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Corresponding author: A. Porporato, Department of Civil and Environmental Engineering, Duke University, Box 90287, Durham, NC 27708-0287, USA. (firstname.lastname@example.org)
 While seasonally dry conditions are typical of large areas of the tropics, their biogeochemical responses to seasonal rainfall and soil carbon (C) sequestration potential are not well characterized. Seasonal moisture availability positively affects both productivity and soil respiration, resulting in a delicate balance between C deposition as litterfall and C loss through heterotrophic respiration. To understand how rainfall seasonality (i.e., duration of the wet season and rainfall distribution) affects this balance and to provide estimates of long-term C sequestration, we develop a minimal model linking the seasonal behavior of the ensemble soil moisture, plant productivity, related C inputs through litterfall, and soil C dynamics. A drought-deciduous caatinga ecosystem in northeastern Brazil is used as a case study to parameterize the model. When extended to different patterns of rainfall seasonality, the results indicate that for fixed annual rainfall, both plant productivity and soil C sequestration potential are largely, and nonlinearly, dependent on wet season duration. Moreover, total annual rainfall is a critical driver of this relationship, leading at times to distinct optima in both production and C storage. These theoretical predictions are discussed in the context of parameter uncertainties and possible changes in rainfall regimes in tropical dry ecosystems.
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 Dry forests cover roughly 17% of tropical and subtropical regions [Holdridge, 1967], playing an important role in providing resources and services, and for sustaining biodiversity. Seasonally dry tropical forests are also considered the most threatened of all tropical forest types [Janzen, 1988] with most of the remaining approximately 106 km2 at risk [Miles et al., 2006]. The development of sustainable management practices for these forests requires a better understanding of their productivity and carbon (C) storage potential. However, such understanding is hampered by the inherent complexity of biogeochemical feedbacks and their responses to climatic drivers. In particular, seasonally dry ecosystems are subjected to extreme rainfall variability [Feng et al., 2013], with severe water limitation during the dry season and enhanced biological activity during the wet season. Total annual rainfall in seasonally dry ecosystems ranges from 250 to 2000 mm, usually distributed over a 4–9 month wet season [Murphy and Lugo, 1986], with primary productivity and biogeochemical dynamics largely driven by this seasonality in precipitation and the related soil moisture dynamics [Jaramillo et al., 2011; Murphy and Lugo, 1986; Feng et al., 2012, Runyan and D'Odorico; 2013]. Annual aboveground litter biomass production in seasonally dry ecosystems ranges from 1.5 Mg ha−1 yr−1 in the drier environments to 12.6 Mg ha−1 yr−1 in the more mesic ones [Martinez-Yrizar, 1995], roughly 50–75% less than a wet tropical forest [Murphy and Lugo, 1986].
 For a particular total annual rainfall, the seasonal distribution of rainfall events—especially the frequency of daily rainfall occurrence—is a dominant driver of primary productivity in these water-limited ecosystems [Fay et al., 2003; Knapp et al., 2008; Porporato et al., 2006]. On the one hand, the effects of changes in rainfall distribution on net primary productivity (NPP) [Feng et al., 2012] propagate to the soil C pools through litterfall and thus affect C sequestration. On the other hand, rainfall distribution impacts soil moisture and thus also regulates soil organic matter decomposition [e.g., Fierer and Schimel, 2002; Miller et al., 2005]. Hence, water availability during the wet season drives both C accumulation through primary production and C loss through respiration, which ultimately balances long-term soil C storage. As a consequence of this trade-off between productivity and respiration, different seasonal rainfall patterns (for a given annual rainfall) might alter the potential C sequestration. Notably, some seasonal patterns that allow plants to efficiently use limited rainfall and optimize production could also maximize C sequestration. In contrast, other less efficient seasonal patterns may result in more respiration than can be compensated by production, thus favoring C losses. Moreover, as climate change is projected to alter seasonal rainfall distributions, with increased dry season length in tropical dry regions [Hulme and Viner, 1998; IPCC, 2007], the question arises whether any shifts in distribution (as well as the total amount) of rainfall can change the balance of production and C storage with respect to current conditions.
 To address these questions and explore the effect of rainfall seasonality on soil C storage in seasonally dry ecosystems, a model is proposed that captures the essential elements of the coupled dynamics of soil moisture, biomass production, and soil C stocks based on a given annual rainfall and its distribution throughout the year. Different from previous works focusing on growing season dynamics [D'Odorico et al., 2003; O'Donnell and Caylor, 2012; Wang et al., 2009], here the whole seasonal cycle, including the alternation of wet and dry seasons, is explicitly included. We estimate the model parameters from available field data and discuss related parameter uncertainties, focusing in particular on the sensitivity to the rooting depth, C decomposition rate, and soil moisture thresholds. Based on the proposed model, the seasonal rainfall patterns that allow highest ecosystem productivity and C storage are quantified. We conclude by discussing the implications of predicted changes in seasonality and rainfall on these ecosystem fluxes and pools.
 To describe the hydrologic controls on the mean behavior of plant production and soil C cycling including both seasonal and intraseasonal random variability in rainfall, a stochastic hydrologic model is coupled to an ecosystem-level C cycle model. The hydrologic model first determines the seasonal variations in average soil moisture, from which biomass production is calculated. Productivity fuels the soil C pool, which is in turn depleted by moisture-dependent heterotrophic respiration. Limiting our description to tropical seasonally dry ecosystems ensures that temperature seasonality may be neglected compared to rainfall variability. Moreover, while nutrient limitations are important, their seasonal effect may be assumed to be decoupled from that of water availability. Thus, while we do not neglect nutrient limitation per se, we assume that it affects the long-term average fluxes instead of the seasonal ones. That is, different nutrient levels may alter model parameters (such as the plant growth rate and the maximum decomposition rate), but temporal changes are assumed to be driven by fluctuations in soil water content. The same rationale also applies to temperature, which might vary across sites, but tends to remain stable throughout the year in tropical regions. Fluxes and variables are defined in Figure 1 and Tables 1 and 2.
Table 1. Summary of Seasonally Variable Parameters (Subscript i Refers to Either Dry or Wet Season)
Mean event frequency
Ensemble average daily rainfall rate
Table 2. Summary of Seasonally Invariant Parameters
 A stochastic soil water balance is used to capture the key soil-water interaction in a simplified framework valid at the daily time scale [Rodríguez-Iturbe and Porporato, 2004]. Soil moisture at a point is lost to evapotranspiration, runoff, and leakage while being recharged by intermittent rainfall pulses of random depth (Figure 1). When vertically averaged over the rooting depth, Zr, the soil moisture balance becomes [see Porporato et al., 2004; Laio et al., 2001; Daly et al., 2004a, 2004b]
where wo is the maximum effective plant available soil moisture capacity per unit ground area, equal to (s1 − sw)nZr, is the effective plant-available soil water with s the relative volumetric water content, sw is the plant wilting point, and s1 is the point above which soil water is assumed to be immediately lost to leakage and runoff (i.e., the actual infiltration rate is bounded by the available pore space). R is the rate of precipitation, ET is evapotraspiration, and LQ is the rate of leakage/runoff.
 The rainfall regime is modeled as a marked Poisson process with interarrival times of rain events drawn from an exponential distribution of mean (e.g., 1/day) and rainfall depth drawn from an exponential distribution of mean α (e.g., mm) [Porporato et al., 2004; Rodriguez-Iturbe et al., 1999], so that the average daily rainfall rate is λα. For simplicity, we assume rainfall depth (α) to be seasonally invariant, leaving temporal changes in rainfall frequency (λ) as the controlling parameter of rainfall seasonality. In particular, the rainfall frequency in the dry season (λd) is assumed constant across all seasonal variations, such that all dry seasons are similar in their daily rainfall rate and variable only in duration. Thus, for a given annual rainfall, the longer the dry season, the more concentrated the rainfall in the wet season. The rainfall frequency in the wet season is modeled using a symmetric triangular distribution
where Td and Tw are the durations of the dry and wet seasons, respectively, and the hydrologic year is assumed to start with the dry season. This rainfall model provides a minimal, yet realistic representation of the temporal distribution of empirical mean rainfall rates in seasonally dry ecosystems (see Figure 3a).
 Due to the stochastic nature of the rainfall regime, we interpret seasonal changes in soil moisture, plant productivity, and soil C in an ensemble-average sense over the rainfall variability [see Feng et al., 2012]. Thus, for example, the probability density function of effective soil moisture x ∈ [0,1] will be indicated as p(x,t), and its ensemble average as . An ensemble average of a generic variable u ∈ [umin,umax] over a period T is denoted by . For instance, the mean annual C concentration is expressed as , and the mean annual rainfall rate is .
 The macroscopic stochastic equation describing the temporal evolution of the ensemble average of the effective soil moisture is [Laio et al., 2002; Feng et al., 2012]
in which γ=w0/α, and the terms on the right-hand side of the equation are the ensemble averages of rainfall input and soil moisture losses. Thus, equation (3) can be written as
ET(x,t) is modeled as a linear function of x, ranging from 0 to ETmax(t), the seasonally dependent maximum evapotranspiration, as x increases from 0 to 1 [Porporato et al., 2004; Feng et al., 2012]. Accordingly, the evapotranspiration term of equations (4) and (5) can be written as,
 The runoff/leakage term, LQ, can be approximated as [Feng et al., 2012]
which is a closed-form nonlinear differential equation forced by periodic rainfall inputs (through λ(t)) and outputs (through ETmax(t)). Equation (8) can be solved numerically for periodic statistically steady-state conditions. Figure 2a shows the general seasonal trend in the time evolution of the ensemble average of the effective soil moisture for two seasonal variations using parameters described later in section 2.5 and Tables 1 and 2.
2.2 Biomass Growth
 To describe the effects of soil moisture on plant productivity, we follow previous work linking plant C assimilation and productivity to soil moisture [Daly et al., 2004b; Porporato et al., 2004; Feng et al., 2012]. We assume that mean plant C assimilation is unrestricted by water availability and maintained at maximum capacity when mean soil moisture is above the threshold x*. As the mean soil moisture declines below x*, stomata progressively close until transpiration and net average plant growth rate, B (g C d−1 m−2), cease at the wilting point, xw, such that
in which Bmax (g C d−1 m−2) is the maximum daily growth rate, which already accounts for plant respiration (see section 2.5). We assume that temperature is not a limiting factor in these tropical ecosystems and that the effects of nutrient limitation are controlled only by Bmax (i.e., nutrient-rich sites would have higher Bmax). Coupling biomass productivity (equation (8)) with the stochastic soil moisture model of section 2.1 allows for computing the temporal evolution of the ensemble mean rate of biomass production, B. Figure 2b illustrates the general seasonal trend of the plant biomass production rate, for two seasonal variations based on parameters described in section 2.5 and Tables 1 and 2. Moreover, B is integrated over a year to compute the NPP (g C m−2 yr−1), which is in turn used as the input to the C pool through litterfall during the dry season. We focus here on productivity rather than plant standing biomass, which is assumed to be at steady state—i.e., Bmax is constant through time. This assumption is justified in natural, undisturbed dry forests as well as in aggrading forests where the rate of biomass increase is stable through time, for instance due to water (rather than leaf or root biomass) limitation.
2.3 Soil Carbon
 Using a single soil C compartment, the mean soil carbon balance equation can be expressed as (Figure 1),
where C is the concentration of soil carbon expressed in mass of soil organic C per unit volume of soil, ADD is the mean carbon input from plant litterfall (distributed over the depth Zr), and RESP represents the mean heterotrophic respiration from soil organic carbon decomposition.
 Because here we focus on large spatial scales and neglect patch-scale heterogeneities [see to this regard O'Donnell and Caylor, 2012; Wang et al., 2009] and consider time averaged dynamics, a linear model for RESP is justified [Manzoni and Porporato, 2009]. By averaging the daily fluctuations, the short-term pulses of respiration that may be responsible for a large fraction of the annual soil C balance [e.g., Carbone et al., 2011] are accounted for in an ensemble-average sense. In other words, each year, respiration pulses trigger large C losses at different times during the year, but when averaging across years, the changes in respiration through time are more regular and allow for a simplified mathematical treatment. At these scales, soil microbial biomass can be assumed to be in equilibrium with soil C, so that C is the main driver of respiration [Manzoni and Porporato, 2009; Olson, 1963]. As moisture decreases, the decomposition rate also decreases from the maximum rate (kC,max) due to reduced substrate diffusivity and water stress [Manzoni et al., 2012]. Thus, assuming that the first-order decay rate depends linearly on mean soil moisture content [e.g., Rodrigo et al., 1997],
 Because we focus on tropical seasonally dry ecosystems, temperature can be assumed not to be limiting, whereas soil moisture availability can be regarded as the most constraining environmental factor. In dry forest ecosystems, the majority of decomposition takes place during the rainy season [Martinez-Yrizar, 1995]. Moreover, peak decomposition occurs near field capacity, x = 1, at which both water and oxygen availabilities are near optimal [Moyano et al., 2013].
 Typically, in tropical seasonally dry ecosystems, the majority of leaf fall and thus litter input to the soil occurs when rainfall is at a minimum, after the end of the growing season [Martinez-Yrizar, 1995; Murphy and Lugo, 1986] (see section 3.2 for specific data on the case study location). To capture this pattern, the rate of litter input, ADD, is assumed to increase linearly from zero at the start of the dry season before beginning a symmetric linear decline after the midway point of the dry season. The total maximum litterfall is computed such that the total litter deposition equals NPP/Zr, or the rate of biomass production integrated over the rooting depth, assuming that this is the soil depth where the bulk of C residue is also located. The assumption that all C fixed through photosynthesis on an annual basis is transferred to the soil is justified by the limited C resorption during leaf senescence (approximately 20% resorption in tropical ecosystems, [see Vergutz et al., 2012]), which is further reduced to about 6% on a whole plant basis. Thus, the complete soil C mass balance reads,
 For illustration, the time series of soil C simulated over two years, for two seasonal variations, are shown in Figure 2c.
2.4 Field Data
 Soil samples from the wet and dry seasons along with mean monthly rainfall and litterfall data from a caatinga ecosystem were obtained at the Fazenda Tamandua in the state of Paraiba (Northeastern Brazil) and will be used to parameterize the model (section 2.5) and test the piecewise linear approximations to the rainfall and litterfall inputs (section 3.2). The site is a composite of natural preserve (approximately 30% of the original caatinga), intensive organic agriculture and mixed caatinga, and open pasture. The caatinga ecosystem is an expanse of seasonally dry mix of semiarid thorn scrub and deciduous forest that covers 735,000 km2 in Northeast Brazil. Tall caatinga forests are now scarce, small, and fragmented [Prado, 2003], with the landscape predominated by branched and spiny shrubs, succulents (especially Euphorbiaceae), bromeliads, and cacti.
 The hydroclimatic conditions of the Fazenda Tamandua are characterized by prolonged dry seasons (approximately June to January) followed by short wet seasons characterized by intense rainfall events (February to May). Rainfall data, collected over 70 years from a meteorological station close to Fazenda Tamandua (at Santa Terezinha, 7.11°S, 37.45°W; source: SUDENE), show that while receiving on average 741 mm of rainfall annually, large interannual fluctuations around the mean occur. Over the span of record, the wettest year occurred in 1985 with 1.775 m of rainfall, while the driest, 1958, saw only 228 mm and the region has experienced a significant standard deviation of 294 mm of annual rainfall.
 The rainfall data collected at Santa Terezinha were averaged on a monthly basis (Figure 3a). The data were then fit to a piecewise linear regression function representative of the modeled distribution pattern. The average rainfall rates in the dry and wet seasons are, respectively, 0.3 and 3.8 mm d−1, while the average wet season length is Tw =182 days. (Figure 3a)
 Estimation of NPP was based on litterfall data collected over four years in 72 litter traps placed within plots at different stages of vegetation recovery after pasture abandonment. For each stage of recovery (16, 38, or 50+ years of regeneration), three 1000 m2 (20 × 50 m) plots were established; within each plot, eight litter traps with 0.5 m2 of area (0.5 × 1 m) were placed and arranged in two transects, each containing four traps with a distance of 7.5 m between traps and 10 m between the transects. The traps were made of nylon cloth with 0.5 mm mesh size and a frame of PVC tubes standing 0.4 m above ground. Litter collection was carried monthly, separately for each trap, and taken to the laboratory to be air dried, sorted as “leaves,” “wood,” or “miscellaneous” and weighed.
 Here we use the average seasonal pattern from these plots to obtain a representative estimate for the whole range of age classes present at Fazenda Tamandua (Figure 3c). Litterfall (including woody components) averaged 524 g m−2 yr−1on a dry weight basis, or assuming 50% carbon content [Clark et al., 2001], roughly 262 g C m−2 yr−1. In addition to leafy and woody components collected by the litter traps, allometric relations suggest an increase by a factor of about three halves to account also for root turnover [Niklas and Enquist, 2002], leading to a total NPP of roughly 392 g C m−2 yr−1. These productivity values are in line with other neo-tropical dry forests receiving comparable amounts of rainfall [Jaramillo et al., 2011].
 Finally, composite soil samples taken from the topsoil during the wet and dry seasons in the three most mature plots were used to estimate soil organic C concentrations. For this, in each of the three mature plots, eight soil samples were collected from the 0–15 cm soil layer using a soil-sampling shovel. The sampling points were determined a priori and were placed at a distance of 1 m from each of the eight litter traps. The samples were taken to the northern side of the traps in the wet season and to the southern side in the dry season. Carbon concentration averaged 12.89 g C kg−1 of soil in the dry season and 11.44 g C kg−1 of soil in the wet season. Assuming an intermediate bulk density for a sandy loam, typical to the region, of 1.4 g cm−3 [Meek et al., 1992], yields soil C concentrations of approximately 1.8 × 104 g C m−3 in the dry season and approximately 1.6 × 104 g C m−3 in the wet season for an annual average concentration of 1.7 × 104 g C m−3, a value slightly lower than in other deciduous neo-tropical dry forests [Jaramillo et al., 2011].
2.5 Model Parameterization
 Numerical values for model parameters representative of seasonally dry ecosystems are reported in Tables 1 and 2. The parameters are assumed either to be invariant annually or vary between the wet and the dry seasons. For the most part, the seasonally invariant parameters describe biogeochemical processes while the seasonally varying parameters describe the seasonal hydroclimatic forcing imposed on the ecosystem. The model sensitivity to key parameters is assessed in section 3.3.
 All results refer to a loamy soil with porosity n=0.45 [Laio et al., 2001]. Representative soil moisture thresholds for this soil were chosen (after Laio et al.  and Porporato et al. ) as s1= 0.8, sw = 0.2 and x* = 0.4, while we assumed a rooting depth Zr=0.35 m—a typical value for dry tropical savannas [Jackson et al., 1996].
 Beyond the parameters assumed to be variable to control the rainfall seasonality (Tw and 〈Ryr〉), the other hydroclimatic parameters are assumed constant. In particular, based on the available rainfall time series, we approximate the mean rainfall depth and frequency in the dry season by α=15 mm and λd=0.02 events per day. Maximum evapotranspiration rates are computed using the Penman-Monteith equation [Brutsaert, 2005] for the vegetated fraction of the surface, and assuming equilibrium evaporation rate from the bare soil fraction [Kelliher et al., 1995]. In absence of more detailed information, we assumed a bare soil fraction of 10% in the wet season and of 30% in the dry season, and a wet-season leaf area index of 1.5 m2 m−2 (consistent with similar dry forests in Brazil [see, Miranda et al., 1997; and Bucci et al., 2008]). Time averaged net radiation, air temperature, and wind speed were obtained from a meteorological station installed at Tamandua in March 2011. The sensitivity of stomatal conductance to vapor pressure deficit was obtained from Bucci et al. . As a result, ETmax,w and ETmax,d were obtained as 5.9 and 4.7 mm d−1, respectively.
 The maximum rate of carbon decomposition is approximated using the data discussed in section 2.4. The annual carbon input received through litterfall and root turnover is equal to approximately 392 g C m−2 yr−1 or, assuming the bulk of residue production is distributed over the rooting depth (ZC=0.35 m) and converting to cubic meters per day, approximately 3.07 g C m−3 d−1. The annual mean rate of C decomposition, 〈kC〉, can be estimated by dividing the annual carbon input by the steady-state C concentration (1.7 × 104 g C m−3), yielding a value of 1.8⋅10−4 d−1. Because the annual mean soil moisture modeled with Tamandua rainfall data (section 3.2) is approximately 0.3, assuming 〈kC〉 = kC,max 〈x〉, we can approximate kC,max = 6.0 × 10−4 d−1. Compared to a tropical savanna, the obtained value is intermediate between the rates of litter and organic matter decomposition [D'Odorico et al., 2003], lending support to our estimate. However, because spatial and biogeochemical heterogeneities, both within a site and across sites, may affect the value of kC,max, model sensitivity to this parameter is discussed in section 3.3.2.
 The maximum daily NPP, Bmax, can be estimated in two independent ways: (i) based on ecosystem-level net C exchanges, and (ii) based on leaf-level photosynthesis, scaled up to the whole canopy. Assuming a maximum gross plant C uptake of roughly 4 mol CO2 m−2 d−1 computed from the first approach [Miranda et al., 1997] and accounting for a 50% reduction due to plant respiration [Cannell and Thornley, 2000], this leads to Bmax= 2.4 g C m−2 d−1. Following the second approach, Bmax is calculated by multiplying leaf-level light-saturated photosynthesis (roughly 10 µmol CO2 m−2 d−1 [see Franco et al., 2005]) by the leaf area index (about 1.5 [see Miranda et al., 1997; Bucci et al., 2008]), and after accounting for the daily cycle of solar radiation (reduction of the light-saturated rate by about 50%) and plant respiration (50% carbon use efficiency as before), we obtain Bmax = 2.0 gC m−2 d−1. Hence, depending on leaf area index and nutrient availability, Bmax may range between 1 and 3 gC m−2 d−1. To support this approximation, in the particular case of Tamandua, we found that when considering measured rainfall data from Santa Terezinha averaged over 70 years (see section 2.4), our model requires Bmax = 2.0 g C m−2 d−1 to match the NPP measured in the field (392 g C m−2 yr−1). While this value is in line with our estimates, this specific value will be used only in the analyses specifically involving the Fazenda Tamandua ecosystem (Figures 3, 5, 6, and 7). In the other analyses (Figures 2 and 4), an average value of Bmax = 2.2, found by averaging our independent estimates (2.4 and 2.0), will be used. However, since the values of Bmax could vary significantly from site to site, model sensitivity to this parameter will be discussed in section 3.3.
3 Results and Discussion
3.1 Annual Cycles of Production and Soil C
 Using the parameters described in section 2.5, and summarized in Table 1 and 2, and assuming a constant total annual rainfall of 700 mm, the model was first analyzed for two hypothetical rainfall regimes—one characterized by a short wet season of 100 days and the other by a long wet season of 200 days. Note that because total rainfall is maintained constant, the rainfall frequencies for the wet season in the two cases are different, with higher frequencies occurring in the short wet season. Figure 2 shows the temporal evolution of the ensemble average soil moisture, plant productivity, and soil C concentration for both seasonal variations beginning from the start of the hydrologic year (defined here as the onset of the dry season) and through two years of the annually periodic cycle.
 The average soil moisture quickly decreases at the start of the dry season and remains low in both scenarios until the onset of the rainy season (Figure 2a). Because rainfall is more concentrated in the case of the short wet season, soil moisture reaches a higher seasonal peak than in the long wet season regime; however, more time is spent in conditions of water stress if the wet season is shorter. Figure 2b presents the evolution of the plant productivity: while the condition 〈x(t)〉 ≥ x* is desirable for maximum productivity, additional water inputs above x* do not further enhance productivity, whereas the mean leakage and runoff increase. As a result, a shorter growing season results in higher soil water content for a short time, during which productivity is high but mean annual NPP is lower than when rainfall is more evenly distributed. However, excessively low rainfall rates, even over a long period, cannot sustain high productivity because soil moisture does not reach x*. These two contrasting scenarios suggest that some intermediate wet season durations and rain intensities likely maximize 〈NPP〉. This trade-off is further discussed in section 3.3.
 Figure 2c illustrates the temporal evolution of soil C for the same two seasonal scenarios. Soil C accumulates during the dry season when litter is deposited, and low soil moisture levels restrict heterotrophic decomposition, whereas it declines during the wet season when litterfall ceases and high levels of soil moisture support fast decomposition. The magnitude of the mean annual C concentration is largely driven by 〈NPP〉, which enters the C mass balance as litterfall. Accordingly, lower 〈NPP〉 such as in the short wet season case lowers the mean C storage, even for the same annual rainfall.
3.2 Application to the Caatinga Ecosystem
 In the caatinga ecosystem of the Fazenda Tamandua, the rainfall trends are first compared to the litterfall data in Figure 3a. A peak in litterfall occurs roughly 120 days after the peak in rainfall, and well into the dry season, which closely corresponds to the period of minimum rainfall, as also shown in other studies [Jaramillo et al., 2011; Martinez-Yrizar, 1995]. Over two months, more than 40% of the 524 g m−2 yr−1 of total annual litterfall has fallen. This relatively concentrated litterfall duration and the fact that during the dry season soil moisture limitations inhibit decomposition justify our approximation that litter input is limited to the dry season and concentrated toward the center of the dry period.
 To further assess the validity of the proposed input distributions, we compare the temporal evolution of soil moisture and soil C using measured data against those forced with the modeled triangular distributions. In the case driven by data, linearly interpolated monthly rainfall and litterfall field data from the Fazenda Tamandua (section 2.4) are used as rainfall and soil C inputs to the numerical model. In the latter theoretical case, the modeled distributions described in sections 2.1 and 2.3 are used for rainfall and soil carbon inputs.
 Despite simplifications to the input data (see Figures 3a and 3c), the trajectories resulting from modeling using the interpolated or empirical input distributions (Figures 3b and 3d) yield very similar mean yearly soil moisture and soil C, as well as similar trends in their temporal evolution. Also, the occurrence of the maximum in soil C during the dry season is consistent with the observed seasonal pattern at Fazenda Tamandua (section 2.4). The only significant qualitative differences are a small shift in peak carbon toward the wet season and a slightly higher amplitude in the soil carbon trend driven by the modeled input distributions (see Figure 3d). Both of these discrepancies are related to the simplified timing of litter distribution, but do not significantly affect mean annual values. Thus, in what follows, we will focus on the annual average C concentration, , and explore its dependence on rainfall seasonality.
3.3 Effect of Seasonality and Optimal Plant Conditions
 Here we explore the effects of seasonality on annual NPP and mean soil C by varying rainfall intensity and seasonality, while keeping the other parameters fixed. For given total annual rainfall, changes in the length of the wet season, Tw, result in large quantitative differences in C cycling patterns (see Figure 2), leading to the possible existence of favorable seasonal durations in terms of maximum production and mean annual soil C. Furthermore, attributes of these optima are largely driven by total annual rainfall. Thus, we will examine seasonal trends not only within a particular annual rainfall but also across a range of annual rainfall inputs. We limit the wet season to a period of at least 20 days to ensure a distinct seasonality. Moreover, because rainfall rates in the dry season are fixed and ETmax,w is greater than ETmax,d, we limit our exploration to annual rainfall rates high enough so that soil moisture in the dry season never exceeds that in the wet season (i.e., 〈Ryr〉 ≥ 0.2 m yr−1). Finally, rainfall is also kept lower than an upper limit (〈Ryr〉 = 1.2 m yr− 1) over which certain seasonal variations cause little to no annual water stress, creating an inherent lack of seasonality.
 We are now in a position to explore how total annual rainfall and its seasonal distribution control plant productivity, possibly giving rise to maxima in 〈NPP〉. Figure 4a illustrates the effects of the annual rainfall rate, 〈Ryr〉, and wet season duration, Tw, on 〈NPP〉 by plotting six traces of 〈NPP〉 as a function of Tw for six annual rainfall rates. At high annual rainfall rates, 〈NPP〉 increases almost linearly as the wet season is extended. In these scenarios, total annual rainfall is high enough to prevent water stress throughout the wet periods; thus, any shortening of the wet season only increases losses to runoff and deep percolation while lengthening the dry period. However, as annual rainfall (and thus rainfall frequency) decreases, the trend begins to lose its linearity. Lengthening the wet season still increases production, though at a declining rate as there is not sufficient rainfall to maintain maximum growth for the duration of a long wet season. In other words, even during the “wet” season, water availability becomes insufficient to sustain maximum production. Hence, as annual rainfall continues to decrease any wet season longer than a particular optimum yields no further growth, but rather hinders production. At this optimum, the active growth period is maximized while water losses by percolation and runoff are minimized (see Figure 4a).
 At these low to moderate rainfalls, as 〈Ryr〉 increases, the magnitude of the maxima increases roughly linearly. Moreover, the maxima are achieved with longer and longer wet seasons, until rainfall is high enough (〈Ryr〉 ≈ 0.6 m yr−1—the third darkest line in Figure 4a) to sustain high production throughout the whole year. At this point, a longer wet season is always favorable, and any further precipitation input only increases the rate at which production benefits from a lengthened rainy season.
 Previous theoretical studies have also reported peaks in production under an optimal rainfall distribution. Daly et al. [2004b] and Feng et al.  have shown the development of similar peaks using comparable models on carbon assimilation and biomass production, respectively. Furthermore, empirical studies linking precipitation to primary productivity have shown that NPP can vary greatly among ecosystems despite comparable annual rainfall [Huxman et al., 2004; Martinez-Yrizar, 1995; Knapp and Smith, 2001], suggesting a role of seasonal rainfall distributions. The range of production levels found by Huxman et al.  is comparable to results from our model. For instance, with 600 mm of total annual rainfall, the model predicts a range of 〈NPP〉 approximately equal to 230 to 500 g C yr−1 m−2. Huxman et al.  report NPP in the order of 150 to 450 g C yr−1 m−2 (converting dry weight to C by assuming 50% C concentration in plant tissue and accounting for belowground productivity through an allometric factor of 3/2). Moreover, assuming that the Huxman et al.  data do not entirely account for woody matter, the allometric factor would increase and the data would even more closely approach the modeled range.
 It is also important to understand how biogeochemical variability (in soil texture, vegetation type, resilience to drought, etc.), expressed through the model parameters, affects these trends. Increasing the value of Bmax (as would be the case in nutrient-richer conditions) shifts the productivity values upward, while leaving their shape qualitatively unaffected. Conversely, increasing the threshold on water stress, x*, leads to declines in mean production. Additionally, adjusting this threshold alters the relation between production and wet season duration. Namely, as x* is increased, the optimal production occurs at shorter wet season durations, because higher daily rainfall rates in the wet season are needed to reach maximum rates of plant growth (for a given 〈Ryr〉). Likewise, x* is linked to the magnitude of annual rainfall required at the production peak. Larger x* in fact implies that more rainfall is needed for plants to reach maximum production throughout an extended wet period. It is important to note, however, that such variations in these parameters do not affect the nature of the trends obtained here.
3.3.2 Soil C Storage
 Similar to biomass production, particular seasonal patterns of rainfall may be “optimal” with regard to the mean annual soil C concentration, (Figure 4b). In fact, while increasing NPP positively affects C input via litterfall, higher soil moisture levels also increase C output via respiration. The competing effects of soil moisture on plant productivity (thus litterfall) and respiration complicate the relationship between wet season length, Tw, and , leading to a nonlinear relationship between and Tw.
 For the same six annual rainfall rates plotted in Figure 4a, is plotted as a function of Tw in Figure 4b. At higher rainfall levels (solid black line), an initial lengthening of the wet period leads to a decrease in C stocks, but as the wet season is further extended C stocks start rising. In this scenario, slightly extending a very short wet season increases mean annual soil moisture, , positively affecting respiration more than 〈NPP〉, such that declines. As the lengthening of the wet season continues, water is used more efficiently, increasing 〈NPP〉, while increases at a declining rate. Thus, higher 〈NPP〉 begins to outweigh changes in respiration, causing C accumulation and to rise at an almost linear rate. However, as annual rainfall decreases, the initial dip in diminishes, and eventually disappears. This pattern is due to the fact that short wet seasons concentrate rainfall and stimulate production more than respiration. Moreover, similar to the trend in production, as rainfall is decreased, begins to decline during extended wet periods, and an optimal seasonality is established which appears at a shorter and shorter wet season length with decreasing rainfall (Figure 4b).
 Furthermore, for all levels of annual rainfall, the seasonality marking the transition to declining gains in C stocks corresponds to that which optimizes production. The convergence of these optima suggests that the effect of seasonal rainfall distributions on NPP is a more critical driving factor of C stocks than the effect on decomposition. Using a more complex coupled hydrologic-biogeochemical model to assess the effect of woody plant encroachment on C stocks in arid regions, O'Donnell and Caylor  also found that while a change in vegetation structure affects both productivity and decomposition, the effect on productivity appeared to be the driving factor of changes in C stocks.
 Similar to 〈NPP〉, the wet season duration associated with peak increases with rainfall; however, the magnitude of peak does not consistently increase. Up until roughly 600 mm yr−1, increasing rainfall rates improve at the optimum. However, further increasing annual rainfall does not permit the C input to outweigh respiration; thus, the magnitude of at all seasonalities begins to decline. Eventually, at very high rainfall levels, respiration rates heavily outweigh diminishing gains in 〈NPP〉 and mark a transition away from seasonally dry ecosystems. Hence, different rainfall distributions during the hydrologic year may lead to increased or decreased C stocks as mean rainfall increases. When the wet season lengthens proportionally to the increase in mean rainfall, C stocks may remain steady or increase, as observed along the Kalahari transect [Ringrose et al., 1998]. However, if the wet season duration changes little and only rainfall intensity increases, C stocks are often predicted to decrease. The combined effects of Tw and 〈Ryr〉 are further discussed in section 3.3.3 in the context of climate change and plotted in Figure 6.
 Before discussing in depth the potential implications of seasonal changes in rainfall, it is important to understand how model parameterization could affect the trends in C stocks. First, the parameters discussed in relation to production have no effect on mean soil moisture values; thus, their influence will only be propagated to C stocks indirectly through their effect on production, as discussed in section 3.2.1. The most important direct control on C stocks is the decomposition rate, kC,max. As expected, increasing the rate of decomposition dramatically lowers across all seasonal patterns, for any given annual rainfall. Although kC,max is an empirical coefficient approximating the effects of a large number of edaphic characteristics, it is helpful to understand how ecosystems with varying decomposition levels react to seasonal shifts. Changing kC,max affects the sensitivity of to mean soil moisture at a fixed C input from NPP—causing lower sensitivities to hydrologic changes when kC,max is higher (not shown).
 Mean rooting depth also plays an important role to define soil C storage, because it alters the soil hydrologic regime [Rodríguez-Iturbe and Porporato, 2004; Guswa, 2010]. In Figure 5, we explore the effect of rooting depth for different climatic scenarios (though assuming the bulk of C residue remains distributed over the same 35 cm). We start by looking at the average scenario from Tamandua (dashed black line in Figures 5a and 5b). Increasing the rooting depth reduces until around 50 cm, while it improves C storage thereafter. In Figure 5a, the annual rainfall rate is decreased, while maintaining Tw = 182 days, whereas, in Figure 5b, Tw is decreased while maintaining 〈Ryr〉 = 0.74 m. These minima in soil C storage are due to soil moisture favoring respiration more than production at intermediate Zr. Moreover, the values of Zr at the minimum depend on the climate. The existence of a climate-dependent optimal rooting depth is supported by previous results [Guswa, 2010] showing that intermediate rooting depths may maximize productivity. Here we suggest that maximizing productivity does not lead necessarily to larger C stocks because respiration could balance C inputs and possibly lead to minima in C storage at intermediate Zr.
3.3.3 Potential Effect of Climatic Changes on Soil C
 Climate change projections for the tropics predict increased dry season length and decreased annual rainfall, and hence decreased mean soil moisture [Hulme and Viner, 1998; IPCC, 2007]. Figure 6 shows how these changes, isolated or in tandem, affect the predicted C stocks in the caatinga at Fazenda Tamandua (currently characterized by Tw = 182 days and 〈Ryr 〉= 0.74 m, indicated by TAM in Figure 6). It is first important to note that seasonality at this site is not optimal for C storage at the moderate annual rainfall rate of 0.74 m yr−1, so that longer wet seasons could improve C stocks (Figure 6). Extending the dry season by 20% without decreasing rainfall, thus shortening the wet season and intensifying the rain events, leads to lower C storage, from = 1.70 × 104 g C m−3 to = 1.63 × 104 g C m−3 (scenario TAMA). In contrast, lowering the annual rainfall rate without increasing Tw increases storage to = 1.88 × 104 g C m−3 (scenario TAMB). The short, suboptimal wet season durations at the Fazenda Tamandua do not allow using rainfall efficiently. Hence, decreasing annual rainfall without a change in wet season duration will lead to lower losses to leakage and runoff and only a mild decrease in NPP. On the other hand, decreasing annual rainfall will still lower decomposition rates accounting for the overall improvement of C stocks in ecosystems with suboptimal Tw. Assuming for the sake of comparison that a 20% decrease in rainfall would be linked to a 20% decrease in Tw, a small mitigating effect would appear, leading to an only slightly improved = 1.77 × 104 g C m−3 (scenario TAMC in Figure 6). Thus, it appears decreasing rainfall from current average conditions at Fazenda Tamandua, even if associated with some lengthening of the dry season, would increase soil C stocks because of reduced decomposition and better rain use efficiency in the wet season, despite slightly reduced productivity driven by the prolonged dry period. It should be noted that the proposed model neglects photodegradation, which could become an important component of C losses as vegetation cover decreases [Austin and Vivanco, 2006]. When this pathway is important, the C storage at low rainfall could be lower than predicted. In other savanna ecosystems, soil C tends to correlate positively to mean annual rainfall [Ringrose et al., 1998]. Our model also predicts this pattern if increases in rainfall (from the conditions identified by TAM in Figure 6) are matched by a sufficiently rapid lengthening of the wet season.
 It is important to emphasize that the effects on soil C due to shifts in seasonal distributions and rainfall rates are highly dependent on the initial hydroclimatic regime. In Figure 7, we start with either the average seasonal scenario at Fazenda Tamandua (Tw=182 days, Ryr=0.74 m yr−1) or a drier scenario at Fazenda Tamandua (with the same Tw for the sake of comparison) comparable to the recorded years of minimal annual rainfall (Ryr=0.3 m yr−1, Tw=182 days). Based on these two scenarios, is shown as a function of declining Tw or 〈Ryr〉. As discussed above, decreasing the wet season length from the average scenario (thin dashed gray line in Figure 7) slowly reduces while decreasing rainfall actually improves C stocks (thin solid gray line). However, the opposite effect occurs when starting from the drier case. Here, slightly decreasing Tw (dashed black line) concentrates rainfall, leading to improved water use efficiency and increased NPP despite small changes in mean soil moisture (thus respiration) resulting in slight gains in C storage. On the other hand, decreasing rainfall (thick solid black line) would hinder already low production to the point that despite a reduction in respiration, C stocks would also decrease due to a significant decrease in C input. It is important to note that in both scenarios, the reduction of both Tw and 〈Ryr〉 results in little change in C stocks, as also shown in Figure 6.
 In a modeling study, Wang et al.  also found different sensitivities of long-term soil C storage to changes in rainfall amounts, depending on the presence of woody vegetation and the initial rainfall patterns. In relatively mesic savanna sites, C was lost when rainfall decreased, whereas in drier sites, some C gains were predicted in under-canopy environments. Thus, in addition to the combined, and potentially mitigating, effects of declining rainfall and increasing dry periods, the initial hydroclimatic regime of a particular ecosystem is important in predicting the effects of shifting seasonal distributions. Consideration of future changes in soil C storage will have to account for both the current climatic conditions and the direction and extent of future changes.
 Using a minimal model of coupled water and C fluxes we assessed the relations between biomass growth, soil carbon cycling, and rainfall seasonality in tropical dry forests. We quantified the trade-off between annual productivity and soil respiration (both affected by water availability, but in contrasting ways) and described the resulting patterns in soil C storage as rainfall patterns shift.
 Our results suggest that, for a given annual rainfall, there is a rainfall seasonality that maximizes plant productivity. Wet seasons longer than this optimum lead to lower daily rainfall frequencies that cannot sustain soil moisture levels high enough to overcome water stress and achieve maximum production. In contrast, wet seasons shorter than the optimum are characterized by high leakage and runoff, limiting plant-available soil moisture. Consequently, as annual rainfall increases, maximum production occurs at an increasing wet season duration that minimizes losses to leakage and runoff created by high daily rainfall rates. Annual mean C concentrations exhibit more complicated trends. Increasing soil moisture is associated with both increasing production (and hence C input through litterfall) and respiration, the balance of which ultimately determines C storage in these water-limited ecosystems. For a given rainfall, very short wet seasons favor respiration over NPP, causing low C storage. However, as the wet season is lengthened, the balance is shifted toward C accumulation via rapidly increasing NPP. Soil C levels increase until production is maximized, and further increasing wet season length beyond this point decreases both production and . As with NPP, the optimum wet season duration corresponding to the maximum in production increases with annual rainfall.
 Predicted future shifts in rainfall regimes toward longer dry seasons and lower annual rainfall will alter the balance of productivity and respiration. If dry season length increases and rainfall remains stable, soil C depletion would likely ensue (however, in some cases, soil C could improve depending on the initial hydroclimatic state). In contrast, if dry season length remains constant but the annual rainfall rate declines, soil C could increase or decrease, depending on initial conditions. While highly productive ecosystems will likely only experience declining C storage with predicted climate shifts, those currently operating well below peak production could potentially see improved C stocks with the onset of declining rainfall due to reduced soil respiration.
 We would like to acknowledge the Pratt Fellows program of Duke University for providing funding to TR. Funding was provided in part by the United States Department of Energy (DOE) through the Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes (TCP) program (DE-SC0006967), the Agriculture and Food Research Initiative Competitive Grant 2011-67003-30222 from the USDA National Institute of Food and Agriculture, and the National Science Foundation (NSF-CBET-1033467 and DEB-1145875/1145649 and the Graduate Research Fellowship Program). The authors acknowledge the InterAmerican Institute for Global Change Research (Grant CRN2-021) for the support to the field data generation. The support of Instituto Fazenda Tamandua is also acknowledged. We thank Giulia Vico for help analyzing the meteorological data and the two anonymous reviewers for constructive comments.