Belinda E Medlyn
email: b.medlyn@unsw.edu.au

Erwin Dreyer

D Ellsworth

M Forstreuter

P C Harley

M U F Kirschbaum

Xavier Le Roux

Pierre Montpied

J Strassemeyer

A Walcroft

K Wang

D Loustau

Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data

Keywords: electron transport, model parameters, photosynthesis, ribulose-1,5-bis phosphate carboxylaseoxygenase, ribulose-1,5-bis phosphate regeneration, temperature acclimation

Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data

INTRODUCTION

Many of the models used to study effects of global change on plant function and growth incorporate the [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF] model of C 3 photosynthesis (e.g. [START_REF] Cramer | Global response of terrestrial ecosystem structure and function to CO 2 and climate change: results from six dynamic global vegetation models[END_REF]). This model is particularly useful in this context because it represents mechanistically the effects of elevated atmospheric [CO 2 ], a major factor in global change, on photosynthesis. The model has two major parameters, the potential rate of electron transport ( J max ) and the maximum rate of ribulose-1,5-bis phosphate carboxylase-oxygenase (Rubisco) activity ( V cmax ). There is now a large database of values of J max and V cmax [START_REF] Wullschleger | Biochemical limitations to carbon assimilation in C 3 plants -a retrospective analysis of A/C i curves from 109 species[END_REF] and the effects of elevated [CO 2 ] on these parameters [START_REF] Medlyn | Effects of elevated [CO 2 ] on photosynthesis in European forest species: a meta-analysis of model parameters[END_REF]. The model also has the potential to accurately represent the effects of elevated temperature, a second major factor in global change that directly affects plant growth. However, as many modellers are aware, there is a dearth of information regarding the temperature responses of J max and V cmax [START_REF] Leuning | Scaling to a common temperature improves the correlation between the photosynthesis parameters J max and V cmax[END_REF].

We know that these temperature responses are likely to vary, because the temperature response of photosynthesis itself varies with genotype and environmental conditions, and may acclimate to changes in growth temperature [START_REF] Slatyer | Altitudinal variation in the photosynthetic characteristics of snow gum Eucalyptus pauciflora Sieb. ex Spreng. I. Seasonal changes under field conditions in the Snowy Mountains area of South-eastern Australia[END_REF][START_REF] Berry | Photosynthetic response and adaptation to temperature in higher plants[END_REF]. To date, however, there has been a fairly limited number of studies examining temperature responses in the context of the Farquhar model [START_REF] Leuning | Scaling to a common temperature improves the correlation between the photosynthesis parameters J max and V cmax[END_REF]. The limited amount of information available can result in possibly inappropriate parameter choices. The database of temperature responses of model parameters has the potential to expand in the near future, given recent improvements in temperature control in commercially available gas exchange systems. However, there is a second obstacle to identifying variation in these responses between species, which is that parameter values obtained from data can differ according to the method used to derive them, as is shown below. Direct comparison of parameter values between different studies can therefore be misleading. [START_REF] Wullschleger | Biochemical limitations to carbon assimilation in C 3 plants -a retrospective analysis of A/C i curves from 109 species[END_REF] solved this problem when compiling a database of J max and V cmax by deriving all parameter values himself directly from A -C i curves, thus ensuring consistency between parameters.

The aim of this study was to improve modelling of photosynthetic temperature responses by compiling and comparing existing information on the temperature response of the parameters of the [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF] model of photosynthesis. Few studies have compared variation of these parameters among species, so a broad understanding of temperature responses and their relationship to species characteristics and growth environment is lacking. We adopted the approach of [START_REF] Wullschleger | Biochemical limitations to carbon assimilation in C 3 plants -a retrospective analysis of A/C i curves from 109 species[END_REF], using consistent methods to derive model parameters from the original data sets. Some 19 data sets were obtained. In order to draw some generalizations from these data sets, we attempted to link variation in the parameters between data sets to ecological factors such as functional type and growth environment.

METHODS

Data

Estimates of the parameters J max and V cmax may be obtained in several ways including gas exchange [START_REF] Kirschbaum | Temperature dependence of whole-leaf photosynthesis in Eucalyptus pauciflora Sieb. ex Spreng[END_REF][START_REF] Harley | Use of an analytical model to study limitation on net photosynthesis in Arbutus unedo under field conditions[END_REF], in vitro methods [START_REF] Badger | Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions, with particular reference to the effect of temperature on kinetic parameters[END_REF][START_REF] Armond | Photosynthetic acclimation to temperature in the desert shrub, Larrea divaricata. II. Light-harvesting efficiency and electron transport[END_REF] or chlorophyll fluorescence [START_REF] Niinemets | Shape of leaf photosynthetic electron transport versus temperature response curve is not constant along canopy light gradients in temperate deciduous trees[END_REF]. In order to ensure that responses were comparable, we chose only to include gas exchange data. In this method, values of J max and V cmax are obtained from the response of photosynthesis under high light ( A ) to intercellular CO 2 ( C i ). A family of A -C i curves at different temperatures will thus give the temperature response of the two parameters J max and V cmax . Obtaining such a family of curves is very time-consuming and hence several authors have attempted to estimate the temperature responses of J max and V cmax using reduced data sets (e.g. [START_REF] Hikosaka | Balancing carboxylation and regeneration of ribulose-1,5-bisphosphate in leaf photosynthesis: temperature acclimation of an evergreen tree, Quercus myrsinaefolia[END_REF][START_REF] Wohlfahrt | Inter-specific variation of the biochemical limitation to photosynthesis and related leaf traits of 30 species from mountain grassland ecosystems under different land use[END_REF]. We attempted to include some of these studies here, but we found that such shortcuts considerably reduced the accuracy of the parameter values, and therefore decided against their inclusion.

We required the original A -C i curves from each study, for reasons illustrated below. However, in two cases the original data were no longer available [START_REF] Kirschbaum | Temperature dependence of whole-leaf photosynthesis in Eucalyptus pauciflora Sieb. ex Spreng[END_REF][START_REF] Harley | Modelling photosynthesis of cotton grown in elevated CO 2[END_REF]. Temperature responses from these two studies have been extensively used in modelling, so we thought it important to include them in the comparison. Therefore, in these two cases, typical A -C i curves were reconstructed from reported parameter values and the model was re-fitted to these curves. Statistical information on parameters obtained in this way is necessarily missing. Details of all data sets used are given in Table 1.

In most cases, temperature responses were obtained by applying temperature control to leaves for the duration of the gas exchange measurements. In contrast, in the experiments carried out by [START_REF] Dreyer | Temperature response of leaf photosynthetic capacity in[END_REF] and [START_REF] Robakowski | Temperature response of photosynthesis of silver fir (Abies alba Mill.) seedlings[END_REF] (Table 1), temperature changes were applied to the whole seedlings for the night preceding the measurements. This procedure could potentially have modified the temperature response, as there is evidence that the thermal properties of photosystem II (PSII) and of electron transport may begin to acclimate after even a few hours at a given temperature (e.g. [START_REF] Havaux | Rapid photosynthetic adaptation to heat stress triggered in potato leaves by moderately elevated temperatures[END_REF]). The results presented below, however, do not appear to indicate any difference between the experiments carried out by this group and other experiments.

Model

Overview of the [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF] model of photosynthesis [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF] proposed that net leaf photosynthesis, A n , could be modelled as the minimum of two limiting rates:

(1) A c is the rate of photosynthesis when Rubisco activity is limiting and A j the rate when ribulose-1,5-bis phosphate (RuBP)-regeneration is limiting. R d is the rate of mitochondrial respiration. Rubisco-limited photosynthesis is given by:

(2) where V cmax is the maximum rate of Rubisco activity, C i and O i are the intercellular concentrations of CO 2 and O 2 , respectively, K c and K o are the Michaelis-Menten coefficients of Rubisco activity for CO 2 and O 2 , respectively, and Γ* is the CO 2 compensation point in the absence of mitochondrial respiration. This formulation of the model assumes that the cell-wall conductance, the conductance between the intercellular space and the site of carboxylation, is negligible. Some authors have argued that this conductance is significant and may vary with leaf temperature (e.g. [START_REF] Makino | Effects of growth temperature on the responses of ribulose-1,5-bisphosphate carboxylase, electron transport components, and sucrose synthesis enzymes to leaf nitrogen in rice, and their relationships to photosynthesis[END_REF]. For most species considered here, we did not have access to appropriate data to evaluate the cell-wall conductance and hence were obliged to use the form of the model given above. The rate of photosynthesis when RuBP regeneration is limiting is given by:

A A A R n c j d = ( )- min , A V C C K O K c cmax i i c i 0 = - ( ) + + Ê Ë È Î Í G *
(3) where J is the rate of electron transport. J is related to incident photosynthetically active photon flux density, Q, by: (4)

where J max is the potential rate of electron transport, θ is the curvature of the light response curve and α is the quantum yield of electron transport. The value of α was fixed at 0•3 mol electrons mol -1 photon, based on an average C 3 photosynthetic quantum yield of 0•093 and a leaf absorptance of 0•8 [START_REF] Long | Quantum yields for uptake of carbon dioxide in C 3 vascular plants of contrasting habitats and taxonomic groupings[END_REF]. The value of θ was taken to be 0•90. These parameter values have only a slight effect on the estimated value of J max .

The key parameters of the model, which vary among species, are J max and V cmax . It is the temperature dependences of these parameters that we set out to examine. In addition, it is known that the parameters K c , K o and Γ* vary with temperature. These parameters, by contrast, are thought to be intrinsic properties of the Rubisco enzyme and are generally assumed constant among species, thereby minimizing the number of parameters to be fitted [START_REF] Harley | Use of an analytical model to study limitation on net photosynthesis in Arbutus unedo under field conditions[END_REF].

T-dependence of K c , K o , and Γ*

The in-vivo temperature dependence of the Michaelis-Menten coefficients of Rubisco, K c (µmol mol -1 ) and K o (mmol mol -1 ), was recently measured in transgenic tobacco over the temperature range 10-40 °C [START_REF] Bernacchi | Improved temperature response functions for models of Rubisco-limited photosynthesis[END_REF] and the following relationships obtained:

(5) (6) T k denotes leaf temperature in K and R is the universal gas constant (8•314 J mol -1 K -1 ). Previous parameterizations of the photosynthesis model have been based on in vitro determinations of these functions, carried out by [START_REF] Badger | Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions, with particular reference to the effect of temperature on kinetic parameters[END_REF] and [START_REF] Jordan | The CO 2 /O 2 specficity of ribulose-1,5-bisphosphate carboxylase/oxygenase: dependence on ribulose bisphosphate concentration, pH and temperature[END_REF], which are given here for comparison. [START_REF] Badger | Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions, with particular reference to the effect of temperature on kinetic parameters[END_REF] determined carboxylase and oxygenase activities over the temperature range 5-35 °C of Rubisco purified from leaves of Atriplex glabriscula. They obtained the following relations (as given in [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF]):

(7) (8) (9) A J C C j i i = Ê Ë ˆ¥ - ( ) + ( ) 4 2 G G * * q a a J Q J J QJ 2 0 - + ( ) + = max max K T RT c k k = ◊ - ( ) ( ) È Î Í 404 9 79430 298 298 exp K T RT o k k = ◊ - ( ) ( ) È Î Í 278 4 36380 298 298 exp K T RT T c k k C = - ( ) ( ) È Î Í ˘> ∞ ( ) 460
K m = K c (1 + O i /K o )
, at an intercellular O 2 concentration of 210 mmol mol -1 , using each of these three sets of equations.

Similarly, the temperature dependence of the CO 2 compensation point, Γ* (µmol mol -1 ), was estimated by [START_REF] Bernacchi | Improved temperature response functions for models of Rubisco-limited photosynthesis[END_REF] to be:

(12)
Alternative expressions of the temperature dependence of the CO 2 compensation point, Γ*, are generally based on the work of either Badger and colleagues [START_REF] Badger | Effects of CO 2 , O 2 and temperature on a high-affinity form of ribulose diphosphate carboxylase-oxygenase from spinach[END_REF][START_REF] Badger | Studies on the kinetic mechanism of ribulose-1,5-bisphosphate carboxylase and oxygenase reactions, with particular reference to the effect of temperature on kinetic parameters[END_REF], [START_REF] Jordan | The CO 2 /O 2 specficity of ribulose-1,5-bisphosphate carboxylase/oxygenase: dependence on ribulose bisphosphate concentration, pH and temperature[END_REF] or [START_REF] Brooks | Effect of temperature on the CO 2 /O 2 specificity of ribulose-1,5-bisphosphate carboxylase/ oxygenase and the rate of respiration in the light: estimates from gas-exchange experiments on spinach[END_REF]. These three alternative temperature dependences are illustrated in Fig. 1b. The CO 2 compensation point is related to K c and K o and to the maximum oxygenation activity of Rubisco, V omax [START_REF] Farquhar | A biochemical model of photosynthetic CO 2 assimilation on leaves of C 3 species[END_REF]):

(13) [START_REF] Badger | Effects of CO 2 , O 2 and temperature on a high-affinity form of ribulose diphosphate carboxylase-oxygenase from spinach[END_REF] observed that the ratio V omax / V cmax = 0•21, independent of temperature, allowing the temperature dependence of Γ* to be determined from that of K c and K o . [START_REF] Jordan | The CO 2 /O 2 specficity of ribulose-1,5-bisphosphate carboxylase/oxygenase: dependence on ribulose bisphosphate concentration, pH and temperature[END_REF] studied the CO 2 specificity factor τ = K c V omax /(K o V cmax ) of Rubisco purified from spinach and obtained (equation derived by [START_REF] Harley | Modelling photosynthesis of cotton grown in elevated CO 2[END_REF]): ( 14) [START_REF] Brooks | Effect of temperature on the CO 2 /O 2 specificity of ribulose-1,5-bisphosphate carboxylase/ oxygenase and the rate of respiration in the light: estimates from gas-exchange experiments on spinach[END_REF] estimated the CO 2 compensation point of spinach in vivo using a gas-exchange technique and obtained the following relation, valid over the range 15-30 °C:

(15) They report that this relationship closely resembles that obtained by [START_REF] Jordan | The CO 2 /O 2 specficity of ribulose-1,5-bisphosphate carboxylase/oxygenase: dependence on ribulose bisphosphate concentration, pH and temperature[END_REF].

We explored the significance of the differences between these alternative formulations when fitting the parameters J max and V cmax . We found that the parameter J max was only very slightly sensitive to the formulation of either K m or Γ* (not shown). However, the parameter V cmax was highly sensitive to the formulation of K m chosen (Fig. 1c). The ratio of J max : V cmax was thus also highly sensitive to K m (Fig. 1d). This sensitivity is the reason why we considered it necessary to

K T RT c k k = ◊ - ( ) ( ) È Î Í
T RT k k G * = ( ) K V O V c omax i o cmax 2K t = ◊ - - ( ) ( ) È Î Í 2 321 29 000 298 298 exp T RT k k G * = ◊ + ◊ - ( )+ ◊ - ( ) 42 7 1 68 298 0 0012 298 2 T T k k
use a consistent method to derive all parameters in a consistent fashion from original A-C i curves before comparing the temperature responses.

In the current work, we chose to use the temperature functions obtained by [START_REF] Bernacchi | Improved temperature response functions for models of Rubisco-limited photosynthesis[END_REF], because these functions were measured in vivo, without disturbance of the leaf, and are hence more likely to reflect accurately activity within the leaf. When using the temperature dependences of J max and V cmax presented below, it is important to also use the [START_REF] Bernacchi | Improved temperature response functions for models of Rubisco-limited photosynthesis[END_REF] temperature dependences for K c , K o and Γ*, because of the sensitivity of the model to these functions illustrated in Fig. 1.

T-dependence of J max and V cmax

On reviewing the literature, it is daunting to observe the number of alternative functions that have been used to model the temperature dependences of J max and V cmax (compare, for example, [START_REF] Harley | Use of an analytical model to study limitation on net photosynthesis in Arbutus unedo under field conditions[END_REF][START_REF] Long | Modification of the response of photosynthetic productivity to rising temperature by atmospheric CO 2 concentrations: has its importance been underestimated?[END_REF][START_REF] Harley | Modelling photosynthesis of cotton grown in elevated CO 2[END_REF][START_REF] Harley | Scaling carbon dioxide and water vapour exchange from leaf to canopy in a deciduous forest. I. Leaf model parameterization[END_REF][START_REF] Lloyd | A simple calibrated model of Amazon rainforest productivity based on leaf biochemical properties[END_REF]. However, all these equations are actually just alternative expressions of two basic functions. The first is the Arrhenius function:

(16) which has parameters k 25 (the value at 25 °C) and E a (the exponential rate of rise of the function). The second is a peaked function [START_REF] Johnson | The nature of enzyme inhibitions in bacterial luminescence: sulphanilamide, urethane, temperature, pressure[END_REF], which is essentially the Arrhenius equation (Eqn 16) modified by a term that describes how conformational changes in the enzyme at higher temperatures start to negate the on-going benefits that would otherwise come from further increasing temperature. This equation can be written in two equivalent forms: The first form has parameters k 25 , H a , H d and DS, whereas the second form has parameters k opt , H a , H d and T opt . H a and H d are the same between the two forms, whereas DS and T opt are related by: (19)

(17) (18) f T k E T RT k a k k ( )= - ( ) ( ) È Î Í 25 298 298 exp f T k E T RT S H R T S H T R k a k k d k d k ( )= - ( ) ( ) È Î Í ˘+ - Ê Ë + - Ê Ë 25
f T k H H T T T RT H H H T T T RT ( )= - ( ) Ê Ë Á - - - ( ) Ê Ë Á Ê Ë Á êxp exp 1
The parameters can be interpreted as follows: k 25 and k opt are the values of J max or V cmax at temperatures 25 °C and T opt , respectively; H a gives the rate of exponential increase of the function below the optimum (and is analogous to parameter E a in the Arrhenius function); H d describes the rate of decrease of the function above the optimum; and T opt is the optimum temperature. DS is known as an entropy factor but is not readily interpreted.

Model fitting

The first step in fitting the model was to obtain a value of J max and V cmax for each individual A-C i curve. This step was carried out by fitting Eqns 1, 2, 3 and 4 to each curve using the non-linear regression routine with Gaussian algorithm in SAS (SAS Institute Inc., Cary, NC, USA). The parameter R d was also fitted but was not used further, because this parameter was found to be poorly estimated by the model.

Temperature response parameters were then obtained by fitting Eqns 16, 17 and 18 to response curves of J max and V cmax to leaf temperature, using SigmaPlot (SPSS Inc. Chicago, IL, USA). It was assumed that J max and V cmax at a given temperature could vary between leaves (according to factors such as leaf nitrogen per unit area) but that relative temperature responses of the parameters would be constant. This assumption was incorporated in the model by introducing dummy variables l i to represent each leaf and putting: (20) in Eqns 16, 17 and 18 [START_REF] Kleinbaum | Applied Regression Analysis and Other Multivariable Methods[END_REF]. Here, l i = 1 for leaf i and 0 otherwise, and k i is the value of k 25 or k opt for leaf i. Reported values of the parameters k 25 and k opt are mean and standard deviation of values of k i .

The Arrhenius model is a subset of the peaked model (compare Eqns 16 and 17). Therefore, an F-test was used to determine whether the peaked model gave a significantly better fit to data than the Arrhenius model [START_REF] Kleinbaum | Applied Regression Analysis and Other Multivariable Methods[END_REF]. As others have found, the four-parameter peaked model was often over-parameterized, i.e. there was insufficient data to determine all parameters [START_REF] Harley | Modelling photosynthesis of cotton grown in elevated CO 2[END_REF][START_REF] Dreyer | Temperature response of leaf photosynthetic capacity in[END_REF]. Hence, this model was also fitted under the assumption that H d = 200 kJ mol -1 , and an F-test used to determine whether H d was significantly different from this value.

Implied temperature response of photosynthesis

We wanted to identify the implications for photosynthesis of differences in the temperature responses of model

T H S R H H H opt d a d a = - - ( ) È Î Í D ln k lk i i i = Â
parameters. To do so, Eqns 1, 2, 3 and 4 were used to calculate a typical temperature response of net photosynthesis from the derived parameter values. This calculation was made by assuming standard ambient environmental conditions for light-saturated photosynthesis: an atmospheric [CO 2 ] concentration of 350 µmol mol -1 , a constant C i : C a ratio of 0•7, and a value for J of 0•9J max . Leaf respiration was modelled for all species using a base rate of 0•01 V cmax and a Q 10 of 2.

RESULTS

Temperature response of V cmax

Fitted parameters of the temperature response of V cmax are given in Table 2. In most cases, the peaked function (Eqn 17) with H d fixed at 200 kJ mol -1 gave a significantly better fit to the data than the Arrhenius function (Eqn 16). In no case, however, did relaxing the constraint on H d significantly improve the fit to the data. Species for which no peak in the temperature response of V cmax was discernible were Fraxinus excelsior, Prunus persica, Pinus taeda and Pinus radiata. Note, however, that measurements on P. radiata did not go above 30 °C (Table 1), and that peak values close to 40 °C (maximal measurement temperature) are statistically difficult to estimate (e.g. for F. excelsior); in all cases a peak may well occur above the highest measurement temperature.

Values of k 25 , the maximum rate of Rubisco activity at 25 °C, varied across data sets by a factor of three. Some of this variation is probably caused by variations in leaf nitrogen content between data sets. Values were highest for crop species, but were comparable for coniferous and deciduous species. Note that all rates are expressed on a one-sided leaf area basis.

The activation energy H a was generally in the range 60-80 kJ mol -1 , implying a similarity in the temperature responses of V cmax across data sets. Two data sets had values of H a slightly below this range (F. excelsior and fertilized P. radiata) whereas another two had values of H a considerably above this range (Gossypium hirsutum and Juglans regia).

The optimum temperature for V cmax , T opt , was undetermined for those experiments where the peaked function was not a significantly better fit than the Arrhenius function. Among the other experiments, T opt was generally in the range 35-41 °C, with no clear pattern in the variation, with two exceptions. Betula pendula and Pinus sylvestris, grown in Finland, experienced the lowest growing temperatures and showed significantly lower values of T opt (27-29 °C).

The variability in the temperature response of V cmax is illustrated in Fig. 2a, which shows the temperature responses normalized to 1 at 25 °C. Most of the temperature responses lie between the two curves shown for Juglans regia and Acer pseudoplatanus. The exceptions are cotton, Gossypium hirsutum, which has a much steeper V cmax -T response owing to its high value of H a , and the )

E a (kJ mol -1 ) r 2 k 25 (µmol m -2 s -1 ) k opt (µmol m -2 s -1
)

H a (kJ mol -1
)

H d (kJ mol -1 ) T opt (°C) r 2 P Crops Glycine max
Finnish plants, B. pendula and P. sylvestris, which have a much lower optimal temperature for V cmax .

Temperature response of J max

The peaked function (Eqn 17) described the temperature response of J max significantly better than the Arrhenius function (Eqn 16) for all experiments other than P. radiata and P. taeda. Parameters for the peaked function are given in Table 3.

Values of the activation energy H a were in general highest for crop species (80-90 kJ mol -1 ), intermediate for deciduous species (40-60 kJ mol -1 ) and lowest for coniferous species (30-40 kJ mol -1 ). The major exceptions to this pattern were again the cold-climate trees from Finland, B. pendula and P. sylvestris, which both had high values of H a , and F. excelsior. Values of H d were significantly less than 200 kJ mol -1 for these three species and for soybean.

The optimal temperature for J max is generally in the range 30-38 °C, with no clear pattern among species, with the exception again of the Finnish plants. Betula pendula and P. sylvestris had much lower optimal temperatures for J max of about 20 °C.

The variability in the temperature response of J max is illustrated in Fig. 2b. The two Finnish species have similar responses, with low optimal temperatures. The other conifers have responses resembling that of P. pinaster, with a relatively low slope owing to low values of H a . Deciduous tree responses generally lie between those of F. excelsior and F. sylvatica. Crop species responses are steeper again, as illustrated by the G. hirsutum response.

Ratio of J max : V cmax

Figure 3 shows the relationship between values of J max and V cmax at 25 °C. Most of the data points fall close to a straight line with a slope of 1•67. The major exceptions to this pattern are soybean, with a ratio of 2•4, and the two Finnish plants, which both have ratios of about 1. For each experiment, a linear function was fitted to the relationship between the J max : V cmax ratio and leaf temperature. There was a significant negative slope in all cases, ranging from -0•045 to -0•08, highlighting the difference in activation energies for J max and V cmax .

Implications for the temperature response of light-saturated photosynthesis

The temperature response of photosynthesis was modelled for each data set, under the assumption of a constant C i : C a ratio. From the resulting curves, the optimal temperature for photosynthesis and its rate of increase over the range 15-30 °C were calculated, and these are plotted in Figs 4 and 5 against growth temperature. Figure 4 illustrates that for the majority of broadleaf and coniferous trees, the optimal temperature for photosynthesis varies between 23 and 30 °C and is largely unrelated to growth temperature. However, the trees grown in cold conditions in Finland had considerably lower optimal temperatures. The optimal temperatures for the two crop species, which were grown in warm conditions, were comparable to the highest optimal temperatures obtained for the tree species. The rate of increase of photosynthesis between 15 and 30 °C was also similar for most plants in the survey, ranging from 1•2 to 1•6 (Fig. 5). The exceptions were the Finnish trees, again, for which photosynthesis actually decreased over this temperature range, and walnut (J. regia) and cotton (G. hirsutum), which had particularly high rates of increase. From Figs 4 and 5 we can identify three broad classes of implied photosynthetic temperature response (Fig. 6). Most plants had fairly similar responses, falling between those of A. pseudoplatanus and Q. petraea. The two Finnish trees, B. pendula and P. sylvestris, had distinctly different responses, with much lower optimal temperatures. Finally, cotton (and to a lesser extent J. regia) differed in having a much steeper response curve.

DISCUSSION

The aim of this review was to investigate variability in the temperature responses of the model parameters J max and V cmax , with a view to improving parameter choice when modelling photosynthetic processes. The major factors thought to affect these responses are growth temperature and genotype or species [START_REF] Berry | Photosynthetic response and adaptation to temperature in higher plants[END_REF]. It has also been suggested that nutrition [START_REF] Martindale | Acclimation of photosynthesis to low temperature in Spinacia oleracea L. II. Effects of nitrogen supply[END_REF] and light availability [START_REF] Niinemets | Shape of leaf photosynthetic electron transport versus temperature response curve is not constant along canopy light gradients in temperate deciduous trees[END_REF]) may play a role. We found that the temperature responses of J max and V cmax obtained in gas exchange experiments were quite similar across many of the species included in the review (Tables 2 and3), a promising finding as it potentially simplifies parameter choice. Parameter values obtained by alternative means (in vitro, chlorophyll fluorescence) are included for comparison in Table 4, and generally fall within the range of values reported in Tables 2 and3. Responses of coniferous and broadleaf trees were broadly similar, with only a slight trend for lower H a of J max in conifers. However, the responses of the two crop species, par- ticularly cotton, differed from tree species in several aspects including activation energies of both J max and V cmax and the ratio of J max : V cmax at 25 °C, suggesting that alternative parameter sets are required for modelling these two plant types. This result needs to be clarified by expansion of the database on herbaceous species and crops, however.

It is not possible to draw inferences about acclimation of photosynthesis to growing conditions from such a diverse set of studies, because several alternative explanations are possible for any observed differences, such as differences in experimental protocol or genotypic differences. Nevertheless some interesting comparisons can be made which can serve as a preliminary basis for generalizations about temperature responses in different environments.

For example, we can compare studies on the same species growing in different environmental conditions. Both Fagus sylvatica and Quercus robur were the subject of two different studies, one with seedlings growing individually in pots and one with seedlings growing densely in mini-ecosystems. Low foliar nitrogen in the mini-ecosystem studies led to low values of k 25 for both J max and V cmax . The relative temperature response of V cmax was unchanged, but T opt of J max was lower in the mini-ecosystem experiment. This result parallels that of [START_REF] Niinemets | Shape of leaf photosynthetic electron transport versus temperature response curve is not constant along canopy light gradients in temperate deciduous trees[END_REF] who found that the temperature optimum of J max was positively correlated with light availability and suggested that the correlation was a result of photosynthetic acclimation to microclimate.

There was generally a poor relationship between parameter values and growth temperature, with the clear exception of the lowest-temperature-grown plants, B. pendula and P. sylvestris, which had distinctly different temperature responses compared to plants of the same genus grown in temperate climates. The low-temperature-grown plants had low optimal temperatures for both J max and V cmax , and low J max : V cmax ratios. Although not completely comparable, a study on alpine grasses growing in low temperature environments [START_REF] Wohlfahrt | Inter-specific variation of the biochemical limitation to photosynthesis and related leaf traits of 30 species from mountain grassland ecosystems under different land use[END_REF] does not show such dramatic differences in the temperature optima of J max and V cmax . Further research is required to clearly establish the effects of growth in a cold climate on the temperature responses of J max and V cmax . No data were available for tropical species; it would be interesting to see how optimal temperatures for such species compare with those reported here.

Another key requirement for future research highlighted by this study is the need for more information on the temperature dependence of K c and K o , the Michaelis-Menten coefficients for Rubisco activity. We have illustrated the fact that values of V cmax derived from gas exchange data depend strongly on the assumed values of K c and K o and hence are not readily comparable between studies. In the absence of a clear resolution of the temperature dependence of these parameters, it is important, particularly when modelling, to ensure that parameter sets are consistent [START_REF] Medlyn | Effects of elevated [CO 2 ] on photosynthesis in European forest species: a meta-analysis of model parameters[END_REF].

It should be noted that photosynthetic rates are determined not only by biochemical processes, but also by stomatal conductance to CO 2 . In this study we have omitted to consider the effects on photosynthesis of possible acclimation of stomatal conductance to temperature. (Figs 4-6 were constructed assuming a constant C i : C a ratio.) In the companion paper [START_REF] Medlyn | Temperature response of parameters of a biochemically-based model of photosynthesis. I. Seasonal changes in mature maritime pine (Pinus pinaster Ait.)[END_REF], we showed that changes in stomatal conductance could contribute considerably to photosynthetic temperature acclimation. A similar result was found by [START_REF] Ferrar | Photosynthetic temperature acclimation in Eucalyptus species from diverse habitats, and a comparison with Nerium oleander[END_REF] for Eucalyptus species and [START_REF] Ellsworth | Seasonal CO 2 assimilation and stomatal limitations in a Pinus taeda canopy[END_REF] for Pinus taeda. [START_REF] Berry | Photosynthetic response and adaptation to temperature in higher plants[END_REF] suggested stomatal acclimation to temperature was uncommon but also noted that information on this topic was scarce. Even without acclimation, photosynthetic rates at ambient CO 2 concentration at optimum temperature, and the temperature of optimum photosynthesis itself, can be strongly affected by stomatal responses to temperature and water vapour pressure deficits [START_REF] Kirschbaum | Temperature dependence of whole-leaf photosynthesis in Eucalyptus pauciflora Sieb. ex Spreng[END_REF]. Hence, even with identical photosynthetic parameters, leaves can have different photosynthetic rates under ambient conditions due to different stomatal conductances caused by internal (e.g. water stress) or external (e.g. water vapour pressure deficits) factors. It has also been suggested that changes in the temperature response of cell-wall conductance may be a factor in temperature acclimation [START_REF] Makino | Effects of growth temperature on the responses of ribulose-1,5-bisphosphate carboxylase, electron transport components, and sucrose synthesis enzymes to leaf nitrogen in rice, and their relationships to photosynthesis[END_REF]. We were unable to evaluate this possibility owing to lack of data.

CONCLUSION

The primary aim of this review of the temperature responses of model parameters J max and V cmax was to highlight variability in these responses among species and growth environments in order to improve parameter choice when modelling temperature effects on photosynthesis and growth. In general, it was found that parameters for crop species, temperate trees, and boreal trees, fell into three distinct groups (see Tables 2 and3), suggesting that modellers should use a set of parameters from the appropriate group. The limited data analysed here also revealed differences in photosynthetic temperature response parameters among growth environments, suggesting that equations should be chosen, where possible, to be appropriate for given radiation and temperature conditions. However, to better model temperature responses, a greater understanding of the functional significance of differences among broad plant types and growth environments is needed, which will require more careful experimental comparisons of withinversus among-species variation in temperature response parameters.

  is the total number of data points used. Growth T is the mean temperature in the month preceding the measurements. Growth conditions: GH, greenhouse; GH -T, temperaturecontrolled greenhouse; N, nursery; OTC, open-top chamber (control treatment); ME, mini-ecosystem (control treatment); FACE, free-air CO

  Figure1aillustrates the temperature dependence of the effective Michaelis-Menten coefficient for CO 2 ,K m = K c (1 + O i /K o ), at an intercellular O 2 concentration of 210 mmol mol -1 , using each of these three sets of equations.Similarly, the temperature dependence of the CO 2 compensation point, Γ* (µmol mol -1 ), was estimated by[START_REF] Bernacchi | Improved temperature response functions for models of Rubisco-limited photosynthesis[END_REF] to be:

Figure 1 .

 1 Figure 1. (a) Alternative forms for the response of K m = K c (1 + O i /K o ) to leaf temperature. (b) Alternative forms for the response of Γ* to leaf temperature. (c) Response of V cmax to leaf temperature obtained by fitting a sample data set using alternative forms for K m . (d) Response of ratio J max : V cmax to leaf temperature obtained by fitting a sample data set using alternative forms for K m . Key: Solid line: data from Badger & Collatz (1977). Dotted line: data from Jordan & Ogren (1984). Dashed line: data from Bernacchi et al. (2001).

Figure 2 .

 2 Figure 2. Sample responses of (a) V cmax and (b) J max to leaf temperature. Values are normalized to 1 at 25 °C.

Figure 4 .

 4 Figure 4. Modelled optimal temperature of light-saturated net photosynthesis plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Figure 5 .

 5 Figure 5. Modelled ratio of lightsaturated net photosynthesis at 30 °C to that at 15 °C, plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Figure 6 .

 6 Figure 6. Sample responses of modelled leaf photosynthesis to leaf temperature. Values are normalized to 1 at 25 °C.

1

  Temperature response of photosynthetic parameters -review 1169 © 2002 Blackwell Publishing Ltd, Plant, Cell and Environment, 25, 1167-1179

Table 1 .

 1 Details of experimental data sets used

	Age of plants Notes		O 2 varied also seedlings		Raw data seedlings	unavailable	seedlings
	Growth T Growth conditions		25 GH -T		29 GH -T		16 N (France)
	Points		48				28
	Plants		3		2		5
	Measurement T		20,25,30,35,40		18,26,29,35		10,18,25,32,36,40	5,10,22,26,32
	Author		Harley, Weber & Gates	(1985)	Harley et al. (1992)		Dreyer et al. (2001)	Wang (unpub.)
	Common name		Soybean		Cotton		Sycamore	Silver birch
	Species	Crops	Glycine max		Gossypium hirsutum	Deciduous trees	Acer pseudoplatanus	Betula pendula

Table 2 .

 2 Parameters of the temperature response of V

	Peaked model
	cmax
	Arrhenius model	k 25 (µmol m -2 s -1
		Species

Table 3 .

 3 Parameters of the temperature response of J max

	Species	k 25 (µmol m -2 s -1 )	k opt (µmol m -2 s -1 )	H a (kJ mol -1 )	H d (kJ mol -1 )	T opt (°C)	r 2

Figure 3. Relationship between J max and V cmax at 25 °C. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species. Fitted regression line has slope of 1•67.

Table 4 .

 4 Comparable parameter values obtained by other methods

© 2002 Blackwell Publishing Ltd, Plant, Cell and Environment , 25 , 1167-1179

exchange (control ring).

© 2002 Blackwell Publishing Ltd, Plant,Cell and Environment, 25, 1167-1179

in vitro;

in vivo measurements with transgenic low-Rubisco plants;

chlorophyll fluorescence.

ACKNOWLEDGMENTS

B.M. acknowledges financial support from the French Institut National de la Recherche Agronomique and the Australian Research Council. D.E. was supported by funds from the US Department of Energy, Office of Biological and Environmental Research under the Forest-Atmosphere Carbon Transfer and Storage (FACTS) project. We thank Georg Wohlfahrt for helpful discussion and Michael Battaglia for insightful comments on the manuscript.


C L

S L

Y L B

Aggregate breakdown dynamics under rainfall compared to aggregate stability measurements

Aggregate breakdown due to rainfall action causes crusting and interrill erosion. Erodibility is, seemingly, determined by the capacity of surface aggregates to resist the effects of rainfall. In this paper, we evaluated the relevance of an aggregate stability measurement, which comprises three treatments, in order to characterize aggregate breakdown dynamics. Two cultivated soils were studied: a clay loam slightly sensitive to erosion and a more susceptible silt loam. We compare the size distributions of micro-aggregates produced by the three aggregate stability treatments to the results from a rainfall simulation. The behaviour of four initial aggregate size classes (< 3 mm, 3-5 mm, 5-10 mm, and 10-20 mm) was also compared to study the influence of the initial aggregate size on the nature of resulting aggregates. The Mean Weight Diameter was from 200 to 1400 µm for the silt loam, and from 600 to 7000 µm for the clay loam. The two experiments, aggregate stability measurements and aggregate breakdown dynamics under rainfall, yielded similar results. Qualitative analysis showed that for both soils, the sizes of fragments produced by breakdown with the aggregate stability tests and under rainfall were similar and seemed to be qualitatively independent of the size of initial aggregates. We first schematized the structural organization of aggregates in cultivated horizons with a simple hierarchical model at two levels: (i) < 250 µm micro-aggregates, (ii) > 250 µm macro-aggregates made by the binding together of micro-aggregates. We then developed a model of aggregate breakdown dynamics under rainfall which gives, for various rainfall durations, the size distributions of resulting fragments on the basis of aggregate stability measurements. We obtained a correlation coefficient of 0.87 for the silt loam and of 0.91 for the clay loam, showing that the experimental and predicted mass percentages were linearly related for each size fraction.

Introduction

Crusting and interrill erosion on cultivated soils result from aggregate breakdown and transfer of soil fragments by rain and runoff. Aggregate stability influences several aspects of a soil's physical behaviour, in particular water infiltration and soil erosion. Sealing results in decreased infiltration and increased overland flow and erosion. The relationship between crusting and erosion was investigated by [START_REF] Hairsine | Relating soil erosion by water to the nature of the soil surface[END_REF], who concluded that there was much in common between both processes, and that erosion rates were controlled in great part by aggregate breakdown processes. Soil erodibility can be estimated from some measured soil properties that are often correlated with erosion [START_REF] Amézketa | Testing a new procedure for measuring water-stable aggregation[END_REF] such as texture [START_REF] Bradford | Interrill soil erosion processes: II. Relationship of splash detachment to soil properties[END_REF], the percentage of Fe and Al (Le [START_REF] Le Bissonnais | Seal formation, runoff and interrill erosion from 17 California soils[END_REF], exchangeable Ca or sum of exchangeable bases [START_REF] Meyer | Susceptibility of agricultural soils to interrill erosion[END_REF], exchangeable sodium [START_REF] Emerson | A classification of soil aggregates based on their coherence in water[END_REF], and organic matter [START_REF] Tisdall | Organic matter and water-stable aggregates in soils[END_REF][START_REF] Haynes | Effect of sample pretreatment on aggregate stability measured by wet sieving or turbidimetry on soils of different cropping history[END_REF]. All these parameters have sometimes statistically significant relationships with soil erosion. In addition, statistical modelling is very difficult because of the large number of parameters and the complexity of their interactions.

An aggregate stability measurement combines and integrates the effect of all these textural and chemical parameters with their interactions in a single value. Various aggregate stability measurements have been proposed in order to predict soil surface behaviour and erosion (Le Bissonnais, 1996;[START_REF] Amézketa | Testing a new procedure for measuring water-stable aggregation[END_REF]. The relationship between aggregate stability and erosion has generally been dealt with at an empirical level without considering the different aggregate breakdown processes that occur under specific initial conditions [START_REF] Fox | Process-based analysis of aggregate stability effects on sealing, infiltration, and interrill erosion[END_REF]. This could explain why positive correlations between aggregate stability and soil erodibility [START_REF] Coote | Seasonal variation of erodibility indices based on shear strength and aggregate stability in some Ontario soils[END_REF], as well as negative correlations, have been reported [START_REF] Bajracharya | Interrill erodibility of some Ohio soils based on field rainfall simulations[END_REF].

To measure aggregate stability, Le Bissonnais (1996) proposed a method consisting of three treatments applied to 3-5 mm aggregates, that differentiate between the various mechanisms of breakdown: slaking due to fast wetting (treatment I), microcracking due to slow wetting (treatment II) and mechanical breakdown by stirring of pre-wetted aggregates (treatment III). The results are expressed as the resulting fragment size distribution and as the mean weight diameter (MWD), which is the sum of the mass fraction remaining on each sieve after sieving, multiplied by the mean aperture of the adjacent sieves.

De [START_REF] De Noni | Proposal of soil indicators for spatial analysis of carbon stocks evolution[END_REF] compared the results from different methods of aggregate stability measurements to erosion rates obtained on experimental parcels. The model correlation coefficients were as follows: r = 0.90 for Le Bissonnais (1996); 0.76 for [START_REF] Yoder | A direct method of aggregate analysis of soils and a study of the physical nature of erosion losses[END_REF]; 0.72 for [START_REF] Kemper | Aggregate stability and size distribution[END_REF]; and 0.66 for [START_REF] Hénin | Méthode pour l'étude de la stabilité structurale des sols[END_REF]. [START_REF] Amézketa | Testing a new procedure for measuring water-stable aggregation[END_REF] found equally good correlations between results from Le Bissonnais's method and splash erosion mass. In a recent paper, Le [START_REF] Bissonnais | Topographic dependance of aggregate stability, overland flow and sediment transport[END_REF] showed that the three aggregate stability treatments allowed assessment of the spatial variation of aggregate stability at the field scale with respect to the topography, and determination of the seasonal variations in the structural behaviour of soil.

As described by [START_REF] Hairsine | Rainfall detachment and deposition: Sediment transport in the absence of flow-driven processes[END_REF], current conceptual models of interrill erosion consider three processes: (i) rainfall detachment, (ii) sediment deposition, and (iii) entrainment of sediment. Soil detachment is supposedly due to raindrop impacts, and the only role of shallow overland flow is to transfer downslope the detached aggregates [START_REF] Kinnell | The mechanics of raindrop-induced flow transport[END_REF][START_REF] Hairsine | Unsteady soil erosion due to rainfall impact: A model of sediment sorting on the hillslope[END_REF]. At greater flow depth, the role of overland flow becomes more important and rill erosion can be initiated by detachment due to overland flow. Cohesive soil is considered to be composed of a number, n, of fragment size classes. The rate of rainfall detachment per unit area of soil, e, for sediment size class, i, is expressed as a power function of the rainfall rate, P, according to:

e i = a i P p , ( 1
)
where a is the detachability of the original soil, p a non-dimensional exponent, and a is an empirical parameter, which is not based on physical measurements. Moreover, the process named "detachment" by [START_REF] Rose | A mathematical model of soil erosion and deposition processes. I. Theory for a plane land element[END_REF] regroups two sub-processes and can be conceptually divided into the aggregate breakdown process, and the splash process which puts the resulting fragments in motion (Figure 1). Aggregate breakdown determines the size distribution of fragments available for mobilization by raindrop splash and then transported by splash and by overland flow. We propose, therefore, to use the fragment size distributions resulting from aggregate stability treatments, measured using the method of Le Bissonnais (1996), to express the aggregate breakdown dynamics.

This paper describes the investigation of the potential of aggregate stability measurements for the assessment and modelling of aggregate breakdown dynamics under rainfall.

As aggregate stability is measured on various aggregate sizes depending on the method, four initial aggregate size classes: 0-3 mm, 3-5 mm, 5-10 mm and 10-20 mm have been used in order to test the influence of initial aggregate size on the size distribution of breakdown fragments. For each of these four initial aggregate size classes, two series of experiments were performed: (i) Aggregate Stability measurements (AS), and (ii) Aggregate Breakdown induced by rainfall measurements(AB) for comparison between the fragment size distribution obtained under rainfall simulation and from aggregate stability measurements.

Materials and methods

Soils

Samples were collected from the A horizons (upper 15 cm) of two cultivated soils (Alfisols), a silt loam and a clay loam. Clay content was 112 g kg -1 for the silt loam and 360 g kg -1 for the clay loam. The organic C content was 20 g kg -1 for the silt loam and 18 g kg -1 for the clay loam. The silt loam was formed from aeolian deposits of the western part of the Paris Basin (Normandy, France), which is a zone very sensitive to erosion.

The clay loam was formed from a marly molasse of the Basin of Aquitaine (Lauragais, France). The silt loam was collected in April 2001, after ploughing to establish potato mono-culture, and the clay loam was collected in July 2001, after stubble ploughing following the wheat harvest. After removal from the field, both soils were air-dried and sieved at 20 mm.

For both series of experiments, the soils were segregated into four initial aggregate size classes by dry sieving: < 3 mm, 3-5 mm, 5-10 mm, and 10-20 mm and aggregates were oven dried for 24 h at 40 • C in order to limit moisture variations. Water content was 0.07 g kg -1 for the silt loam and 0.17 g kg -1 for the clay loam.

Aggregate stability measurements (AS)

The three aggregate stability treatments were applied to each of the four initial aggregate size classes, according to the method proposed by Le Bissonnais (1996) and tested by [START_REF] Amézketa | Testing a new procedure for measuring water-stable aggregation[END_REF], [START_REF] Le Bissonnais | Aggregate stability and assessment of soil crustability and erodibility: II. Application to humic loamy soils with various organic carbon contents[END_REF], [START_REF] Bissonnais | Topographic dependance of aggregate stability, overland flow and sediment transport[END_REF] and [START_REF] De Noni | Proposal of soil indicators for spatial analysis of carbon stocks evolution[END_REF]. In this method, three treatments are applied to aggregates in order to distinguish between mechanisms of breakdown: slaking due to fast-wetting (fast-wetting treatment), occurring, for example, during heavy storms on dry soils; micro-cracking due to slow-wetting (slow-wetting treatment), which may occur during low-intensity rain; and mechanical breakdown by the stirring of pre-wetted aggregates (stirring treatment), which corresponds to aggregate behaviour during continuously wet periods. Each treatment was replicated three times for each initial aggregate size class.

Aggregate breakdown induced by rainfall (AB)

Simulated rainfall with deionised water was applied at 30.3 mm h -1 (standard error = 1.2 mm h -1 and spatial variability < 5 %). The rainfall simulation device and its characteristics are described by [START_REF] Chaplot | Field measurements of interill erosion under different slopes and plot sizes[END_REF]. The kinetic energy was 16.2 J mm -1 and the peak raindrop size was 1.5 mm. Three replicated rainfall simulations were performed for each initial aggregate size class for both soils. The rain duration was chosen from previous experiments performed on these soils using the same rainfall intensity and corresponded to the length of time before runoff begins, i.e. 40 minutes for the silt loam and 60 minutes for the clay loam (Leguédois & Le Bissonnais, 2004).

Experimental devices (Figure 2) were built with an inner ring to hold the aggregates and a large ring to keep all the splashed fragments inside. Filter paper ensured sufficient infiltration, so that water was recovered for each device. Once weighed, we knew the exact cumulative rainfall amount for each device.

As for the aggregate stability measurements, the experiments were performed on 5 g of aggregates. For each rainfall simulation and for each initial aggregate size class, nine devices with 5 g of aggregates were submitted to rainfall. The whole fragments produced by aggregate breakdown and splash were collected after receiving various rainfall amounts, so that we obtained nine samples with different levels of breakdown.

Fragment size distribution measurements

The fragment size measurements were performed after AS and AB experiments, for each treatment or rainfall duration and for each initial aggregate size class. Ethanol was used for collecting the fragments in order to preserve the structure of the whole fragments produced. The fragment size distributions were obtained by combining sieving and laser diffraction. Fragments up to 500 µm were sieved in ethanol at 2000, 1000, and 500 µm.

Fragments smaller than 500 µm were analysed with a laser diffraction sizer as 12 fractions, from 0.05 µm to 500 µm. These 12 fractions corresponded to volume frequencies of the different size fractions. The four coarsest size fractions (>2000 µm, 1000-2000 µm, 500-1000 µm, and < 500 µm) were then collected and oven dried at 105 • C to obtain their masses. The calculation of the size distribution, including 16 size fractions, was made by combining the volume frequencies obtained with the laser diffraction sizer with the masses of the different size fractions. For this calculation, it was assumed that the bulk density of the different size fractions was similar. Then, fragment size distributions were expressed using the Mean Weight Diameter (MWD), which is the sum of the mass percentage of each size fraction multiplied by the mean size of the fraction [START_REF] Kemper | Aggregate stability and size distribution[END_REF].

Statistical analysis

An overall test of coincidence of two non-linear regressions was made to assess if two data sets were significantly different. The two data sets correspond to the MWDs obtained for various cumulative rainfalls applied to two distinct initial aggregate size classes. The objective was to test the hypothesis, H 0 , that two regression curves are similar. The principle of this test was the comparison of the residual variability obtained with only one model to the residual variability obtained with two distinct models fitted for each set of experimental data. For this, the two data sets were fitted with two distinct power functions of the rainfall variable and the residual variability S 2 y x a for both fits was calculated. The same was done by fitting a unique model to both data sets and S 2 y x b was calculated. Then the quality of the fitting was calculated by:

S 2 y x c = ((n 1 + n 2 -2) S 2 y x b -(n 1 + n 2 -4) S 2 y x a ) / 2, ( 2
)
where n 1 and n 2 are the number of calculated values for each of the two aggregate size classes. Lastly, we quantified the relative improvement by two distinct models against one by calculating the F value of the Fischer-Snedecor test:

F = S 2 y x c / S 2 y x a . (3) If F > F 2 n 1 +n 2 -4
, H 0 was rejected, meaning that a significantly better fit was obtained by considering two distinct models.

Results

Influence of the initial aggregate size class on the fragment size distribution resulting from AS

The analysis of Mean Weight Diameters, calculated, respectively, with (Figure 3 ). These results show that the variation in the MWDs between initial aggregate size classes are partly due to the effect of the > 2000 µm fraction. In fact, complete aggregate breakdown is not instantaneous. Increasing rainfall duration is probably required to reach complete breakdown when the size of initial aggregates increases (Le [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF] and when clay content increases.

For both soils, the lowest MWD is obtained for the fast-wetting treatment applied to the smallest size of initial aggregates (< 3 mm). The fast-wetting treatment is also the most destructive whatever the initial aggregate size. In addition, this treatment differs from the two others because, even if we calculate the MWD without the > 2000 µm fraction (Figure 3), the MWD increases when the size of initial aggregates increases.

For the three treatments performed on the silt loam, the fragment size distribution analysis shows a bimodal frequency curve with two modes: one around 750 µm and the other one around 75 µm (Figure 5a). For the clay loam (Figure 5b), the 75 µm peak almost vanished, but another one is visible around the > 2000 µm fraction. The clay loam produces coarser fragments than the silt loam.

Compared to the other treatments, the fast-wetting treatment generated the greatest amount of aggregates from 50 to 500 µm. Aggregates resulting from breakdown were coarser for the clay loam than for the silt loam. The slow-wetting treatment produced the smallest quantity of fine fragments. The stirring treatment generated the greatest quantity of fine fragments < 50 µm. These fragments result from the abrasion of the periphery of aggregates due to the mechanical energy applied during the treatment. This is a cumulative process and the quantity of fine fragments (< 50 µm) is proportional to the duration of the mechanical energy (Le [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF]).

The differences observed in the MWDs analysis between both soils result from differences in the intensity of the breakdown mechanisms, especially due to clay content (Le [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF]. For slow-wetting and stirring treatments, the same fragment size distributions resulting from aggregate breakdown is found, irrespective of the initial aggregate size class, particularly for the clay loam (Figure 3(b)). These fragment size distributions resulting from aggregate breakdown could be considered as characteristic signatures of soils, and related to an elementary fabric of the material.

Dynamics of aggregate breakdown under rainfall simulation (AB)

As we obtained fragment size distributions for increasing cumulative rainfall values, the dynamics of aggregate breakdown were analyzed by calculating an indicator of the MWD decrease. Each value of the indicator corresponds to the difference between the MWD before a rainfall simulation and the MWD at x mm of cumulative rainfall divided by x. We obtained the aggregate breakdown kinetics based on the mean decrease of the MWD for 1 mm of rainfall. These kinetics are similar for both soils (Figure 6), with two different stages during a rainfall event. The first is named "quasi-instantaneous" aggregate breakdown because of the rapid decrease of the MWDs. This rapid stage is particularly present for the silt loam, where the MWD of 3-5 mm aggregates decreases from 3500 µm to 980 µm under 3 mm of rainfall. It corresponds to a 70 % decrease of the MWD value for all the initial aggregate size classes of the silt loam. There is only a 40 % decrease for the clay loam. After 5 mm of rainfall, the second stage shows a slower decrease of the MWDs. During this last stage, the MWDs decrease for the silt loam is twice that of the clay loam.

As for the analysis of aggregate stability measurements, the MWDs have been calcu-lated without the > 2000 µm fraction (Figure 7). For the silt loam, the MWD of the fragments resulting from aggregate breakdown is higher for larger initial aggregates. For the clay loam, only the MWD of the < 3 mm class seems to be smaller than the three other classes. Statistical tests of regression coincidence were performed to determine if the models fitted for each of the four initial size classes (Figure 7) were significantly different. The comparisons have been made for the couples of initial aggregate size class with close tendancy curves. It shows that each initial aggregate size class has different breakdown dynamics, except for both largest classes of the clay loam (Table 1). The computation of the ratio F / F 2 n 1 +n 2 -4 enabled us to evaluate the sensitivity of the statistics. This ratio is close to one for the three largest initial aggregate size classes of the clay loam. It shows that the difference between classes of the MWD decrease is much more marked for the silt loam than for the clay loam.

For both soils, the analysis of the dynamics of each fraction resulting from aggregate breakdown can be described by a power function of the cumulative rainfall variable. We can distinguish three size ranges with a specific dynamics (Figure 8

Discussion

Comparison between AB and AS: initial aggregate size class and breakdown mechanisms

The behaviour of each soil and aggregate size class under rainfall simulation is in agreement with the results of aggregate stability measurements. For the rainfall experiment applied to the silt loam, the MWDs calculated without the > 2000 µm fraction are greater when the size of initial aggregates is larger. This relationship is less marked for the clay loam (Figure 7). We can explain this response, depending on the initial aggregate size, by considering the mechanism of micro-cracking. Micro-cracking is the result of two different mechanisms with different physical processes: differential swelling and partial slaking (Le Bissonnais, 1996). Both processes produce micro-aggregates of the same size and type but they occur in soil with different clay content [START_REF] Chan | Slaking characteristics of some Australian and British soils[END_REF]: as the clay content increases, partial slaking decreases and breakdown by differential swelling increases. Partial slaking is directly related to the wetting stage in the presence of air, and is particularly intense when the porosity is bigger and also when the clay content is small (Le [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF]. For the silt loam, we inferred that micro-cracking is the result of breakdown by partial slaking. As with the slaking mechanism, partial slaking is caused by the compression of air entrapped inside aggregates but at a smaller rate. Because of a bigger porosity in the silt loam and a sufficient rainfall rate, air can be trapped. For the silt loam, it explains why we obtain a gradual response for each initial aggregate size similar to the response to the fast-wetting treatment.

Furthermore, considering the rapid MWD decrease of the < 3 mm class for both soils (Figure 6), we can say that our rainfall simulation is destructive for the finest aggregates regardless of the soil aggregate stability. According to [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF], the finest aggregates are the most vulnerable because the ratio between the rainfall intensity and the pore volume is large. In our experiment, the mode of the raindrop size distribution produced by the simulator is 1.5 mm diameter (78 % of the volume of rainfall corresponds to raindrops from 1 to 2 mm). The MWD of the < 3 mm class before rainfall is 1.3 mm for the silt loam and 1.4 mm for the clay loam. For both soils, the ratio raindrop size : initial aggregate size is close to one. For < 3 mm aggregates, our rainfall conditions are close to those of the fast-wetting treatment. That is the reason why slaking is more prevalent in the < 3 mm aggregate size class than in the other classes. It explains why the MWDs for the < 3 mm size class (Figure 7) are so small and why their decrease is so rapid (Figure 6).

To explain the greater resistance of the largest aggregates, we hypothesise that the clay content and/or the organic matter content increases as the aggregate size increases. During sieving, the silt loam produced a very small quantity of 10-20 mm aggregates. The 10-20 mm aggregates we obtained were probably high in organic matter and in clay content, which possibly explains their "survival". In many studies, stable macro-aggregates of cultivated soils are often enriched in total C as compared to soil micro-aggregates [START_REF] Puget | Total and young organic matter distributions in aggregates fo silty cultivated soils[END_REF] and in particulate organic matter [START_REF] Cambardella | Carbon and nitrogen dynamics of soil organic matter fractions from cultivated and native grassland soils[END_REF][START_REF] Puget | Dynamics of soil organic matter associated with particle-size fractions of water-stable aggregates[END_REF]. Considering the clay content, [START_REF] Puget | Dynamics of soil organic matter associated with particle-size fractions of water-stable aggregates[END_REF] found that water-stable macroaggregates were not enriched in clay or silt when compared to microaggregates, the converse of the [START_REF] Dormaar | Chemical properties of soil and water-stable aggregates after sixtyseven years of cropping to spring wheat[END_REF] study. To verify these hypotheses, it is necessary to measure and characterise the organic matter and clay contents contained in the aggregates of each initial aggregate class.

Regarding the global pattern of the fragment size distributions, we observed a relative independence of the fragment size distributions resulting from breakdown from initial aggregate size (Figure 4). In the resulting fragment size distributions, the relative importance of each mode varies in relation to the clay content. As described by [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF], clay content seems to explain differences in the MWDs of both soils. As the duration of the energy applied is the same for all initial aggregate sizes, and considering that breakdown occurs progressively from the periphery to the centre of aggregates [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF], it is logical to obtain a greater MWD for the coarsest initial aggregate classes, even if the MWD is expressed without the > 2000 µm fraction.

Comparison between AB and AS: temporal dynamics of breakdown mechanisms

The fast-wetting treatment is more destructive than the rainfall applied in the AB exper-iments. For both soils, the size distribution of fragments produced quasi-instantaneously with the fast-wetting treatment is very different from the one obtained during the first millimetres of rainfall. Slaking, which is responsible for aggregate breakdown in the fastwetting treatment, occurs on dried aggregates [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF]. Thus this mechanism could only happen during the first millimetres of rainfall, which is not the case.

The clay loam yielded almost the same response for all initial aggregate size classes submitted to rainfall. This confirms that slaking is not dominant under our rainfall conditions.

If it were, the MWD of the four initial size classes obtained under rainfall would be different from each other, as it is so for the fast-wetting treatment. Therefore, we can conclude that the breakdown we observe under rainfall simulation corresponds to the cumulative effect of microcracking and mechanical breakdown mechanisms. These mechanisms are simulated by the slow-wetting treatment and the stirring treatment, respectively.

As we can see for the 3-5 mm aggregates of the silt loam (Figure 8), the fragment size distribution resulting from the slow-wetting treatment is similar to the fragment size distribution obtained after 3.2 mm of rainfall. During the first three millimetres of rainfall, the microcracking mechanism is also predominant and its intensity seems to be at a maximum at about 3 mm of cumulative rainfall. The fragment size distribution obtained for the stirring treatment, enriched in fine fragments around the 75 µm peak, which is typical of this treatment, is similar to the fragment size distribution obtained after 21.2 mm of rainfall.

Mechanical breakdown due to raindrop impact is an important process for wet soils because the aggregates are weaker (Le Bissonnais, 1996). The breakdown is proportional to the duration of the mechanical energy applied (Le [START_REF] Bissonnais | Analyse des mécanismes de désagrégation et de mobilisation des particules de terre sous l'action des pluies[END_REF]. We observed differences in the quantities of fine fragments (about 75 µm) produced between the four initial aggregate size classes. For both soils, comparing the fragment size distribution obtained at the end of the rainfall simulation to the fragment size distribution obtained from the stirring treatment, we observed that the < 3 mm aggregate class produces more fine fragments under rainfall than during the stirring treatment. This tendency is reversed for the 10-20 mm class. For the 3-5 mm class, size distributions are similar for the stirring treatment and the rainfall simulation. This means that the mechanical energy applied during the stirring treatment is equivalent to the effect of 30 mm of rainfall at 30 mm h -1 . This also shows that the raindrop effect is particularly important and rapid when the size of the aggregates is small. During the stirring treatment, the aggregates receive mechanical energy once they are completely wet. The difference between AB and AS experiments is, that under rainfall simulation, the wetting is more progressive than during the stirring test. The saturation of large aggregates under rainfall is particularly slow.

Relation between aggregate structural organisation and aggregate breakdown

Regarding the dynamics of each of the 16 fragment size fractions resulting from breakdown, the mass percentage of the whole < 250 µm size fractions increases during rainfall (Figure 8). This means that the > 250 µm aggregates are progressively broken down into < 250 µm aggregates. Our results confirm those of [START_REF] Tisdall | Organic matter and water-stable aggregates in soils[END_REF], Oades &[START_REF] Oades | Aggregate hierarchy in soils[END_REF][START_REF] Puget | Dynamics of soil organic matter associated with particle-size fractions of water-stable aggregates[END_REF], who proposed a hierarchical model of soil aggregation in which macroaggregates are made by the binding together of microaggregates.

We can assume a very simple hierarchical organisation at two levels for aggregates of ploughed layers of cultivated soils: microaggregates (< 250 µm) are brought together in macroaggregates [START_REF] Plante | A modelling approach to quantifying soil macroagregate dynamics[END_REF] and progressively separated during breakdown (Figure 9).

In our case, aggregate breakdown results from physical mechanisms. Aggregates have pores of different sizes, which determine the distribution and strength of failure zones [START_REF] Perfect | Fractal theory applied to soil aggregation[END_REF]. Physical breakdown mechanisms occur at the weakest points of aggregate structure. For a given energy input, the probability of aggregate failure increases with increasing aggregate size [START_REF] Marshall | Stability of structural aggregates of dry soil[END_REF][START_REF] Coughlan | Aggregation in swelling clay soils[END_REF].

For both soils, we obtained a continuous enrichment in < 250 µm aggregates during rainfall. We conclude that the aggregate structure of both soils is made by the binding together of < 250 µm aggregates. We also consider that the energy applied during our rainfall simulations corresponds to the energy required to break down coarse aggregates in < 250 µm aggregates, but is not sufficient to break down these 250 µm aggregates into smaller units.

Modelling soil detachment dynamics using aggregate stability measurements

The hierarchical model of soil aggregation allows categorisation of the dynamics of 16 size fractions into two size ranges. The > 250 µm size range, whose total mass percentage decreases during rainfall, P, includes the four coarsest fractions, j. This total mass percentage can be written as B j with j = 1, 2 . . . 4. The total mass percentage corresponding to the < 250 µm size range, with the finest size fractions, k, can be written as B k with k = 5, 6 . . . 16, with B k increasing during rainfall. The conservation of sediment mass percentage in fragment size fractions j and k can be written as:

4 1 B j (P) + 16 5 B k (P) = 1. (4)
Considering that the three mechanisms (slaking, microcracking, and mechanical breakdown) reproduced by the three aggregate stability treatments are dominant at different times during a rainfall event (Figure 10), we propose equation ( 5), which gives the mass percentage, B i , of fragments of each of the 16 size fractions, i, available at P millimetres of cumulative rainfall:

B i (P) = α [Fast-wetting] i (P) + β [Slow-wetting] i (P) + χ [Stirring] i (P), (5)
where α, β, and χ are constants.

Results obtained for aggregate stability measurements showed that the fast-wetting treatment was more destructive than that observed during the rainfall experiment. This means that the fragment size distributions obtained from the fast-wetting treatment do not correspond to the size distribution of fragments resulting from aggregate breakdown under a 30 mm h -1 rainfall rate (Figure 8). For greater rainfall intensities, the slaking process, which is simulated by the fast-wetting treatment, would probably be present and dominant during the first millimetres of rainfall [START_REF] Concaret | Étude des mécanismes de la destruction des agrégats de terre au contact de solutions aqueuses (2)[END_REF]. In this case, the use of the fastwetting treatment variable would better describe the fragment size distribution obtained under rainfall. This would also be true for larger raindrops such as those observed during heavy storms. In our case, the dynamics of soil detachment are modelled without the fast-wetting term of equation ( 5), using only the slow-wetting and stirring treatments, as represented in Figure 6. Dynamics are modelled with power functions of the rainfall variable as:

B i (P) = [Slow-wetting] i m P n + [Stirring] i r P s , (6)
where [Slow-wetting] as clay content could certainly be used to explain the differences in the parameter values between both soils [START_REF] Meyer | Susceptibility of agricultural soils to interrill erosion[END_REF].

Conclusions

The aim of this study was to investigate the potential of aggregate stability measurements for the assessment and modelling of aggregate breakdown dynamics under rainfall which is the first step of the interrill erosion process.

We showed that the fragment size distribution resulting from breakdown were very similar for the four initial aggregate size class, indicating that the same mechanisms were involved. The differences observed from one class to another resulted essentially from the duration of these mechanisms while the differences between soils were in terms of the intensity of the breakdown mechanisms.

Another result was that the fragment size distributions obtained with the aggregate

  (a)) and without (Figure 3(b)) the > 2000 µm size fraction, shows the difference in aggregate stability between both soils for the three treatments. It shows the higher stability of the clay loam. A noticeable point is that, for the three treatments, the MWD increases as the size of initial aggregates increases. The fragment size distribution analysis of the four initial aggregate size classes shows that the greatest diffference is observed for the largest > 2000 µm fraction (Figure 4). For the clay loam, the MWDs calculated without the > 2000 µm fraction for the slow-wetting and stirring treatments are not significantly different for the four initial aggregate size classes, except for the slow-wetting treatment applied to 3-5 mm aggregates (Figure 3(b)). For the silt loam, the comparison between the MWDs calculated without the > 2000 µm fraction for the three treatments shows that only the < 3 mm size class is significantly different from the other initial aggregate size class (Figure 3(b)

  (a)): 1. > 2000 µm: The mass percentage of this size range decreases rapidly during the first three millimetres of rainfall. 2. 250-2000 µm: During the first three millimetres of rainfall, the mass percentage of fragments increases due to the breakdown of > 2000 µm aggregates. Then, this quantity decreases because the aggregates are themselves broken down into finer aggregates; after three millimetres of rainfall there are few > 2000 µm aggregates remaining to be broken down into 250-2000 µm fragments. 3. < 250 µm: This size range grows because of the progressive breakdown of > 250 µm aggregates into < 250 µm fragments. This size range could correspond to the panel of elementary micro-aggregates which are put together to form the > 250 µm macroaggregates.

  i and[Stirring] i are the percentage of the fraction i obtained for each aggregate stability treatment, P the cumulative rainfall, m, n, r and s are constants characteristic of each soil.As the fragment size distributions resulting from breakdown are qualitatively independent from the size of initial aggregates, non-linear regression was made for the breakdown of 3-5 mm aggregates. This modelling consists of fitting the measured percentage to equation (6), which is based on the mass percentage of each of the 16 size fractions measured from aggregate stability treatments. The values of the m, n, r and s parameters have been optimised for each soil by minimising the distance:16 i=1 B i exp(P) -B i mod(P) 2 , (7)with B i exp the experimental value of the mass percentage of a fraction i, and B i mod, the predicted value of the mass percentage of a fraction i. The optimisation of m, n, r and s parameters was made on a data set corresponding to one replicate, the model obtained from which (n = 135), was then used to predict the mass percentage of the validation set corresponding to the two other replicates (n = 270). We obtained excellent coefficients of correlation for both soils (r=0.87 for the soilt loam and r=0.91 for the clay loam), as presented for the silt loam in Figure11. These first results show it is possible to express the aggregate breakdown,B i ,on the basis of aggregate stability measurements. It makes it possible to know the size distribution of fragments available to be put in motion by raindrop impacts and then transported by splash or runoff (Figure1) for various cumulative rainfall values, from the fragment size distribution obtained with the aggregate stability measurements.In equation (6), the dynamics are modelled with the rainfall variable in terms of cumulative rainfall and, so, it doesn't take the rainfall intensity into account. The rainfall energy, coupling cumulative rainfall and rainfall intensity, would certainly describe the aggregate breakdown dynamics more generally. The relevance of the fast-wetting treatment in soil detachment modelling has to be tested for greater rainfall intensities. It would be interesting to determine ranges of rainfall rate where combinations of the three aggregate stability treatments describe correctly the fragment size distribution dynamics of breakdown products. Complementary experiments could also be performed on other types of soils in order to assess the validity range of this model. Variables such

  stability measurements were similar to those obtained under rainfall experiments. The gradual response obtained for various cumulative rainfall values was due to the relative magnitude of the different physical mechanisms simulated by the three aggregate stability treatments.We have identified a similar structural organisation of aggregates from ploughed layers for the clay loam and the silt loam. The macroaggregates are constructed from < 250 µm microaggregates, which progressively detach at the weakest point of the aggregate structure under rainfall action.These results allowed modelling of the dynamics of aggregate breakdown under rainfall on the basis of the fragment size distributions resulting from aggregate stability measurements. This aggregate breakdown model could be combined with temporal data or models of fragment size distributions of splashed fragments and sediments transported by overland flow. This should enable the evaluation of the size selectivity of the mobilisation and transport processes, and development of a global model of sediment transfer in interrill erosion.

Fig. 1

 1 Fig. 1Conceptual modelling of interrill erosion as three sub-processes: breakdown, mobilisation and transport/sedimentation. Initial aggregates (a) break down into fragments (b). Raindrops mobilise fine fragments (c), available for transport by overland flow for the finest (d) or sedimentation for the coarsest (e).Fig.2Aggregate breakdown holder and collector. Fig.3Aggregate stability measurements expressed as Mean Weight Diameters (MWD) computed for each fraction (a) and without the > 2000 µm fraction (b). Str: stirring treatment; SW: slow-wetting treatment; FW: fast-wetting treatment. Bars are standard errors. MWD values followed by a different lowercase letter within the same treatment and between the four initial aggregate size classes are significantly different at P < 0.05. Values followed by * within the same initial aggregate size class and between treatments are significantly different at P < 0.05. Fig. 4 Fragment size distribution resulting from the fast-wetting treatment performed on the clay loam aggregates. Bars are standard errors. Fig. 5 Fragment size distributions resulting from the three aggregate stability treatments on 3-5 mm initial aggregates for (a) the silt loam and (b) the clay loam. Bars are standard errors. Fig. 6 MWD decrease indicators during rainfall simulation for each initial aggregate size, corresponding to the decrease of the MWD at each millimetre of rainfall for (a) the silt loam and (b) the clay loam. Curves are power functions of the cumulative rainfall. Fig. 7 Dynamics of the MWDs resulting from breakdown under rainfall for (a) the silt loam and (b) the clay loam. The MWDs are calculated without the > 2000 µm fraction. Curves are power functions of the cumulative rainfall variable. Fig. 8 Fragment size distribution resulting from breakdown of 3-5 mm aggregates for the silt loam. Comparison between size distribution of breakdown products resulting from various cumulative rainfall heights (a) and aggregate stability measurements (b). Bars are standard errors (b).Fig. 9 Relationship between aggregate breakdown and aggregate structural organisation of ploughed layers of cultivated soils. Fig. 10 Theoretical schemas for the organisation and evolution of aggregate breakdown mechanisms, where (a) represents the supposed predominance of each of the three physical mechanisms responsible for breakdown at specific moments of a rainfall event, (b) corresponds to the simplified schema of what we really observe during the rainfall simulations at 30 mm h -1 . Fig. 11 Comparison of the modelled mass percentage of breakdown fragments vs measurements, for 3-5 mm aggregates of the silt loam and for various cumulative rainfall values.

Fig. 2

 2 Fig. 1Conceptual modelling of interrill erosion as three sub-processes: breakdown, mobilisation and transport/sedimentation. Initial aggregates (a) break down into fragments (b). Raindrops mobilise fine fragments (c), available for transport by overland flow for the finest (d) or sedimentation for the coarsest (e).Fig.2Aggregate breakdown holder and collector. Fig.3Aggregate stability measurements expressed as Mean Weight Diameters (MWD) computed for each fraction (a) and without the > 2000 µm fraction (b). Str: stirring treatment; SW: slow-wetting treatment; FW: fast-wetting treatment. Bars are standard errors. MWD values followed by a different lowercase letter within the same treatment and between the four initial aggregate size classes are significantly different at P < 0.05. Values followed by * within the same initial aggregate size class and between treatments are significantly different at P < 0.05. Fig. 4 Fragment size distribution resulting from the fast-wetting treatment performed on the clay loam aggregates. Bars are standard errors. Fig. 5 Fragment size distributions resulting from the three aggregate stability treatments on 3-5 mm initial aggregates for (a) the silt loam and (b) the clay loam. Bars are standard errors. Fig. 6 MWD decrease indicators during rainfall simulation for each initial aggregate size, corresponding to the decrease of the MWD at each millimetre of rainfall for (a) the silt loam and (b) the clay loam. Curves are power functions of the cumulative rainfall. Fig. 7 Dynamics of the MWDs resulting from breakdown under rainfall for (a) the silt loam and (b) the clay loam. The MWDs are calculated without the > 2000 µm fraction. Curves are power functions of the cumulative rainfall variable. Fig. 8 Fragment size distribution resulting from breakdown of 3-5 mm aggregates for the silt loam. Comparison between size distribution of breakdown products resulting from various cumulative rainfall heights (a) and aggregate stability measurements (b). Bars are standard errors (b).Fig. 9 Relationship between aggregate breakdown and aggregate structural organisation of ploughed layers of cultivated soils. Fig. 10 Theoretical schemas for the organisation and evolution of aggregate breakdown mechanisms, where (a) represents the supposed predominance of each of the three physical mechanisms responsible for breakdown at specific moments of a rainfall event, (b) corresponds to the simplified schema of what we really observe during the rainfall simulations at 30 mm h -1 . Fig. 11 Comparison of the modelled mass percentage of breakdown fragments vs measurements, for 3-5 mm aggregates of the silt loam and for various cumulative rainfall values.

Fig. 9

 9 Fig. 1Conceptual modelling of interrill erosion as three sub-processes: breakdown, mobilisation and transport/sedimentation. Initial aggregates (a) break down into fragments (b). Raindrops mobilise fine fragments (c), available for transport by overland flow for the finest (d) or sedimentation for the coarsest (e).Fig.2Aggregate breakdown holder and collector. Fig.3Aggregate stability measurements expressed as Mean Weight Diameters (MWD) computed for each fraction (a) and without the > 2000 µm fraction (b). Str: stirring treatment; SW: slow-wetting treatment; FW: fast-wetting treatment. Bars are standard errors. MWD values followed by a different lowercase letter within the same treatment and between the four initial aggregate size classes are significantly different at P < 0.05. Values followed by * within the same initial aggregate size class and between treatments are significantly different at P < 0.05. Fig. 4 Fragment size distribution resulting from the fast-wetting treatment performed on the clay loam aggregates. Bars are standard errors. Fig. 5 Fragment size distributions resulting from the three aggregate stability treatments on 3-5 mm initial aggregates for (a) the silt loam and (b) the clay loam. Bars are standard errors. Fig. 6 MWD decrease indicators during rainfall simulation for each initial aggregate size, corresponding to the decrease of the MWD at each millimetre of rainfall for (a) the silt loam and (b) the clay loam. Curves are power functions of the cumulative rainfall. Fig. 7 Dynamics of the MWDs resulting from breakdown under rainfall for (a) the silt loam and (b) the clay loam. The MWDs are calculated without the > 2000 µm fraction. Curves are power functions of the cumulative rainfall variable. Fig. 8 Fragment size distribution resulting from breakdown of 3-5 mm aggregates for the silt loam. Comparison between size distribution of breakdown products resulting from various cumulative rainfall heights (a) and aggregate stability measurements (b). Bars are standard errors (b).Fig. 9 Relationship between aggregate breakdown and aggregate structural organisation of ploughed layers of cultivated soils. Fig. 10 Theoretical schemas for the organisation and evolution of aggregate breakdown mechanisms, where (a) represents the supposed predominance of each of the three physical mechanisms responsible for breakdown at specific moments of a rainfall event, (b) corresponds to the simplified schema of what we really observe during the rainfall simulations at 30 mm h -1 . Fig. 11 Comparison of the modelled mass percentage of breakdown fragments vs measurements, for 3-5 mm aggregates of the silt loam and for various cumulative rainfall values.

  Figure 3

Table 1

 1

	Clay loam	11.12	1.85	0.09	1.22
	Silt loam	18.58	5.47	14.23	33.82

Acknowledgements

The authors appreciate the skilled assistance of B. Renaux and L. Prud'Homme for rainfall simulations, H. Gaillard for aggregate stability measurements, F. Darboux for scientific discussions, and K. Wein and T. Ellis for English language corrections.

List of Tables

Statistical ratios between calculated and theoretical values of the F-test at P < 0.05 for each couple of initial aggregate size class compared to each other. If F > F 2 n 1 +n 2 -4 , the two data sets are significantly different. . . . . . 25