HYDROL 3629

Journal of Hydrology 212–213 (1998) 268–286

A model for hydrological equilibrium of leaf area index on a global scale Laurent Kergoat 1 CESBIO (CNES/CNRS/UPS), 18 Av. E. Belin, bpi 2805, F-31055 Toulouse cedex, France Received 23 November 1995; accepted 1 October 1997

Abstract In this paper, a model for hydrological equilibrium of leaf area index (LAI) is presented. The central assumption is that adaptation of vegetation to the local climate leads to a development of the canopy, which ensures a large light absorption but prevents severe soil water depletion. Particular attention has been paid to the processes which strengthen or weaken the basic LAI/evapotranspiration relationship, including soil moisture feedback on transpiration and evaporation, deciduousness of the canopy and interception losses. The annual water balance has been compared to stream flow data. A general agreement was found between simulated and observed run-off averaged over 28 large river basins. This shows that a water exchange scheme with explicit canopy processes can be used on a global scale. Vegetation aridity gradients are well defined by the hydrological equilibrium theory. An additional light availability constraint shows that the LAI, for wet tropics, some wet temperate and boreal areas, is not primarily water limited. An interesting point arises from an underestimation of the LAI and evapotranspiration in the rain forest margins and dry forests. This suggests that these areas are prone to recurrent droughts, and that drought resistance and avoidance strategies are of uppermost importance for vegetation function and therefore water cycle modelling. In particular, deep rooting may play a crucial role. The objective of modelling vegetation response to resources availability—here the water and light resources—is to improve our understanding of the biosphere as a resource-based system on a global scale, in the perspective of a change in atmospheric CO2 and corresponding climate modifications. The exact role of below-ground functioning, its links with carbon allocation, and especially the cost of deep rooting, emerge from this study as critical questions. 䉷 1998 Elsevier Science B.V. All rights reserved. Keywords: Leaf area index; Hydrological equilibrium; Global scale

Nomenclature

W

LAI PAR L(z)

Sn ETr Eveg Esoil Tr E0 Epot tint

S(z) 1

projected leaf area index photosynthetically active radiation cumulated LAI between level z and top of the canopy absorbed PAR at level z in the canopy

Present address: Laboratoire d’Ecologie Terrestre, 13 av. Col. Roche, BP 4403, 31405 Toulouse cedex, France. E-mail: [email protected]

0022-1694/98/$ - see front matter 䉷 1998 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(98)00211-X

extractable water content in the root zone (m) snow pack water content (m) evapotranspiration (mm/day) wet canopy evaporation (mm/day) soil evaporation (mm/day) plant transpiration (mm/day) equilibrium evaporation (mm/day) potential evapotranspiration (mm/day) period of day-time used by evaporation of wet canopy (s)

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Pi DR Pr T D S0 Sg Rn Rveg n Rsoil n Smelt n Sfall n tday k Rz raveg rasoil rc rl gl gmax st rs rsmin S1 W1 W2 W3 b D Lv Lf r Cp g Ca –G rstc

intercepted rainfall (mm/day) drainage run-off (mm/day) daily precipitation (mm/day) daily mean air temperature (⬚C) air water vapour pressure deficit (Pa) daily mean incoming surface PAR (W/m 2) daily mean incoming surface global radiation (W/m 2) daily mean surface net radiation (W/m 2) net radiation for the vegetation (W/m 2) net radiation for the soil (W/m 2) water from snow melt (mm/day) snow fall (mm/day) day length (s) extinction coefficient for PAR and net radiation rooting depth (m) aerodynamic resistance of the canopy (s/m) aerodynamic resistance of the soil (s/m) canopy resistance (s/m) leaf stomatal resistance (s/m) leaf stomatal conductance (mm/s) leaf maximum stomatal conductance (mm/s) soil surface resistance (s/m) minimum soil surface resistance (s/m) constant for light effect on stomatal conductance (W PAR/m 2) soil water constant for stomatal closure (mm) soil water constant for evaporation reduction (mm) soil water constant for zero evaporation (mm) rainfall interception coefficient temperature derivative of the saturated vapour pressure curve latent heat of vaporization latent heat of fusion air density specific heat of air psychrometric constant CO2 gradient between atmosphere and carboxylation site Leaf stomatal resistance to CO2 diffusion (s/m)

269

1. Introduction—Objectives Many studies have recognized strong links between the water cycle and vegetation functioning. Dickinson (1991), for example, reviewed some studies showing the influence of land surface on global scale terrestrial water cycle and atmospheric circulation. From a complementary point of view, Woodward (1987), Prentice et al. (1992) and Neilson (1995), among others, have developed models of vegetation distribution and function which are largely based on water availability. In the general context of rising CO2 and possible associated climate perturbations, it is of special interest to investigate to what extent the ecological and physiological functioning of vegetation (e.g., gas exchange) is dependent on resource availability. In that context, this paper presents a model for hydrological equilibrium of leaf area index (LAI) on a global scale. The LAI is the surface of leaves per surface of ground, and is viewed as an important variable of vegetation function. Indeed, the LAI measures the surface involved in radiation absorption and turbulent transfers between vegetation and the atmosphere. Therefore, this variable is a key variable for models of evapotranspiration and photosynthesis at the stand, regional and global levels (e.g., Running and Coughlan, 1988; Aber and Federer, 1992; Janecek et al., 1989). As the LAI shows high variability even within a vegetation type (e.g., Gholz, 1982), it is therefore difficult to prescribe a priori values for the different biomes. Remote sensing provides an opportunity to estimate the absorption of photosynthetically active radiation (PAR) and, to some extent, LAI (Sellers et al., 1996). However, predictive capabilities are required for prognostic modelling. This study investigates a functional relationship between LAI and water availability, using the large variability of current climate found on a global scale. The concept of equilibrium between vegetation and water availability has been proposed and tested by several authors (Eagleson, 1982; Specht and Specht, 1989; Grier and Running, 1977; Gholz, 1982; Poole and Miller, 1981; Rambal and Leterme, 1987). The basic idea is that the water losses, resulting from evapotranspiration processes, increase when vegetation develops, so that adaptation to local climate promotes canopy development until water shortage prevents further growth. Indeed, these studies showed

270

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Table 1 Biome-dependent parameters Biomes 1. Evergreen needle-leaved forest 2. Evergreen broad-leaved 3. Dry deciduous forest 4. Cold deciduous forest 5. Mediterranean veg. shrubs 6. Grasslands 7. Tundra

gst (mm/s)

ra (s/m)

Rz (m)

Drought tolerance period (days)

b

Pmax (mmol CO2/m 2/s)

Ta (⬚C)

Tb (⬚C)

5.6

15

1.2

1

0.06

12.3

0

35

6.0 4.8 4.6 5.3 7.8 6.6

20 20 20 20 50 50

1.5 1.5 1.2 1.5 0.6 1.2

30 1 1 80 1 1

0.02 0.02 0.06 0.02 0.01 0.03

10.5 11.6 10.9 13.1 33.0 10.0

5 5 0 5 0 0

40 40 40 40 40 35

that, for different ecosystems along aridity gradients, there were significant relationships between a measure of vegetation density (e.g., LAI) and a water balance index. The vegetation types encompassed coniferous forests, chaparral, eucalyptus woodlands, evergreen oaks and temperate grasslands, and the results were largely independent of plant species. Woodward (1987) was the first to apply this concept on a global scale, thus deriving a global LAI map. The biome model of Prentice et al. (1992) also largely makes use of the relationships between vegetation distribution and soil water availability. Recently, Neilson (1995) developed a model focused on global vegetation distribution related to this approach: different types of vegetation are competing for resources, and their LAI development is constrained, among many other rules, by water availability. Some of these studies used a water balance index, precipitation minus potential evapotranspiration. This is a convenient variable, but it may mask two important phenomena. (1) In the case of dry deciduous vegetation, the main relationship between the annual water balance index on the vegetation development probably involves indirect effects: during the dry season, the water balance is highly negative, but vegetation largely avoids water stress. The influence of growing season length on the carbon budget and life cycle may be more important than any real water shortage which could limit growth. (2) As pointed out by Prentice et al. (1992), vegetation has to cope with real (not potential) water stress and therefore modelling soil moisture, and its feedback on evapotranspiration, is an important step. Woodward (1987) suggested that accounting for dry deciduousness

could have significant effects on the estimation of vegetation sustainable LAI. The purpose of this paper is to present a model of hydrological equilibrium LAI and to examine the results that are obtained at the global scale. This model attempts to account for drought avoidance and drought resistance strategies, and to address the role of soil water content. In addition to the water constraint on LAI development, a light availability constraint was also introduced. This simply states that vegetation would not display leaves whose annual carbon balance is negative, as a result of withincanopy shading effects. Section 2 details the model development. Section 3 shows the main results, and presents a comparison between both modelled run-off and evapotranspiration and the water budget of large rivers. Section 4 discusses these results and underlines those theoretical or modelling issues still requiring further attention.

2. Model development 2.1. Algorithm The projected LAI of potential vegetation is estimated for every grid point, at a resolution of 0.5⬚ × 0.5⬚. The vegetation is characterized by its physiological and physical properties (Table 1) and evergreen versus deciduous phenology. Deciduousness is modelled as a leaf-on/leaf-off transition. The hydrological equilibrium LAI is determined by a critical water stress that occurs during the ‘leaf-on’ season. For each pixel, discrete projected LAI values of 15, 8,

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

271

Fig. 1. Algorithm for equilibrium LAI estimation. Thirteen discrete values of the LAI are used to compute the seasonal water balance and the carbon budget of the lowest canopy layer. The process stops when the water and light criteria are both fulfilled.

6, 5, 4, 3, 2.5, 2, 1.5, 1, 0.6, 0.3 and 0 are used successively to assess the soil water content under mean climate conditions (Fig. 1). Water stress is defined as the ratio of extractable soil water to maximum extractable soil water. A ratio of 0.25 has been retained to define critical water stress. As plant stomatal closure occurs when this ratio is below 0.4 (see Section 2), this threshold corresponds to a significant stomatal closure, which is assumed not to be sustainable when occurring during the leaf-on period. Drought tolerance strategy is accounted for by allowing an n-day period during which this ratio can be less than 0.25. A second criterion is imposed by a light availability constraint. So, starting from a value of 15, which represents a reasonable upper boundary for the LAI, the LAI is successively reduced until the two criteria are both fulfilled. As detailed hereafter, particular attention has been paid to processes which influence (either strengthen or weaken) the relationship between evapotranspiration and canopy LAI. 2.2. Model description The variation of available soil water W, defined as the difference between field capacity and permanent

wilting point, is the balance between precipitation Pr and snow melt Smelt minus evapotranspiration ETr and n a drainage run-off term DR: dW ˆ Pr ⫹ Smelt ⫺ ETr ⫺ DR: n dt

…1†

The model is run with a daily time-step with climate data interpolated using monthly mean values. This means that input data place a strong constraint on model development (see Section 2.3). The maximum value for W is the relative available water content multiplied by the biome-dependent rooting depth Rz. Drainage or run-off simply empty the soil reservoir when water content is larger than field capacity. Evapotranspiration ETr consists of evaporation of intercepted rainfall Eveg, transpiration by the plants Tr and soil evaporation Esoil: ETr ˆ TR ⫹ Eveg ⫹ Esoil :

…2†

These terms are estimated by a simple two-layer resistance scheme (Fig. 2). This scheme has been used, for example, by Persson and Lindroth (1994) to simulate transpiration and evaporation of a willow stand.

272

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

consumed by wet canopy evaporation is given by "

tint

Pi ˆ min ;t Epot day

# …5†

and this leads to interception losses: Fig. 2. Resistances of the transpiration (left), soil evaporation (middle) and wet canopy evaporation (right) schemes.

2.2.1. Evapotranspiration 2.2.1.1. Interception losses Rainfalls are intercepted by the canopy and are evaporated at the potential rate. Interception losses often reach 30% of the annual precipitation and therefore affect the soil moisture availability, especially when the canopy is rough (and strongly coupled to the atmosphere) and the precipitation events are frequent but not intense. Interception losses of 20– 40% are common for temperate broad-leaved and needle-leaved forests (e.g., Shuttleworth, 1989; Kelliher et al., 1993; Jarvis, 1993). Estimates for tropical forests are usually lower, due to the intensity of rainfall events: 10–25% of annual rainfall (Doley, 1981; Shuttleworth, 1989). For grasslands, the interception losses are of lower importance, because these canopies are weakly coupled to the atmosphere, so that transpiration and wet foliage evaporation are not very different. Interception generally increases along with the LAI. Here, interception is considered to be proportional to LAI and to the incoming precipitation: Pi ˆ b·LAI·Pr:

…3†

The coefficient b is biome dependent (Table 1) and is a proxy for the rainfall regimes effect. For an LAI of 5, interception is then 30% of incoming rainfall for a boreal evergreen forest and 10% for a tropical evergreen forest. Net radiation Rn is partitioned between the canopy soil …Rveg n † and the ground surface …Rn †, assuming a Beerlike extinction with LAI: ⫺k·LAI †·Rn : Rveg n ˆ …1 ⫺ e

…4†

Day-time canopy available energy is first used to evaporate intercepted water at the potential rate (during time tint). The fraction of day length (tday)

Eveg ˆ Epot ·tint ˆ

rCp raveg D ·tint ; Lv …D ⫹ g†

DRveg n ⫹

…6†

where D is the air water vapour saturation deficit, D is the temperature derivative of the saturated vapour pressure curve, g the psychrometric constant, r is the density of air, Cp the specific heat of air and Lv the latent heat of vaporization of water. The canopy aerodynamic resistance raveg depends on the biome (Table 1). Night-time fluxes are neglected, and the remaining day-time canopy available energy is used by plant transpiration as follows.

2.2.1.2. Transpiration combination equation transpiration:

The Penman–Monteith is used to estimate

rCp DRveg n ⫹ veg D  ra  ·…tday ⫺ tint †: Tr ˆ  rc Lv D ⫹ g 1 ⫹ veg ra

…7†

The canopy conductance gc ˆ 1/rc is computed by analytical integration, with the depth of the leaf level stomatal conductance, gst, accounting for within-canopy light extinction (Eq. 9). Stomatal conductance depends on the environmental conditions (Eq. 8), as proposed by Jarvis (1976). The for the differmaximum stomatal conductances gmax st ent biomes (Table 1) are taken from a review by Ko¨rner (1994). Ko¨rner’s analysis showed that the leaf conductances, per unit projected leaf area, were rather similar among the different life forms, and also stated that the seasonal course of transpiration is mainly driven by canopy development and by soil moisture. Stomatal closure in response to high vapour pressure deficit is also generally observed, especially when the surface roughness is high and the soil water depleted. At depth z in the canopy, the stomatal

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

and Finnigan, 1988):

conductance is: gst …z† ˆ ˆ gmax st ·

1 rst …z†

E0 ˆ

    S…z† W 3500 ⫺ D :max 1; : ·max 1; S…z† ⫹ S1 W1 3000 …8†

The PAR absorbed at level z, within the canopy, follows a classical Beer extinction: S…z† ˆ k·S0 ·e⫺k·L…z† :

…9†

Thus, an analytical integration from the leaf to the canopy level gives:   ZLAI gmax S1 ⫹ k·S0 gst …z† dz ˆ st ·log · gc ˆ k S1 ⫹ k·S0 ·e⫺k·LAI 0     W 3500 ⫺ D : ·max 1; × max 1; W1 3000 …10† As incoming surface PAR S0 is interpolated from the monthly mean value, the seasonal variation of the light factor is weak, but integration with depth ensures a curvilinear response of the canopy conductance with LAI. This modelling may not capture the underlying mechanisms, but was suggested by Saugier and Katerji (1991) to reproduce field measurements on the canopy scale. This curvilinear relation was also identified by Schulze et al. (1994). 2.2.1.3. Soil evaporation Soil evaporation may significantly contribute to the land/atmosphere water exchanges (e.g., Kelliher et al., 1993), particularly in the case of sparse or deciduous canopies. Evaporation is estimated by a combination equation which introduces a soil surface resistance rs:

Esoil

rCp DRsoil n ⫹ soil D  ra  ·tday : ˆ  rs Lv D ⫹ g 1 ⫹ soil ra

273

…11†

The same soil aerodynamic rasoil and minimum surface resistance rsmin values are prescribed to the seven biomes (Table 1). As rasoil is an order of magnitude larger than rsmin (see Kelliher et al., 1993; Schulze et al., 1994), this leads to a maximum soil evaporation rate which is close to the equilibrium rate (Raupach

D …1 ⫺ Rveg n †: l…D ⫹ g†

…12†

However, the soil surface resistance rs decreases rapidly when the soil dries (e.g., Wetzel and Chang, 1987; Kelliher et al., 1993):   1 W ⫺ W2 ˆ gmax ·max 1; : …13† gsoil ˆ soil W3 ⫺ W2 rsoil The parameters W2 and W3 correspond to 60% and 100% of the maximum available water in the root zone (Wetzel and Chang, 1987). This mimics the decrease in soil evaporation following surface drying and mulch formation. 2.2.2. Snow pack For high latitudes and mountainous regions, the water balance is largely controlled by snow processes. A very simple snow (Sn) submodel is used to account for winter snow accumulation, soil water freezing and for spring snow melt Smelt n . When air temperature is below 0⬚C, precipitation is considered to be snowfall and the soil water is assumed to be frozen (W Sfall n constant): dSn melt ˆ Sfall n ⫺ Sn : dt

…14†

When air temperature T is above 0⬚C and when a snow pack is present, a simple energy budget relates snow melt to air temperature and soil-level net radiation: Rsoil n ⫹ ˆ Smelt n

rCp …T ⫺ 0† rasoil ·tday when T ⬎ 0; …15† Lf

where Lf is the latent heat of fusion of the ice. This scheme aims at simulating snow dynamics very simply, and more physically sound schemes can be used in cases where the focus is on snow physical processes (e.g., Bonan, 1991). 2.2.3. Light limitation submodel Several studies focused on LAI/water availability relationships have recognized that the water constraint was unable to explain LAI variations for alpine and mountainous sites (Grier and Running, 1977; Gholz, 1982). Nemani and Running (1989) suggested that

274

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Table 2 Biome-independent parameters k

Rsoil (s/m) a

Rsoil (s/m) s

W1/Wmax

S1 (W PAR/m 2)

Ca –G (kg CO2/m 2)

0.5

100

50

0.4

10

576 × 10 ⫺6

light limitation for the lowest leaves or needles could favour self-pruning and LAI adjustment. The light limitation submodel follows this suggestion. It relies, however, on much more elusive parameterizations and poorly known parameters compared to those of the water relations (e.g., Cannell and Grace, 1993). The objective is mainly to isolate regions where the water constraint is not satisfactory. For a layer dL at depth z in the canopy, daily photosynthesis dPn is estimated with a simple resistance scheme (Running and Coughlan, 1988). A constant CO2 gradient ca –G (Table 2) is divided by the sum of two resistances: a stomatal resistance to CO2 diffusion rstc and a residual or non-stomatal resistance rrc , which includes the mesophyll resistance and the biochemical processes: …ca ⫺ G†·tday : dPn ˆ c rst …W; D; S…z†† ⫹ rrc …T; S…z††

…16†

The stomatal resistance for CO2 is proportional to the resistance to water diffusion, and thus depends on soil water, absorbed PAR and vapour pressure deficit (Eq. 8): rstc ˆ 1:6rst :

…17†

The non-stomatal resistance depends on PAR absorption, and displays a parabolic response to air temperature which is biome dependent (Table 1): rr ˆ

rrc min

S2 ⫹ S…z† …Ta ⫺ Tb †2 : : S…z† 4…Ta ⫺ T†…T ⫺ Tb †

yield plays an important role in the estimate of annual photosynthesis. Estimating the respiration cost of leaves is a difficult task. For sun leaves, the ratio of dark respiration rate to light-saturated photosynthesis rate usually ranges from 0.06 to 0.10. Little is known, however, for shade leaves, and hence for the ‘lowest’ leaves. Indeed, these two rates (photosynthesis and respiration), as well as nitrogen content, often display a within-canopy gradient (e.g., Hirose and Werger, 1987; Sprugel et al., 1994). Here, it is assumed that the ratio between respiration rate and light-saturated photosynthesis rate does not change with depth within the canopy, and lies close to 0.08. The annual carbon budget for the lowest layer is then proportional to: LCB…LAI† /

dayˆ365 X dayˆ1

…ca ⫺ G†·tday c rst …W; D; S…LAI†† ⫹ rrc …T; S…LAI††

…19†

! …ca ⫺ G†·t24h ; ⫺ 0:08 c rst min ⫹ rrc …T; S ˆ ∞† where LAI is the total leaf area index of the canopy. The first term on the right-hand-side is the daily photosynthesis at the bottom of the canopy, the second term is the 24 h respiration cost. 2.3. Input data

…18†

c is obtained The minimum residual resistance rrmin by equating the maximum photosynthetic rate to biome-dependent values (Table 1), which also follows Ko¨rner (1994). The light response factor S2 is derived by assuming a quantum yield a ˆ …dPn=dS†S!0 of 0.04 mmol CO2/mol PAR (see Ruimy et al., 1996 for discussion on canopy level quantum yields.). As shade leaves receive low irradiance, the quantum

A minimal set of seven vegetation types was defined, to account for major differences in the above-described processes. (1) Evergreen needle-leaved forest, (2) evergreen broad-leaved forest, (3) dry deciduous forest, (4) cold deciduous forest, (5) evergreen Mediterranean forest and shrubs, (6) grasslands and (7) tundras. These biomes are characterized by different behaviours or properties, like the aerodynamic resistance, evergreen versus deciduous phenology, drought resistance adaptation, photosynthetic capacity and

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

275

Fig. 3. Sensitivity of water stress versus LAI. F is the minimum over the year of the ratio water content/maximum water content. Resistance and dry deciduousness are accounted for (see text), so that a ratio of 0.25 (dotted line) determines the critical water stress and the hydrological equilibrium of the LAI. Pixels belong to biomes 1 (57.75 N, 44.75 E), 2 (0.25 N, 65.25 W), 3 (20.25 S, 20.25 E), 4 (47.25 N, 3.75 E), 5 (29.75 S, 119.75 E) and 6 (38.75 S, 96.75 W).

stomatal conductance, as detailed in Table 1. The vegetation map is therefore simplified after a Matthews map (Matthews, 1983) (see Appendix B for details). The phenology is defined by a leaf-on/ leaf-off transition. The dates of transition are derived from an analysis of satellite normalized difference vegetation index (NDVI) time series (Moulin et al., 1997). Outside the leaf-on season, LAI is zero. Climate data consist of monthly mean precipitation and air temperature fields from Cramer and Leemans, (update of Leemans and Cramer, 1991; Cramer, personal communication). These data are gridded on a 0.5⬚ × 0.5⬚ basis, and interpolated to the daily time-step. Incoming surface solar radiation is derived from Cramer–Leemans cloudiness fields. This dataset is the standard dataset for the IGBP/GAIM NPP models intercomparison (Lurin et al., 1994). Photosynthetically active radiation (0.4–0.7 mm) comprises 48% of solar radiation. A global map of the soil maximum available water content (% volume) is derived from the Zobler (1986) soil texture map following Prentice et al. (1992).

Using energy budget or combination equations to estimate evaporation and transpiration rates requires surface net radiation (the all-wavelength surface downward flux) and air water vapour pressure deficit. Obtaining these global fields is, however, very difficult. The reasons for the net radiation come mainly from a sparse ground monitoring network and a dependence on local surface and atmosphere properties. Furthermore, modelling this variable is equally difficult. For vapour pressure deficit, the problem is mostly the temporal variability and spatial sampling. As a result, many studies of the surface water balance promote the use of potential evapotranspiration derived from empirical formulae based, for instance, on temperature and day length. The motivation for using energy budget in this paper is primarily to explain the role of the canopy (LAI, physiological properties) on water fluxes. Extensive discussion on surface processes, and on the advantages and drawbacks of these different approaches, can be found in Mintz and Walker (1993) and Koster and Suarez

276

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Fig. 4. Annual transpiration (dashed line), soil evaporation (dotted-dashed line) and interception losses (dotted line) are plotted against LAI. The solid curve is the total evapotranspiration and the solid straight line is the annual precipitation, for a temperate deciduous forest site (47.25 N, 3.75 E), case 4 of Fig. 3.

(1994). Here, the net radiation is simply derived from solar radiation (Woodward, 1987): Rn ˆ 0:81 × Sg ⫺ 90 …W=m2 †:

…20†

Monthly mean vapour pressure fields from 1927 network stations (Spangler and Jenne, 1990) are averaged over the period 1960–1989 and gridded using a four-nearest-neighbours linear interpolation. These data are first-order approximations of the micrometeorological inputs required by energy budget calculations. However, the assumption is made that they significantly capture the large variability of climate found on a global scale. The atmosphere is viewed here as an external forcing and feedback or upscaling issues are not considered (Jarvis, 1993).

3. Results and comparison with river basins data 3.1. LAI Drought intensity is represented by the ratio of soil

water to maximum extractable water (F). The minimum value of F reached during the leaf-on period is plotted as a function of LAI in Fig. 3, for contrasting climate and vegetation types. Drought-induced stomatal control occurs when this ratio is below 0.4, and the critical stress is, by assumption, 0.25. Consequently, the intersection of the curves with F ˆ 0.25 defines the equilibrium LAI. For an a priori tolerant ecosystem with an n-day tolerance period, increasing values of F are sorted and the value at rank n is plotted against LAI, thus being directly comparable to the other curves. A sharp increase in drought intensity with canopy LAI (curves 3, 5 and 6 in Fig. 3) shows that an equilibrium is found, at the same time implying that errors in the water exchange model (LAI effects on ETr) will cause small changes in the retrieved LAI. For the temperate deciduous forest (4) and the high latitude boreal (4) sites, the curves tend to flatten. No drought is experienced for the tropical rain forest site (2), even for an LAI of 15. LAI values are determined by the light constraint (not shown) for sites 1 and 2, and close to the water

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

277

Fig. 5. Global projected LAI derived from the water equilibrium concept only.

constraint curve for site 4. These curves illustrate different behaviour of the response of the water status to increasing LAI. The asymptote of F for high LAI reflects the soil control over transpiration and evaporation, and also results from the limitation caused by low atmospheric demand (site 2; sites 1 and 4 for winter conditions). Fig. 4 displays annual evapotranspiration and its three components versus LAI for site 4. It clearly shows curvilinear relationships between transpiration and LAI, even when transpiration and interception losses are cumulated. Moreover, the soil evaporation strongly buffers the ETr versus LAI curve for sparse canopies. In that respect, the ETr–LAI curve is similar to the surface conductance–LAI curve proposed by Schulze et al. (1994) after analysis of canopy-level latent heat flux measurements. Two experiments were carried out on the global scale. The first (noted ‘water’) consists of retrieving LAI using the water constraint only. The second involves both water and light constraints. The LAI

maps in Fig. 5 and Fig. 6 thus share the regions where the water constraint is the strongest constraint on canopy development. Evaluation of these maps with the help of remote sensing global archives will be detailed elsewhere. Briefly, the ‘water’ experiment distinctly identifies aridity gradients: East–West over North America, North–South in inner Asia, and more generally the transitions between desert areas and adjoining vegetated areas. The tropics display very strong contrasts between wet areas, where LAI is not water limited, and drier regions, where rather low LAI values are found (extreme cases are Austral Africa Miombo woodlands and Brazilian Cerrados). A large spatial variability is found in the dry deciduous tropics. This is related to dispersion in the leafon season detected by NDVI time series (e.g., residual cloud contamination; Moulin et al., 1997). The main effect of the ‘light’ constraint is to cut off LAI above 5 or 6. This takes place in a large part of the boreal zone, some moist temperate areas and moist tropics: the Amazon basin, Central Africa, Indonesia and also

278

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Fig. 6. Global projected LAI derived from water and light availability constraints.

China. These results were expected for energy-limited high latitudes (Grier and Running, 1977; Woodward, 1987). A more surprising result is the sharp contrast found in the margins of the evergreen rain forest. As a first evaluation, the consistency of the water balance model has been compared to stream flow data. 3.2. Water balance Over a large river basin, the long-term water balance reduces to: Pr ⫺ ETr ˆ DR;

…21†

where DR is the annual long-term average stream flow, Pr and ETr basin-averaged precipitation and actual evapotranspiration. In the long term, water storage is assumed to be negligible. Basin discharges have been used to build up continental water balance (Baumgartner and Reichel, 1975). Moreover, it is one of the rare large-scale datasets available for global

biogeochemical model evaluation. As stream flow data present a strong year-to-year variability, 30year average river discharges were taken from Probst and Tardy (1987). These data mainly follow UNESCO reports (UNESCO, 1977). The annual evapotranspiration and the basins contours are shown in Fig. 7, and Appendix A provides river names. For these 28 rivers, the run-off simulated by the LAI model is plotted against the measured run-off (Fig. 8). Simulated evapotranspiration is plotted against the difference between observed precipitation and observed run-off (Fig. 9). The overall result is that the large variability of both run-off and evapotranspiration is well reproduced by the model. Two caveats, however, have to be considered. (a) Both run-off and precipitation observations can display significant errors. For example, precipitation data reviewed by Salati and Nobre (1991), for the Amazon basin ranges from 2000 to 2400 mm/year, and the station network sampling may introduce

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

279

Fig. 7. Annual evapotranspiration and river basin contours (see list in Appendix A).

some biases. (b) On a basin scale, climate ‘alone’ obviously exerts a strong constraint on the water balance, and the surface process effects are therefore bounded. Nevertheless, the general agreement found in Figs. 8 and 9 suggests that using an explicit canopy scheme and general physiology leads to reasonable results, considering that no parameter calibration has been performed. Consequently, canopy scale studies focused on vegetation function, e.g., long-term water and CO2 flux measurements, can significantly contribute to the modelling of the global biogeochemical cycle (Schulze et al., 1994; Saugier and Katerji, 1991). Besides the general agreement between modelled and observed water budgets, this comparison suggests two possible residual model biases. The first concerns arid areas, where run-off simulation is almost nil, whereas measured discharge is not, e.g., Colorado (3) and Limpopo (12). This may be due to intense storminess, which can generate run-off but is not suffi-

cient to fill the bucket when monthly mean climate data are used. The bucket assumption may simply be inadequate for these areas. The second possible bias concerns the dry tropics rivers. Indeed, run-off simulated for the Zambezi (28), Nile (17), Sao Fransisco (24), Senegal (25), Godavari (8) and also Zaire (27) are systematically larger than the measured values (Fig. 8). This case is different from the former, in so far as dry tropics have a well-defined rainy season, and precipitation is sufficient to fill the soil reservoir even on a monthly basis. This suggests that evapotranspiration could be slightly underestimated. This may also be related to the above-mentioned low LAI found for the dry forests surrounding the rain forest. One reason may thus be an underestimation of LAI, but this underestimation of LAI can in turn reflect a bias toward insufficient rooting depth, and subsequent excess run-off (see Section 4). Land use is generally considered an important determinant of river hydrology. Therefore, disagreement

280

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

Fig. 8. Modelled versus observed basin-averaged run-off, for 28 large rivers (see list in Appendix A).

Fig. 9. Modelled evapotranspiration versus observed rainfall minus run-off (see list in Appendix A).

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

281

Fig. 10. Change in basin-averaged run-off versus change in basin-averaged LAI following a ^ 30% change in rooting depth.

between run-off simulated for a natural potential vegetation and actually observed stream flow data can be expected. This does not appear clearly in Figs. 8 and 9. However, data for the Si Kiang river (Southern China), which were not retained because of a too short time series, may reveal land use effects. Indeed, simulated run-off is 667 mm/year and observed run-off is 839 mm/year, according to Baumgartner and Reichel (1975). The most striking effect could be expected in regions where perennial evergreen vegetation is replaced by short rotation agriculture. This occurs in the Si Kiang basin, where potential vegetation is evergreen broad-leaved forest. However, the net effect of tropical forest replacement on water yield is a complex problem and is still controversial (Bonell, 1993). Rooting depth (Rz) is often cited as an important but elusive parameter of vegetation water relations (Running, 1994) and terrestrial water balance (Milly and Dunne, 1994). Sensitivity of the model to a 30% change in Rz has been studied. As shown in Fig. 10, the sensitivity of estimated run-off (Drun-off) closely follows the sensitivity of LAI (DLAI), and displays a linear dependency: Drun-off ˆ ⫺ 91·DLAI ⫺ 1, r 2 ˆ

0.81. Increasing the size of the soil water reservoir directly favours evapotranspiration, and also allows an additional development of canopy LAI, which in turn increases evapotranspiration. The boreal basins are relatively insensitive to the rooting depth (Ob, Amur, Kolyma, Lena and Ienissei) and the arid zones (Colorado and Limpopo). To separate the respective roles of LAI and Rz, the sensitivity of run-off to a 30% change in Rz, with constant LAI, was also tested. The corresponding decreases in runoff were 60% of previous values. The streams which flow, at least partially, in the dry tropics exhibit a significant sensitivity (e.g., Mekong, Zaire and Godavari) and also the largest change in run-off relative to the change in LAI (Fig. 10).

4. Discussion The comparison of the model outputs and streamflow data, as well as the analysis of the water and light constraints, suggests some comments and also raises some questions on vegetation/water relations on a global scale. According to this model, the LAI for

282

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

the tundras, for a significant part of the boreal zones and also for some temperate zones is not primarily limited by water availability. Inclusion of the light constraint leads to reasonable simulation of high-latitude river discharges. Vegetation in these regions is assumed to be ‘energy limited’ (Woodward, 1987; Neilson, 1995). In this study, the light constraint reflects only one side of the ‘energy’ limitation, and it is not sufficient (i.e. allows for high LAI), e.g., for North-East Canada (Fig. 5). In this step, the growth process is not modelled, and temperature control on growth combined with growing season length can be additional constraints. Growing degree days (cumulative temperature above a given threshold; e.g., 0⬚C) are commonly used as a benchmark for these limitations, but Woodward (1987) pointed out that this could be difficult to translate in the context of changing CO2 atmospheric concentration or climate, because the underlying mechanisms are not described. Modelling the whole-plant carbon budget and also the temperature limited nitrogen mineralization may provide complementary constraints (Vitousek and Howarth, 1991; Field et al., 1992). On the other hand, LAI values greater than 6 are not uncommon for coniferous and tropical stands. This shows that the light constraint requires refined modelling. Accounting for foliage clumping and diffuse irradiance tends to increase the light penetration in the canopy (e.g., Cannell and Grace, 1993). The main uncertainties, however, concern the modelling of carbon gains and losses of the lowest canopy layer. Also, the temperate forests respond to water and light constraints in a close way. Both criteria mainly result in LAI values of 4–8. This suggests that the ‘climatic space’ of temperate deciduous forest favours a co-limitation of these two constraints. Tropical evergreen forests present a very contrasting picture. First, for the wet areas, the water constraint does not seem relevant: evapotranspiration, limited by net radiation and low vapour pressure deficit (VPD), is significantly lower than precipitation. For these regions, there is some evidence that the light constraint is sound (e.g., Alexandre, 1981), though modelling uncertainties are presently too large to provide accurate LAI estimates. Second, this study shows that a large part of this biome pertains to a recurrent dry season, especially severe for the margins. Consequently, corresponding equilibrium

LAI values are low (2–4) and probably underestimated. This confirms that drought avoidance or drought resistance mechanisms may play an important role in the functioning of these forests. In addition to the drought-induced and VPD-induced stomatal closure, and with the 30-day resistance period (Table 1) taken into account, at least two more mechanisms may be involved: semi-deciduousness and deep rooting. The partial defoliation of the canopy may significantly reduce evapotranspiration during the dry season (Medina, 1983), especially because it concerns emergent trees (more exposed to atmospheric demand). One can note that the margins of the rain forest are classified by Olson et al. (1983) as rain-green forest, and that Prentice et al. (1992) successfully reproduced rain-green forest distribution by adjusting thresholds using an off-line water balance model. Quantification of semi-deciduous function, however, is poorly documented (Medina, 1983). The second mechanism is deep rooting. This hypothesis is supported by Nepstad et al. (1994). They showed that a large part of the Amazon basin is exposed to a severe dry season, and presented clear evidence of deep roots tapping deep water during the dry spell. These results were established for trees and degraded pastures. They also investigated the consequences on the carbon cycle. This is in agreement with a review of maximum rooting depth across the different biomes (Canadell et al., 1996). One conclusion of the present study is that evergreen tropical forests are exposed to very different climates, and that their functioning (e.g., gas exchange) reflects this variability. The impact of drought stress and drought avoidance on both water and carbon cycles warrants further study. The rooting depth issue also holds for tropical dry forests. In that case, deep rooting and drought resistance obscure the relation between water availability and phenology. For instance, leaf flushing often occurs long before the beginning of the rainy season (Borchert, 1994; Sobrado, 1993; Machado and Tyree, 1994, Chidumayo, 1994). These studies, however, established strong relations, though sometimes complex, between water availability and phenology. This confirms that accounting for dry deciduouness cannot be avoided. Considering the comparison with river discharges (Fig. 9) and the sensitivity of the basin-averaged evapotranspiration (Fig. 10), it can be anticipated that deep rooting is a

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

major determinant of water balance for tropical dry forests as well. Previous studies have recognized the importance of the water-holding capacity of the plant root zone on the global water cycle. Using a general circulation model, Milly and Dunne (1994) found a 70-mm increase of evapotranspiration for a doubling of water-holding capacity in the range of 10–600 mm. They defined hydrological ‘thriftiness’ as the ability to retain water for later release by evaporation and proposed thriftiness as a simple characteristic of land/atmosphere water exchanges. As it is strongly dependent on rooting depth, accurate estimates of this variable are required. Developing models which are based on ecological assumptions, and thus considering the vegetation ‘point of view’ on the water cycle, clearly gives interesting insights into this question and may provide consistent parameter sets for climate/vegetation interaction studies.

5. Conclusions In this paper, a model of hydrological equilibrium of the LAI is presented. The central assumption is that adaptation of vegetation to the local climate leads to a development of the canopy, which ensures a large light absorption but prevents severe soil water depletion (e.g., Woodward, 1987). Particular attention has been paid to the processes which strengthen or weaken the basic LAI–evapotranspiration relationship, including soil moisture feedback on transpiration and evaporation, deciduousness of the canopy and interception losses. The annual water balance has been compared to stream flow data. A general agreement was found between simulated and observed run-off averaged over 28 large river basins. This shows that a water exchange scheme with explicit canopy processes can be used on a global scale. The interest of using such a scheme is to take advantage of canopy level studies (see reviews by Schulze et al., 1994 and Ko¨rner, 1994, among others) and to allow the testing of ecological assumptions on vegetation function. Aridity gradients are well defined by the hydrological equilibrium theory. An additional light availability constraint shows that, for wet tropics and some wet temperate and boreal areas, LAI is not primarily water limited. An interesting point arises

283

from an underestimation of LAI and evapotranspiration in the rain forest margins and dry forests. This suggests that these areas are prone to recurrent droughts, and that drought resistance and avoidance strategies are of utmost importance for vegetation functioning and therefore water cycle modelling. In particular, deep rooting may play a crucial role. The objective of modelling vegetation response to resources availability—here the water and light resources—is to improve our understanding of the biosphere as a resource-based system on a global scale, with the perspective of a change in atmospheric CO2 and corresponding climate modifications (Field et al., 1992). The exact role of below-ground functioning, its links with carbon allocation and especially the ‘cost’ of deep rooting emerge, from this study, as critical points. As many questions concern the carbon cycle, the coupling of biogeochemistry and biogeography models (Neilson and Marks, 1994; Neilson and Running, 1996; Woodward et al., 1995) is a promising approach to further investigate the issues of functional coupling between the carbon and water cyles.

Acknowledgements Ge´rard Dedieu, Bernard Saugier and two anonymous reviewers are acknowledged for their helpful comments. Thanks also to Be´atrice Berthelot, Ste´phane Adam and Wolfgang Ludwig for their contributions to climate and streamflow data collection. This work was supported by CNES, the European Community ESCOBA project and the French Programe National d’Etude de la Dynamique du Climat. Appendix A. List of river basins 1. 2. 3. 4. 5. 6. 7. 8. 9.

Amazon Amur Colorado Columbia Danau Don Garonne Godavari Ienissei

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Kolyma Lena Limpopo Loire Mekong Mississipi Niger Nile Ob Orange Parana Po Rhine Rhone Sao Fransisco Senegal St Lawrence Zaire Zambezi

Mean Annual Global, Continental and Maritime Precipitation, Evaporation and Runoff. Elsevier, Amsterdam, p. 179. Bonan, G.B., 1991. A biophysical surface energy budget analysis of soil temperature in the boreal forests of interior Alaska. Water Resources Research 27 (5), 767–781. Bonell, M., 1993. Progress in the u56.5.75.c(97.1ngn)-297.2(of)(197.4rRunof593

Appendix B. Simplification of Matthews vegetation map Biomes 1. Evergreen needle-leaved forest 2. Evergreen broad-leaved forest 3. Dry deciduous forest and woodland 4. Cold deciduous forest 5. Mediterranean veg., evergreen shrubs 6. Grasslands, savannahs, steppes, hot desert 7. Tundras, cold desert

Matthews classes 7, 8, 14 1–5 9, 12, 15 10, 11, 16 6, 13, 17, 18, 21 19, 23–29 20, 22, 30, 31

References Aber, J.D., Federer, C.A., 1992. A generalized, lumped-parameter model of photosynthesis, evapotranspiration and net primary production in temperate and boreal forest ecosystems. Oecologia 92, 463–474. Alexandre, D.Y., 1981. L’indice foliaire des foreˆts tropicales. Acta Oecologica, Oecol. Gener. 2 (4), 299–312. Baumgartner A., Reichel E., 1975. The World Water Balance:

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286 scheme and their effects on a GCM’s hydrological cycle. Advances in Water Resources 1, 61–78. Leemans, R., Cramer, W.P., 1991. The IIASA data base for mean monthly values of temperature, precipitation and cloudiness on a global terrestrial grid. Research Report RR-91-18, International Institute for Applied Systems Analysis, Laxenburg, Austria. Lurin, B., Rasool, S.I., Cramer, W., Moore, B., 1994. Global Net Primary Productivity. Global Change Newsletter, IGBP Newsletter 19, September 1994, Stockholm, Sweden. Machado, J.-L., Tyree, M.T., 1994. Patterns of hydraulic architecture and water relations of two tropical canopy trees with contrasting leaf phenologies: Ochroma pyramidale and Pseudobombax spetenatum. Tree Physiology 14, 219–240. Matthews, E., 1983. Global vegetation and land use: new highresolution data bases for climate studies. J. Clim. Appl. Meteor. 22 (3), 474–487. Medina, E., 1983. Adaptation of tropical trees to moisture stress. In: Golley, F.B. (Ed.), Tropical Rain Forest Ecosystems, Structure and Function, Ecosystems of the World 14A. Elsevier, Amsterdam, pp. 225–238. Milly, P.C.D., Dunne, K.A., 1994. Sensitivity of the global water cycle to the water-holding capacity of land. Journal of Climate 7, 506–526. Mintz, Y., Walker, G.K., 1993. Globals fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature. Journal of Applied Meteorology 32, 1305–1334. Moulin, S., Kergoat, L., Viovy, N., Dedieu, G., 1997. Global scale assessment of vegetation phenology using NOAA/AVHRR satellite measurements. Journal of Climate 10 (6), 1154–1170. Neilson, R.P., 1995. A model for predicting continental-scale vegetation distribution and water balance. Ecological Applications 5, 362–385. Neilson, R.P., Marks, D., 1994. A global perspective of regional vegetation and hydrologic sensitivities from climatic change. Journal of Vegetation Science 5, 715–730. Neilson, R.P., Running, S.W., 1996. Global dynamic vegetation modeling: coupling bioheochemistry and biogeography models. In: Walker, B., Steffen, W. (Eds.), Global Change and Terrestrial Ecosystems; International Geosphere–Biosphere Programme Book Series. Cambridge University Press, Cambridge, pp. 566–591. Nemani, R.R., Running, S.W., 1989. Testing a theoretical climate– soil–leaf area hydrologic equilibrium of forests using satellite data and ecosystem simulation. Agricultural and Forest Meteorology 44, 245–260. Nepstad, D.C., De Carvalho, C.R., Davidson, E.A., Jipp, P.H., Lefebvre, P.A., Negreiros, G.H., Da Silva, E.D., Stone, T.A., Trumbore, S.E., Vieira, S., 1994. The role of deep roots in the hydrological and carbon cycles of Amazonian forests and pastures. Nature 372, 666–669. Olson, J.S., Watts, J.A., Allison, L.J., 1983. Carbon in live vegetation, of major world ecosystems. ORNL-5862, Oak Ridge National Laboratory, Oak Ridge, TN. Persson, G., Lindroth, A., 1994. Simulating evapotranspiration from a short-rotation forest: variations within and between seasons. Journal of Hydrology 156, 21–45.

285

Poole, D.K., Miller, P.C., 1981. The distribution of plant water stress and vegetation characteristics in southern California chaparral. Am. Midl. Nat. 105, 32–43. Prentice, I.C., Cramer, W., Harrison, S.P., Leemans, R., Monserud, R.A., Solomon, A.M., 1992. A global biome model based on plant physiology and dominance, soil properties and climate. Journal of Biogeography 19, 117–134. Probst, J.-L., Tardy, Y., 1987. Long range streamflow and world continental runoff fluctuations since the beginning of this century. Journal of Hydrology 94, 289–311. Rambal, S., Leterme, J., 1987. Changes in aboveground structure and resistance to water uptake in Quercus coccifera along a rainfall gradient, 1987. In: Tenhunen, J.D., et al. (Eds.), Plant Response to Stress, NATO ASI Series. Springer, Berlin, 668 pp. Raupach, M.R., Finnigan, J.J., 1988. Single-layer models of evaporation from plant canopies are incorrect but useful, whereas multilayer models are correct but useless: discuss. Aust. J. Plant Physiol. 15, 705–716. Ruimy, A., Kergoat, L., Field, C., Saugier, B., 1996. The use of CO2 flux measurements in the models of the global terrestrial carbon budget. Global Change Biology 2, 287–296. Running, S.W., 1994. Testing Forest–BGC ecosystem process simulations across a climatic gradient in Oregon. Ecological Applications 4 (2), 238–247. Running, S.W., Coughlan, J.C., 1988. A general model of forest ecosystem processes for regional applications. I. Hydrological balance, canopy gas exchange, and primary production processes. Ecol. Model. 42, 125–154. Salati, E., Nobre, C.A., 1991. Possible climatic impacts of tropical deforestation. Climatic Change 19, 177–196. Saugier, B., Katerji, N., 1991. Some plant factors controlling evapotranspiration. Agricultural and Forest Meteorology 54, 263– 277. Schulze, E.-D., Kelliher, F.M., Ko¨rner, C., Lloyd, J., Leuning, R., 1994. Relationship between maximum stomatal conductance, ecosystem surface conductance, carbon assimilation rate and plant nitrogen nutrition: a global ecology scaling exercise. Ann. Rev. Ecol. Syst. 25, 629–660. Sellers, P.J., Los, S., Tucker, C.J., Justice, C.O., Dazlitch, D.A., Collatz, G.J., Randall, D.A., 1996. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part 2. The generation of global fields of terrestrial biophysical parameters from satellite data. Journal of Climate 9, 706–737. Shuttleworth, W., 1989. Micrometeorology or temperate and tropical forest. Phil. Trans. R. Soc. Lond. B324, 299–334. Sobrado, M.A., 1993. Trade-off between water transport efficiency and leaf life-span in a tropical forest. Oecologia 96, 19–23. Spangler, W.M., Jenne, R.L., 1990. World Monthly Surface Station Climatology, Computer Tape Documentation. National Center for Atmospheric Research, Boulder CO. Specht, R.L., Specht, A., 1989. Canopy structure in eucalyptusdominated communities in Australia along climatic gradients. Acta Oecologica, Oecol. Plant. 10 (2), 191–213. Sprugel, D.G., Ryan, M.G., Brooks, J.R., Vogt, K.A., Martin, T.A., 1995. Respiration from the organ level to the stand. In: Smith, W.K., Hinckley, T.M. (Eds.), Resource Physiology of Conifers, Academic Press, 396 pp.

286

L. Kergoat / Journal of Hydrology 212–213 (1998) 268–286

UNESCO, 1977. Atlas of World Water Balance. UNESCO, Paris. Vitousek, P.M., Howarth, R.W., 1991. Nitrogen limitation on land in the sea: how can it occur?. Biogeochemistry 13, 87–115. Wetzel, P.J., Chang, J.-T., 1987. Concerning the relationship between evapotranspiration and soil moisture. Journal of Climate and Applied Meteorology 26, 18–27.

Woodward, F.I., 1987. Climate and Plant Distribution. Cambridge University Press, Cambridge. Woodward, F.I., Smith, T.M., Emanuel, W., 1995. A global land productivity and phytogeography model. Global Biogeochemical Cycles 9, 471–490. Zobler, L., 1986. A world soil file for global climate modelling. NASA Technical Memorandum 87802, 32p.