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Corresponding author: T. Kumagai, Hydrospheric Atmospheric Research Center, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan. (firstname.lastname@example.org)
 Drought-related tree mortality at a regional scale causes drastic shifts in carbon and water cycling in Southeast Asian tropical rain forests, where severe droughts are projected to occur more frequently, especially under El Niño conditions. We examine how the mortality of a Bornean tropical rain forest is altered by projected shifts in rainfall, using field measurements, global climate model (GCM) simulation outputs, and an index developed for drought-induced tree mortality (Tree Death Indexη) associated with a stochastic ecohydrological model. All model parameters have clear physical meanings and were obtained by field observations. Rainfall statistics as primary model forcing terms are constructed from long-term rainfall records for the late 20th century, and 14 GCM rainfall projections for the late 21st century. These statistics indicate that there were sporadic severe droughts corresponding with El Niño events, generally occurring in January–March, and that seasonality in rainfall will become more pronounced, e.g., dry (January–March) seasons becoming drier and wet (October–December) seasons becoming wetter. The computedη well reflects high tree mortality under severe drought during the 1997–1998 El Niño event. For the present, model results demonstrate high and low probabilities of mortality in January–March and October–December, respectively, and they predict that the difference in such probabilities will increase in the future. Such high probability of mortality in the dry season is still significantly high, even considering the beneficial effect of increased soil water storage in the wet season (which is projected to increase in the late 21st century).
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 Although tropical forests in Southeast Asia represent only about 11% of the world's tropical forests in terms of area [World Resources Institute, 2007], they have the highest relative deforestation rate in tropical areas [Houghton and Hackler, 1999; Laurance, 1999; Malhi and Grace, 2000; Canadell et al., 2007]. Therefore, the impact of these forests is of great concern for global and regional climate and hydrologic cycling [Kanae et al., 2001; Malhi and Wright, 2004; Mabuchi et al., 2005; Werth and Avissar, 2005]. An analysis of climatic trends in global tropical rain forest regions over the period 1960–1998 showed that rainfall has declined more significantly in Southeast Asia than in Amazonia, and that the El Niño Southern Oscillation (ENSO) may be the primary driver of drought in Southeast Asia [Malhi and Wright, 2004] (the Indian Ocean Dipole (IOD) may also cause drought in this region). As summarized by the Intergovernmental Panel on Climate Change , the projected growth of atmospheric greenhouse gases in this century will significantly impact global and regional temperatures, with concomitant modifications to precipitation patterns. Global climate models (GCM) have shown more frequent El Niño-like conditions from human-induced greenhouse warming [Timmermann et al., 1999], linked to mechanisms of tropical droughts [Neelin et al., 2003]. Thus, an understanding of how tropical rain forest ecosystems in Southeast Asia respond to climate change and El Niño-induced drought will significantly impact our ability to predict Earth system processes under climate change.
 Tree mortality and die-offs at the landscape/regional scale are among the most important forest responses to severe drought. Such regional scale mortality may cause rapid and large-scale shifts in ecosystem structure and function, resulting in drastic changes in carbon, water and energy exchange between biosphere and atmosphere [e.g.,Bonan, 2008]. Drought-induced tree mortality can be amplified by climate change directly through increasing temperature and drought, and indirectly through favoring demographics of insects and pathogens [Breshears et al., 2005, 2009; McDowell et al., 2008; Adams et al., 2010; Allen et al., 2010]. Furthermore, such profound effects of tree mortality on Earth system processes could generate positive feedbacks that exacerbate climate change [Betts et al., 2004; Malhi et al., 2009; Adams et al., 2010; Allen et al., 2010]. Thus, physiological mechanisms underlying tree survival and mortality during drought should be considered in the context of climate change, but such mechanisms remain poorly understood despite numerous scientific investigations [McDowell et al., 2008; Allen et al., 2010].
 Categorizing plants by “isohydric” and “anisohydric” regulation of water status helps link basic drought physiological traits to climate-induced mortality and die-off [e.g.,McDowell et al., 2008; Breshears et al., 2009; Kumagai and Porporato, 2012]. Isohydric plants regulate transpiration by stomatal closure to maintain constant midday leaf water potential, thus avoiding drought-induced hydraulic failure. However, stomatal closure over longer droughts causes carbon starvation and low production of defensive chemicals against biotic agents, resulting in tree mortality. Further, a rise in temperature and severe drought could accelerate carbon starvation for isohydric plants, because of increased respiration costs [e.g.,Damesin, 2003; Metcalfe et al., 2010a, 2010b]. In contrast, anisohydric plants have less stomatal sensitivity, and allow midday leaf water potential to decline with soil moisture decrease. Thus, hydraulic failure for these plants occurs at a much more negative water potential than for isohydric species [e.g., Linton et al., 1998; West et al., 2007]. This fact may help anisohydric species to stave off carbon starvation during moderate but long droughts, but it makes them more susceptible to hydraulic failure.
 Previous studies and an ongoing throughfall exclusion experiment indicate that the studied tropical rain forest ecosystem tends to have little regulation of forest water use, regardless of sporadically severe soil drying [Kumagai et al., 2004c, 2005; Kumagai and Porporato, 2012]. Although it is generally thought that anisohydric behavior is an adaptation to more drought-prone habitats, we showed that anisohydric plants are more favored than isohydric plants under very moist environments where there is little risk of hydraulic failure [Kumagai and Porporato, 2012]. Furthermore, there is recent evidence that avoiding the risk of hydraulic failure is the best strategy for water use, in both isohydric and anisohydric species [Meinzer et al., 2009; McDowell, 2011]. Thus, here we use a “Tree Death Index,” η [Kumagai and Porporato, 2012], which focuses on tree death induced only by hydraulic failure assuming anisohydric behavior in the studied forest, and evaluates the impact of climate factors on forest mortality. Nevertheless, in some cases of isohydric plants, one should take into consideration the effect of carbon starvation on tree death [e.g., Fisher et al., 2010].
 Our major goal is to clarify how the mortality of a Bornean (Southeast Asia) tropical rain forest will respond to current and projected rainfall patterns. With this goal in mind, we use the Tree Death Index η, which is thought to be the best index for describing tree mortality risk in this region. However, using simply ηis insufficient because of its inadequate description of seasonality in rainfall (detailed later). The index is useful for defining actual tree mortality, and for development of a vegetation dynamics model that considers effects of climate-change drought on tree death and survival. Thus, a secondary goal is to show the development, correction and usefulness ofη.
 The studied rain forest is among the moistest biomes in the world [see Kumagai et al., 2005, Figure 3]. It has been reported that in tropical rain forests of Malaysia and Indonesian Borneo, severe drought associated with the ENSO event of 1997–1998 caused extremely high tree mortality [Nakagawa et al., 2000; Potts, 2003; van Nieuwstadt and Sheil, 2005; Allen et al., 2010; Phillips et al., 2010]. For the studied Bornean tropical rain forest, we use tree mortality before and after the 1997–1998 El Niño, rainfall records from 1968 to 2001, GCM simulation outputs of current and future rainfall statistics, and η. Based on the anisohydric behavior observed in this forest and the soil–plant–atmosphere continuum (SPAC) concept, η allows use of information from previous detailed field measurements [Kumagai et al., 2004a, 2004b, 2004c, 2005, 2009; Manfroi et al., 2006] and provides model parameters with clear physical meanings. The tree mortality analysis using ηis based on stochastic representation of rainfall constructed from long-term rainfall records for the current rainfall scenario, and is linked to GCM simulation outputs for the future rainfall scenario. It thus provides an index of drought-induced mortality,η, for the tropical rain forest, under current climate conditions including sporadic El Niño events, and under future scenarios of global change. We expect that η was larger in the period 1997–1998 and under global change conditions. Furthermore, global change is projected to affect seasonality in rainfall, and thus seasonality in η. In this study, we will confirm these hypotheses and explain the occurrence probability of η under the hypotheses.
 Soil moisture dynamics is a key control on hydrologic fluxes through the SPAC, and is fundamental for describing ecosystem processes such as plant water stress [Porporato et al., 2001, 2004; Rodríguez-Iturbe and Porporato, 2004]. Accounting only for changes in mean responses to climatic variability is inadequate for realistic investigation of climate change impacts on ecosystems. One must also account for the stochastic component of hydrologic forcing and possible alterations in frequency and amount of rainfall events, which in turn impact soil moisture dynamics and temporal characteristics (i.e., intensity, duration, and frequency) of periods of plant water stress, plant productivity and mortality [Porporato et al., 2001, 2004]. Such probabilistic descriptions of ecosystem process dynamics are useful for assessing the impact of climatic fluctuations, such as severe drought brought on by current ENSO cycles and global change, whose characterization is inherently affected by uncertainty.
 In this study, we use a simple SPAC model linked to probabilistic descriptions of soil moisture and plant water stress [Porporato et al., 2001]. We also develop the index η, representing anisohydric plant mortality (i.e., neglecting carbon starvation-type mortality) produced by climate change-type drought [Kumagai and Porporato, 2012]. A review and description of the modeling scheme is presented below for completeness.
2.1. Stochastic Soil Moisture Dynamics Model
 The stochastic soil moisture model of this study was originally proposed by Rodríguez-Iturbe et al. , and improved by Laio et al. . Under conditions where lateral movement can be neglected, the daily, vertically integrated soil moisture balance equation is given by
where n is soil porosity; Zr is rooting depth (mm); s is the degree of saturation between 0 and 1; t is time (day); φ is rate of infiltration into the rooting zone (mm day−1), which is represented by the rainfall rate minus the rate of rainfall loss through canopy interception and rate of infiltration-excess; andχ is the rate of water loss from the soil (mm day−1), i.e., the evapotranspiration rate E(s, t) (mm day−1) plus the leakage L(s) (mm day−1). The frequency of rainfall events can be assumed to be a stochastic variable expressed as an exponential distribution, with mean time interval between precipitation events 1/λ (day). The amount of rainfall, when it occurs, is also assumed an independent random variable described by an exponential probability distribution, with mean depth of rainfall events α (mm). Losses to the atmosphere from canopy interception are represented using a threshold of rainfall depth Δ (mm) that denotes interception capacity determined by forest stand throughfall and stemflow measurements [e.g., Manfroi et al., 2006], below which effectively no water reaches the ground. Saturation overland flow is derived from rainfall excess, which occurs when rainfall depth exceeds water storage capacity in the rooting zone soil layer.
 Leakage losses are assumed to occur through gravitational flow. L(s) is assumed to be at its maximum for saturated soil moisture conditions. It can be expressed as the hydraulic conductivity K(s) (mm day−1), i.e., the exponential function of Ksat, the saturated hydraulic conductivity (mm day−1), sfc, s at “field capacity,” the water content held in the soil after gravity drainage where K(s) is zero, and β, a parameter that can be obtained by fitting the power law unsaturated hydraulic conductivity to field data [Laio et al., 2001].
 In this model, it is considered that the main control on evapotranspiration is s, giving
where EW and Emax are soil evaporation and the maximum evapotranspiration (mm day−1), respectively; and sh, sW and s* are s at “hygroscopic point,” “plant wilting point,” and “plant stress point,” respectively. The primary forcing variable for evapotranspiration in the tropics is net available energy [Kumagai et al., 2005]. Thus, we use a modified expression of Priestley and Taylor  to compute EW and Emax, given by
where i denotes W or max; αPT_W and αPT_max are the Priestley–Taylor coefficients (αPT) for EW and Emax, respectively; κ is a unit conversion factor (mm day−1 (m s−1)−1); δ is the rate of change of saturation water vapor pressure with temperature (Pa K−1); Lv is the latent heat of vaporization of water (J kg−1); ρw is the density of water (1000 kg m−3); ε is the psychrometric constant (66.5 Pa K−1); and Rn is net radiation above the canopy (W m−2). A major uncertainty in equation (3) is αPT, which for forested ecosystems is usually less than its typical 1.26 value because of additional boundary layer, leaf, xylem, and root resistances. Measured daily evapotranspiration and daily averaged Rn are used to obtain daily αPT, and then we derive a relationship between s and daily αPT. αPT_W and αPT_max are parameterized by fitting equations (2) and (3) to the relationship. For the stochastic model computations, all thermodynamic variables in equation (3) are assumed constant, and Rn is obtained by averaging seasonally observed values, to maintain analytical tractability.
 Owing to the stochastic rainfall forcing in equation (1), its solution can be represented only in a probabilistic manner. In this framework, the steady state probability density function (PDF) of s, pdf(s), can be derived from the master equation of the process [see Rodríguez-Iturbe and Porporato, 2004].
2.2. Plant Water Stress Dynamics and Mortality Model
 Following Porporato et al. , a (static) plant water stress ζ can be defined as zero when soil moisture is greater than the level of incipient stomatal closure, s*, and as a maximum of one when soil moisture reaches the level of complete stomatal closure, sW. A nonlinear curve between s* and sW is
where q is a measure of nonlinearity of the effect of soil moisture deficit on plant conditions, varying with plant species. Plants with a higher q value, i.e., stronger nonlinearity, can have lower ζ with decreasing s, but abruptly increase ζ in the immediate vicinity of sW. This means that such plants can allow their leaf water potential to approach the xylem cavitation threshold without suffering from water stress [Porporato et al., 2001].
 The probabilistic structure of ζ can be derived from pdf(s) by substituting equation (4) for s. The PDF of ζ, fZ(ζ), has an atom of probability at ζ = 0, FZ(0) = 1 − P(s*), and one at ζ = 1 equal to FZ(1) = P(sW) (where P is the cumulative density function of s). The continuous part of fZ(ζ) between zero and one, corresponding to sW < s < s*, can be written as [Porporato et al., 2001]:
where Cζ is an integration constant that can be found by imposing the condition FZ(0) + FZ(1) + ∫ 01fZ(ζ)dζ = 1.
 Mean water stress can be calculated as = ∫ 01ζfZ(ζ)dζ + FZ(1). However, since the value of also takes into consideration periods of ζ = 0, we thus consider the mean value of water stress (assuming the plant is under stress) as [Porporato et al., 2001]:
where P(s*) denotes only that part of the PDF corresponding to ζ above 0.
 The information on plant conditions given by the mean and the PDF of water stress must be completed by a description of the temporal characteristics of periods of water stress. The length of the periods in which soil moisture is below a threshold is among the important stochastic variables in the treatment of this temporal dimension of water stress. The analytical expression for the mean duration of an excursion below the threshold sW (; day) can be obtained using the crossing analysis as [Porporato et al., 2001]:
where λ′ is the frequency of rainfall events (day−1) given by λ exp(−Δ/α); and γ[·,·] is the lower incomplete Gamma function.
Porporato et al.  defined a measure of vegetation water stress by combining with the mean duration and frequency of water stress during the growing season, calling it “dynamic” water stress or mean total dynamic stress during that season, . Likewise, to describe plant mortality and survival caused by hydraulic failure under severe drought conditions, we define a “Tree Death Index” η, using equations (7) and (8) as
where kis a parameter representing an index of plant resistance to drought, which can vary with plant species. The mortality of plants with a higher-k value is insensitive to drought conditions described by and . Tseas is the number of days in a season (day). Tree mortality described by ηis related to permanent damage from drought-induced hydraulic failure. Unlike the given by Porporato et al., we use instead of the mean duration of an excursion below s*. Moreover, we do not take into account the effect of frequency of water stress in equation (9), because permanent damage leading to tree mortality occurs at maximum water stress, and tree mortality is a single event in time.
 With seasonal variation in rainfall, i.e., wet and dry seasons, the effect of wet season soil moisture storage on subsequent dry season forest water use becomes crucial in the strategy of vegetation to cope with stochastic water availability [Kumagai et al., 2009]. To account for this effect, we use the mean time s*(s0) (day) to reach the threshold of water stress s*, from an arbitrary soil water content s0 at the dry season start, as given by Rodríguez-Iturbe and Porporato :
where ρ(u) is the normalized loss function described as χ(u)/nZr. To explain the effect of possible water storage at growing season start on plant water stress during the season, Rodríguez-Iturbe et al.  extended , assuming that water stress is zero at that start, until s(t) reaches s*, when it equals . Likewise, to describe the dry season η affected by the preceding wet season water storage, using s*(s0), we defined a corrected η as
Here, we use the steady state η during a season and a specific period (e.g., El Niño event), its interannual variation, and the corrected η to account for the effect of preceding wet season water storage η′, in the analysis of plant mortality and survival under drought conditions caused by a historical El Niño event and climate change.
3. Materials and Methods
3.1. Site Description and SPAC Model Parameters
 Vegetation–atmosphere exchange and meteorological data, which are well suited for estimating the SPAC model parameters, were obtained for a natural forest in Lambir Hills National Park (LHNP; 4°12′N, 114°02′E, 200 m a.s.l.), 30 km south of the city of Miri in Sarawak, Malaysia. The mean annual temperature in LHNP is around 27°C, with little seasonal variation. The rain forest in LHNP consists of two types of original vegetation common to Borneo, mixed dipterocarp and tropical heath forest. The former contains various genera of the family Dipterocarpaceae, which covers 85% of LHNP. Average canopy height at the study site is about 40 m, but heights of emergent treetops can reach 50 m. The leaf area index (LAI) ranged spatially from 4.8 to 6.8 m2 m−2, with mean 6.2 m2 m−2. The monthly amounts of litterfall were similar throughout the year, suggesting small variations in LAI. Soils consist of red-yellow podzolic (Malaysian classification) or Ultisols (United States Department of Agriculture Soil Taxonomy), with high sand content (62–72%), accumulation of nutrient content at the surface horizon, low pH (4.0–4.3), and high porosity (54–68%). Oxisols are widely distributed in the African and South American tropics, and are rarely seen in the Southeast Asian tropics. Ultisols, however, which are classified as an argillic soil, prevail in the Southeast Asian tropics, suggesting the representative soil type in this region.
 A 4 ha experimental plot gridded into 400 subplots of 10 m × 10 m was established in LHNP. An 80-m-tall (to the gondola base) canopy crane with a 75-m-long rotating jib was constructed at the center of this plot, to provide access to the upper canopy. Some observational floors of the canopy crane were devoted to eddy covariance flux measurements and above-canopy meteorological measurements, such as radiation flux, air temperature and humidity, wind velocity and rainfall. The subplots were used for throughfall and stemflow measurements, in-canopy micrometeorological measurements and soil moisture measurements.
Table 1 gives model parameters for evapotranspiration and soil characteristics, for computing soil moisture dynamics in LHNP. Derivation of these parameters and how computation results were validated are described elsewhere [Kumagai et al., 2009], but a brief description is provided here for completeness.
Table 1. Model Parameters of Evapotranspiration and Soil Characteristics in Lambir Hills National Park
Nonlinearity of soil moisture deficit effect on plant conditions, in equation (4)
 We used eddy covariance-measured transpiration to derive relationships betweens and daily αPT for the present vegetation, according to the procedure in the description of equation (3) (see section 2.1) [Kumagai et al., 2004b]. Given the high LAI at the site (>3), bulk surface conductance (Gs) is strongly related to the behavior of leaf stomatal conductance (gs), and can be fixed at a value about three times that of gs, independent of LAI [Kelliher et al., 1995]. The equilibrium evaporation term in equation (3) represents evaporation at the limit of complete decoupling between vegetation surface and atmosphere [McNaughton and Jarvis, 1983]. In our previous studies [Kumagai et al., 2004c, 2005], we found large decoupling coefficient values because of relatively large Gs compared with aerodynamic conductance, and that net available energy is the primary forcing variable for evapotranspiration at the studied forest. Thus, the αPT coefficient as a function of s well reflects observations that the LHNP tropical rain forest ecosystem tends to have little regulation of forest water use, despite episodic severe soil drying. This is unlike Eastern Amazonian forests, which tend to show isohydric behavior [Fisher et al., 2006]. In addition, using the nonlinear parameter q = 3 [Kumagai and Porporato, 2012], we assumed that plants with little regulation of water use can allow their water potential to approach the hydraulic failure threshold without sensing water stress [see McDowell et al., 2008]. Thus, the increment rate of ζ with soil moisture deficit (see equation (4)) for the studied vegetation can be taken as a relatively strong nonlinear increase [Porporato et al., 2001].
 Roots concentrate in a soil depth less than 0.5 m (T. Kume, personal observation, 2008). Principal soil moisture dynamics are mainly the result of root water absorption to a depth around 1.0 m, as supported by findings from a soil penetration test (T. Wakahara, personal observation, 2008). Thus, we assumed a Zr of 1.0 m for LHNP. The parameters n and sh, corresponding to saturated and residual water contents, respectively, were estimated using the soil water retention curve obtained in the field [Kumagai et al., 2004a, 2004b].
 The Ultisols at LHNP have a very high sand content, and therefore act like sand in terms of water movement at high soil matric potential. However, they retain water like clay soils at lower potential [Kumagai et al., 2004c]. In fact, Ksat and β at this site, which were estimated using nonlinear least squares regression between the time courses of s by numerical solution of equation (1) and the observations [Kumagai et al., 2004a, 2004b], are typical for sandy clay–silty clay loam and sand, respectively [see Campbell and Norman, 1998].
sfc was assumed to be s when L(s) in χ in equation (1) (=L(s) + E(s, t)) could not be ignored, and thus L(s) = K(s) = 0.1 mm day−1. Also, values of sh and sW were estimated using the s − αPT relationship [Kumagai et al., 2004a, 2004b]. Since there was no evapotranspiration plateau at high s at the site, s* was assumed equal to sfc.
 Mean daily Rn values in wet and dry seasons were obtained; in LHNP, Rn in the wet season (October–May) is lower than that in the dry season (April–September), owing to cloud cover effects.
 Throughfall and stemflow only occur when rainfall exceeds certain thresholds, and can be described as linear functions of rainfall. Consequently, daily interception loss was related to incident rainfall in a single storm event by subtracting both the throughfall and stemflow functions from rainfall in LHNP [Manfroi et al., 2006]. Thus, Δ, the amount of rainfall that can accumulate on forest canopy during a rainfall event, was calculated from the daily interception functions of rainfall.
 Using the model parameters for present vegetation and time series of rainfall as local forcing data, the soil moisture balance model (equation (1)) was validated in a deterministic mode (i.e., without use of probabilistic descriptions). As a result, we found that the model reproduced well the measured s, including under severe drought conditions (Figure 1). This was despite all simplifying assumptions, such as the use of averaged Rn for calculating evapotranspiration (equation (3)). The figure reveals that modeled and measured s were not significantly different (P = 0.37, slope = 1.01, R2 = 0.80). Again, soil moisture dynamics is a main determinant of hydrologic fluxes in this model, and thus the validation of measured s time series should be sufficient. Also, in the context of s model validation, we confirmed that model estimation of total annual evapotranspiration was consistent with measurements (∼1400 mm year−1, provided by Kumagai et al. [2004a]).
3.2. Rainfall Characteristics
 Mean annual rainfall was around 2740 mm at Miri Airport, 20 km from LHNP, for the period 1968–2001, whereas in LHNP it was around 2600 mm for 2000–2006. This small spatial difference in mean annual rainfall was not detected in 0.25° resolution Tropical Rainfall Measuring Mission (TRMM) 3B42 data for 2000–2009 (data not shown). Thus, we assumed that we could substitute the long-term rainfall record at Miri Airport for that at LHNP. This rainfall record shows significant interannual rainfall variability in the region. For example, maximum and minimum annual rainfalls for 1968–2001 were 3499 mm in 1988 and 2125 mm in 1976, respectively. Although the study site is in a region with one of the smallest seasonal rainfall variations in the world [seeKumagai et al., 2005, Figure 3], there is a slight seasonal cycle. It is drier from February to September, and wetter from October to January [see Kumagai et al., 2009, Figure 1a].
 In the tropical part of the Indian monsoon area, dry spells of 15–30 days are not uncommon [Yasunari, 1979]. To identify severe droughts, we calculated a 30-day shifting average of rainfall, based on daily data at Miri for the period 1968–2001 (Figure 2). This calculation was based on the method of Duchon , who forwarded the time series requirement to analyze the rainfall cycle at a period shorter than half a year [see Kumagai et al., 2005, Figure 3], and Sakai et al. , who indicated that a dry period of at least 30 days is most closely linked to drought stemming from ecohydrological aspects like regional soil moisture dynamics and plant water relations. The results show that there were sporadic but severe dry spells with persistence of at least 30 days, which typically corresponded with El Niño events defined by Sea Surface Temperature (SST) anomaly from 5°S–5°N and 150°W–90°W.
 To assess drought-induced mortality for each dry and wet season, we also evaluated the primary forcing terms of the stochastic ecohydrological model, i.e., the arrival rate of rainfallsλ and rainfall depth α, for each season. Seasons are typically represented by sequences of three months, i.e., December–February, March–May, June–August and September–November. However, three-month seasonal means of Θ,λ and α using the above representations could not sufficiently describe their seasonal variations. Thus, we computed time series of total precipitation (Θ: mm), λ and α over the period 1968–2001, for each of the four seasons, January–March, April–June, July–September and October–December. In this way, variances of yearly time series of seasonal averaged values (Θ, λ and α) were maximized. We defined interannual and seasonal variations in rainfall characteristics using box plots for Θ, λ and α (Figure 3). On average, all rainfall parameters had slight seasonal variations. Outliers, and thus interannual variations, were especially prominent from January–March. Furthermore, as stated previously, severe drought conditions were generally present during El Niño events (Figure 3).
 The effects of interannual climate fluctuations were then incorporated into the index η, using the time series of λ and α obtained for each season. Fluctuations of these parameters are represented by gamma distributions based on their means and standard deviations, and are obtained from the respective yearly time series (Table 2). For each season, steady state η are calculated with pairs of λ and α generated by Monte Carlo sampling, using gamma distributions [D'Odorico et al., 2000; Porporato et al., 2006; Kumagai et al., 2009].
Table 2. Total Seasonal Rainfall (Θ), Mean Yearly Rate of Arrival of Rainfalls (λ), Rainfall Depth (α), and Standard Deviations, for Each Season of 1968–2001 in Lambir Hills National Park
541.3 ± 279.9
0.47 ± 0.15
12.0 ± 4.5
583.3 ± 136.9
0.49 ± 0.075
13.1 ± 2.6
642.5 ± 183.2
0.49 ± 0.080
14.2 ± 2.7
973.5 ± 241.2
0.68 ± 0.064
15.5 ± 3.1
3.3. High Mortality Under a Severe Drought Condition Associated With 1997–1998 El Niño
 The forests of LHNP experienced a severe drought associated with the 1997–1998 El Niño, and drought-induced mortality increase was observed [Nakagawa et al., 2000; Potts, 2003]. To examine usefulness of Tree Death Index η for the LHNP tropical rain forest, we used the results of Nakagawa et al. , summarized as follows.
 The strong 1982–1983 El Niño caused very severe drought. However, the 1997–1998 El Niño was the strongest in the 20th century, and its associated drought was the most severe (statistically, the Kolmogorov-Smirnov test showed that a drought such as in 1998 may occur once in about 360 years) (seeFigure 2). Mortality rates during that drought were 6.37% year−1, as compared with 0.89% year−1during the pre-drought period (1993–1997); the basal area lost during the drought was 3.4 times that of the annual increase in basal area during the pre-drought. Notably, the dominant family in the study forest, Dipterocarpaceae, had a 12–30 times higher in the drought than the pre-drought period. The mortalities shown here are among the highest ever observed in world tropical rain forests [Phillips et al., 2010].
3.4. GCM Projections of Rainfall in Late 21st-Century
 Rainfall characteristics for the late 21st century (2080–2099) scenario were taken from model outputs at approximate coordinates 4°12′N, 114°02′E, simulated by 14 IPCC GCMs (listed in Table 3), available through a public website (http://www.ipcc-data.org/). The GCM runs used here follow the Special Report on Emissions Scenarios (SRES) A2 [Nakicenovic et al., 2000], which assumes a very heterogeneous world with continuously increasing population and regionally oriented economic growth that is more fragmented and slower than in other storylines. There are well-known uncertainties regarding comparison of point-scale field observations to the coarse-resolution GCM grid cell [Miralles et al., 2010]. Here, specific values projected by each GCM are not important, unlike the variance and mean of the values. In addition, topography of the study site is widespread lowland, and climatic factors might be somewhat homogeneous within the GCM grid cell. Therefore, we assumed that the difference between point-scale observations and grid cell-scale simulations was included in the GCM-to-GCM variation of projected value, and there was no correction for this difference in each projection.
Table 3. Total Seasonal Rainfall (Θ), Mean Yearly Rate of Arrival of Rainfalls (λ), and Rainfall Depth (α) for Each Season at Lambir Hills National Park, from Global Climate Model (GCM) Simulations for the Period 2080–2099a
All values were taken as relative changes in rainfall predicted by each GCM, but offset by changes to rainfall observed in 1968–2001, according to Malhi et al. .
14 Intergovernmental Panel on Climate Change (IPCC) GCMs used: NCPCM, NCCCSM, MRCGCM, MPEH5, MIMR, IPCM4, INCM3, GIER, GFCM21, GFCM20, ECHOG, CSMK3, CNCM3, and HADCM3 (see http://www.ipcc-data.org/).
Standard deviations of Θ simulated from 14 GCMs are shown in parentheses.
 Based on an assumption that GCM simulations capture future seasonal changes in relative rainfall intensity in spite of their current tendency to underestimate absolute rainfall, we followed Malhi et al.  and accepted relative changes in rainfall predicted by each GCM, but offset them using rainfall observed from 1968 to 2001:
where m and jdenote a season and a GCM, respectively. Subscripts 21, obs_20, GCM_20 and GCM_21 denote an objective value for the late 21st century (2080–2099), observations in the late 20th century (1968–2001), and GCM-simulations for the late 20th (1961–1990) and 21st (2080–2099) centuries, respectively. ΘGCM_20is GCM-simulated rainfall under Non-SRES 20C3M assuming increasing greenhouse gases, as observed through the 20th century. The future rainfall parametersλ21 and α21 were calculated using tuning parameter a obtained to minimize b, given by
where σα and σλ are standard deviations of αobs_20 and λobs_20, respectively. Here, we assumed that λ21 and α21 vary linearly with each slope of σα and σλbetween GCM-simulated Θ values.
 With the revised calculation using equation (12), many GCM simulations show a tendency in the late 21st century for increased seasonality in Θ, i.e., a wet season becomes wetter, and a dry season drier (Tables 2 and 3). On the other hand, HADCM3 showed the most severe change in rainfall regime, projecting dry seasons to become much drier, with little change in the wet season. HADCM3 has a different model weighting, based on capturing interannual variability, and has many advantages in projecting climate-induced drought; thus, this extreme simulation result is likely [Malhi et al., 2009]. Hence, we constructed two types of future scenarios for 2080–2099, outputs averaged over 14 GCM simulations and from HADCM3 only (Table 3). Here, we assumed that the different periods, for observations (1968–2001) and GCM runs (1961–1990), can represent late 20th century precipitation characteristics, and that the GCM runs for the late 21st (model period 2080–2099) can be compared with observations of different period duration (1968–2001), because model outputs were translated to PDFs through the stochastic treatments. Again, interannual variations in the parameters λ21 and α21 are represented by gamma distributions using σλ and σα, respectively. For each season, steady state η under future climate conditions were calculated with the pairs of λ21 and α21 generated by Monte Carlo sampling, using gamma distributions.
 Interannual variation in steady state η for each season is shown in Figure 4. Although mean η for January–March, April–June and July–September do not have significant differences (around 0.07; Figures 4a–4c), interannual rainfall fluctuation in January–March (Figure 3) appreciably increases the frequency of higher η values (referred to as the “fatal mode” of η, because mortality might be higher under conditions with such high η values) (Figure 4a). Notably, the atom of probability at η = 1 in January–March reaches 10.0% (Figure 4a). On the other hand, mean η in October–December is around 0.01, and about 85% of its frequency is below 0.01 (Figure 4d). The steady state η estimated under the El Niño conditions of 1997–1998 were around the mean, or at the boundary of at least 35% of the upper tail of the PDF of η, pdf(η) for April–June, July–September and October–December (Figures 4b–4d). For January–March it was one, representing the most fatal situation (Figure 4a).
Figure 5 compares interannual variations in the steady state η for each season in the late 20th century, and projected for the late 21st century. Owing to appreciable reduction in rainfall in January–March under the GCM rainfall projections, especially that of HADCM3, the frequencies of η fatal mode and atoms of probabilities at η = 1 significantly increase in the 21st century (Figure 5a). The PDFs of η for April–June and July–September are almost the same in calculations for the 20th century. Compared with the 20th century simulations, the rainfall decrease in April–June in the HADCM3 simulation (Tables 2 and 3) increases the frequency of greater η (Figure 5b), and the rainfall increases in July–September in the projection by the 14 GCM average (Tables 2 and 3) augments contributions to small η and decreases large η (Figure 5c). In October–December, moister environments projected for the 21st century do not significantly alter pdf(η) (Figure 5d).
 The study site has slight seasonality in rainfall (Table 2), and the GCMs projected that this seasonality will amplify in the late 21st century (Table 3). Here, higher η appear in January–March, the driest season (Figures 4 and 5), and the preceding October–December is the moistest season of the year. Thus, it is logical to expect that soil water storage in October–December affects η in the following January–March, and this effect will be modified by climate change. The extended definition of η accounting for the high soil moisture at the start of the preceding season (η′: equation (11)), for different total seasonal rainfall in January–March (ΘJFM), are calculated using rainfall parameters λ21 and α21 obtained from ΘJFM = Tseasλ21α21 and equations (14) and (15) (Figure 6a). The η′ has a maximum value at s*, equal to the steady state η (see equation (11)), and decreases with increasing s0. As Figure 6a shows, η′ can reach one when ΘJFM < 200 mm, shows little difference when ΘJFM < 50 mm, and has a lower value with average climate conditions in January–March, i.e., ΘJFM = 513.2 mm. In addition, pdf(s0) for October–December in Figure 6b shows that whereas there is little difference between soil moisture conditions in the 20th century and the HADCM3 projection, increased rainfall in the projection by the 14 GCM average increases the frequency of greater s, and that the study site under El Niño conditions in 1997 experienced very dry conditions compared with normal.
 Here, using Figures 6a and 6b, we compute the mean total η′ in January–March, taking into consideration the effect of water storage in the preceding October–December as JFM = ∫01η′JFMpdfOND(s0)ds0 (where η′JFM and pdfOND(s0) define η′ in January–March as a function of s0 and pdf(s) in October–December, respectively). Figure 7 plots JFM against ΘJFM. The JFM abruptly increases when ΘJFM < 270 mm, and reaches a plateau and maximum (around 0.64) when ΘJFM < 50 mm. It is interesting that the JFM calculated using rainfall parameters under El Niño conditions in 1998 lies on the plateau (Figure 7). In Figure 7, we indicate possible ranges of ΘJFM obtained from 1968 to 2001 observation and GCM projections for 2080–2099. This shows that while the maximum value of JFM in 1998 is somewhat an outlier when considering the ΘJFM in 1968–2001, such a high JFM is more likely to occur in the late 21st century, especially in the HADCM3 projection.
5. Discussion and Conclusions
 Using a combination of field measurements and theoretical considerations, the index for drought-induced tree mortality (Tree Death Indexη), associated with a stochastic ecohydrological model and GCM projections of rainfall, allows us to examine how future rainfall shifts will affect ecosystem water budgets and related drought-induced mortality of a Bornean tropical rain forest. The concept ofηis close to a water stress integral (WSI) involving temporal accumulation of deviation in leaf water potentials relative to the maximum observed value, providing a long-term index of plant water stress [Myers, 1988]. Nepstad et al. effectively explained the drought-induced death and survivorship of trees in a large throughfall exclusion experiment, using the WSI. Unlike the WSI, theηmodel has as its primary forcing terms rainfall statistics, which describe the impact of global-change-type drought.
 The field measurements permitted derivation of realistic relationships that link the rainfall forcing term generated from historical data and GCM projections with ecosystem water cycling, including tree water stress. For example, field data were used to derive relationships between transpiration and extractable soil water content, and between rainfall and interception, seasonal evaporative demand, and drainage flow parameters [e.g., Kumagai et al., 2004b, 2009]. As a result, we could describe ecosystem water cycling using the parameters (Table 1), and formulate a hypothesis about the relationship between plant water stress and soil moisture.
 Mechanistic or semi-mechanistic modeling of tree death [e.g.,Martínez-Vilalta et al., 2002; Fisher et al., 2010] has received less attention, mainly because of sparse data on the relationship between environmental conditions and tree health [Keane et al., 2001]. Our present ability to determine emergence of global changes in forest mortality is constrained by a lack of systematic global monitoring [Allen et al., 2010]. Widely used empirical mortality models [e.g., Bugmann and Solomon, 2000; Horner et al., 2009] are effective for current climatic conditions but are likely inadequate for future climate change conditions, because they lack insight into the relationship between changing environmental factors and responding physiological mechanisms. Improvements for mortality modeling problems should include a biologically reasonable predictor in a stochastic algorithm that can account for plant stresses in response to environmental changes [Hawkes, 2000].
 There are promising indexes for examination of the relationship between climate-induced forest die-off and drought intensity and duration, as follows. Tree mortality abruptly increases when the index exceeds environmental and/or physiological thresholds. Many researchers have used the maximum climatological water deficit (MCWD), defined as the most negative value of monthly precipitation minus monthly evapotranspiration over a year, to explain the drought sensitivity of forest die-off [e.g.,Aragão et al., 2007; Malhi et al., 2009; Phillips et al., 2009, 2010]. Nepstad et al. tested the hypothesis that tree mortality increases abruptly during drought, when plant-available soil water (PAW) declines below a critical minimum threshold. They effectively used PAW, which accounts for soil moisture conditions and the ability of different types of access to soil water. The indexη was developed here as a simple mechanistic tree mortality model based on ecophysiological (both aboveground and belowground processes) and soil physics properties, and was related to directly measured quantities in the studied forest ecosystem, as well as to stochastic rainfall properties and global climatic events (e.g., El Niño).
 Practically, such an index must be translated into actual tree mortality, such as fraction of tree deaths per year. For example, to simulate tree death from carbon starvation, Fisher et al. formulated drought-induced tree mortality (M: % year−1) as a function of stored carbon pool, background mortality (Bm: % year−1), and single cohort mortality rate (Sm: % year−1). In their model, M = Bm and M = Bm + Sm occur when mean cohort carbon storage is equal to leaf biomass, i.e., irrespective of stress on the carbon store, and when carbon storage is zero, respectively. Also, in the ecosystem demography model by Moorcroft et al. , mortality rate is calculated as the sum of two terms: an individual's density-independent mortality rate, related to its longevity, and its density-dependent mortality rate, associated with its current net carbon production. The first term could correspond toBm. These concepts are based on death from carbon starvation, including isohydric behavior in response to drought. Here, drought-induced mortality from hydraulic failure might be similarly modeled as
where ηmax is the possible maximum value of η, and Sm is the value when η is ηmax. Note that M = Bm occurs when η = 0, i.e., irrespective of the hydraulic failure. This modeled M increases linearly with η, but η is a nonlinear function of ecophysiological and environmental factors.
 Further, generalization of η modeling, such as its application to other sites or creation of global ηmaps, is needed for predicting the extent and patterns of future alteration in forests affected by drought-induced mortality. For example, using daily precipitation values on a global 0.25° latitude-longitude resolution grid from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis [seeKistler et al., 2001], we can obtain global and temporal patterns of precipitation statistics, i.e., α and λ, which drive the stochastic soil moisture and η model. Global assessments of evapotranspiration characteristics, e.g., validation and parameterization, could be done using tower eddy covariance and meteorological data from the FLUXNET data archive (http://www.fluxnet.ornl.gov/). Also, the relationship between evapotranspiration and soil moisture could be obtained from combination of the FLUXNET data and outputs from the Second Global Soil Wetness Project (GSWP-2) [seeDirmeyer et al., 2006]. Also needed are an improved network of observations, e.g., a global network of sap flow measurements for drought physiology, and global and annual maps of actual tree mortality (M) [see Allen et al., 2010] for translating the η map to an M map.
 We found that future rainfall shifts cause higher and lower frequencies of the fatal mode of η in January–March and October–December, respectively (Figure 5). This finding is attributed to a projected reduction and increase in rainfall in January–March and October–December, respectively. Thus, we examined the effect of a projected increase in soil water storage in October–December on tree water stress the following January–March (Figure 6). Despite the stored water effect, the computed η for January–March 1998 (strong ENSO event) reached the maximum possible; the likelihood of this η value was found very small in the 20th century (Figure 7). Interannual rainfall variation simulated by the GCMs (especially HADCM3) demonstrated that tree mortality as great as in the 1998 ENSO event is more likely in the late 21st century (Figure 7). Furthermore, Phillips et al.  suggested a mortality more sensitive to drought in Bornean forests than in Amazonian forests. This motivates greater consideration of the influence of severe drought on forest mortality in the 20th century at our Borneo study site. More extensive and technically difficult experiments are required to explain the meaning of η in M (see equation (16)) and the applicability of η and M modeling to other forest sites.
 T. K. is grateful to the Forestry Department, Sarawak, for their support during the fieldwork for this study. T. K. also thanks Tohru Nakashizuka, Masakazu Suzuki and Tetsukazu Yahara for their support, and numerous colleagues who helped with this fieldwork. This study was funded by Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency (JST), the Global COE (Centers of Excellence) Program (GCOE) of the Japan Society for the Promotion of Science (JSPS), grants from the Ministry of Education, Culture, Sports, Science and Technology, Japan (21255001, 20248016, 20380090 and 19255006), and the Excellent Young Researcher Overseas Visit Program under the sponsorship of the JSPS.