment Systems Conference and 5th International Water Sensitive Urban Design Conference, BlueScope Water, Sydney, New South Wales, Australia, 2007) and only a brief summary is reported here for completeness. Four biofilter columns were built in January 2006 in a greenhouse using 375 mm diameter PVC columns, as schematically shown in Figure 1. The columns were filled with 4 levels of different filtration media and seven plants of tall sedge, Carex appressa, were planted in each column [Read et al., 2008]. At the very bottom of the columns, a pipe allows for the control of the water flow, thereby permitting the creation of a 450 mm deep saturated zone. The experiments were done on two columns without saturated zone (−SZ) and two columns with saturated zone (+SZ).
 The experiment consisted of artificially generating wetting and drying cycles of different durations, by dosing at various frequencies the columns with 25 liters of semi-synthetic storm-water. Soil volumetric water content, θ, was measured at 250 mm from the top of the filtration media, using Theta Probes (model ML2x, Delta-T Devices, Cambridge, UK). In one of the columns with SZ, θ was also measured at two depths in the unsaturated zone, 100 and 350 mm respectively. Instruments were sampled every 30 seconds and 10 minutes averages were recorded. In what follows we will often refer to the relative soil moisture, s = θ/n (0 ≤ s ≤ 1), where the effective porosity of the sandy-loam at the top of the columns is assumed to be n = 0.4.
3. Experiment Results
 Soil moisture at 250 mm from the surface behaves very differently depending on whether the underlying saturated zone is present or not. Figure 2 compares soil moisture in soils with and without SZ for two different sequences of wetting and drying cycles. Even when starting at approximately the same soil water content, the columns without SZ experience faster dry-downs, being commonly drier than the columns with SZ. Such a difference is due to capillary rise, which maintains the soil above the water table in a consistently wetter state. This is particularly evident for s≤0.3 during the night, when transpiration losses are very low. In fact, in the columns without SZ, the soil water content keeps decreasing during the night, although at a lower rate, while soil moisture actually increases in the columns with SZ. As the soil dries-down, the water table drops and the depth of the unsaturated zone increases. The effect of the capillary rise thus becomes less significant for the soil near the surface.
 To better show the difference between columns with and without SZ, we analyzed the series of daily averages of the measured soil moisture during the drying periods. The derivative with respect to time of these series may be interpreted as the daily water-loss rate in the soil layer at 250 mm. Figure 3 reports these water losses (e.g., −ds/dt) as a function of soil moisture itself.
 As expected, in the columns without SZ, the rate of water losses increases with s [e.g., Rodriguez-Iturbe and Porporato, 2004]. When soil moisture equals sw, to which we will refer as the wilting point, vegetation is under a strong water stress and transpiration stops. As s grows, transpiration (i.e., −ds/dt) increases approximately linearly from 0 to a value corresponding to the potential evapotranspiration when s = s*. The rate of water losses remains constant at this level for soil moisture values between s* and the field capacity, sfc, above which vertical percolation predominates with a consequent considerable growth in the loss rates.
 In the columns with SZ, this pattern appears greatly modified (Figure 3). When soil moisture is high (the situation commonly associated with a shallow water table) the capillary rise largely compensates the losses due to evapotranspiration and vertical percolation. As soil moisture decreases, accompanied by a consequent water table drop, the capillary rise reduces its effect and evapotranspiration becomes predominant, thereby leading to higher water-loss rates. Below s* the water-loss rates diminish because of the reduced transpiration rate, similar to the columns with no SZ.
 The effect of the capillary rise thus appears to be the generation of a maximum in the water losses for s about s*. This suggests that during a long dry-down from s > sfc to s ∼ sw, soil moisture spends long periods above and below s*, transiting quickly through s = s* (see, for example, Figure 2). By forcing these dynamics with a series of rainfall events, one may reasonably expect that over the long term, unless the climatic conditions are persistently either wet (s > s*) or dry (s < s*), the soil moisture in the unsaturated zone presents pdfs with two preferential states above and below s*, respectively.
4. Stochastic Modeling
 In order to better clarify the dynamics previously discussed, in the following we will empirically adapt the stochastic model by Laio et al. , developed for arid or semi-arid environments, to humid lands. Under the assumption that lateral soil water flows are negligible, as in the case of the columns used in the laboratory, the daily soil water balance at a point can be written as [Laio et al., 2001]
where n is the effective porosity, Zr is a depth over which soil moisture is averaged, I(s, t) is infiltration from rainfall, and ρ[s(t)] represents the (daily) soil water dynamics between rainfall events within the depth Zr.
 In order to use equation (1), ρ[s(t)] and I(s, t) need to be defined. In what follows we present how we modeled such functions.
4.1. Water Loss Function
 Soil moisture at different depths during a dry-down is modeled using Richards equation [e.g., Hillel, 1998]. The results from this detailed simulation permits the evaluation of the water losses (e.g., −ds/dt) at different depths at a fine timescale. Averaging such results over a depth Zr and over the day gives the function ρ[s(t)]. The used version of Richards equation reads
where t is time, z denotes the vertical direction (positive downward), K the hydraulic conductivity, Ψ the soil water potential, and E represents evapotranspiration losses. K and Ψ are assumed to depend on θ according to [e.g., Dingman, 2002]
with Ks and Ψs conductivity and water potential at saturation, respectively, and b a parameter dependent on soil texture. Evapotranspiration E is modeled as E = Ew + T, where Ew is a constant that represents the sum of cuticular transpiration and direct evaporation from the soil, and T = Emax(z)f1(θ)f2(t) is transpiration. Emax(z) is assumed to decrease linearly with depth and is estimated from the time series measured at 100 and 350 mm depths (not shown). The function f1(θ) is a piecewise linear function, increasing from 0 at θw = sw/n to 1 at θ* = s*/n, and remaining constant and equal to 1 for s > s* (see Figure 3). The function f2(t) is a simplification of the daily cycle of transpiration and reads f2(t) = 4/dd2[−t2 + (dd + 2t0) t − t0 (t0 + dd)], where t0 is the time in the morning at which stomata start opening and dd is the number of hours that they remain open.
Equation (2) is solved adopting the method described by Celia et al. . The initial soil water profile was evaluated by fitting the measurements at 100 and 350 mm with saturated conditions at 450 mm. The two measured series were used as boundary conditions for the depths between 100 and 350 mm. The boundary conditions for the upper part were the measured series at 100 mm and soil moisture at the surface. The latter was assumed to decrease because of evapotranspiration up to s = sw, after which it remained constant at this value. Results of this simulation are reported in the auxiliary material.
 The previous analysis allows us to estimate the averaged value of daily soil water content within the top layer of soil of thickness Zr = 350 mm, and thus to estimate the function ρ[s(t)] of equation (1), as shown in Figure 4a (dots). Daily soil water dynamics between rainfall events are schematically due to three components: evapotranspiration, leakage, and capillary rise.
 Evapotranspiration can be modeled as a piecewise function, linearly increasing from sw to s* and remaining constant at the value Ep when s > s*. Leakage is modeled after Laio et al.  as
with β = 2b + 4 (b is the coefficient in equation (3)). Since the water table is considered to be deeper than 450 mm, we assume that, when the unsaturated zone is above field capacity, leakage is very high and overcomes the capillary rise.
 The mathematical description of the capillary rise accounts for the main interactions between the saturated and unsaturated zones. When the unsaturated zone is wet, the water table is shallow, and it gradually drops as the unsaturated zone dries down. For high soil moisture (i.e., s ≈ sfc), the difference in the water potential between the unsaturated and the saturated zones is relatively low, thus limiting upward water movement. As the unsaturated zone becomes drier, capillary rise increases because of the larger difference in the water potential between saturated and unsaturated zone. Contemporarily, the saturated zone loses water and the water table drops. The concomitant occurrence of the water-table deepening and the drying of the unsaturated zone generates a maximum in the capillary rise, which occurs at a soil moisture value between s* and sfc. Below this soil moisture level, the capillary rise reduces to become negligible with respect to transpiration when s < s*. For simplicity and to allow exact results the capillary rise, Cr, is modeled as a parabola (Figure 4a).
 According to the previous considerations, the function ρ(s) can thus be written as
where Cr = 4Emax/[2.5(sfc − s*)2] and L(s) is expressed in equation (4).
4.2. Infiltration and Long-Term Soil Moisture PDF
 We assume that the environmental conditions are similar to those in our experiment. Therefore, the water table never reaches the depth Zr and the soil hydraulic conductivity is very high, so that, at the daily timescale, water ponding is very unlikely to occur. According to these assumptions, the whole amount of water carried by each rainfall event infiltrates the soil, and thus I(s,t) in equation (1) equals rainfall.
 Rainfall is modeled as a marked Poisson process with events occurring at a frequency λ and the water amount per rainfall event is exponentially distributed with average α (see Laio et al.  for more details).
 Because I(s, t) is not known deterministically, the solution of equation (1) is only meaningful in probabilistic terms. Following Laio et al. , the pdf of s can be calculated as
where N is a normalization constant obtained imposing p(s)ds = 1 and γ = nZr/α.
Figure 4b shows three examples of pdfs for increasing values of rainfall frequency calculated using equation (6). Rainfall events induce a sequence of soil moisture decays, which occur at relatively slow rates when s > s* and s < s*, transiting quickly through s ∼ s*. This sequence of slow soil water decays in wet and dry conditions induces the bimodality reported in Figure 4b. As expected, the two distinct modes disappear when the capillary rise term is not include in the dynamics (Cr = 0), as shown in Figure 4b.