V Shcherbakov
email: shcherbakov@moniut.univ-bpclermont.fr

J.-F Gayet

G Febvre

A J Heymsfield

G Mioche

Probabilistic model of shattering effect on in-cloud measurements

A probabilistic model of the ice shattering effects on in-cloud measurements performed with instruments designed with inlets, which have the circular cross-section, is presented. Applications are made for the Polar Nephelometer and PMS FSSP instruments. The model provides rough estimates of the effects on microphysical measurements and assigns the key parameters that govern the efficiency of ice shattering. It is shown that experimental data are less affected by the shattering for clouds that have a lower proportion of large particles. The effects on derived integral microphysical parameters are shown to be very sensitive to the effective diameter of the ice fragments. The smaller the fragments from a given cloud particle are, the higher their effects are.

Errors on Polar Nephelometer measurements were evaluated. It is shown that the ice particle shattering leads to the overestimation of the extinction coefficient. For example, for a given distribution with the effective diameter of 68 µm and with fragment effective diameters of 10 µm the extinction is overestimated by 25%. With larger particles having an effective diameter of 89 µm, the error increases up to 37%. As for the FSSP-300 instrument, under the same conditions the extinction coefficient is overrated by 17% and the number particle concentration is overestimated by 30%. The discussion of the results points out the main hypothesis which may seriously limit the reliability of the modelling results. Nevertheless, the magnitudes of the errors on extinction and particle concentration are of the same orders of those reported in the literature from experimental assessments.

Introduction

Airborne in situ instruments have intensively been used on aircraft to measure microphysical characteristics of warm, mixed and ice clouds for several decades. The observed experimental data are widely used for cloud parameterizations for many applications such as cloud process studies, general circulation models, validation of remote sensing techniques, assessment of cloud radiative forcing and so on. At the same time, for many years it has been recognized that some aircraft cloud microphysical measurements may be contaminated by hydrometeors shattering or splashing when they collide with the probe inlets [START_REF] Heymsfield | On measurements of small ice particles in clouds[END_REF]. [START_REF] Gardiner | Degradation of in-cloud Forward Scattering Spectrometer Probe measurements in the presence of ice crystals[END_REF] showed that in the presence of large, irregular ice crystals the FSSP droplet spectra may be artificially enhanced by 2-3 orders of magnitude. [START_REF] Gayet | The reliability of the PMS FSSP in the presence of small ice crystals[END_REF] compared FSSP and 2D-C measurements and concluded that FSSP concentrations are exaggerated in cirrus with large crystals (i.e., maximal particle size up to 700 µm). [START_REF] Field | Ice particle interarrival times measured with a fast FSSP[END_REF] came to the conclusion that shattering may result in overcounting of ice particles measured by FSSP in the midlatitude cirrus by factor of 2 to 5. Techniques were proposed by [START_REF] Field | Ice particle interarrival times measured with a fast FSSP[END_REF][START_REF] Field | Shattering and interarrival times measured by optical array probes in ice clouds[END_REF] to separate genuine small particles from shattering artefacts using ice particle interarrival times (from either Fast-FSSP or 2D-C probes), thus making objective corrections possible. [START_REF] Korolev | Shattering during sampling by OAPs and HVPS. Part I: Snow particles[END_REF] concluded that the fraction of shattered particles may make up more than 10% of the total number of particles sampled by the OAP-2DP. [START_REF] Heymsfield | On measurements of small ice particles in clouds[END_REF] showed that there are linear relationships between the ice water content (IWC) in large particles and those detected by the FSSP and the cloud and aerosol spectrometer (CAS). The within-cloud condensation nuclei measurements may be an artifact of the sampling process because of droplet splashing on the edge of the inlet [START_REF] Hudson | Cloud condensation nuclei near marine stratus[END_REF]. [START_REF] Baker | Drop size distributions and the lack of small drops in RICO rain shafts[END_REF] pointed out that splashing events on the 2D-S probe are a regular occurrence in the presence of raindrops. Moreover, [START_REF] Jensen | On the References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion importance of small ice crystals in tropical anvil cirrus[END_REF] emphasized that the observed difference in 2D-S measurements from DC-8 and WB-57 flight legs during the Tropical Composition, Cloud, and Climate Coupling (TC4) campaign may be an indication of shattering off the leading edge of the WB-57 wing affecting the 2D-S measurement at the wing-hatch location. In the following, we discuss only shattering artifacts, which are directly related to the instrument itself. On the other hand, it is reasonable that not all data of in-cloud measurements should be considered as erroneous. For example, [START_REF] Garrett | Comments on "Effective radius of ice cloud particle populations derived from aircraft probes[END_REF] concluded that the Cloud-Integrating Nephelometer (CIN) is insensitive to shattering of precipitation-sized particles on its aperture. At the same Figures

Back Close Full Screen / Esc

Printer-friendly Version Interactive Discussion time, [START_REF] Heymsfield | Responses to comments on "Effective radius of ice cloud particle populations derived from aircraft probes[END_REF] suggested that measurements from both the cloud integrating nephelometer (CIN) and the FSSP instruments may be similarly contaminated by ice particle shattering.

A large dataset of microphysical and optical characteristics of cirrus clouds (see Gayet et al., 2006 and citations therein) was obtained during the INCA (INterhemispheric differences in Cirrus properties from Anthropogenic emissions) experiment [START_REF] Str Öm | Aerosol and cirrus measurements at midlatitudes on the Southern hemisphere: An overview based on the first INCA experiment[END_REF]. The instruments used for the measurements have already been thoroughly described by [START_REF] Gayet | Cirrus cloud microphysical and optical properties at southern and northern midlatitudes during the INCA experiment[END_REF]. Three independent techniques were used in that study: (1) the PMS (Particle Measuring System) FSSP-300 (Forward Scattering Spectrometer Probe) operated by the DLR (Deutsches Zentrum f ür Luft-und Raumfahrt), (2) the PMS 2D-C and (3) the Polar Nephelometer (PN) probes, both operated by the LaMP (Laboratoire de M ét éorologie Physique). The same set of instruments was employed in several campaigns during recent years. Thus, it is of importance to estimate the ice shattering effects in relation to those instruments. This work concerns only the Polar Nephelometer and the FSSP instrument. As for the PMS 2D-C probe, we note in passing that since 2001 the LaMP's operational algorithm rejects frames with three and more isolated images. Consequently, shattering could result in an undercounting of real large particles (see, [START_REF] Korolev | Shattering during sampling by OAPs and HVPS. Part I: Snow particles[END_REF].

The shattering of actual ice particles into several smaller ice fragments may occur due to 1) mechanical impact with the probe arms (PN, FSSP, 2D-C) and/or the inlet shroud (PN, FSSP) prior to their entering the sampling volume, and 2) fragmentation due to interaction with turbulence and wind shear generated by the probe housing (see, e.g., [START_REF] Korolev | Shattering during sampling by OAPs and HVPS. Part I: Snow particles[END_REF]. The shattering efficiency depends on a large set of parameters, namely, the habit, size, and density of cloud particles, probe inlet-shroud design [START_REF] Korolev | Shattering during sampling by OAPs and HVPS. Part I: Snow particles[END_REF], the airspeed and the impact angle with respect to the airflow [START_REF] Weber | Spurious aerosol measurements when sampling from aircraft in the vicinity of clouds[END_REF]. Thus, a number of physical processes have to be considered in an effort to evaluate effects of the shattering on airborne measurements. The exact solution of this problem is extremely arduous, if not to say impossible, task. Thus, the use of simplified models or approximations could be useful tools that are able to provide rough estimates of the shattering effects on in-cloud measurements.

Because the Polar Nephelometer and the FSSP probes have inlets with circular crosssection (see sketches on Fig. 1) a common model of the shattering can be proposed for these two instruments. The aim of this paper is to present a probabilistic model of ice shattering effects on Polar Nephelometer and FSSP measurements. This work is a first attempt to obtain rough estimates of measurement errors caused by the shattering or the splashing of cloud particles. The concept and the results may initiate more sophisticated models and may be used for the design of oriented wet wind tunnel experiments.

The paper is organized as follows: the probabilistic model is described first, thereafter the results of case study are presented. Finally, the last section is devoted to the discussion and to the practical application.

2 The model of ice particle shattering

Description of the probabilistic model

When the shattering effect is discussed in the literature, the emphasis is usually on fragments that are measured as cloud particles. In other words, the main attention is given to the additional component that may result in overestimation of derived cloud properties (extinction coefficient for instance) and in overcounting of ice particles concentration measured by the FSSP. Generally, impacting cloud-particles are identified as the source of fragments. At the same time, the question whether the ensemble of the sampled non-shattered particles differs from the ensemble of actual cloud particles is usually neglected.

To get an answer on this question, it will suffice to imagine an instrument inlet having a crosssection diameter, for example, of 100 µm. It is obvious that such an instrument cannot measure particles having a size of 100 µm or higher. Therefore, for all in-cloud instruments which are designed with an inlet to drive cloud particles into the sampling section, not only ice fragments resulting from the shattered particles may affect the measured data, but the size distribution of the sampled cloud particles may be altered as well. Consequently, we consider the shattering effects on in-cloud measurements that are governed by two processes. The first one is the loss of cloud particles (which are assumed to be shattered) due to collisions with the tip of the probe inlet shroud.

Thus, the measured size distribution of the particles, which are not shattered, is not equal to the actual size distribution of cloud particles. Moreover, we consider the loss of cloud particles as the unavoidable source of fragments for an instrument designed with an inlet or a shroud. The second process is a direct consequence of the first one, that is, some fragments of the shattered particles are sampled by the probe as cloud particles.

Hereafter, we will use the term "shattered particles" to mean actual cloud particles that will impact with the probe inlet tube and shatter. The term "fragments" will be used for particles resulting from shattering. A "sampled" or "measured" particle (nonshattered particle and/or fragment) is a particle, which goes through the probe sampling volume and then is recorded.

As it was mentioned above, the use of simplifications or approximations is inevitable in an effort to evaluate effects of the shattering on measurements. At the same time, any approach has to take into account the stochastic nature of the problem. Our simple, if not to say simplest, model does not consider physical processes associated with the air flow through an instrument. The model is wholly probabilistic, i.e., it is based on the probability that a particle is shattered and on the probability that a fragment is sampled as a cloud particle.

In this study the Polar Nephelometer [START_REF] Gayet | A new airborne Polar Nephelometer for the measurements of optical and microphysical cloud properties. Part I: Theoretical design[END_REF] and the FSSP [START_REF] Baumgardner | Interpretation of measurements made by the Forward Scattering Spectrometer Probe (FSSP-300) during the airborne arctic stratosphere expedition[END_REF] probes will be considered. They both have inlets designed with a circular cross-section (see sketches on Fig. 1). We note in passing that the methodology described in this paper can easily be applied to airborne instruments, which also have circular inlets, for example, the Cloud Particle Imager (CPI, [START_REF] Lawson | An overview of microphysical properties of Arctic clouds observed in May and July 1998 during FIRE ACE[END_REF].

Let us consider the idealized Polar Nephelometer (PN) and FSSP inlet-shroud cross- sections shown by the bold circle labelled A (see scheme on Fig. 2). Therefore the particles go in the direction that is perpendicular to the figure plane.

The spatial distributions of cloud particles and of all fragments (which result from of the shattered particles) within the inlet cross-section are assumed to be homogeneous. Generally, the homogeneous distribution of particles in a sampled cloud is not a simplification.

The spatial distribution of the fragments is likely related to the design of the probe inlet and/or shroud via both the aerodynamic flow inside the probe inlet and/or shroud and the aerodynamic size (and morphology) of the particles [START_REF] King | Air flow around PMS canisters[END_REF]. Therefore the spatial distribution of the fragments will depend on the airspeed and the distances (i) between the sampling volume (represented by red lines on Fig. 1) and the inlet inner-edge, and (ii) between the sampling volume and the leading edge of the inlet (see Fig. 1). Specific modelling of fragments trajectories inside of probe inlets is not available to our knowledge. This issue is beyond the scope of this paper and could be the object of forthcoming works. Oriented wet wind tunnel tests could also help in a better understanding of the spatial distribution of the fragment particles along the probe inlet. The spatial distribution of fragments is assumed to be homogeneous in our model for simplicity sake. The PN data are expected to be less sensitive to that simplification because the PN sampling area is large with regard to the inlet cross-section (50 mm 2 versus 80 mm 2 respectively) and thus most of fragments are sampled (see Fig. 1).

The FSSP sampling area is much smaller than the inlet cross-section (0.5 mm 2 versus 1300 mm 2 respectively). Therefore, if the fragments are inhomogeneously distributed, the ice water content (IWC) carried by the sampled fragments could significantly differ from the IWC of the shattered particles. In the case when most of fragments go preferentially along the inlet axis and are measured by the FSSP, the IWC of fragments will be larger than the IWC of shattered particles. That is, the ratio of the IWC of fragments to the IWC of shattered particles will be greater than one. This IWC ratio will be smaller than one when most of fragments go preferentially near the inlet border and miss the sampling volume. In the following, that ratio is assumed to be equal to one. The width of the inlet leading edge schematized by the width of the line A on Fig. 2, is assumed to be a negligibly small quantity. The validity of that assumption depends on the design of the inlet tip. It seems to be appropriate for the Polar Nephelometer, but not for some designs of the FSSP (see Fig. 1). The larger the width of the leading edge (represented by the line A) is, the higher the shattering effect should be.

All particles in a sampled cloud and all fragments are assumed to be spheres. Despite the fact that particle fragments and ice crystals of cirrus or mixed clouds are not spherical, this assumption is used because it provides a radical simplification of all following calculations.

Because the spatial distribution of particles is homogeneous, the 2D distribution of centre-of-masses of the cloud particles over the cross-section (see Fig. 2) is homogeneous as well. The particles having their centre-of-masses inside the circle A, hereafter are referred to as the particles that "have to be sampled". That term and the corresponding quantity serve for the normalization, i.e., they allow the determination of the considered probabilities in the following.

The probability that a cloud particle is shattered, i.e., is withdrawn from the sampled population due to a collision with the probe inlet, strongly depends on the particle diameter d with respect to the diameter of the inlet. For example, a particle with the diameter higher than the diameter D of the inlet (i.e., the diameter of the A circle on Fig. 2) is always shattered. The inlet diameter D values are of 10 mm and of 40 mm for the Polar Nephelometer and the FSSP-300, respectively. The both values are large with respect to cloud-particles sizes. That is why the case d > D is ignored in our model.

In order to illustrate the determination of the loss-process probability, we use in the inlet without interaction with the tip. Such a particle is referred to as a particle that has to be sampled and it is measured without shattering (case 1 on Fig. 2).

(2) If the centre-of-mass of a particle falls inside the ring between the circles B and A, the particle collides with the inlet tip and shattering occurs. All subsequent fragments will be sampled and measured. Such a particle is referred to as a particle that has to be sampled and it is shattered (case 2 on Fig. 2).

(3) If the centre-of-mass of the particle is inside the ring between the circles A and C, shattering happens. Because the centre-of-mass is outside of the circle A, such a particle is referred to as a particle that must not be sampled and it is shattered (case 3 on Fig. 2).

The probability p 1 (d ) that a cloud particle is measured without shattering (case 1) is proportional to the area S B of the circle B. As it was mentioned above, we use for the normalization the area S A of the circle A. That is,

p 1 (d ) = S B S A = (D -d ) 2 D 2 , d ≤ D (1)
For d >D, p 1 (d ) is set to zero. The probability p 1 (d ) depends on the diameter of a particle and on the inlet diameter. It follows from Eq. ( 1) that the larger a particle is, the lower the probability p 1 (d ) is. The probability p 2 (d ) that a particle has to be sampled and it is shattered (case 2) is proportional to the area S 2 of the ring between the circles B and A; and it is inversely proportional to the area S A of the circle A:

p 2 (d ) = S 2 S A = D 2 -(D -d ) 2 D 2 = 2Dd -d 2 D 2 , d ≤ D. (2) For d > D, p 2 (d ) is set to zero. It is reasonable that p 1 (d ) + p 2 (d ) = 1. It is seen from Eq.
(2) that p 2 (d ) tends to zero when the diameter of the particle tends to zero. That is, the smaller a particles is (with respect to the diameter D of the inlet), the lower the shattering effect is. By the same way the coefficient p 3 (d ) can be determined. The coefficient p 3 (d ) is proportional to the probability that a particle must not be recorded and it is shattered (case 3). It is proportional to the area S 3 of the ring between the circles C and A:

p 3 (d ) = S 3 S A = (D + d ) 2 -D 2 D 2 . ( 3
)
Strictly speaking, the quantity p 3 (d ) is not a probability because it can be greater than 1. Nevertheless, we consider it as a useful coefficient. It should be pointed out another time that Eqs. ( 1), ( 2) and ( 3) are the direct consequence of the homogeneity of the cloud-particle spatial distribution. When a particle collides with the inlet tip (the cases 2 and 3), its fragments can go inside or outside the inlet. Generally, the proportion and the size distribution of fragments, which go inside, are governed by a number of characteristics and, first of all, they strongly depend on the design of the tip. As for a particle of a given diameter d , the proportion depends on the position of the centre-of-mass of the particle with regard to the A circle. Having no basis to estimate that proportion and for simplicity sake, we assume that all fragments of case 2 enter into the inlet, and all fragments of the case 3 go outside the inlet. This assumption overestimates the proportion for case 2. That overestimation is partly compensated by the underestimation of the number of the fragments, which are related to the case 3 and could be sampled by the instrument.

We recall that the size distribution of particles that are measured by an instrument consists of two parts. The first part is the cloud particles that are not shattered; and the second one is the fragments of shattered particles. As it was mentioned above, the particle number size distribution n 1 (d ) of the measured particles, which were not shattered, is not necessary equal to the actual size distribution n 0 (d ) of the cloud particles. This feature is a consequence of the loss process. It follows from Eq. ( 1) that the size distribution n 1 (d ) (case 1) is as follows: Equation ( 4) shows a non-linear relationship between n 1 (d ) and n 0 (d ). In other words, the larger the diameter d is, the higher the difference between n 1 (d ) and n 0 (d ) is. And, it is important to keep in mind that the distribution n 1 (d ) represents a fraction of particles, which are measured by an instrument.

n 1 (d ) = n 0 (d )p 1 (d ) = n 0 (d ) (D -d ) 2 D 2 . ( 4
The second part of particles, which are measured, consists of fragments of the shattered particles (case 2 in our model). Generally, the size distribution of the measured fragments depends on the size distribution of the shattered particles. Therefore we define the number size distribution n 2 (d ) of the shattered particles, which produce all subsequent measured fragments. According to Eq. ( 2) n 2 (d ) can be expressed as follows:

n 2 (d ) = n 0 (d )p 2 (d ) = n 0 (d ) D 2 -(D -d ) 2 D 2 . ( 5
)
The relationship

n 1 (d ) + n 2 (d ) = n 0 (d ) is valid, it follows from the equality p 1 (d ) + p 2 (d ) = 1.
It should be emphasized that the number size distribution n 2 (d ) of the shattered particles is generally much smaller than the actual size distribution n 0 (d ) of the cloud particles as we will see below.

Effects on integral microphysical parameters

When the particle size distribution n 0 (d ) is known, Eqs. ( 4) and ( 5) serve to compute the integral parameters like the particle total concentration N, the extinction coefficient Ext, the ice water content IWC, and the effective diameter d eff . For example, the extinction coefficient Ext 2 and the effective diameter d eff2 are computed on the basis of the size distribution n 2 (d ).

As for the effect of fragments, additional simplifications and assumptions have to be introduced because the size distribution of the fragments depends on a number of physical processes and parameters, some of which are not known. We list some, but not all of them: the habit, size, and density of particles [START_REF] Korolev | Shattering during sampling by OAPs and HVPS. Part I: Snow particles[END_REF], the airspeed and the impact angle [START_REF] Weber | Spurious aerosol measurements when sampling from aircraft in the vicinity of clouds[END_REF] subsequent effects on the recorded and derived cloud properties depend on the spatial distribution of fragments over the inlet cross-section with respect to the effective sampling area of the probe. The Polar Nephelometer data are expected to be less sensitive to that feature while it is of particular importance for instruments with relatively small sampling area regarding the inlet diameter, e.g., the FSSP. As previously indicated, for simplicity sake the spatial distribution of fragments is supposed to be homogeneous in our model. Furthermore, it is assumed that conservation of mass holds true. That is, the total volume of the shattered particles (the case 2) is converted into fragments, which are measured as cloud particles. Under the assumption that the spatial distribution of the fragments is homogeneous, conservation of mass leads to the property that the IWC of the fragments is equal to the IWC of shattered particles (conservation of IWC). This assumption could be justified from the estimates by [START_REF] Heymsfield | On measurements of small ice particles in clouds[END_REF] who suggest that IWC from FSSP measurements could be overestimated by only 15% by shattering effects. It is self-evident that a shattering model cannot employ the fragment size distribution in an analytic or tabulated form. There are too many unknown parameters and characteristics. That is why only integral parameters of the size distribution are used in our model. Such a choice is based on the fact that the concept of the integral parameters works well in ice-clouds physics (see e.g., Heymsfield et al. 2006 and citations therein).

The effective diameter d eff of an ice particle population is composed of two variables: extinction (Ext) and the ice water content (IWC):

d eff = α • IW C E xt , ( 6
)
where α is a coefficient. Generally, both Ext and IWC, as well as α, are dependent upon the particle size distribution and the ice particle habit. For example, from [START_REF] Gayet | Cirrus cloud microphysical and optical properties at southern and northern midlatitudes during the INCA experiment[END_REF] α is of 3.0 from with Ext and IWC expressed in m -1 and g m -3 , respectively.

In our model, the coefficient α is supposed to be constant, i.e., it is of the same value for cloud particles and fragments. It follows from Eq. ( 6) that :

E xt = α • IW C d eff , (7)
i.e., when IWC is fixed, the extinction is inversely proportional to the effective diameter.

In other words, the smaller the fragments of a given cloud particle, the higher their effect on the measured extinction. If the conservation of IWC holds true, the key parameter is the effective diameter d effF R of the fragments with respect to the effective diameter d eff2 of the shattered cloud particles; and the extinction coefficient E xt F R of the fragments can be expressed as follows:

E xt F R = E xt 2 d eff2 d effF R , ( 8
)
where E xt 2 is the extinction coefficient of the shattered particles (the case 2).

The Polar Nephelometer measures the scattering phase function of an ensemble of particles from a few micrometers to about 1 mm diameter. Thus, all assumptions taken together lead to the following value E xt mes of the extinction coefficient measured by the PN:

E xt mes = E xt 0 + E xt F R -E xt 2 , ( 9
)
where E xt 0 is the actual extinction coefficient of the cloud particles. It follows from Eqs. ( 8) and ( 9) that the shattering effect can be written for the Polar Nephelometer in fraction terms as:

δE xt P N = E xt mes -E xt 0 E xt 0 = E xt 2 E xt 0 d eff2 d effF R -1 , ( 10
)
Considering now the FSSP, the size range of that instrument is typically from 2 µm to 22 µm with the series 300 used during cirrus studies [START_REF] Gayet | Cirrus cloud microphysical and optical properties at southern and northern midlatitudes during the INCA experiment[END_REF]. This limited Figures

Back Close Full Screen / Esc

Printer-friendly Version Interactive Discussion size range must be considered for the estimation of the shattering effect on FSSP-300 measurements. For example, Eq. ( 9) is rewritten as:

E xt mesFSSP = E xt 0FSSP + E xt F R FSSP -E xt 2FSSP , ( 11
)
where the subscript "FSSP" means that the corresponding values are computed for the sampling size range of the FSSP-300 instrument. If the size of all fragments is within that range, the shattering effect on the extinction coefficient deduced from FSSP-300 data is expressed as follows:

δE xt FSSP = E xt F R FSSP -E xt 2 FSSP E xt 0 FSSP = E xt 2 E xt 0 FSSP d eff 2 d eff F R - E xt 2 FSSP E xt 0 FSSP , ( 12
)
It follows from Eq. ( 10) that the key parameters of the shattering effect on PN data are: (i ) the ratio d eff2 / d effF R of the effective diameters of the shattered particles and of the fragments, and (ii) the ratio Ext 2 / E xt 0 of the extinction coefficients of the shattered particles and of the cloud particles. Concerning the FSSP, our simulations revealed that the second term on the right-hand side of Eq. ( 12) is, as a rule, negligibly small. Thus, the key parameters of the shattering effect δ Ext FSSP are the same. The difference is that the extinction coefficient Ext 0FSSP should be used in the ratio Ext 2 / Ext 0FSSP .

The last part of this section deals with the shattering effect on the number concentration measured by the FSSP instrument. The effect is estimated under all assumptions discussed above. Let N 0FSSP be the actual number concentration of cloud particles within the FSSP size range and N mesFSSP be the number concentration recorded by the instrument. Then, the shattering effect written in percentage terms is:

δN FSSP = N mesFSSP -N 0FSSP N 0FSSP = N F R -N 2FSSP N 0FSSP , ( 13
)
where following relationship between the extinction coefficient Ext and the number concentration N of particles (see, e.g., [START_REF] Korolev | Microphysical properties of continental clouds from in-situ measurements[END_REF]):

N mesFSSP = N 0FSSP + N F R -N 2FSSP , N F R
E xt = β • N • d 2 eff , ( 14
)
where β is the coefficient, which is expressed as β = π Q/ 4 for spherical particles; Q is the extinction efficiency (equal to 2 according to the large particle approximation).

In our model, the coefficient β is supposed to have the same value for cloud particles and fragments. It follows from Eqs. ( 8), ( 13), and ( 14) that the shattering effect on the number concentration δN FSSP can be written as:

δN FSSP = E xt 2 E xt 0FSSP • d eff2 d effF R • d 2 eff0FSSP d 2 effF R - E xt 2FSSP E xt 0FSSP • d 2 eff0FSSP d 2 eff2FSSP . ( 15
)
As above, it is supposed that the size of all fragments is within the FSSP's sampling size range. It should be mentioned that the shattering effect is expressed by Eqs. ( 10), ( 12) and ( 15) in relative units, that is, the relationships are independent of the absolute value of the total concentration of cloud particles.

Estimation of the effects of ice particle shattering on in-cloud measurements

The model discussed above, treats of the shattering effect as a direct problem, i.e., all characteristics are computed on the basis of the size distribution n 0 (d ) of cloud particles. On the other hand, all experimental data on cloud particles reported in the scientific literature are more or less affected by an instrument or a set of instruments. Thus, any case study must uses a size distribution that could already be affected by the shattering. Nevertheless, experimental data provide opportunities to obtain quite distribution labelled D2 and represented on Fig. 3 is the average cirrus ice-crystal size distribution computed for the dataset, which was recorded during the field campaign performed at midlatitudes in the Southern Hemisphere. The particle size distributions D1 and D3 (see Fig. 3) were generated using the technique of principal component analysis (PCA) (see details in [START_REF] Shcherbakov | Assessment of cirrus cloud optical and microphysical data reliability by applying statistical procedures[END_REF]. We recall that the PCA provides the possibility of reproducing almost all the variability of a dataset with reasonably good accuracy while considering only a few principal components. The number size distributions are shown on Figure 3 and they are considered as n 0 (d ) functions in subsequent calculations. The size ranges from 3.0 to 21.8 µm and from 22.5 to 800 µm correspond to the FSSP-300 and to the PMS 2D-C data, respectively. We note in passing that the jump in the concentration from the FSSP and the 2D-C on Fig. 3 may be due to shattering effects on FSSP measurements and/or 2D-C problems at small size due to electronic probe response [START_REF] Strapp | Laboratory measurements of the response of a PMS OAP-2DC[END_REF]. We consider in a first guess these size distributions as representative in order to assess shattering effects on FSSP and Polar Nephelometer measurements. The corresponding values of the integral parameters are shown on Table 1 and they agree well with the data reported by [START_REF] Gayet | Microphysical and optical properties of midlatitude cirrus clouds observed in the southern hemisphere during INCA[END_REF]. It should be mentioned that the effective diameter d eff0 values vary from 36 µm to 89 µm (see Table 1), that is, the proportion of large particles varies within a large range.

The number size distributions n 1 (d ) and n 2 (d ) were computed according to Eqs. ( 4 the same time, the proportion of the large particles (see the effective diameter values in Table 3) is much higher in n 2 (d ) because the probability p 2 (d ) increases with the particle diameter d . The main properties of the distributions n 2 (d ), computed for the FSSP-300 inlet diameter D = 40 mm, are the same. The difference is in the absolute values that are about four times lower because the FSSP inlet diameter is four times larger compared to the PN geometry.

Effect of the Ext 2 / Ext 0 ratio

In order to quantify the shattering effect in reference to the cloud particles, we will first deal with the integral parameters of particles, which are shattered and produce measured fragments (the case 2), relative to the corresponding values of the actual cloud particles. We recall that n 2 (d ), which is obtained from Eq. ( 5), is not the size distribution of fragments, but addresses the shattered cloud particles. The particle total concentrations (N 0 and N 2 ), the extinction coefficient (E xt 0 and E xt 2 ), and the ice water content (IW C 0 and IW C 2 ) were computed on the basis of the number size distributions (n 0 (d ) and n 2 (d )) according to well-known relationships (see, e.g., [START_REF] Korolev | Microphysical properties of continental clouds from in-situ measurements[END_REF].

Table 2 shows the percentages (δ) of the shattered particles to actual particles expressed in terms of particle concentration, extinction and ice water content for the Polar Nephelometer and FSSP inlets. We recall that on all figures and tables, the notations D1, D2, and D3 correspond to the three size distributions n 0 (d ) shown on Fig. 3. For example the percentages are 0.19%, 1.34% and 3.81% for the particle concentration, extinction and ice water content, respectively, with the Polar Nephelometer inlet. As expected, the values for the FSSP-300 instrument are lower than those for the Polar Nephelometer. As already indicated, the four-fold increase of the inlet diameter resulted in a four-times decrease of the integral parameters of the shattered particles.

These relative values depend on the size distributions of cloud particles, i.e., they increase with increasing d eff0 . We recall that the total volume (or IWC) of the shattered particles is assumed to be converted into fragments, which are measured as cloud 11025 Figures

Back Close

Full 2 means that the higher the proportion of the large cloud particles is, the higher the shattering effect is, all other factors being the same.

As follows from Eq. ( 10), the ratio δE xt = E xt 2 / E xt 0 is one of the key parameters that govern the shattering effect on PN data. At first glance the values of δExt would seem small. Nevertheless, we show below that such values would have a significant importance in shattering effects on measurements.

Effects of the effective diameter of the particle fragments and of large particles

Another key parameter of the shattering effect is the ratio In contrast to d eff2 , the assessment of the effective diameter d effF R is the challenge since microphysical parameters of fragments are not sufficiently studied to date. There is little information on this matter. [START_REF] Vidaurre | Particle Impact and Breakup in Aircraft Measurement[END_REF] concluded that the impact kinetic to surface energy ratio serves as a useful breakup criterion and indicates that both drops and ice crystals larger than a few microns often break apart if they happen to impact on any aircraft-mounted instrument. And, they showed that an ice crystal of a few hundreds microns diameter can be broken up into hundreds of fragments. Moreover, [START_REF] Vidaurre | Particle Impact and Breakup in Aircraft Measurement[END_REF] speculated that a total conversion of impact kinetic energy into surface energy could be achieved by breaking the entire crystal into hexagonal columns of 30-nm dimension. On the other hand, Heymsfield et al. (2007, Appendix A) found that that the mass-weighted mean diameters were around 14-16 µm for particles recorded by the Cloud and Aerosol Spectrometer (CAS) in the conditions 11026 Introduction

d eff2 / d effF

Conclusions Figures

Back Close

Full Screen / Esc

Printer-friendly Version Interactive Discussion that were favourable to the shattering. As a consequence of such a large uncertainty, we estimated the shattering effect on integral parameters for a set of values of d effF R that are in the most expected size range.

Polar Nephemometer measurements

The effects on the extinction coefficient derived from the Polar Nephelometer data, were computed according to Eq. ( 10). The estimated values of δExt P N are shown on Fig. 4 as function of d effF R for the three considered size distributions (D1, D2 and D3). As expected, the results highlight that ice particle shattering leads to the overestimation of the extinction coefficient. The effect is very sensitive to the value of the effective diameter of the fragments (d effF R ) and it depends on the actual particle size distributions (D1 to D3), i.e. on the proportion of the large cloud particles. For example, with the distribution D2 (characterized by the effective diameter of 68 µm see Table 1), δExt P N increases from 12% to 50% with d effF R decreasing from 20 µm to 5 µm. The effects of the proportion of large particles are exemplified on Fig. 5 (upper panel). For a given effective diameter of the particle fragments (d effF R = 10 µm for instance), the overestimation factor (δExt P N ) increases from 9% to 37% as the effective diameter of the actual particle size distribution (d eff0 ) increases from 36 µm to 89 µm respectively.

FSSP-300 measurements

The shattering effects on FSSP-300 data were computed according to Eqs. ( 12) and ( 14). The values of δN FSSP and δ Ext FSSP are given on Figure 6 5 µm, these values increase to 235% and 34% respectively. If the effective diameter of the fragments is of 5 µm, the errors on the particle concentration also increase significantly from 50% to 550% with the proportion of the large cloud particles (D1 d eff0 = 36 µm and D3d eff0 = 89 µm, respectively). This result is in support of the conclusion that shattering may result in large overcounting of ice particles measured by FSSP in midlatitude cirrus by factor of 2 to 5 [START_REF] Field | Ice particle interarrival times measured with a fast FSSP[END_REF]. As for extinction, the results on Fig. 5 (bottom panel) show a similar feature regarding the Polar Nephelometer but with smaller errors for d effF R = 5 µm.

It is interesting to highlight that the extinction overestimations are of the same orders for the Polar Nephelometer and the FSSP (25% and 20% respectively) for identical simulated conditions (d effF R = 10 µm and d eff0 = 68 µm, D2). This could nicely explain the very good consistency of comparison results between extinctions calculated from two different techniques (combination of FSSP-300 and CPI probes and Polar Nephelometer) even in presence of large ice crystals in cirrus clouds where shattering is likely occurring with a similar efficiency on the two instruments [START_REF] Mioche | Validation of the CALIPSO/CALIOP extinction coefficients from in situ observations in mid-latitude cirrus clouds during CIRCLE-2 experiment[END_REF] see their Fig. 7). This consistency could be fortuitous but may also give an indication that the ice water content (IWC) of fragments over the sampling cross section of the FSSP-300 is close to the IWC of the shattered particles.

Furthermore, [START_REF] Mioche | Validation of the CALIPSO/CALIOP extinction coefficients from in situ observations in mid-latitude cirrus clouds during CIRCLE-2 experiment[END_REF] compared CALIOP and airborne PN co-located observations in terms of extinction coefficient in different cirrus cloud situations. Very good agreements were observed when small irregularly-shaped ice crystals (d eff0 ∼20-40 µm) are present, while systematic larger PN extinction values (with regard to CALIOP data) were evidenced for cirrus with large irregularly-shaped ice crystals (d eff0 ∼80 µm). Assuming the CALIOP data to be unbiased, the shattering of larger ice crystals seems to be a plausible explanation for the PN large extinction values (∼38% of overestimation). If this hypothesis holds true for the PN overestimation of 38% and for an actual effective diameter of 80 µm, the effective diameter of the fragments would be around 10 µm following the results on Fig. 5a. With these inputs the overestimation of the FSSP extinction would also be about 30% (confirming the results above) and the error on the measured particle concentration would be about 70% (see Fig. 6a).

Considering that the mean effective diameter (d eff0 ) of 68 µm (see Table 1 and size distribution D2 on Fig. 3) is representative of the observations made during INCA, the above estimated errors on PN and FSSP measurements are, on the average, of the same order of the usual random uncertainties (i.e., 85% and 75% on the extinction and the particle concentration respectively, see Table 1 in [START_REF] Gayet | Quantitative measurement of the microphysical and optical properties of cirrus clouds with four different in situ probes: Evidence of small ice crystals[END_REF]. Therefore most of the published results on mid-latitude cirrus during INCA would be reliable within the measurements accuracies. Only about 20% of the observations made at temperatures higher than -40 • C could have greater shattering errors due to subsequent larger effective diameters of cloud particles [START_REF] Gayet | Cirrus cloud microphysical and optical properties at southern and northern midlatitudes during the INCA experiment[END_REF].

As for previous results obtained in contrails [START_REF] Febvre | On optical and microphysical characteristics of contrails and cirrus[END_REF], we believe that the observations are not affected by shattering effects because small particles were measured with effective diameter smaller than 25 µm.

Discussion and practical application

Discussion

It was pointed out above that our model is simple, it is wholly probabilistic, and a number of simplifications and assumptions were used. The validity of the assumptions is under question. In this section, we discuss point by point the possible consequences.

(i ) The spatial distribution of all fragments is supposed to be homogeneous, it doesn't depend on the size of a cloud particle or of a fragment, and there is no any correlation. Generally, the spatial distribution of the fragments should be inhomogeneous and it should depend on the distances (i) between the sampling volume and the inlet inner-edge and (ii) between the sampling volume and the leading edge of the inlet. In addition, it should depend on the inlet design, on the airspeed through the probe, on the change in the flow field due to the probe itself, and on physical characteristics of cloud particles. The PN data are expected to be insensitive to that simplification be- cause the PN sampling area is large and thus most of fragments are recorded. To the contrary, the FSSP sampling area is small with reference to the inlet diameter. It might be expected that most of fragments go preferentially near the inlet border and miss the sampling volume. In this case, our assumption leads to overestimation of the shattering effect. At the same time, it could lead to underestimation, because we cannot exclude that the fragments go preferably along the probe axis due to the lateral forces involved in the breakup of a cloud particle. If experimental data demonstrate spatial inhomogeneous distribution of fragments, a coefficient, which relates IWC of the fragments to IWC of the shattered particles, should be assumed.

(ii) The width of the tip of the inlet is assumed to be a negligibly small quantity. Largewall leading edges may significantly increase the shattering effect. Thus, it should be highly recommended to optimize the inlet design of FSSP instruments.

(iii) All particles in a sampled cloud and all fragments are supposed to be spheres. That assumption is widely used in our model. Ice breakup mechanisms may occur likely depending on the ice particle structure (dense graupels or delicate branched crystals).

(iv) The fragments, which go inside the inlet, originate from and only from the particles that have to be sampled and are shattered (case 2). Generally, some fragments of particles of the case 2 can go outside the inlet, and some fragments of the case 3 can go inside the inlet.

(v) The model is probabilistic and physical processes are not considered. It could be expected that airflow modelling could improve the assessment of the shattering effect. In our opinion, the most important question to be addressed by airflow modelling is the spatial distribution of fragments inside the inlet. Of course, the modelling should be based on a reliable model of breakup of ice particles.

(vi) It is assumed that the conservation of mass holds true. That is, the total volume of the shattered particles is transformed into fragments, which are recorded as cloud particles. This assumption seems to be quite reliable for the Polar Nephelometer because it measures the cloud property of an ensemble of particles ranged from a few microns to 1 mm. As for the FSSP instrument, the fragments, which have a size beyond the sampling range (2-22 µm for the series 300), do not affect the recorded data. Thus, a portion of the mass of the shattered particles is definitively lost and this decreases the shattering effect.

(vii) In our estimations, we employed experimental data that are already somewhat affected. Generally, the shattering decreased the fraction of large particles in favour of the small ones, and in turn this somewhat decreased the estimated values.

Practical application

As it was pointed out above, our model treats the shattering effect as a direct problem, that is, the equations employ an unaffected size distribution of cloud particles. On the other hand, there is an obvious need to quantify the shattering effect on the basis of measured data.

Our simulations with a thorough analysis of the Eqs. ( 10), ( 12), and (15) revealed that the principal contribution to the shattering is from the size range of large particles. Thus, a size distribution, which is measured by 2D-C, CPI or 2D-S probes, can be used for rough assessments. In absolute units, the shattering effect on Polar Nephelometer and FSSP data can be expressed as follows:

∆E xt P N = E xt 2 • d eff2 d effF R -1 , ( 16
) ∆N FSSP = IW C 2 π 6 ρd 3 effF R , ( 17
) ∆E xt FSSP = α • IW C 2 d effF R , ( 18
)
where ρ is the ice density, α is a coefficient (see Eq. 6 its turn, is calculated using Eq. ( 5), where n 0 (d ) is the size distribution measured by 2D-C or 2D-S probe. Equations ( 17) and ( 18) were obtained from Eqs. ( 12) and ( 15) by neglecting small quantities, i.e., the second terms in the right-hand side.

If one deals with data measured by a FSSP instrument having the usual inlet design, the value C 2D,F SSP • IW C 2D-C should be used instead IWC 2 in Eqs. ( 17) and ( 18), where IWC 2D-C is the ice water content of the size distribution n 0 (d ) measured by 2D-C probe. C 2D,F SSP is an empirically derived-shattering coefficient; the basis assumption being that large particles shatter and increase the mass (IWC) or extinction (Ext) of ice in the probe measurements (see details in [START_REF] Heymsfield | On measurements of small ice particles in clouds[END_REF].

At the same time, that coefficient should depend on the effective diameter of n 0 (d )

because the larger particles are, the higher the probability of the breakup is.

Conclusions

We present in this paper a probabilistic model of the effects of ice particle shattering on in-cloud measurements performed with instruments designed with inlets which have circular cross-section. The model provides rough estimates on microphysical measurements and assigns the key parameters that govern the efficiency of ice particle shattering. The model disclosed for the first time that not only cloud IWC governs the shattering effect, but a number of other factors as well. Due to the model we specified the priority factors such as the effective diameter of fragments, the effective diameter of shattered cloud particles, and the spatial distribution of the fragments inside the FSSP inlet.

The results show that experimental data are less affected by the shattering for clouds that have a lower proportion of large particles and confirm the results from previous studies [START_REF] Field | Ice particle interarrival times measured with a fast FSSP[END_REF][START_REF] Heymsfield | On measurements of small ice particles in clouds[END_REF][START_REF] Mcfarquhar | Ice properties of single-layer stratocumulus during the Mixed-Phase Arctic Cloud Experiment[END_REF]). The effects on the derived integral parameters are very sensitive to the effective diameter of the fragment particles and to the proportion of the large cloud particles, i.e., to the effective diameter of cloud particles. The smaller fragments of a given cloud particle are, the Figures

Back Close Full Screen / Esc

Printer-friendly Version Interactive Discussion higher their effect is. It is expected that the effective diameter of fragments depends on the inlet design and on the habit, size, and density of cloud particles. A reliable model of breakup of an ice particle is sorely needed. The airspeed should also play a key part in that model. Concerning the Polar Nephelometer measurements, the ice particle shattering leads to the overestimation of the extinction coefficient. For example for a given distribution with an effective diameter of 68 µm and with a fragment effective diameter of 10 µm the extinction is overestimated by 25%. With larger particles (d eff = 89 µm) the error increases up to 37%.

As for the FSSP-300 instrument, with the same conditions the extinction coefficient is overrated by 17% and the number particle concentration is overestimated by 30%. It is interesting to underline that the extinction overestimations above are of the same orders for the two instruments. This could explain the very good consistency of comparison results between extinctions calculated from two different techniques (FSSP-300 and Polar Nephelometer) even in presence of large ice crystals in cirrus clouds where shattering is likely occurring with a similar efficiency on the two instruments.

Most of the published results on mid-latitude cirrus during INCA would be reliable within the measurements accuracies. Only observations made at temperatures higher than -40

• C could have greater shattering errors due to subsequent larger effective diameters of cloud particles. As for previous results obtained in contrails [START_REF] Febvre | On optical and microphysical characteristics of contrails and cirrus[END_REF], the observations are likely not affected by shattering effects because small particles were measured. The discussion of the results points out the main hypothesis which may seriously limit the reliability of our modelling results. Nevertheless, the magnitudes of the errors on extinction and particle concentration are of the same orders of those reported in the literature from experimental assessments. Some of the hyphothesis could be verified from oriented experiments for instance by using cloud wind tunnels with controlled conditions for the assessment of different inlet designs, airspeed, range of particle size distributions, and so on.

  Fig. 2 the dashed B and C circles that are concentric with the A circle. The diameters of B and C are D -= Dd and D + = D + d , respectively, and therefore depend on the diameter d of a particle.For a cloud particle of diameter d , there are three following possibilities:(1) If the centre-of-mass of a particle falls inside the B circle, this particle goes into

  and N 2FSSP are the number concentrations of the fragments and of the shattered cloud particles, respectively. All magnitudes are computed only within the FSSP size range. In addition to Eq. (13), we employ the

  reliable estimates and to assign key parameters that govern the shattering effect.The results below are based on the data obtained during the INCA experiment[START_REF] Str Öm | Aerosol and cirrus measurements at midlatitudes on the Southern hemisphere: An overview based on the first INCA experiment[END_REF]) and reported by[START_REF] Shcherbakov | Assessment of cirrus cloud optical and microphysical data reliability by applying statistical procedures[END_REF]. For comparison purposes, three following particle number size distributions were chosen. The particle size 11023

  ) and (5) for the inlet diameter D values of 10 mm and of 40 mm for the Polar Nephelometer and the FSSP-300, respectively. The both values of the inlet diameter are large with respect to cloud-particles sizes. This explains the fact that the size distributions of actual cloud particles (n 0 (d )) and non-shattered particles (n 1 (d )) are close together on Fig. 3 and cannot be clearly distinguished in log-log scale. The size distributions n 2 (d ) of the shattered particles, computed for the PN inlet diameter D=10 mm, are shown on Fig. 3 as well. We note in passing that the same colour convention is used for the size distributions n 0 (d ) and n 2 (d ). There is an analogy between n 2 (d ) and n 0 (d ) because n 2 (d ) is directly related to n 0 (d ) by Eq. (5). At

  increase of the ratio δIW C(%) = 100 • IW C 2 / IW C 0 with d eff0 in Table

  as a function of d effF R for the three considered size distributions (D1, D2 and D3). As with the Polar Nephelometer, the results show that the both parameters are very sensitive to the values of the effective diameter of the fragments and to the proportion of the large cloud particles. For example, considering the size distribution D2 (d eff0 = 68 µm) with a fragment effective diameter (d effF R ) of 10 µm the particle concentration (see Fig. 6a) and the extinction (see Fig. 6b) are overestimated by 30% and 17% respectively. With d effF R =

  This work was funded by the Centre National d'Etudes Spatiales (CNES) and by the Institut Polaire Franc ¸ais Paul Emile Victor (IPEV). This work was funded by a grant from a CNRS/INSU program. We acknowledge C. Gourbeyre and J.-F. Fournol (LaMP) for their active participation to the airborne experiments A. Minikin (DLR) for fruitful discussions. The publication of this article is financed by CNRS-INSU.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Sketches of the inlets of the Polar Nephelometer (upper panel) and FSSP probe (bottom panel). Red lines represent the sampling volume. D is the inlet diameter.

  . Moreover, as indicated above the Figures

	Back	Close
	Full Screen / Esc
	Printer-friendly Version
	Interactive Discussion

  R . The values of the effective diameter d eff2 of the shattered particles (the case 2) are reported in Table3. The first line of numbers of Table3corresponds to the size distributions n 2 (d ) shown on Fig.3. The effective diameter d eff2 is much larger than d eff0 due to the increased proportion of large particles (192 µm against 68 µm for the Polar Nephelometer inlet). It is seen that d eff2 depends on the size distribution of cloud particles and it is less sensitive to the inlet diameter.

Table 1 .

 1 Integral parameters of the size distribution D1, D2, and D3.

		D1	D2	D3
	-3 ) N 0 (cm -1 ) Ext 0 (km IWC 0 (mg m -3 ) 5 2.6 0.47 0.55 0.68 1.8 1.4 11 18
	d eff0 (µm)	36	68	89

ACPD

Full


Amanda Camila Poppi

Gustavo Lazzari

Ana Luiza

Rodolpho Mendonça Gomes

Martin Prado

Rafaela Takako

Ribeiro Almeida

Daniele Maria Zanzarin

Eduardo Jorge Pilau

Cabreira Clóves

Lucas José Jobim

Eric Mari

Chevaux

Ana Luiza Mendonça

Amanda Camila De Poppi

Rodolpho Martin Do Prado

Rafaela Takako Ribeiro De Almeida

Clóves Cabreira

Lucas José Mari

Eric Chevaux

Frédérique Chaucheyras-Durand

Adegbola Tolulope Adesogan

João Luiz

Pratti Daniel

Jlp Daniel
email: jlpdaniel@uem.br

Effects of feeding a live yeast on rumen fermentation and fiber degradability of tropical and subtropical forages

Keywords: cell wall, lactic acid, rumen metabolomics, Saccharomyces cerevisiae

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In diets of high-producing ruminants, forages are included to provide physically effective fiber, to enhance ruminal function, and to maintain animal health. 1 Forages are also important sources of nutrients, depending on their quality, which is mainly determined by its fiber content and digestibility. 2 The content and digestibility of fiber in diets influences feed intake due to physical filling of the rumen, which can influence dry matter (DM) intake and animal performance. 3,4 Forage species, genotype, maturity and harvest management can affect forage composition and digestibility. Crop growth environment may also have an effect on forage quality. Several authors have reported that warmer temperatures increase lignin deposition and decrease in vitro digestibility compared with forage grown at lower temperatures. [5][6][7][8] Hence, growth strategies capable of enhancing fiber digestibility would benefit dairy systems in tropical and subtropical areas.

Post-harvest strategies can also be used to improve forage digestibility, such as the application of exogenous fibrolytic enzymes 9 and chemicals (e.g., sodium hydroxide, anhydrous ammonia, or calcium oxide). 10,11 Moreover, manipulation of ruminal fermentation with probiotics can improve forage digestibility. [12][13][14] Several studies with diets based on forages cultivated in temperate conditions have indicated that supplementation with live yeasts, such as Saccharomyces cerevisiae strains, increases the total number of cellulolytic bacteria, stimulates lactate utilization, and 1 decreases lactate production, increases rumen pH and reduces oxygen concentration in the rumen fluid, resulting in higher fiber degradation, higher synthesis of microbial protein and improved animal performance. [15][START_REF] Ondarza | Case study: mutiple-study analysis of the effect of live yeast on milk yield, milk component content and yield and feed efficiency[END_REF][START_REF] Mosoni | Quantification by real-time PCR of cellulolytic bacteria in the rumen of sheep after supplementation of a forage diet with readily fermentable carbohydrates: effect of a yeast additive[END_REF][START_REF] Desnoyers | Meta-analysis of the influence of Saccharomyces cerevisiae supplementation on ruminal parameters and milk production of ruminants[END_REF][START_REF] Fonty | Establishment of cellulolytic bacteria and development of fermentative activities in the rumen of gnotobiotically-reared lambs receiving the microbial additive Saccharomyces cerevisiae CNCM I-1077[END_REF] De Ondarza et al. showed increased milk yield and feed efficiency in animals supplemented with live yeasts, but their meta-analysis was mainly based on diets with forage cultivated in temperate climates. [START_REF] Ondarza | Case study: mutiple-study analysis of the effect of live yeast on milk yield, milk component content and yield and feed efficiency[END_REF] Meanwhile, potential benefits of live yeast supplementation of the diet on ruminal environment and degradability of different forages grown in tropical and subtropical areas is seldom reported and thus is not well established. [START_REF] Cabrera | Saccharomyces cerevisiae and nitrogenous supplementation in growing steers grazing tropical pastures[END_REF][START_REF] Sousa | Live yeast supplementation improves rumen fibre degradation in cattle grazing tropical pastures throughout the year[END_REF] Nonetheless, field nutritionists have claimed in dairy farms that tropical forages would have a greater improvement of digestibility than forages grown in temperate zones.

Thus, the aim was to evaluate effects of live yeast Saccharomyces cerevisiae strain CNCM I-1077 on ruminal environment and degradability of DM and neutral detergent fiber (aNDF) of several forages commonly found in diets of dairy cows in Brazil and other countries in South America, and especially to determine if a potential improvement in DM and aNDF degradation varies by forage group.

MATERIAL AND METHODS

Forage samples

Fifteen forage samples were collected from dairy farms (one composite sample obtained by mixing 8 to 10 subsamples of each forage in each farm) in different regions of Brazil (13), Argentina (1), and Peru (1), and assigned to one of three groups: tropical grasses (sugarcane silage and tropical grass silage), corn silages, and temperate grasses and alfalfa (oat silage, ryegrass silage, alfalfa silage, and alfalfa hay). The groups were designed to create C4 grasses with low starch content and expected low fiber digestibility (i.e., tropical grasses), C4 grasses with high starch content (i.e., corn silages) and forage with low starch content but expected high fiber digestibility (i.e., temperate grasses and alfalfas). Information about the forages, collection sites, and composition are presented in Tables 1 and2. Immediately after sampling, the forages were dried in a forced-air oven at 55 °C for 72 h at the sampling site, packed into polyethylene bags, and sent to the State University of Maringá, Maringá -PR, Brazil.

Cows, facilities and experimental design Animal care and handling procedures were approved by the ethics committee for animal use of the Maringa State University (protocol number 8208090218 -CEUA/UEM). Four non-lactating rumencannulated Holstein cows (two primiparous and two multiparous); weighing 545 ± 177 kg were housed in a tie-stall barn with rubber bedding, individual feedbunks, and a water trough. The proportion of ingredients and the chemical composition of the diet offered are presented in Table 3. Every morning, ingredients were mixed and fed as a total mixed ration (TMR) at 08:00 h, after removing refusals from the previous day. The amount of TMR was adjusted daily to allow 50 to 100 g•kg -1 of orts (ad libitum diet access).

The experimental treatments were (i) control and (ii) live yeast supplemented at 1 × 10 10 colony forming units (CFU day -1 per cow) (SC; Saccharomyces cerevisiae strain CNCM I-1077; Lallemand Animal Nutrition, Aparecida de Goiânia, GO, Brazil). The dose offered to animals was established after yeast plating in laboratory, as described below for the rumen fluid. Immediately before supplementing, the live yeast (10 g) was diluted in 250 mL of distilled water at 40 °C and dosed directly into the rumen, through the rumen cannula, every morning before TMR feeding. The application through the rumen cannula ensured the target yeast amount was supplied daily. Cows receiving the control treatment The treatments were compared in a switchback design, with three periods of 30 days including 24 days of adaptation and 6 days of sampling. Cows were paired according to parity and randomly assigned to each treatment sequence. There were two treatment sequences within the parity pair: Control-SC-Control or SC-Control-SC.

In situ degradability

From Day 25 to 28 of each period, two 2 day runs were used to measure the in situ disappearance of DM and aNDF of the 15 forage samples (7 or 8 forages randomly allocated in each run). Dry forage samples were ground in a Wiley mill (Marconi MA340, Piracicaba, SP, Brazil) with a 5 mm screen and 5 g were weighed into polyfilament polyester in situ bags (10 × 20 cm; 50 μm porosity; Ankom Technology, Macedon, NY, USA). Each forage was incubated in triplicate in each cow for 12, 24 and 36 h after feeding. Such times were intended to represent a range of retention times in dairy cows, considering fractional passage rates of 0.027 to 0.083 h -1 . [START_REF] Krizsan | A meta-analysis of passage rate estimated by rumen evacuation with cattle and evaluation of passage rate prediction models[END_REF] Before incubation, bags were soaked in warm water (39 °C) for 20 min to simulate rumen temperature and remove the soluble fraction. Two blank bags were included for each time point. Bags were inserted in reverse order and recovered together. Immediately after removal, all bags were submerged in cold water (0 °C) for 5 min and washed with water only in a washing machine (three cycles with water at room temperature, followed by a final spin). Washed bags were dried in a forced-air oven at 55 °C for 72 h, weighed, and their contents were ground through a 1 mm screen using a Wiley mill.

Sampling of feed and rumen fluid

Approximately 500 g of dietary ingredients were collected from day 25 to day 30 of each period and subsequently composited by period (n = 3). Samples were oven-dried at 55 °C for 72 h and ground (1 mm screen; Wiley mill) prior to chemical analyses.

On day 30 of each period, rumen fluid was collected from the ventral sac at 0, 2, 4, 8, and 12 h after feeding to measure pH, ammonia, lactate, volatile fatty acids (VFA) and for metabolomics. Yeast counts were also measured in samples collected at 0, 2, and 8 h after feeding. The pH was measured immediately after sampling using a pH meter (Tec5, Tecnal, Piracicaba, Brazil). After measuring the pH, a sub-sample was used for enumeration of yeasts as described below (only in samples collected at 0, 2, and 8 h). Another sub-sample (100 mL) was used for metabolomics analysis, as described below. A third sub-sample was centrifuged at 10 000×g for 15 min at 4 °C and the supernatant was frozen at -80 °C for further analyses of ammonia, lactate, and VFA.

Laboratory analyses

Forage samples were analyzed for DM (method 934.01), [START_REF]Association of Official Analytical Chemists -AOAC, Official Methods of Analysis[END_REF] crude protein (CP) by the Kjeldahl procedure (method 984.13), [START_REF]Association of Official Analytical Chemists -AOAC, Official Methods of Analysis[END_REF] ash (method 942.05), [START_REF]Association of Official Analytical Chemists -AOAC, Official Methods of Analysis[END_REF] aNDF with a heat stable amylase and expressed inclusive of residual ash, [START_REF] Mertens | Gravimetric determination of amylase-treated neutral detergent fiber in feeds with refluxing in beakers or crucibles: collaborative study[END_REF] indigestible NDF (iNDF) by in situ incubation for 288 h, [START_REF] Huhtanen | The use of internal markers to predict total digestibility and duodenal flow of nutrients in cattle given six different diets[END_REF] acid detergent fiber (ADF; assayed sequentially and expressed inclusive of residual ash) and lignin(sa) (expressed inclusive of residual ash). [START_REF] Van Soest | Collaborative study of acid-detergent fiber and lignin[END_REF] Hemicellulose was calculated as aNDF minus ADF and cellulose as ADF minus lignin(sa). Samples of TMR were analyzed for starch, [START_REF] Hall | Determination of dietary starch in animal feeds and pet food by an enzymatic-colorimetric method: collaborative study[END_REF] and DM, CP, ash, aNDF, and ADF as described for forage samples. Samples of rumen fluid and SC product were used to enumerate yeasts in malt extract agar (M137, Himedia®, Mumbai, India) acidified to pH 3.5 with lactic acid. Plates were incubated aerobically for 2 days at 30 °C. The number of colony forming units (CFU) was expressed as log 10 CFU mL -1 .

After thawing the supernatant of rumen fluid samples, VFA were determined by gas chromatography (GCMS QP 2010 plus, Shimadzu, Kyoto, Japan) using a capillary column (Stabilwax, Restek, Bellefonte, PA, USA; 60 m, 0.25 mm ø, 0.25 μm crossbond carbowax polyethylene glycol). Ammonia and lactate were determined by colorimetric methods as described by Chaney and Marbach and Pryce respectively. [START_REF] Chaney | Modified reagents for determination of urea and ammonia[END_REF][START_REF] Pryce | A modification of Barker-Summerson method for the determination of lactic acid[END_REF] Liquid-liquid extraction of rumen fluid metabolites The fresh rumen fluid samples for metabolomics were first centrifuged at 1000×g for 30 min at 4 °C. Then, the supernatant was centrifuged at 13 000×g for 60 min at 4 °C. The clarified rumen fluid was filtered using a 0.45 and 0.22 μm pore size membrane filter (Merck Millipore; Burlington, MA, USA).

An aliquot (10 mL) was mixed with 10 mL of ethyl acetate and 1.0 g of NaCl for the liquid-liquid extraction (LLE). The solution was vortexed for 2 min and allowed to separate into two phases. The upper organic layer was decanted, and the bottom layer was mixed with another 10 mL of ethyl acetate and 1.0 g of NaCl. This procedure was repeated a third time. The organic phases were combined and concentrated under nitrogen flow. Similar procedures were repeated, but using ethyl acetate with 1% acetic acid (v:v); and ethyl acetate with 1% ammonium hydroxide (v:v).

Extracts were kept at -20 °C until untargeted metabolomics analysis was performed.

Untargeted metabolomic analysis

Extracts were analyzed using an ultra-high performance liquid chromatograph (UHPLC) (Shimadzu, Nexera X2, Japan) coupled to a hybrid quadrupole time-of-fight high resolution mass spectrometry (Impact II, Bruker Daltonics Corporation, Germany) equipped with an electrospray ionization source. Chromatographic separation was performed with an Acquity UHPLC CSH C18 packed with 135 Å pore size, 1.7 μm particle size, 2.1 × 100 mm column (Waters, UK), at a flow rate of 0.2 mL•min -1 . The gradient mixture of solvents A (H 2 O with 0.1% formic acid; v:v) and B (acetonitrile with 0.1% formic acid; v-v) was as follows: 5% B 0-1 min, 50% B 1-5 min, 95% B 5-10 min, maintained at 95% B 10-16 min, 5% B 16-18 min, and maintained at 5% B 18-21 min at 40 °C. The capillary voltage was operated in positive ionization mode, set at 4500 and 3000 V, respectively; with an end plate offset potential of -500 V. The dry gas parameters were set to 8 L•min -1 at 180 °C with a nebulization gas pressure of 4 bar. Data were collected from m/z 50 to 1300 with an acquisition rate of 5 Hz, and the four ions of interest were selected by auto MS/MS scan fragmentation. Molecular networking approach required the conversion of mass spectrometry raw data into mzXML file format followed by upload to the Global Natural Products Social Molecular Networking (GNPS) to generate the molecular networking. [START_REF] Wang | Sharing and community curation of mass spectrometry data with global natural products social molecular networking[END_REF]

Statistical analysis

Statistical analysis were performed using the mixed procedure of the SAS 9.4 software (SAS Institute Inc., Cary, NC, USA, 2015). [START_REF]Base SAS® 9.4 Procedures Guide[END_REF] Data regarding the DM intake determined on days 24 to 30 of each period were averaged per cow and analyzed using a model that included fixed effects of treatment, period, treatment × period, and random effects of cow and cow × treatment. Rumen fluid parameters (yeast count, ammonia, pH, VFA) were analyzed with the same model, including fixed effects of time and treatment × time. For the in situ assay, forages were assigned to one of three groups: corn silages, tropical grasses (sugarcane silage and tropical grass silage) and temperate grasses and alfalfa (oat silage, ryegrass silage, alfalfa silage and alfalfa hay). Outcomes were analyzed with the model described for DM intake but including fixed effects of the forage group and the interaction between the forage group and treatment. The fixed effect of treatment × period was not significant for any variable (P ≥ 0.22), and then removed from the model. Differences between treatments were declared if P ≤ 0.05 and trends accepted if 0.05 < P ≤ 0.10. Metabolomics data were evaluated qualitatively for the presence or absence of putative compounds. Each spectrum was manually verified to check precursors and product ions.

RESULTS

The SC addition did not affect (P = 0.53) DM intake (10.1 versus 10.8 kg day -1 for control and SC, respectively). Cows supplemented with SC had higher (P = 0.05) counts of yeast in rumen fluid (Table 4). There was an interaction (P = 0.04) between yeast supplementation and time after feeding for lactate concentration (Fig. 1). At 8 h after feeding, cows receiving SC had a lower lactate concentration in rumen fluid (P < 0.01). Cows fed SC had a higher (P = 0.05) acetate: propionate ratio in the rumen fluid, but concentrations of acetate, propionate, butyrate, iso-butyrate, iso-valerate, valerate, and total VFA did not differ between treatments (P > 0.10). There was a tendency for there to be lower ammonia (P = 0.10) and higher pH (P = 0.09) when SC were fed to cows.

There was no interaction (P > 0.10) between forage group and yeast supplementation for the in situ degradability of DM and aNDF (Table 5), but SC feeding increased aNDF (P = 0.04) and DM degradability (P = 0.03) at 24 h. There was a trend for higher DM (P = 0.09) and aNDF degradability (P = 0.08) at 12 h for SC. No differences occurred for in situ degradability of DM and aNDF at 36 h of incubation (P > 0.10).

Untargeted metabolomics revealed that a chemical entity with the putative molecular formula of C

DISCUSSION

Supplementation of live Saccharomyces cerevisiae strains has been reported to increase fiber degradation and animal performance. 15,[START_REF] Ondarza | Case study: mutiple-study analysis of the effect of live yeast on milk yield, milk component content and yield and feed efficiency[END_REF] Benefits of live yeast supplementation are often associated with improved rumen function due to factors such as reduced redox potential by oxygen scavenging, [START_REF] Marden | How does live yeast differ from sodium bicarbonate to stabilize ruminal pH in high-yielding dairy cows?[END_REF] pH due to decreased lactic acid production and increased utilization of lactic acid, [START_REF] Williams | Effects of the inclusion of yeast culture (Saccharomyces cerevisiae plus growth medium) in the diet of dairy cows on milk yield and forage degradation and fermentation patterns in the rumen of steers[END_REF][START_REF] Chaucheyras | Effects of a strain of Saccharomyces cerevisiae (Levucell® SC), a microbial additive for ruminants, on lactate metabolism in vitro[END_REF][START_REF] Chaucheyras-Durand | Effect of the microbial feed additive Saccharomyces cerevisiae CNCM I-1077 on protein and peptide degrading activities of rumen bacteria grown in vitro[END_REF][START_REF] Guedes | Effects of a Saccharomyces cerevisiae yeast on ruminal fermentation and fiber degradation of maize silages in cows[END_REF] higher availability of growth factors (e.g., organic acids and vitamins) 15,37-39 and stimulation of rumen microbial growth. [START_REF] Sousa | Live yeast supplementation improves rumen fibre degradation in cattle grazing tropical pastures throughout the year[END_REF][START_REF] Newbold | Mode of action of the yeast Saccharomyces cerevisiae as a feed additive for ruminants[END_REF][START_REF] Moya | Effects of live yeast (Saccharomyces cerevisiae) and type of cereal on rumen microbial fermentation in a dual flow continuous culture fermentation system[END_REF] However, potential benefits of live yeast supplementation on ruminal degradability of forages grown in tropical and subtropical areas are seldom reported and there is no information on the potential improvement in DM, and aNDF degradation varies by forage group in dairy cows, whether they are lactating or not.

An important result in this study was the higher rumen in situ degradability of aNDF in cows fed SC, especially in early incubation times (i.e., 24 h), which is in line with the modifications in the rumen environment. Cows fed SC had higher counts of yeasts, tended to have higher pH values, and lower concentrations of ammonia and lactate at comparable concentrations of VFA in the rumen fluid. These findings indicate that SC improved the rumen environment and might have stimulated the growth of cellulolytic and anaerobic bacteria and hastened their colonization onto fiber particles. [START_REF] Harrison | Influence of addition of yeast culture supplement to diets of lactating cows on ruminal fermentation and microbial populations[END_REF][START_REF] Erasmus | Effect of yeast culture supplement on production, rumen fermentation, and duodenal nitrogen flow in dairy cows[END_REF] The increase in rumen pH in animals supplemented with SC is attributable at least partly to the lower concentration of lactate and may have increased activity of fibrolytic bacteria and fungi in the ruminal digesta, 14,[START_REF] Moya | Effects of live yeast (Saccharomyces cerevisiae) and type of cereal on rumen microbial fermentation in a dual flow continuous culture fermentation system[END_REF][START_REF] Harrison | Influence of addition of yeast culture supplement to diets of lactating cows on ruminal fermentation and microbial populations[END_REF] resulting in the greater aNDF degradability in such cows. The concomitant reduction of ammonia nitrogen suggests a greater uptake of the available nitrogen pool in the rumen by the fibrolytic bacterial populations, which are known to utilize ammonia as an important nitrogen source. [START_REF] Fonty | Establishment of cellulolytic bacteria and development of fermentative activities in the rumen of gnotobiotically-reared lambs receiving the microbial additive Saccharomyces cerevisiae CNCM I-1077[END_REF] Although there was no difference in the concentration of total VFA and most individuals' VFA, cows fed SC had a lower concentration of lactate and higher acetate: propionate ratio due to a numerical reduction in propionate concentration. In the rumen, propionate is synthetized via succinyl-CoA and acrylyl-CoA pathways. [START_REF] Russell | Energy yielding and consuming reactions[END_REF] In the latter pathway, lactic acid produced by rumen bacteria or ingested with fermented feedstuffs can be converted to propionate by lactate-fermenting bacteria. [START_REF] Mackie | An in vivo study of ruminal microorganisms influencing lactate turnover and its contribution to volatile fatty acid production[END_REF] Yeast supplementation has been associated with either a decreased production or increased utilization of lactic acid. [START_REF] Williams | Effects of the inclusion of yeast culture (Saccharomyces cerevisiae plus growth medium) in the diet of dairy cows on milk yield and forage degradation and fermentation patterns in the rumen of steers[END_REF][START_REF] Chaucheyras | Effects of a strain of Saccharomyces cerevisiae (Levucell® SC), a microbial additive for ruminants, on lactate metabolism in vitro[END_REF][START_REF] Chaucheyras-Durand | Effect of the microbial feed additive Saccharomyces cerevisiae CNCM I-1077 on protein and peptide degrading activities of rumen bacteria grown in vitro[END_REF][START_REF] Guedes | Effects of a Saccharomyces cerevisiae yeast on ruminal fermentation and fiber degradation of maize silages in cows[END_REF] In our study, although lactate concentrations were relatively low (<1 mM), indicating nonacidotic conditions in our non-lactating cows, two lactate peaks were detected in the rumen fluid. The first occurred immediately after feeding, reflecting the intake of lactic acid present in the corn silage. At 8 h after feeding, lactate concentration increased again, likely as an intermediate of ruminal fermentation, which coincided with the highest concentrations of VFA and the pH nadir (not shown). Though the size of the first peak immediately after feeding did not differ across treatment, that for SC cows was much lower at 8 h than the peak for control cows, in support of previous studies in which SC reduced lactate concentration in cows. Hence, the lower lactate concentration at the second peak associated with the numerical trend of lower propionate concentration suggest that decrease in lactate might have occurred due to a lower production of lactate rather than a stimulation of lactate utilizer microorganisms. The higher acetate: propionate ratio might have been a consequence of this pattern. The numerically lower concentration of valerate is in line with the numerically lower concentration of propionate, due to fact that valerate is partially formed by the condensation of propionate and acetate. [START_REF] Gray | The nature and origin of the volatile fatty acids in the rumen of the sheep[END_REF] Moreover, the greater fiber degradation in cows fed SC may have contributed to their greater acetate: propionate ratio. This is likely due to stimulation of ruminal fibrolytic microorganisms, which generally increases the molar proportion of acetate to a greater extent than non-fiber fermenting ruminal microorganisms. [START_REF] Russell | Energy yielding and consuming reactions[END_REF][START_REF] Wolin | Microbe-microbe interaction[END_REF] In our study, these benefits were observed even in a nonacidogenic diet. Thus, SC supplementation is likely to assist the ruminal fermentation in dairy cows having high DM intake of diets with great proportion of rumen fermentable carbohydrates. De Ondarza et al. reported greater milk yield for cows supplemented with live yeast than non-supplemented cows and with the effect being greater for cows <100 days in milk than for cows >100 days in milk. [START_REF] Ondarza | Case study: mutiple-study analysis of the effect of live yeast on milk yield, milk component content and yield and feed efficiency[END_REF] It has been claimed that forage type can influence the SC effect on ruminal fiber degradation. Guedes et al. [START_REF] Guedes | Effects of a Saccharomyces cerevisiae yeast on ruminal fermentation and fiber degradation of maize silages in cows[END_REF] described a larger response to SC supplementation in corn silages of lower fiber degradability than in corn silages with higher fiber degradability in situ. Recently, Sousa et al. [START_REF] Sousa | Live yeast supplementation improves rumen fibre degradation in cattle grazing tropical pastures throughout the year[END_REF] reported a higher relative benefit of SC for tropical forages of lower fiber degradability. However, the absolute increase in fiber degradability (g•kg -1 ) reported by these authors was higher in forages with increased quality, with higher increase in fiber degradability in Palisade grass (+25 g•kg -1 ), Guineagrass (+ 23 g•kg -1 ), and corn silage (+ 26 g•kg -1 ), than in sugarcane silage (+ 17 g•kg -1 ) and bermudagrass hay (+ 19 g•kg -1 ). In fact, Chaucheyras-Durand et al. 14 showed a higher benefit for SC after 24 h on fiber degradation for soybean hulls (+ 32.8 g•kg -1 ) with a higher fiber digestibility than in wheat bran (+ 20.7 g•kg -1 ), alfalfa hay (+17.6 g•kg -1 ), or wheat silage (+14.0 g•kg -1 ) with lower digestibility coefficients. As SC benefits are likely based on increased fibrolytic activity by stimulation of bacteria and fungi, acting synergistically, 14 it seems likely that plant tissues with greater recalcitrance would be more affected than those with a less lignified cell wall by SC supplementation, at least under realistic digesta retention times.

In the current trial, there was no interaction between forage group and yeast supplementation for in situ degradability; meanwhile, the SC supplementation increased in situ degradability of DM by 4.6% at 24 h of incubation, mainly due to an increase of aNDF degradability by 10.3% at 24 h of incubation. Previous studies have indicated that fiber degradation is better predicted assuming that fiber is the sum of iNDF and potentially digestible neutral detergent fiber, and that potential digestible fiber is represented by two digestible fractions, with rapidly degradable and slowly degradable fractions. [START_REF] Ellis | Models for estimating parameters of neutral detergent fiber digestion by ruminal microorganisms[END_REF][START_REF] Huhtanen | Prediction of in vivo neutral detergent fiber digestibility and digestion rate of potentially digestible neutral detergent fiber: comparison of models[END_REF][START_REF] Raffrenato | Development of a mathematical model to predict pool sizes and rates of digestion of 2 pools of digestible neutral detergent fiber and an undigested neutral detergent fiber fraction within various forages[END_REF] In our study, it is likely that the degradation rate of aNDF of the forage sources was faster when SC was fed. Several reports have suggested that SC supplementation increases the rate of fiber degradation, with a more pronounced effect at shorter incubation times. [START_REF] Sousa | Live yeast supplementation improves rumen fibre degradation in cattle grazing tropical pastures throughout the year[END_REF][START_REF] Williams | Effects of the inclusion of yeast culture (Saccharomyces cerevisiae plus growth medium) in the diet of dairy cows on milk yield and forage degradation and fermentation patterns in the rumen of steers[END_REF][START_REF] Girard | Stimulation of ruminal bacteria by different fractions derived from cultures of Saccharomyces cerevisiae strain 1026[END_REF][START_REF] Callaway | Effects of a Saccharomyces cerevisiae culture on ruminal bacteria that utilize lactate and digest cellulose[END_REF] The lack of difference between control and SC that was observed when the forage samples were incubated for 36 h suggests that SC acted on the degradation of the potential digestible fiber fast pool.

Non-targeted metabolomics was used as an exploratory approach to prospect ruminal chemical entities affected by SC supplementation. Interestingly, some compounds were suppressed in the rumen of cows that received SC. Among those was one having the molecular formula of C 17 H 29 N 6 O 3 and m/z 365.2284 [M + H] + , which was putatively annotated as lipid and related molecules. This opens a new window of opportunity to understand the mechanisms of improved ruminal metabolism upon SC supplementation. Recently, rumen metabolites involved in linoleic and alpha-linolenic metabolism were linked to feed efficiency in beef [START_REF] Artegoitia | Rumen fluid metabolomics analysis associated with feed efficiency on crossbred steers[END_REF] and dairy cattle. [START_REF] Li | Combined signature of rumen microbiome and metabolome in dairy cows with different feed intake levels[END_REF] De Ondarza et al. [START_REF] Ondarza | Case study: mutiple-study analysis of the effect of live yeast on milk yield, milk component content and yield and feed efficiency[END_REF] reported in a multi-study analysis greater milk fat yield and higher feed efficiency for cows supplemented with SC compared with cows not supplemented. Collectively, those findings may suggest that the ruminal lipid metabolism, including the biohydrogenation pathways, may be involved on the improved rumen function in cows www.soci.org de Poppi et al.

wileyonlinelibrary.com/jsfa receiving SC. In future studies, the integration of rumen metabolomics with other omics techniques is expected to assist describing key metabolic pathways that ultimately improve the ruminal function.

CONCLUSIONS

For dairy cows fed a corn silage based TMR, Saccharomyces cerevisiae strain CNCM I-1077 supplementation decreased ruminal lactate concentrations and increased DM and aNDF degradability after 24 h of incubation regardless of forage group.

Figure 1 .

 1 Figure1. Ruminal lactate concentration in cows supplemented with (▲) or without (□) with live yeast. P = 0.03 for treatment, P < 0.01 for time, P = 0.04 for treatment × time. **P < 0.01 for control versus yeast supplementation at 8 h after feeding.

Table 1 .

 1 Forages sampled

	ID	Forage	Assigned group	Type	Scientific name	Conservation	Locality	Country
	A	Corn	Corn silage	C4 grass Zea mays	Silage	Saladillo	Argentina
	B	Corn	Corn silage	C4 grass Zea mays	Silage	Castro-PR	Brazil
	C	Corn	Corn silage	C4 grass Zea mays	Silage	Bela Vista de Goiás-GO	Brazil
	D	Corn	Corn silage	C4 grass Zea mays	Silage	Mandaguaçu-PR	Brazil
	E	Corn	Corn silage	C4 grass Zea mays	Silage	Arequipa	Peru
	F	Alfalfa	Temperate/	Legume	Medicago sativa	Hay	Lunardelli-PR	Brazil
			Alfalfa
	G	Alfalfa	Temperate/	Legume	Medicago sativa	Silage	Castro-PR	Brazil
			Alfalfa
	H	Oat	Temperate/	C3 grass Avena sativa	Silage	Arapoti-PR	Brazil
			Alfalfa
	I	Oat	Temperate/	C3 grass Avena sativa	Silage	Castro-PR	Brazil
			Alfalfa
	J	Ryegrass	Temperate/	C3 grass Lolium multiflorum	Silage	Castro-PR	Brazil
			Alfalfa
	K	Ryegrass	Temperate/	C3 grass Lolium multiflorum	Silage	Castro-PR	Brazil
			Alfalfa
	L	Sugarcane	Tropical grass	C4 grass Saccharum officinarum	Silage	Nova Andradina-MS	Brazil
	M	Sugarcane	Tropical grass	C4 grass Saccharum officinarum	Silage	Agudos-SP	Brazil
	N	Tropical	Tropical grass	C4 grass Panicum maximum cv.	Silage	São Miguel do Araguaia-	Brazil
		grass			Mombaça		GO
	O	Tropical	Tropical grass	C4 grass Panicum maximum cv.	Silage	Terenos-MS	Brazil
		grass			Mombaça

Table 2 .

 2 Chemical composition of the forage samples (g•kg -1 dry matter, unless otherwise stated)

		Dry matter
	Forage group	(g kg -1 as fed)	Crude protein	Ash	aNDF a	Hemicellulose	ADF b	Cellulose	Lignin(sa)	iNDF c
	A-Corn silage	272	77.7	59.4	536	260	275	238	37.2	177
	B-Corn silage	340	74.5	39.3	431	253	177	156	21.1	133
	C-Corn silage	255	45.8	25.8	590	256	334	284	49.6	205
	D-Corn silage	293	76.0	34.3	403	200	203	177	25.9	138
	E-Corn silage	323	89.6	104	601	246	354	296	58.1	167
	F-Alfalfa hay	907	140	71.8	720	190	530	390	140	473
	G-Alfalfa silage	536	158	87.5	542	162	380	288	92.9	296
	H-Oat silage	217	71.2	77.2	611	247	364	303	59.8	262
	I-Oat silage	290	94.4	87.7	661	266	395	355	38.4	175
	J-Ryegrass silage	490	143	108	595	248	344	298	46.0	188
	K-Ryegrass silage	545	169	121	519	216	303	271	31.9	122
	L-Sugarcane silage	331	25.8	22.5	767	298	448	340	109	373
	M-Sugarcane silage	243	24.9	24.3	805	311	494	389	105	404
	N-Tropical grass silage	285	30.9	83.4	837	285	552	466	85.9	428
	O-Tropical grass silage	390	42.9	72.4	813	325	488	421	66.6	382
	Item		Composition
	Ingredients
	Corn silage		650
	Concentrate a		350
	Nutrients
	Dry matter, g•kg -1 as fed	473 ± 5.7
	Crude protein		124 ± 1.5
	Ash		54 ± 0.1
	Starch		283 ± 2.4
	Neutral detergent fiber		419 ± 3.1
	Acid detergent fiber		221 ± 1.2

a Neutral detergent fiber. b Acid detergent fiber. c Indigestible aNDF. Table 3. Composition of basal diet (g kg -1 DM, unless otherwise stated) a Concentrate based on ground corn, soybean meal and mineralvitamin mix.

Table 4 .

 4 Yeast count, pH, ammonia and VFA concentrations in the rumen fluid of non-lactating cows supplemented with or without live yeast

		Treatment				P-value a
		Control	SC b	SEM	T	H	T × H
	Yeast count (log 10 CFU mL -1 )	4.99	5.40	0.084	0.05	<0.01	0.37
	Ammonia (mg dL -1 )	11.0	9.39	0.50	0.10	<0.01	0.72
	pH	6.13	6.24	0.031	0.09	<0.01	0.91
	Acetate (mM)	72.4	69.4	2.33	0.44	0.01	0.96
	Propionate (mM)	26.2	23.3	0.94	0.12	<0.01	0.98
	Butyrate (mM)	13.1	12.2	0.41	0.23	<0.01	0.88
	i-Butyrate (mM)	1.49	1.37	0.127	0.55	0.99	0.97
	i-Valerate (mM)	0.53	0.56	0.021	0.38	<0.01	0.79
	Valerate (mM)	1.30	1.16	0.050	0.15	<0.01	0.63
	Total VFA (mM)	115	109	3.4	0.27	<0.01	0.99
	Acetate: Propionate	2.82	3.02	0.045	0.05	<0.01	0.42
	Lactate (mM)	0.64	0.47	0.027	0.03	<0.01	0.04

  17 H 29 N 6 O 3 with m/z 365.2284 [M + H] + was completely suppressed (relative abundance zero) in the rumen fluid of all cows supplemented with SC. This compound was annotated in the family of lipids and related molecules. Chemical entities with m/z 198.0394 [M + H] + and 276.0283 [M + H] + from the organoheterocyclic compound family, m/z 355.2578 [M + H] + from the benzenoid family, m/z 373.2217 [M + H] + , 359.2412 [M + H] + and 267.1942 from the lipids and related molecules, and m/z 253.1412 [M + H] + from the phenylpropanoids and polyketides were also exclusively observed in control cows.

Table 5 .

 5 Effect of live yeast and forage group on the ruminal degradability

				Treatment
			Control			SC a				P-value b
		Temp/	Corn	Trop.	Temp/	Corn	Trop.
		Leg c	silage c	grass c	Leg c	silage c	grass c	SEM	T	G	T× G
	DM d degradability (g kg -1
	DM)
	12 h	476	494	249	496	516	271	15.1	0.09 <0.01 0.99
	24 h	560	567	310	594	597	329	15.3	0.03 <0.01 0.85
	36 h	666	652	391	669	661	391	17.8	0.77 <0.01 0.97
	aNDF e degradability (g kg -1
	NDF)
	12 h	194	108	89	218	127	105	14.9	0.08 <0.01 0.89
	24 h	314	210	162	350	250	178	19.0	0.04 <0.01 0.70
	36 h	461	355	260	473	366	252	23.4	0.78 <0.01 0.87

a Saccharomyces cerevisiae strain CNCM I-1077 supplied at 1 × 10 10 CFU day -1 . b T: effect of yeast supplementation, G: effect of forage group, T × G: interaction between yeast supplementation and forage group. c Forage group: Temp/Legoat silages, ryegrass silages, alfalfa silage and alfalfa hay; Trop. grasssugarcane silages and tropical grass silages; Corn silagecorn silages. d Dry matter. e Neutral detergent fiber.

© 2021 Society of Chemical Industry.J Sci Food Agric 2021

J Sci Food Agric 2021 © 2021 Society of Chemical Industry.wileyonlinelibrary.com/jsfa

ACKNOWLEDGEMENTS

The authors thank the GESF team and the staff of the Iguatemi Experimental Farm (FEI-UEM) for assistance with the study. We gratefully acknowledge financial support from Lallemand SAS (Blagnac, France).

CONFLICT OF INTEREST

The authors declare no real or perceived conflicts of interest. The co-authors from the live yeast supplying company (L.J.M, E.C. and F.C.D.) have only been associated with the design of the study.

1 Mertens DR, Creating a system for meeting the fiber requirements of dairy cows. J Dairy Sci