Åke Andersson

Mathias Poline

Meena Kodambattil

Oleksii Rebrov

Estelle Loire

Philipe Maître

Vitali Zhaunerchyk
email: vitali.zhaunerchyk@physics.gu.se

Structure of Proton-bound Methionine and Tryptophan Dimers in the Gas Phase Investigated with IRMPD Spectroscopy and Quantum Chemical Calculations

The structures of three proton-bound dimers: Met 2 H + , MetTrpH + , and Trp 2 H + are investigated in the gas phase with infrared multiple photon disassociation (IRMPD) spectroscopy in combination with quantum chemical calculations. Their IRMPD spectra in the range of 600 -1850 cm -1 are obtained experimentally using the FT-ICR mass spectrometer and the CLIO free electron laser as an IR light source. The most abundant conformers are elucidated by comparing the IRMPD spectra with harmonic frequencies obtained at the B3LYP-GD3BJ/6-311++G** level of theory. Discrepancies between the experimental and theoretical data in the region of 1500 -1700 cm -1 are attributed to the anharmonicity of the amino bending modes. We confirm the result of a previous IRMPD study that the structure of gas phase Trp 2 H + is charge-solvated, but find that there are more stable structures than originally reported. 1 In addition, gas phase Met 2 H + and MetTrpH + have been revealed to have charge-solvated structures. For all three dimers, the most stable conformer is found to be of type A. The spectrum of Met 2 H + , however, cannot be explained without some abundance of type B charge-solvated conformers as well as salt-bridged structures.

Introduction

Amino acids are ubiquitous building blocks for life. They consists of amino group, carboxyl group and a side chain which determines properties of the specific amino acid. In solution, interactions with the solvent molecules cause amino acids to take on a zwitterionic form, meaning that a proton has moved from the carboxyl to the amino functional group. In the context of gas phase studies of isolated and microsolvated amino acids, the question of when and how amino acids become zwitterions has been studied widely. In many of these studies, infrared multiple photon disassociation (IRMPD) spectroscopy has been used as an experimental tool for molecular structure elucidation. Protonated alpha amino acid dimers in the gas phase are of interest because they capture 2 the essence of amino acid interaction while being of relatively small size. They exhibit many conformers, commonly classified as charge-solvated (CS) or salt-bridge (SB) structures.

The CS implies binding of the monomers through an inter-molecular hydrogen bond (Hbond) between the protonated amino group of one amino acid and amino group (type A) or carboxyl group (type B) of another amino acid. In the SB structures one monomer adopts a zwitterionic (type Z) form.

The stability of SB structures is related to the stability of monomer's zwitterionic form, which in turn has been attributed to various factors. Wyttenbach et al. [START_REF] Wyttenbach | On the Stability of Amino Acid Zwitterions 18 Page 18 of 26 ACS Paragon Plus Environment The Journal of Physical Chemistry in the Gas Phase: The Influence of Derivatization, Proton Affinity, and Alkali Ion Addition[END_REF] found a positive correlation between the stability of the zwitterionic form of alkali metal cationized amino acid monomers and proton affinity (PA) of the amino acid. Bush et al. [START_REF] Bush | Proton Affinity and Zwitterion Stability: New Results from Infrared Spectroscopy and Theory of Cationized Lysine and Analogues in the Gas Phase[END_REF] found this correlation to be weaker for alkali metal cationized lysine with additional methyl groups, and argued that PA is not a reliable indication of zwitterionic stability whereas side chain effects are more important. By contrast, studies of proton bound amino acid homodimers have shown that zwitterionic stability is well predicted by PA. [START_REF] Price | Is Arginine a Zwitterion in the Gas Phase[END_REF][START_REF] Kong | Reinvestigation of the Structure of Protonated Lysine Dimer[END_REF][START_REF] Alahmadi | The Protonated and Sodiated dimers of Proline Studied by IRMPD Spectroscopy in the N-H and O-H Stretching Region and Computational Methods[END_REF][START_REF] Wu | Infrared Multiple Photon Dissociation Spectra of Proline and Glycine Proton-Bound Homodimers. Evidence for Zwitterionic Structure[END_REF][START_REF] Yin | Structure of Protonated Threonine Dimers in the Gas Phase: Salt-Bridged or Charge-Solvated?[END_REF][START_REF] Kong | Progressive Stabilization of Zwitterionic Structures in [H(Ser)2-8]+ Studied by Infrared Photodissociation Spectroscopy[END_REF][START_REF] Seo | Side-chain Effects on the Structures of Protonated Amino Acid Dimers: A Gas-phase Infrared Spectroscopy Study[END_REF][11] High PA amino acids, e.g. argenine, lysine, and proline, have been shown to form SB dimers. [START_REF] Price | Is Arginine a Zwitterion in the Gas Phase[END_REF][START_REF] Kong | Reinvestigation of the Structure of Protonated Lysine Dimer[END_REF][START_REF] Alahmadi | The Protonated and Sodiated dimers of Proline Studied by IRMPD Spectroscopy in the N-H and O-H Stretching Region and Computational Methods[END_REF] On the other hand, low PA amino acids, e.g. glycine, threonine, phenylalanine, and tyrosine, form CS dimers. [START_REF] Wu | Infrared Multiple Photon Dissociation Spectra of Proline and Glycine Proton-Bound Homodimers. Evidence for Zwitterionic Structure[END_REF][START_REF] Yin | Structure of Protonated Threonine Dimers in the Gas Phase: Salt-Bridged or Charge-Solvated?[END_REF][START_REF] Kong | Progressive Stabilization of Zwitterionic Structures in [H(Ser)2-8]+ Studied by Infrared Photodissociation Spectroscopy[END_REF][START_REF] Seo | Side-chain Effects on the Structures of Protonated Amino Acid Dimers: A Gas-phase Infrared Spectroscopy Study[END_REF] With a mid PA, glutamic acid has been shown to adopt CS structures at 15 K, but SB dimers at 300 K. 11 A recent study by Feng et al. [START_REF] Feng | Structure of Protonated Tryptophan Dimer in the Gas Phase Investigated by IRPD Spectroscopy and Theoretical Calculations[END_REF] of tryptophan dimers has shown it to favor CS over SB, even though its PA is similar to that of proline.

In this paper we report the results of IRMPD studies performed for Met 2 H + , MetTrpH + , and Trp 2 H + in the frequency range of 600-1850 cm -1 . The tryptophan (Trp, W) homodimer is studied with the aim of revealing its IRMPD spectrum in a previously unexplored frequency range. [START_REF] Feng | Structure of Protonated Tryptophan Dimer in the Gas Phase Investigated by IRPD Spectroscopy and Theoretical Calculations[END_REF] Studies of the methionine (Met, M) homodimer are motivated by the fact that its PA lies in the frontier of amino acids that are known to form CS structures. [START_REF] Seo | Side-chain Effects on the Structures of Protonated Amino Acid Dimers: A Gas-phase Infrared Spectroscopy Study[END_REF][START_REF] Bleiholder | Revising the Proton Affinity Scale of the Naturally Occurring α-amino Acids[END_REF] An additional reason to study Met is its side chain. Dimers of amino acids tend to stabilize their geometry through intermolecular interaction, e.g. H-bonding between side chains, in addition to the CS or SB binding. Methionine has no N, O, or F on its side chain, only S, which forms significantly weaker H-bonds. 31,[START_REF] Biswal | Nature and Strength of Sulfur-centred Hydrogen Bonds: Laser Spectroscopic Investigations in the Gas Phase and Quantum-chemical Calculations[END_REF] It is therefore of interest to study how methionine dimers stabilize. It is also of interest to study Met heterodimers, where the second monomer is prone to intermolecular interactions. For this purpose, the MetTrpH + dimer is studied, which only has the Trp side chain capable of significant intermolecular interaction, presumably N-H• • • N and N-H• • • π to the indole ring.

Methods

Experiment

All experimental data was collected at Centre Laser Infrarouge d'Orsay (CLIO) in Orsay, France. Three amino acid dimers were studied: Met 2 H + , MetTrpH + , and Trp 2 H + . The Trp used for Trp 2 H + was an isotopologue, specifically five deuterium atoms were substituted on the indole ring. The dimer solutions were prepared as 1 mM monomer concentration in a 49:49:2 mixture of water, methanol, and formic acid. Ions were delivered into the gas phase by electrospray ionization (ESI) of the solution, and subsequently stored and accumulated in a linear ion-trap of a mass spectrometer (MS) of model 7 T Bruker Apex Qe. While trapped, ions were subsequently pulse extracted toward the ion cyclotron resonance (ICR) ion trap, where they were irradiated with pulses of the CLIO free-electron laser (FEL), which scanned the 600 -1850 cm -1 frequency range. The FEL had power 20 -30 mW and pulse rate 25 Hz. Irradiation time of the ions was controlled by a mechanical shutter placed between the FEL beam and the ICR ion trap. It is typically chosen to be around 500 ms. The measurements were performed at high, mid, and low irradiation energy, meaning the summed energy of the FEL pulses over the irradiation time was above, in, and below the range of 8 -16 mJ, respectively. Finally, the abundance of dimers and their fragments were analyzed using For a given FEL frequency, the IRMPD intensity was calculated as:

I IRMPD = ln 1 + I fragment I parent ,
where I species is the integrated MS intensity of that species and its isotopologues. A conformational search has been performed using several molecular dynamics (MD) simulations with different initial geometries in order to cover a large conformation space.

The MD calculations were carried out in the microcanonical ensemble employing the density functional-based tight binding method [START_REF] Aradi | a Sparse Matrix-based Implementation of the DFTB Method[END_REF] as implemented in the DFTB+ software package. [START_REF]Density Functional Based Tight Binding (and more[END_REF] The initial velocities were considered to correspond to a Maxwell-Boltzmann distribution at 298 K and a velocity Verlet algorithm with a time step of 1 fs was implemented. For the amino acid heterodimer, MetTrpH + , we considered two sets of structures with either Met or

Trp moiety being protonated.

The most stable structures obtained with the MD simulations were optimized with DFT using the B3LYP functional and 6-311++G** basis set including the GD3BJ empirical dispersion. The harmonic frequency analysis was performed at the same level of theory. For the optimized structures single point energies were calculated with the CBS-4M composite method. To obtain the corresponding Gibbs energies, the CBS-4M calculations were combined with vibrational analysis performed with the B3LYP-GD3BJ/6-311++G** method.

For Met 2 H + dimers, we additionally performed VPT2 anharmonic vibrational analysis as well as single point energy calculations at the G4MP2 level of theory. To reduce computational costs, the VPT2 analysis was performed with the N07D basis set, which has been shown

to perform well under similar circumstances. [START_REF] Yatsyna | Aminophenol Isomers Unraveled by Conformer-specific far-IR Action Spectroscopy[END_REF] We note that for MetTrpH + and Trp 2 H + dimers, which have more complex structures, neither G4MP2 calculations nor the VPT2 analysis were undertaken due to limitations in computational time. All these calculations were carried out with the Gaussian 16 program. 36 When comparing the harmonic frequency analysis of conformers with an experimental spectrum, three modifications are made. First, all frequencies are multiplied by 0.980, to account for anharmonicity. This frequency scaling constant was found by least-square fitting harmonic theory to all experimental spectra, and is consistent with B3LYP frequency scaling for other molecules. [START_REF] Halls | Harmonic Frequency Scaling Factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ Electric Property Basis Set[END_REF] Second, for every conformer, its vibrational frequencies are broadened The Journal of Physical Chemistry 8 cm -1 , or equivalently with a full width at half maximum of 18.8 cm -1 . This broadening was required in order to take into account the FEL pulse linewidth. Last, the spectra of conformers are scaled in proportion to their relative abundances at room temperature, and summed. The relative abundances p i were found as

p i = 1 Z exp - G i k B T ; Z = i exp - G i k B T , (1)
where G i are the Gibbs energies of the conformers, k B = 0.6950 cm -1 /K is the Boltzmann constant, and T is the temperature.

With the goal of understanding and classifying the inter-and weak intramolecular interactions, noncovalent interaction (NCI) analyses were performed for the most abundant conformers of Met 2 H + , MetTrpH + , and Trp 2 H + . The NCI method introduced by Johnson et al. [START_REF] Johnson | Revealing Noncovalent Interactions[END_REF] uses the electron density and its gradient to classify real-space regions as van der Waals interactions, H-bonds, or steric repulsions. The sign(λ 2 )ρ index assigned by the NCI method, where ρ is the electron density and λ 2 is the second largest eigenvalue of its Hessian, can also be related to the binding energy of H-bonds. [START_REF] Contreras-García | Analysis of Hydrogen-bond Interaction Potentials from the Electron Density: Integration of Noncovalent Interaction Regions[END_REF]

Results and discussion

Methionine-methionine dimers

The four most abundant structures of Met (CBS-4M and G4MP2), B3LYP greatly underestimates the energy of SB conformers. A similar tendency was previously reported in studies of serine dimers. [START_REF] Kong | Progressive Stabilization of Zwitterionic Structures in [H (Ser) 2-8]+ Studied by Infrared Photodissociation Spectroscopy[END_REF] The CBS-4M electronic energy calculations of Met 2 H + conformers give results consistent with G4MP2, while having the advantage of being less time consuming. In light of this agreement, CBS-4M is assumed to be suitable for energy calculations for both other proton-bound dimers studied in this paper. The Gibbs energies of Met 2 H + conformers were therefore calculated with CBS-4M, and the corresponding relative abundances are shown in fig. 3a.

The IRMPD spectra of Met 2 H + with different irradiation energies are shown in fig. 4, together with harmonic frequency analyses for the four most abundant conformers. The Gibbs energy analysis based on eq. ( 1) predicts the MM-A1 conformer to be the most abundant species, though its relative population constitutes less than 40%. This is consistent with the experimental data, i.e. by comparing the IRMPD spectrum near 1405 cm -1 to the harmonic frequency analyses, MM-A1 can be ruled out to be the only populated conformer.

Predictions for MM-Z2 lack the second peak observed in the region of 1700 -1800 cm -1 associated with carboxyl group stretching, which is explained by the fact that the peaks in this region correspond to vibrational modes in the carboxyl group, whereas the type Z conformer possesses only one carboxyl group. The observed peak at 1725 cm -1 being unmatched by MM-A1 and MM-Z2, leads us to believe that there is a substantial abundance of MM-B2 1) employing the CBS-4M method for calculating Gibbs energies. The relative abundances do not sum to exactly one because additional conformers were considered when calculating the thermodynamic partition function. Note that because conformers are indexed by type and electronic energies, not by type and Gibbs energies, some low-index conformers e.g. WM-A1 are not among the eight most abundant conformers. The Journal of Physical Chemistry or MM-B1, which both agree well with the experimental IRMPD spectrum. This is again consistent with the Gibbs energy population analysis, which predicts their relative populations to be 11% and 10%, respectively. All conformers except for MM-B1 are predicted to have large peaks in the region of 1500 -1700 cm -1 , but the IRMPD intensity in this region is constrastingly low and flat. The frequencies in this region correspond to bending modes of the amino group. Because the amino group participates in the H-bonding of the dimer and the potential along the proton transfer coordinate is quite flat, we believe these modes to be strongly anharmonic, and harmonic analyses to be insufficient. This anharmonicity is known to play a significant role for H-bonding amino stretching in Lys 2 H + , 40,41 so it is plausible that bending also is affected.

In order to shed more light on the discrepancies in the region of 1500 -1700 cm -1 , a VPT2 anharmonic vibrational analysis was performed. The resulting spectra are shown as dashed magenta lines in fig. 4. The anharmonic analysis of MM-Z2 did not produce a sensible result. For abundant conformers of type A and B, the anharmonic analyses indeed predict flatter and less intense IRMPD spectra in the region of 1500 -1700 cm -1 . Furthermore, the VPT2 bands are red-shifted compared to those predicted by the harmonic analysis. Overall, the anharmonic treatment improves agreement with the experiment.

It is interesting to note that the VPT2 bands of MM-B2 fit the experimental spectra better than those of MM-A1, calling into the question of whether MM-A1 truly is the most abundant. This can point to the non-thermal population of conformers produced upon ESI. Although this phenomenon was observed in previous studies performed with other experimental setups, [START_REF] Almasian | Non-equilibrium Isomer Distribution of the Gas-phase Photoactive Yellow Protein Chromophore[END_REF] this scenario is very unlikely in our case. When the ions accumulate in the linear ion trap of the ICR, multiple low energy collisions with the Ar buffer gas group. For the case when the Met moiety is protonated, its side chain bends due to an H-bond between the S and the amino group, similar to the Met 2 H + case. In MW-A1, there is an additional cation-π interaction between Met α-H and the phenyl part of the indole ring, making MW-A1 the most stable structure by far.

Following the conclusion drawn from the Met 2 H + results, the electronic energies of MetTrpH + were calculated with CBS-4M, and are shown in tab. 1. The Gibbs energies there is a large peak at 750 cm -1 , substantially larger than the one at 995 cm -1 . According to the harmonic frequency analysis, all conformers are predicted to have a peak near 750 cm -1 , but only the three most abundant conformers are predicted to have a peak near 995 cm -1 , though of magnitude similar to the 750 cm -1 peak. The experimental scan with high irradiation energy revealed a peak at 1085 cm -1 , which is only present for the conformers of type A. As was the case for Met 2 H + , the type Z conformer is predicted to have only a single peak in the region of 1700 -1800 cm -1 . Therefore, it is unlikely to be significantly populated, which is in line with the population analysis based on eq. ( 1). Again, we observe low and flat IRMPD intensity in the region of 1500 -1700 cm -1 , but harmonic analyses predict relatively intense peaks there. Anharmonic analyses were not undertaken due to limitations on com-12

Page 12 of 26

ACS Paragon Plus Environment

The Journal of Physical Chemistry putational time, but we hypothesize that the peaks in the region of 1500 -1700 cm -1 would have become less intense, as they did for Met 2 H + . The harmonic analyses for the three most abundant conformers all fit the experimental spectra adequately, which is consistent with the populations obtained from the Gibbs energies using eq. ( 1).

It is interesting to note that despite the fact that in the most abundant MetTrpH + conformers the proton is located on the Met moiety, as seen in fig. 1b, the IRMPD mass spectra of MetTrpH + do not show MetH + fragments, only TrpH + . A plausible explanation can be suggested based on the multi-photon nature of the IRMPD process. The successive photon absorption is not instantaneous, since it is determined by the intramolecular vibrational energy redistribution time scale. This implies that the dimer can undergo conformational conversion such that the proton might migrate from Met to the Trp moiety. Another explanation for this observation could be that the TrpH + + Met fragmentation channel is more energetically favorable than MetH + + Trp. In order to justify this explanation, we calculated energies of these channels as difference between enthalpies at T = 300 K of the corresponding fragments and the parent dimer assuming the lowest energy conformer, MW-A1. The enthalpies for MetH + , TrpH + , Met and Trp were found with the CBS-4M method (single point energy calculation) for which the geometries were optimized at the B3LYP-GD3BJ/6-311++G** level of theory. According to our calculations the energies of the TrpH + + Met and MetH + + Trp channels are 158 and 160 kJ mol -1 , respectively. Although the TrpH + + Met channel is indeed energetically more favorable, the difference of only 200 J mol -1 is not likely to explain the predominance of the TrpH + + Met fragmentation channel. Therefore we believe that the absence of the MetH + fragment in the mass spectra provides evidence for isomerization occuring during the IRMPD process. Isomerization has been observed in the IRMPD process for other ions, [START_REF] Oomens | Infrared Multiple Photon Dynamics and Spectroscopy of Cationic PABA and its Dehydroxylated Fragment Ion[END_REF][START_REF] Maître | Ultrasensitive Spectroscopy of Ionic Reactive Intermediates in the Gas Phase Performed with the First Coupling of an IR FEL with an FTICR-MS[END_REF] and thus it is not so surprising that it also occurs for proton-bound dimers, which have almost no barrier for the proton transfer. [START_REF] Bouchoux | From the Mobile Proton to Wandering Hydride Ion: Mechanistic Aspects of Gas-phase Ion Chemistry[END_REF] 13

Page 13 of 26

ACS Paragon Plus Environment

The Journal of Physical Chemistry

Tryptophan-tryptophan dimers

The four most stable structures of Trp 2 H + at T = 300 K are shown in fig. 1c. They are all of type A, and are additionally stabilized by cation-π as well as intermolecular H interaction, as is inferred from the NCI analyses (fig. S6 in SI). In addition to the characteristic H-bond of the type A structures, every structure has a stabilizing weak interaction, between either the amino group (WW-A1, WW-A3, WW-A4) or the α-H (WW-A2) of the protonated moiety and carboxyl group. WW-A1 is set apart from the rest by having three relatively strong stabilizing cation-π interactions from each amino group to the indole N on the other moiety.

The electronic energies of Trp 2 H + were calculated with CBS-4M, and are listed in tab. 1.

Two structures previously reported, 1 WW-CS1 and WW-CS4, are included among those found by our conformational search. The Gibbs energies of Trp 2 H + conformers were calculated, and the corresponding relative abundances are shown in fig. 3c. It is interesting to note that even though WW-A1 is the most stable at low temperatures, WW-A2 becomes slightly more abundant at T = 300 K. Such a behavior can be explained in terms of entropy.

The many cation-π interaction in WW-A1 constrain the side chains and limits the entropy, while the relative floppiness of WW-A2 allows for a higher entropy. Our calculations show that the entropy of WW-A1 is indeed 0.6k B (5 J mol -1 K -1 ) lower than that of WW-A2.

For Trp 2 H + the seven most abundant conformers are of type A. Feng et al. there is a reasonable agreement between observations and theoretical predictions outside the region of 1500 -1700 cm -1 for conformers of type A. WW-B1 can be ruled out because of its predicted peak near 1700 cm -1 not seen in experimental IRMPD spectra. WW-Z1 has only one peak in the carboxyl region, i.e. 1700-1800 cm -1 , while two peaks are actually observed.

We thus conclude that the structure of Trp

Conclusions

In this paper, we investigated the structure of Met we further conclude that the most abundant conformers are of type A, but cannot differentiate the most stable type A conformers, because their predicted spectra were quite similar.

In absence of distinct conformer-specific spectral features, the relative abundances of conformers calculated with eq. ( 1) were used, where Gibbs energies are input parameters. The conformer abundances obtained in such a way provide reasonable agreement of the experimental IRMPD spectra with the combined theoretical IR spectra.

For calculating Gibbs energy, three methods were used for the B3LYP-GD3BJ/6-311++G** optimized geometries: B3LYP, CBS-4M, and G4MP2. It was found that CBS-4M behaved similarly to G4MP2 for Met 2 H + while being significantly cheaper, and was therefore utilized for all energy calculations. It was also found that B3LYP underestimates energies of the type Z conformers.

Trp 2 H + was studied previously by Feng et al. The Journal of Physical Chemistry bending vibrational modes, and overestimate their intensities. We believe these modes to be anharmonic as they involve hydrogen bonds between amino groups and the potential for the proton hopping between the two moieties is rather flat. Anharmonic analyses using VPT2 improves the agreement with the experimental data in the region of 1500 -1700 cm -1 , with the notable exception of MM-Z2, for which VPT2 does not produce a sensible result.

As mentioned in the introduction, the aim of this study was to understand how the side chains stabilize. Cation-π interaction is seen for Trp 2 H + between the indole ring and any sufficiently positive hydrogen, e.g. those adjacent to N and α-H, though the latter is rather uncommon. S• • • H bonding in Met 2 H + is concluded to occur between S and protonated amino groups. For the heterodimer MetTrpH + , side chain stabilization occurs through both.

If the Met moiety amino group is protonated, it interacts with (in order of decreasing NCI index ρ) the Trp amino group, S, and indole ring. Otherwise, in many structures including the most abundant, the protonated Trp amino group only interacts with the Met amino and carboxyl group, and the S does not participate in a significant interaction.

Tryptophan and proline may be a remarkable counterexample to the empiric rule which states that the stability of SB structures of homodimers increases with the PA of the monomer. [START_REF] Yin | Structure of Protonated Threonine Dimers in the Gas Phase: Salt-Bridged or Charge-Solvated?[END_REF] The uncertainty lies in which of those amino acids have the greater PA, because they are not consistently ranked across works (see Ref. [START_REF] Bleiholder | Revising the Proton Affinity Scale of the Naturally Occurring α-amino Acids[END_REF] and references therein). The same can be said for methionine and proline. We speculate that while the PA of an amino acid is a mostly reliable indicator for whether the homodimer structure is SB, other properties, e.g. side chains, affect the structure type when the PA is "on the fence". This seems to be the case for amino acids which lie near proline on the PA scale. [START_REF] Seo | Side-chain Effects on the Structures of Protonated Amino Acid Dimers: A Gas-phase Infrared Spectroscopy Study[END_REF] In the future we plan to investigate diastereomer-specific IR features of homo-and het- studies on different amino acid dimers from theoretical perspectives which has also verified the potential of this approach. 46 The results presented in this paper were obtained for homochiral dimers and thus they can readily complement our envisioned studies.

Fourier

Figure 1 : 5 Page 5 of 26 ACS

 1526 Figure 1: The conformers of (a) Met 2 H + , (b) MetTrpH + , and (c) Trp 2 H + with the lowest Gibbs energies at T = 300 K. The distances in Å of possible H-bonds (blue dotted lines) and cation-π interactions (dotted green lines) are shown. The strength of these interactions are investigated in our NCI analysis (fig. S4, S5, and S6 in SI). The shorthand XY-SN denotes a dimer structure. X and Y are one-letter amino acid codes of the protonated and unprotonated moiety, respectively. S is the structure type, which can be A, B, or Z. N is the index when sorted among structures of the same type, with respect to electronic energy at the CBS-4M level of theory.

6 Page 6 of 26 ACS

 626 into a continuous spectrum by convolution with a Gaussian function with parameter σ = Paragon Plus Environment

Figure 3 :

 3 Figure 3: Temperature-dependent relative abundances for the eight most abundant (at 300 K) conformers of (a) Met 2 H + , (b) MetTrpH + , and (c) Trp 2 H + , obtained with eq. (1) employing the CBS-4M method for calculating Gibbs energies. The relative abundances do not sum to exactly one because additional conformers were considered when calculating the thermodynamic partition function. Note that because conformers are indexed by type and electronic energies, not by type and Gibbs energies, some low-index conformers e.g. WM-A1 are not among the eight most abundant conformers.

Figure 4 : 9 Page 9 of 26 ACS

 4926 Figure 4: IRMPD spectra of Met 2 H + . (a) The experimental IRMPD spectra measured at different irradiation energies (black/wine/red solid lines), with local maxima highlighted (green triangles) and traced. The sum of predicted spectra of conformers weighted by relative abundances from fig. 3a (blue line) is included for comparison, offset to ease viewing. (b-e) Scaled harmonic frequencies (solid blue lines) of individual conformers and their relative abundance (blue text) obtained from eq. (1). Predicted spectra (black solid lines) were obtained by convoluting with a Gaussian function with FWHM = 18.8 cm -1 . The anharmonic VPT2 alternative (dashed magenta lines) is included for comparison.

10 Page 10 of 26 ACS

 1026 atoms occur which leads to a thermalization of the ions. On the other hand, a relatively low predicted abundance for MM-B2 conformer might point to deficiencies of the theoretical calculations. Paragon Plus Environment The Journal of Physical Chemistry Methionine-tryptophan dimers The four most abundant structures of MetTrpH + at T = 300 K are shown in fig. 1b. All structures shown are of type A, and, according to our NCI analyses (fig. S5 in SI), are additionally stabilized by a cation-π interaction between the amino group of the Met moiety and the indole ring. A weak intermolecular interaction exists between either the amino group (MW-A1, WM-A5) or the α-H (MW-A2, MW-A3) of the protonated moiety and carboxyl

ofPage 11 of 26 ACSFigure 5 :

 265 Figure 5: Same as fig. 4, but for MetTrpH + and without VPT2. WM-Z1 and WM-B1 are ranked 5 and 16 in abundance, respectively.

2 H 15 Page 15 of 26 ACS

 21526 + is of type A in the gas phase. Because the most stable structures are all of type A, their predicted IRMPD spectra are quite similar (fig.6b-e), and their relative abundances cannot be inferred from the experimental IRMPD spectra unambiguously. Nonetheless, employing abundances based on the Gibbs energy analysis eq. (1), the combined theoretical spectrum (blue line in fig.6a) agrees reasonably Paragon Plus EnvironmentThe Journal of Physical Chemistry well with the experimental IRMPD spectrum.

17 Page 17 of 26 ACS

 1726 erochiral amino acid dimers. Such studies are essential for developing analytical tools for characterizing sample enantiomeric purity. The very recent studies on proton-bound glutamic acid dimers have demonstrated the experimental evidence for chiral recognition of amino acid dimers from their IR spectra. 11 Furthermore, we have recently reported similar Paragon Plus Environment The Journal of Physical Chemistry

  The three dimers Met 2 H + , MetTrpH + , and Trp 2 H + respectively fragment into MetH + , TrpH + , and TrpH + . With high irradiation, these may fragment further. In that case, I fragment is replaced by the sum of all fragments' intensities.

	Calculations
	(a)	MM-A1	MM-Z2	MM-B2	MM-B1
	Met 2 H +	2.26	2.52 1.77	2.24 2.17	1.56 2.22 1.80		2.18	2.56 2.21 2.25 1.74	1.85	2.32	2.20 1.65	1.86
	(b)	MW-A1	MW-A2	MW-A3	WM-A5
	MetTrpH +	2.40	2.33	2.46 2.28 1.49 2.48	2.27	2.28	1.76	2.41	2.16 2.31	1.75 2.36	2.19	1.70 2.60	2.56
	(c)	WW-A2	WW-A1	WW-A3	WW-A4
	2 H + Trp	1.73 2.23 2.35 2.47	2.55	1.70 2 .5 0 2.53 2.32	2.64	2.32	2.40 2.45 1.72 2.46	2.30 2 .4 1	1.75 2.62 2.49

  An energy comparison of the methods is made in fig.2. Compared to the composite methods Figure 2: Electronic energy for Met 2 H + conformers relative to MM-A1, calculated at three levels of theory. The geometries of all Met 2 H + conformers are available as Supporting Information (fig. S1 in SI).

	Page 7 of 26	The Journal of Physical Chemistry
		increasing accuracy and computational expense, they are: B3LYP, CBS-4M, and G4MP2.
		forms an intramolecular H-bond with the protonated amino group, causing the side chain
		to bend. In MM-A1 and MM-B2, the other S weakly interacts with the protonated amino
		group, stabilizing the dimer further. In MM-B1, MM-B2, and MM-Z2, an H-bond is formed
		ACS Paragon Plus Environment

2 H + at T = 300 K are shown in fig. 1a. As inferred from our NCI analyses (fig. S4 in SI), in all four, the S on the protonated moiety between the amino and carboxyl group of the unprotonated moiety.

The single point energies of Met 2 H + were calculated at three levels of theory. In order of 7

Table 1 :

 1 Relative electronic energies (EE) of the most stable MetTrpH + and labeled Trp 2 H + conformers, calculated with CBS-4M. The first letter in dimer notation is the name of the amino acid where the proton is. The geometries of all MetTrpH + and Trp 2 H + conformers are available as Supporting Information (fig.S2and S3 in SI, respectively).

	Conf.	EE (kJ mol -1 ) Conf.	EE (kJ mol -1 )
	MW-A1	0.00 WW-A1	0.00
	MW-A2	4.67 WW-A2	1.14
	MW-A3	7.06 WW-A3	5.87
	WM-A1	10.55 WW-A4	6.89
	WM-Z1	14.98 WW-A5	15.10
	WM-A2	15.76 WW-CS4 1	21.26
	WM-A3	15.77 WW-CS1 1	21.49
	WM-Z2	15.93 WW-A6	29.68
	WM-A4	16.44 WW-Z1	31.33
	WM-A5	17.41 WW-B1	40.43

  [START_REF] Feng | Structure of Protonated Tryptophan Dimer in the Gas Phase Investigated by IRPD Spectroscopy and Theoretical Calculations[END_REF] have already asserted that the most abundant conformers of Trp 2 H + are of type A. The most stable conformer found in the current paper has electronic energy 21.26 kJ mol -1 and Gibbs energy 17.96 kJ mol -1 less than WW-CS4, which we find to be the most stable conformer among those previously reported. To rule out the possibility that the discrepancy between the findings of Feng et al. and ours is caused by using different numerical methods, we also calculated electronic energies at the same level of theory. Employing the M062X functional as used in Ref.,[START_REF] Feng | Structure of Protonated Tryptophan Dimer in the Gas Phase Investigated by IRPD Spectroscopy and Theoretical Calculations[END_REF] the electronic and Gibbs energy of WW-A1 are still lower, by 22.97 and 20.29 kJ mol -1 , respectively, than that of WW-CS1.The IRMPD spectra of Trp 2 H + in the region of 950 -1850 cm -1 for different irradiation 14 energies are shown in fig.6, together with harmonic frequency analyses for the four most abundant conformers. Due to issues arising from a contaminant in the MS, the IRMPD spectra below 950 cm -1 could not be obtained. Similar to the Met 2 H + and MetTrpH + cases, Figure6: Same as fig.4, but for Trp 2 H + and without VPT2. WW-Z1 and WW-B1 are ranked 8 and 9 in abundance, respectively.

	The Journal of Physical Chemistry	Page 14 of 26
	ACS Paragon Plus Environment

  2 H + , MetTrpH + , and Trp 2 H + dimers. For this purpose, we employed IRMPD spectroscopy in combination with theoretical calculations. Based on the comparison of the observed IRMPD spectra with harmonic frequencies of low-energy conformers, scaled by 0.980 to compensate for anharmonicity, it is concluded for all three dimers that the most abundant conformer is CS. For MetTrpH + and Trp 2 H + ,

1

  Our results for Trp 2 H + confirm that the most stable structure of Trp 2 H + is of type A, but include five more stable structures, of which the most stable has electronic energy 21.26 kJ mol -1 and Gibbs energy 17.96 kJ mol -1 less than the most stable among those previously reported.

	The harmonic frequency analyses adequately describe most of the observed IRMPD fea-

tures with the exception of those in the region of 1500 -1700 cm -1 , where the experimental IRMPD features are rather weak and flat. The harmonic analyses assign these peaks to amino 16 Page 16 of 26 ACS Paragon Plus Environment

ACS Paragon Plus EnvironmentThe Journal of Physical Chemistry

Acknowledgement

We are thankful to the CLIO staff for help and assistance with performing the experiment. M. Kodambattil thanks the Erasmus+ EU program for providing her with the scholarship. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 731077. Calculations were performed with resources at the Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC). ACS Paragon Plus Environment The Journal of Physical Chemistry ACS Paragon Plus Environment The Journal of Physical Chemistry

Supporting Information Available

The following files are available free of charge.

• supp_info.pdf : Supporting Information containing figures S1-S6 referred to in this article, and tables of the Cartesian coordinates of each of the 44 conformers.


Thierry Pellarin
email: thierry.pellarin@univ-grenoble-alpes.fr

Carlos Román-Cascón

Christian Baron

Rajat Bindlish

Luca Brocca

Pierre Camberlin

Diego Fernández-Prieto

Yann H Kerr

Christian Massari

Gérémy Panthou

Diego Fernández Prieto

B Perrimond

N Philippon

G Quantin

The Precipitation Inferred from Soil Moisture (PrISM) near real-time

Keywords: Precipitation, Soil moisture, Africa, satellite rainfall products, comparison

come

Introduction

Rainfall is a crucial resource in Africa, where large parts of the population rely on rainfed agriculture. The continent is also known for its vulnerability to rainfall variability that impacts the natural resources (water, vegetation) and subsequently the wellness of populations, in societies where economy is based mainly on agriculture [START_REF] Sultan | Estimating the Potential Economic Value of Seasonal Forecasts in West Africa: A Long-Term Ex-Ante Assessment in Senegal[END_REF]. Knowledge on rainfall spatio-temporal distribution is essential to various applications such as water-resource and land-use management, agricultural crop yield estimates, flood nowcasting, dam management, ground-water recharge estimates and irrigation demand. Rain-gauges provide the most common and most direct measurement of point precipitation at the surface, therefore they are generally assumed as the most accurate method to measure precipitation. Unfortunately, Africa is a region where the ground-based rain-gauge network is of very low density and operational radar installations are almost non-existent [START_REF] Washington | African climate change -Taking the shorter route[END_REF]. Furthermore, the gauge networks have been degrading over the last few decades [START_REF] Nicholson | Validation of TRMM and other rainfall estimates with a high-density gauge dataset for West Africa. Part I: Validation of GPCC rainfall product and pre-TRMM satellite and blended products[END_REF].

In this context, satellite-based precipitation products represent an unavoidable alternative for providing precipitation knowledge in Africa. In recent decades, significant progress has been made in satellite precipitation estimation. This progress is mostly due to the introduction of new sensors (e.g. Global Precipitation Measurement Core Observatory satellite), but also to the improved sensor accuracy, and efficiency of proposed algorithms that take advantage of the many observational data (including multi-channel VIS/IR sensors, and passive microwave). Many studies have been dedicated

to the evaluation of these different satellite precipitation products in Africa [START_REF] Gosset | Evaluation of several rainfall products used for hydrological applications over West Africa using two high-resolution gauge networks[END_REF][START_REF] Camberlin | Evaluation of remotely sensed rainfall products over Central Africa[END_REF][START_REF] Serrat-Capdevila | Evaluation of the Performance of Three Satellite Precipitation Products over Africa[END_REF][START_REF] Pomeon | Evaluating the performance of remotely sensed and reanalysed precipitation data over West Africa using HBV light[END_REF][START_REF] Maidment | Evaluation of satellite-based and model re-analysis rainfall estimates for Uganda[END_REF]. Without being exhaustive, the main conclusions of these studies can be summarized as follows: (i) the state-of-theart products perform relatively well at monthly and decadal time steps [START_REF] Gosset | Evaluation of several rainfall products used for hydrological applications over West Africa using two high-resolution gauge networks[END_REF][START_REF] Roca | Comparing Satellite and Surface Rainfall Products over West Africa at Meteorologically Relevant Scales during the AMMA Campaign Using Error Estimates[END_REF][START_REF] Jobard | An intercomparison of 10-day satellite precipitation products during West African monsoon[END_REF] with a decreasing performances for finer timescales; (ii) most products satisfactorily reproduce the main features of the rainfall regime [START_REF] Gosset | Evaluation of several rainfall products used for hydrological applications over West Africa using two high-resolution gauge networks[END_REF][START_REF] Camberlin | Evaluation of remotely sensed rainfall products over Central Africa[END_REF]; (iii) real-time products exhibit moderate to high (positive or negative) biases [START_REF] Gosset | Evaluation of several rainfall products used for hydrological applications over West Africa using two high-resolution gauge networks[END_REF] whereas adjusted or post-processed products, in which ground precipitation measurements are included in algorithms to correct bias, show lower biases, (iv) there is a clear need to improve the accuracy of satellite products in the estimation of accumulated rainfall [START_REF] Serrat-Capdevila | Evaluation of the Performance of Three Satellite Precipitation Products over Africa[END_REF][START_REF] Maggioni | Estimating Uncertainties in High-Resolution Satellite Precipitation Products: Systematic or Random Error[END_REF].

One potential strategy for improving satellite precipitation products is to use soil moisture measurements from satellite microwave sensors. Soil moisture can be seen as the trace of precipitation, and a knowledge of the temporal and spatial variability of soil moisture could benefit to rainfall retrievals from space. Pioneer studies [START_REF] Pan | Estimation of regional terrestrial water cycle using multisensor remote sensing observations and data assimilation[END_REF][START_REF] Crow | A novel method for quantifying value in spaceborne soil moisture retrievals[END_REF][START_REF] Pellarin | Using spaceborne surface soil moisture to constrain satellite precipitation estimates over West Africa[END_REF][START_REF] Mccabe | Hydrological consistency using multi-sensor remote sensing data for water and energy cycle studies[END_REF][START_REF] Crow | Improving Satellite-Based Rainfall Accumulation Estimates Using Spaceborne Surface Soil Moisture Retrievals[END_REF][START_REF] Pellarin | Soil moisture mapping over West Africa with a 30-min temporal resolution using AMSR-E observations and a satellite-based rainfall product[END_REF] exploited this signal to correct existing satellite precipitation products. Later, [START_REF] Brocca | A new method for rainfall estimation through soil moisture observations[END_REF][START_REF] Brocca | Soil as a natural rain gauge: Estimating global rainfall from satellite soil moisture data[END_REF] developed the SM2RAIN approach to directly derive a rainfall amount from soil moisture variations exclusively. Since 2015, these approaches were improved and applied at the global scale [START_REF] Koster | Precipitation estimation using L-band and C-band soil moisture retrievals[END_REF][START_REF] Massari | An assessment of the performance of global rainfall estimates without ground-based observations[END_REF] and on different locations in the US [START_REF] Wanders | Correction of real-time satellite precipitation with multi-sensor satellite observations of land surface variables[END_REF], in Australia [START_REF] Brocca | Rainfall estimation by inverting SMOS soil moisture estimates: A comparison of different methods over Australia[END_REF], over selected sites [START_REF] Román-Cascón | Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX[END_REF] and in China [START_REF] Zhang | Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time[END_REF]. One of the main advantages of these methodologies based on soil moisture measurement is that they can replace, in near-real-time, scaling procedures of state-of-the-art satellite precipitation and avoid significant latency for dataset availability. This paper aims to present the latest developments in the PrIMS (Precipitation Inferred from Soil Moisture) algorithm originally developed by [START_REF] Pellarin | Soil moisture mapping over West Africa with a 30-min temporal resolution using AMSR-E observations and a satellite-based rainfall product[END_REF][START_REF] Román-Cascón | Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX[END_REF]. The concept of PrISM is to use an existing realtime precipitation product and to correct it using a soil moisture information. In addition to PrISM algorithm, this paper presents an accurate evaluation of its performances for Africa, including a comparison with the performance of ten additional precipitation products at the daily time-scale. In order to improve the evaluation of the product in a region with very low rain-gauge coverage, exclusively local, national and pan-national in situ rain gauge measurements were used to assess PrISM performances and to compare with state-of-the art precipitation products. This was done to avoid traditionally used products that can be tricky at fine time scales, such as the Global Precipitation Climatology Center (GPCC [START_REF] Schamm | Global gridded precipitation over land: a description of the new GPCC First Guess Daily product[END_REF]), the Global Precipitation Climatology Project (GPCP [START_REF] Adler | The version-2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979-present)[END_REF][START_REF] Adler | The Global Precipitation Climatology Project (GPCP) Monthly Analysis (New Version 2.3) and a Review of 2017 Global Precipitation[END_REF]) or the Climatic Research Unit (CRU [START_REF] New | A high-resolution data set of surface climate over global land areas[END_REF]). The paper is organized as follows: section 2 describes the satellite and ground-based rainfall datasets, and the PrISM algorithm; section 3 presents the results and a comparison with existing rainfall products; and section 4 draws conclusions and perspectives.

Ground-based precipitation measurements

Five reference data sets based on in situ rainfall measurements are used in this study (Table 1).

The first two datasets are provided by the AMMA-CATCH Observatory in Niger and Benin [START_REF] Galle | AMMA-CATCH, a Critical Zone Observatory in West Africa Monitoring a Region in Transition[END_REF][START_REF] Lebel | AMMA-CATCH studies in the Sahelian region of West-Africa: An overview[END_REF].

Both sites cover about 1x1° and are composed of 34 gauge stations in Niger and 30 gauge stations in Benin. A spatial interpolation (block kriging) was performed at the 0.25x0.25° spatial resolution in order to obtain a reference rainfall amount at the commonly used satellite spatial scale (0.25°). The selected 0.25° sites in Niger and Benin are respectively centered at 2.625°E; 13.625°N and 1.625°E; 9.625°N (see Figure 1). The number of gauge stations that directly affect the rainfall amount at the 0.25° resolution are 12 in Niger and 10 in Benin. The third data set is composed of 20 in situ gauge stations covering the whole of Burkina Faso. The dataset was provided by National Meteorological Department of Burkina Faso. The fourth dataset is the "WaTFor" data set which documents Western Central Africa. Built-up by [START_REF] Camberlin | Evaluation of remotely sensed rainfall products over Central Africa[END_REF] it contains monthly and daily in situ rainfall data collected from global datasets, national meteorological services and monitoring projects for Cameroon, Gabon, Congo and Central African Republic. Finally, the last data set is a gauge network composed of 78 stations covering 7 countries in East Africa (Ethiopia, Djibouti, Somalia, Kenya, Uganda, Tanzania and Rwanda [START_REF] Camberlin | Temperature trends and variability in the Greater Horn of Africa: interactions with precipitation[END_REF]). The datasets at national scale comprise both synoptic stations (whose data are generally incorporated in post-processed products) and independent stations.

Satellite precipitation products

In addition to the PrISM product, ten existing satellite and ground-based rainfall products have been selected for the inter-comparison (Table 2). All products are provided at the 3-hour and 0.25 degree resolution except TAMSAT (daily, 0.0375°), IMERG (half-hourly, 0.1°), SM2RAIN (daily, 0.25°), CHIRPS (daily, 0.25°) and GPCC (daily, 1°). In order to enable an inter-comparison of the products, all the products were regridded to 0.25° spatial resolution and daily temporal resolution.

Five rainfall products (out of 10) are available in real-time and are not merged with any raingauge observations. The other five products are available after a latency ranging from 7 days to 2 months CMORPH [START_REF] Joyce | A method that produces global precipitation estimates from passive microwave and infrared data at high spatial and temporal resolution[END_REF] is a rainfall estimate product based on geostationary infrared images and passive microwave data from low earth orbiting satellites. Motion vectors are determined from half-hourly geostationary infrared measurements, and used to propagate the estimates obtained from the microwave data. The CMORPH rainfall product is proposed in two modes: the CMORPH-Raw product which is not merged with any raingauge observations and the CMORPH-Adj product which use a monthly ground calibration procedure to remove bias and uncertainties. In this study, the 0.25°

3-hour version of the product was used.

TRMM 3B42 products [START_REF] Huffman | The TRMM multisatellite precipitation analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales[END_REF] originality lies in incorporating precipitation radar and microwave measurements to better evaluate rainfall intensity. It combines these data with polar-orbiting and geostationary satellite images to obtain 3-hourly rainfall estimates at 0.25° spatial resolution. Similar to CMORPH, the TRMM 3B42 products are available in two modes: the TRMM-3B42RT product (hereafter called TRMM-Raw) available in near real-time (latency of about 7 hours) which is not merged with any raingauge observations and the TRMM-3B42 product (hereafter called TRMM-Adj) which includes GPCP monthly gauge aggregations and is available with a latency up to 6-week. The TRMM-3B42 v7 used in this study improves upon the previous ones by incorporating additional microwave and infrared data, revising the relationship between radar reflectivity and rainfall rates, and using better reference data bases for bias correction.

The IMERG product, firstly released in early 2015 [START_REF] Huffman | Day 1 IMERG final run release notes[END_REF], is provided at 0.1°×0.1° spatial and halfhourly temporal resolutions in three modes, based on latency and accuracy: "early" (latency of 4-6 h after observation), "late" (12-18 h), and "final" (~3 months). The main difference between the early and final runs is -beyond the way the different sensor measurements are propagated in time -that the early run has a climatological rain gauge adjustment while the final run uses a month-to-month adjustment based on GPCC gauge data. In this study, we used the IMERG-Early and IMERG-Final products. The two products were upscaled to 0.25° by using a box-shaped kernel with antialiasing, which approach was found to outperform simple spatial averaging and half-hourly rainfall were accumulated to obtain a daily product [START_REF] Massari | A daily/25km short-latency rainfall product for data scarce regions based on the integration of the GPM IMERG Early Run with multiple satellite soil moisture products[END_REF].

TAMSAT (Tropical Applications of Meteorology using SATellite and ground based observations) was developed at the University of Reading specifically for Africa with a spatial resolution of 0.0375°. The TAMSAT method [START_REF] Thorne | Comparison of TAMSAT and CPC rainfall estimates with raingauges, for southern Africa[END_REF][START_REF] Maidment | Data Descriptor: A new, long-term daily satellite-based rainfall dataset for operational monitoring in Africa[END_REF][START_REF] Tarnavsky | Extension of the TAMSAT Satellite-Based Rainfall Monitoring over Africa and from 1983 to Present[END_REF] is based on high resolution (0.0375°) METEOSAT thermal-infrared observations for all of Africa, available from 1983 to the present and updated in near-real time (up to 7 days). Contrary to other merged products, TAMSAT does not use Global

Telecommunication System (GTS) data but historical data from about 4000 stations acquired by various African agencies since the early 1990s [START_REF] Maidment | The 30 year TAMSAT African Rainfall Climatology And Time series (TARCAT) data set[END_REF]. We used the TAMSAT V3.0 version product [START_REF] Maidment | Data Descriptor: A new, long-term daily satellite-based rainfall dataset for operational monitoring in Africa[END_REF] available at the daily time scale. Similar to IMERG, the product was regridded to the 0.25° spatial resolution, and is called TAMSAT_025.

The GPCC daily product is provided by the Global Precipitation Climatology Center [START_REF] Schamm | Global gridded precipitation over land: a description of the new GPCC First Guess Daily product[END_REF], and is available since 1 January 2009 with a spatial sampling grid of 1°. GPCC is a gridded gauge-analysis product derived from quality-controlled station data (more than 85,000 different stations). This dataset is characterized by an uneven spatial distribution: some regions are characterized by dense rain gauge networks (Europe, US, China) while other regions such as Africa, Amazonia and Northern areas suffer from low density networks. To enable comparison with other products, GPCC was downscaled to 0.25° spatial resolution with a linear interpolation method. Telecommunication System (GTS) gauge data are incorporated and a 2-day latency product is available. In the second phase, station data are combined with monthly (and pentadal) high resolution rainfall estimates to produce a second product with a latency of about 3 weeks. The version used in this study is the second product available at the daily and 0.25 degree resolution.

CHIRPS (Climate

Similar to PrISM, SM2RAIN precipitation product [START_REF] Brocca | A new method for rainfall estimation through soil moisture observations[END_REF][START_REF] Brocca | Soil as a natural rain gauge: Estimating global rainfall from satellite soil moisture data[END_REF] takes advantage of satellite soil moisture observations to derive a precipitation product. SM2RAIN is based on the inversion of the soil water balance equation and allows to estimate the amount of water entering the soil by using as input soil moisture observations from in situ or satellite sensors (e.g., [START_REF] Koster | Precipitation estimation using L-band and C-band soil moisture retrievals[END_REF][START_REF] Brocca | Rainfall estimation from in situ soil moisture observations at several sites in Europe: an evaluation of the SM2RAIN algorithm[END_REF][START_REF] Ciabatta | Daily precipitation estimation through different microwave sensors: Verification study over Italy[END_REF][START_REF] Massari | Potential of soil moisture observations in flood modelling: Estimating initial conditions and correcting rainfall[END_REF]. The SM2RAIN product used in this study is the GPM+SM2RAIN precipitation dataset (hereafter called SM2RAIN)

which is based on the integration of IMERG-ER with SM2RAIN-based rainfall estimates derived from ASCAT, SMOS and SMAP L3 soil moisture products. The merging methodology is using an Optimal Linear Combination approach, OLI [START_REF] Bishop | Climate model dependence and the replicate Earth paradigm[END_REF][START_REF] Hobeichi | Derived Optimal Linear Combination Evapotranspiration (DOLCE): a global gridded synthesis ET estimate[END_REF]. This approach provides an analytically optimal linear combination of ensemble members (precipitation products in this case) that minimizes mean square error when compared to a reference dataset. products are in NetCDF format and were regridded from the EASE 25km grid to the 0.25°x0.25° regular grid retained in the present study using the closest neighbor.

The PrISM methodology

The concept of the PrISM (Precipitation Inferred from Soil Moisture) methodology is to exploit remote sensing soil moisture measurements to correct the amount of rainfall estimated by an existing satellite rainfall product (CMORPH-Raw in this study). It makes use of a simple soil moisture / precipitation model and an assimilation scheme.

The API soil moisture / precipitation model

The API (Antecedent Precipitation Index) model is a simple model designed to simulate a soil moisture dynamic based on precipitation data. The API model is defined as:

𝐴𝑃𝐼 (𝑡) = 𝐴𝑃𝐼 (𝑡-1) . 𝑒 ∆𝑡 𝜏 + 𝑃 (𝑡) (Eq.1)
where P(t) is the rainfall accumulation (in mm) during the period Δt (in h) and τ a parameter that describes the drying-out soil moisture velocity (in h). The API index is a simple proxy of the soil moisture dynamic (in mm). Recently, [START_REF] Pellarin | A simple and effective method for correcting soil moisture and precipitation estimates using AMSR-E measurements[END_REF] proposed a slight modification of the original API model in order to improve its accuracy and enable the calculation of volumetric soil moisture in m 3 /m 3 instead of an index expressed in mm. The new version of the API model contains two modifications:

(i) it accounts for the degree of saturation of the soil before a rain event; and (ii) the soil moisture is now limited by the saturation value. These modifications of the relationship add three parameters:

dsoil an equivalent soil thickness (in mm), θsat the soil moisture value at saturation (in m 3 /m 3 ) and θres the residual soil moisture (in m 3 /m 3 ). The new version of the API model (hereafter referred as the API model) is written:

𝜃 (𝑡) = (𝜃 (𝑡-1) -𝜃 𝑟𝑒𝑠 ). 𝑒 -∆𝑡 𝜏 + (𝜃 𝑠𝑎𝑡 -(𝜃 (𝑡-1) -𝜃 𝑟𝑒𝑠 )) . (1 -𝑒 -𝑃(𝑡) 𝑑𝑠𝑜𝑖𝑙 ) + 𝜃 𝑟𝑒𝑠 (Eq.2)
where θ(t) is the surface soil moisture in m 3 /m 3 , τ is the soil moisture drying-out velocity (in h), and P(t) is the cumulative precipitation in mm during the Δt period (in h). It requires the use of a precipitation product at infra-daily resolution (3 hours or less) to determine when rainfall occurs compared to SMOS ascending (6am) or descending (6pm) orbits. A sensitivity study was conducted over 10 sites at the global scale [START_REF] Román-Cascón | Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX[END_REF] to derive the best 4 parameters of the API model. Authors showed that a constant value for θsat = 0.45 m 3 /m 3 provided reliable results. On the contrary, a spatial distribution of the θres and dsoil parameters is required and as well as a spatiotemporal distribution of the τ parameter.

The residual soil moisture is the minimal value of soil moisture on a given pixel. Based on surface soil moisture measurements obtained over the 10 sites presented in [START_REF] Román-Cascón | Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX[END_REF], the simple following formulation was proposed:

𝜃 𝑟𝑒𝑠 = 0.04676 + 0.05936 (𝑁𝐷𝑉𝐼 ̅̅̅̅̅̅̅̅ ) -0.00136 (𝑇𝑎𝑖𝑟 ̅̅̅̅̅̅ ) (Eq.3)

with 𝑇𝑎𝑖𝑟 ̅̅̅̅̅̅ (in °C) is the annual mean 2m air temperature (source MERRA, 2013) and 𝑁𝐷𝑉𝐼 ̅̅̅̅̅̅̅̅ is the annual mean NDVI value provided by ESA-CCI-LC-L4-NDVI (Spot VGT, 2015). Globally, residual soil moisture values range from 0.017 to 0.099 m 3 /m 3 at the global scale and from 0.017 to 0.060 m 3 /m 3 in Africa.

The dsoil coefficient (in mm) describes the rapidity of soil moisture wetting during a rainfall event and is related to the soil thickness. The thinner (thicker) the soil layer, the faster (slower) the soil wetting. Over 9 out of the 10 sites studied in [START_REF] Román-Cascón | Correcting satellite-based precipitation products through SMOS soil moisture data assimilation in two land-surface models of different complexity: API and SURFEX[END_REF], it was found that a dsoil value of 35 mm was adequate compared to in situ soil moisture dynamic. This is consistent with soil moisture depth sensors located (Eq.4)

Globally, dsoil values range from 40 mm (almost everywhere) to 120 mm in arid and semi-arid areas.

The τ parameter in Eq.2 describes the drying-out velocity of the surface soil moisture due to both evapotranspiration and infiltration rate. Consequently, this parameter should depends on both soil hydraulic properties and atmospheric forcing (air temperature, wind velocity, solar radiation). In a first approximation, it was shown in this study that τ value can be appropriately estimated with 30days smoothed air temperature (Tair) using the following relationship:

𝜏(𝑡) = 400 -( 350 (1+𝑒 -0.1(𝑇𝑎𝑖𝑟-7.5) ) ) (Eq.5)
where 30-days smoothed Tair values (°C) are obtained from MERRA-2 database (3-hours, 2013). At the continental scale of Africa, the τ parameter ranges from 80 h to 350 h.

The CDF matching procedure

The PrISM methodology is based on the assimilation of the SMOS soil moisture retrievals into the API model (Eq.2). Thus, a preliminary work consists in scaling the SMOS soil moisture retrievals to the API simulation using a simple CDF-matching procedure. To that end, a reference rainfall dataset was selected to provide a reference soil moisture simulation with the API model at the Africa scale.

The evaluation of two adjusted products (CMORPH-adj and TRMM-3B42) against in situ rainfall measurements in Niger and Benin sites led to the selection of the CMORPH-Adj precipitation product as the reference for the CDF-Matching procedure. Then, the API model (Eq. 2) was run for the whole of Africa using CMORPH-Adj precipitation product and parameters were derived from Eq. 3, 4 and

The Particle Filter assimilation scheme

Among the various existing assimilation schemes, the Particle Filter (PF) is an original method based on random stochastic perturbations of the precipitation forcing that explicitly simulates the consequences of precipitation uncertainties in the associated soil moisture outputs [START_REF] Doucet | On sequential Monte Carlo sampling methods for Bayesian filtering[END_REF][START_REF] Moradkhani | Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter[END_REF][START_REF] Van Leeuwen | Particle Filtering in Geophysical Systems[END_REF]. It is suitable for non-linear models and makes no assumption on the prior and posterior distributions of the model states. This property of the PF makes it more suitable for this study compared to ensemble based data assimilation approaches whose optimality and performance depend on the linearity between input and output variables, having Gaussian distributed errors, as for example in the Ensemble Kalman Filter [START_REF] Evensen | Sampling strategies and square root analysis schemes for the EnKF[END_REF][START_REF] Reichle | Contribution of soil moisture retrievals to land data assimilation products[END_REF]. For a mathematical or formal description of PF, the reader should referred to [START_REF] Yan | Improving Soil Moisture Profile Prediction With the Particle Filter-Markov Chain Monte Carlo Method[END_REF].

The concept is a pixel-based approach. An illustration of the PF assimilation method is shown in Figure 2 (Niger site, 2015). Once there is a new SMOS soil moisture retrieval on a given pixel, an assimilation window which contains the five last SMOS retrievals is defined. The length, i.e. the number of SMOS retrieval within each assimilated sub-period was chosen after a sensitivity study (not shown) and represents a compromise between too short periods (giving much weight to individual SMOS uncertainties) and too long periods which reduce the operational interest of the methodology. Thus, the API model is forced with the real-time satellite rainfall product (CMORPH-Raw in this study) that we aim to correct and which is represented as red "bars" in Figure 2. The red curve in Figure 2 represents the soil moisture simulated by the model forced with this real-time satellite rainfall. Then, the real-time satellite rainfall is used to generate 100 random rainfall time series (number tested in sensitivity experiments) using random stochastic perturbations (grey "bars" in Figure 2). These new rainfall time series are used to force the API model (Eq.2) to obtain an ensemble of soil moisture predictions (i.e., 100 soil moisture time series associated to 100 different rainfall time series, grey curves in Figure 2). The random stochastic perturbations of rainfall is done using the following simple multiplicative relationship: Rain(t,i) = Rain(t)*a(i) with a(i) a random number between 0 and 2 for i=1,100 (uniform distribution). Figure 2 clearly shows that the random rainfall can't exceed twice the amount of the initial rainfall. Then, the SMOS retrievals are used to select the 30 most probable soil moisture trajectories which minimize the RMSE. Finally, the corrected rainfall amount corresponds to the average of the 30 most probable rainfall time-series. The corrected rainfall estimate is associated with an uncertainty calculated as the difference between the maximum and the minimum value of the 30 most probable rainfall time-series. The process is repeated when a new SMOS measurement is available. Consequently, each rainfall event is considered 4 times (a period of 5 successive SMOS measurements provides 4 intervals) and the final rainfall rate correction is the averaged value of the 4 proposed corrected rainfall rates.

As the method is based on a modification of the precipitation rate of an existing product, it is not possible to create any rain event. It is also difficult to completely remove an existing rain event even if it is possible to significantly reduce it. Therefore, the method has a low impact on scores usually used in satellite precipitation product comparisons such as probability of detection (POD)

and false-alarm ratio (FAR).

Results

To enable fair comparison between satellite precipitation products, all products listed in Table 2 were regridded to the 0.25° resolution and daily time-scale. At this spatial scale, a direct comparison with a single raingauge station can be distrusted due to the large spatial scale difference. Thus, we conducted a two-step assessment methodology. First, an accurate assessment was performed on two sites where 10 to 12 raingauge stations are located within the same pixel of 0.25° (i.e. about 25x25 km²) belonging to the AMMA-CATCH Observatory in Niger and Benin. As stated in section 2.1, the use of dense networks of rain gauges allows an accurate estimate of the precipitation rate at this scale.

In a second step, a direct, less relevant comparison between satellite (0.25°) and individual rainfall station was done and results were analyzed at the network scale, i.e. Burkina Faso (20 stations), Central Africa (42 stations) and East Africa (78 stations).

Assessment at the local scale (Niger and Benin)

The eleven selected precipitation products were compared to ground-based precipitation measurements using commonly used statistical scores: the Pearson correlation (R), the Root Mean Square Error (RMSE in mm/day) and the annual bias (in mm). Null values were accounted for in the scores calculation and the comparison was performed at the daily time scale and at the 0.25° spatial resolution. As the ground-based precipitation datasets (Niger and Benin) are available at the hourly time scale whereas some satellite products are provided at the daily time scale, the matching of the two time-series was carefully checked to avoid the known ambiguity between a 6am-6am day (commonly used in precipitation measurements) and a 0-24h day. Lastly, we also examine the number of rainy days (cumulative daily rainfall > 1 mm) compared to in situ measurements.

Results are presented for illustrative purposes for the Benin site (2015) in Figure 3. Statistical scores (R, RMSE and annual bias) are plotted in each graph and are also reported in Table 3. Overall, all products capture relatively well the temporal dynamics of precipitation with a rather high correlation coefficient (R>0.70 except for TRMM-Raw (R=0.65) and GPCC (R=0.42) reported only in ). On the contrary, TAMSAT_025 strongly underestimates the annual precipitation with an estimation of only 731 mm (-36%). Surprisingly, the three adjusted products (CMORPH-Adj, TRMM-Adj and IMERG-Final) provide moderate to strong underestimated precipitation (respectively 828 mm (-28%), 1075 mm (-6.5%) and 1035 mm (-10%) compared to in situ precipitation measurements. Similarly, GPCC exhibits moderate underestimation (1013 mm, -12%). Only the CMORPH-Raw product shows an overestimation of the annual rainfall with 1246 mm (+8%) in Benin in 2015. Lastly, Table 3 includes the difference in term of annual rainy days. In the Benin site, 103 rainy days (> 1mm) were observed in 2015. Table 3 shows that CHIRPS, GPCC and SM2RAIN tends to overestimate this number (112, 135 and 168 days respectively) whereas PrISM and CMORPH-Raw provides similar number of rainy days (101 and 102 days respectively). All other precipitation products exhibit a slight underestimation (from 88 to 94 days). 3.

The same analysis was conducted for the Niger site in 2015. Graphics are shown in supplementary materiel (Figure S1) and the statistical scores are reported in 3.

Lastly, the Taylor diagrams were plotted for the whole period (2010-2016, instead of 2015) except for the two IMERG and SM2RAIN precipitation products that start in March 2014 and are then considered only for 2015-2016 period. Figure 5 reveals some slight differences compared to Figure 4 but leads to similar conclusions. Globally, when a product is provided in two versions, e.g. raw and adjusted, the adjusted product performs better. The "raw" version of TRMM and CMORPH are located far away from their adjusted versions. The PrISM product was found to be among the best products for the Benin site and provides the best performance for the Niger site. TAMSAT_025 and SM2RAIN have similar scores and perform better for the Niger site but their standard-deviations are much lower than in the observation.

Assessment at the regional scale

At the regional scale, scores were calculated using individual raingauge stations compared to 0.25° precipitation products. Scores were calculated at the daily time scale based on the whole available period (see Table 1). Then, the median value of all individual scores (R, RMSE and bias) was calculated. Results are presented separately for the three raingauge networks (Burkina Faso, Central Africa and East Africa) in Figure 6. Results obtained for Benin and Niger are also reported in Figure 6 for comparison. Note that the two IMERG products were not considered for East Africa because the ground rainfall measurements were not available after 2013.

Results show globally that the correlation score is slightly lower for Burkina, Central Africa and East Africa compared to Benin and Niger. Similarly, the corresponding RMSE are respectively greater (worse) for these three networks. On the other hand, the biases are in the same order of magnitude in the five regions. In all regions, PrISM shows good performances according to the 3 scores and is among the best products together with the two IMERG products. It can be observed that PrISM systematically outperforms CMORPH-Raw in term of RMSE (except in East Africa where it is slightly less performant). But the improvement in term of correlation is more modest. CMORPH and TRMM, in their adjusted or raw versions, show similar performances in terms of correlation but provide generally much better results in term of RMSE and biases for their adjusted versions. SM2RAIN and CHIRPS products show lower correlation and higher RMSE scores for Burkina-Faso and Central

Africa but presents a low bias for all regions. Although its biases are small, GPCC, as expected from its low original resolution, generally shows relatively low performances, except in Central Africa.

Finally, TAMSAT_025 globally tends to underestimate the rainfall rate but shows relatively good correlation and RMSE scores.

Limitation of the PrISM methodology

One limitation of the methodology is that it is not able to create a rain event. This is clearly shown in Table 3 where the number of rainy days (> 1 mm) does not change much between the CMORPH-Raw product and the PrISM product. Therefore, it is necessary to use an initial precipitation product that overestimates the number of events since the PrISM algorithm is able to reduce the amount of rainfall.

The PrISM algorithm was also found to be more efficient when the initial rainfall product overestimates the annual rainfall amount. This is particularly true in East Africa where the CMORPH-Raw showed a negative annual bias (see Figure 6) and the PrISM algorithm was not able to correct for that underestimation. On the contrary, on the other 4 sites, the CMORPH-Raw showed positive annual biases which are suitably corrected by PrISM. The reason for this behavior is that a 10 mm rain event (for instance) can easily be reduced to 1 mm, but the PrISM algorithm can't propose a correction greater than 20 mm (correction factor ranging between 0 and 2). Consequently, it is easier to reduce the rainfall amount than to increase it.

The satisfactory results of the PrISM methodology in Central Africa are a pleasant surprise since the SMOS soil moisture retrievals under dense forest are expected to be inaccurate. The explanation of this results is partly due to the large overestimation of the CMORPH-Raw product in Central Africa. The PrISM methodology leads to reduce the rainfall amount of most events and, mechanically, RMSE is reduced as well as the annual bias. Overall, the effect of vegetation cover on the performance of the PrISM algorithm is difficult to evaluate. Indeed, areas of dense vegetation are at the same time areas where the SMOS signal can be inaccurate but also areas of heavy precipitation with a high potential for improvement. PrISM performances are similar in Niger (low vegetation) and in Benin 3.

Figure 1 :

 1 Figure 1: Location of the five reference ground-based rainfall data sets: Burkina Faso (20 stations), Central Africa (42 stations), East Africa (78 stations) and the two AMMA-CATCH sites located in Niger (region of Niamey) and Benin (region of Nalohou). The two squares inside the two left graphs represent the two selected 0.25° pixels in Niger and Benin. Precipitation product on top of land cover on the right map illustrates a time step (3h) of the PrISM precipitation product (2012 July 2 nd 3 to 6 am).

  Hazards group Infrared Precipitation with Stations) dataset is a quasi-global (50°S-50°N), high resolution (0.05°), daily, pentadal, and monthly precipitation dataset [41]. CHIRPS uses the Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis version 7 (TMPA 3B42 v7) to calibrate global Cold Cloud Duration (CCD) rainfall estimates. CHIRPS incorporates station data in a two phase process. In the first phase, Meteorological Organization's Global

at 5

 5 cm depth. However, on the Niger site, a value of dsoil equal to 100 mm was required to reproduce observed in situ soil moisture dynamics. It was concluded that this parameter can be related to the presence/absence of vegetation. In regions without vegetation, soils are often degraded with an impermeable crust associated with a low infiltration rate. A simple sigmoid relationship based on mean annual NDVI (ESA-CCI-LC-L4-NDVI, 2015) was proposed in this study as : 𝑑 𝑠𝑜𝑖𝑙 = 120 -80 1+178482301𝑒 (-100 * 𝑁𝐷𝑉𝐼 ̅̅̅̅̅̅̅̅̅)

5 .

 5 Based on the obtained reference soil moisture simulation (2012), a calculation of the two linear CDF-matching coefficients (p1 and p2) was made to scale the SMOS L3SM to the reference soil moisture. The scaled SMOS values (SMOSCDF) are assumed to be linearly related to SMOS original values as: 𝑆𝑀𝑂𝑆 𝐶𝐷𝐹 = 𝑝1 + 𝑝2. (𝑆𝑀𝑂𝑆)

Figure 2 :

 2 Figure 2: Illustration of the PF assimilation scheme for the Niger site. The initial satellite precipitation rate (in red) produces the associated soil moisture evolution (in red). Stochastic perturbations of the initial satellite precipitation rate produce an ensemble of potential soil moisture evolutions (in grey). The SMOS retrievals (5orange diamonds) are used to select the most probable soil moisture curves (in orange) and to calculate the averaged soil moisture (in blue), which is associated with a specific precipitation rate (in blue). In this case, a decrease of the initial satellite precipitation rate is proposed which is consistent with in situ precipitation measurements (in black).

Figure 3 :

 3 Figure 3 : Example of comparison between in situ precipitation measurements (Benin 0.25° site, 2015, in grey) and the ten precipitation products (PrISM, SM2RAIN, CMORPH (Raw and Adj), TRMM (Raw and Adj), IMERG (Early and Final), CHIRPS-025 and TAMSAT-025). Bars show daily rainfall amounts (left axis), curves show cumulative rainfall (right axis). Statistical scores are reported in Table3.

Figure 4

 4 Figure4shows the Taylor diagrams[START_REF] Taylor | Summarizing multiple aspects of model performance in a single diagram[END_REF] in Benin and Niger sites daily precipitation in 2015.Taylor diagram enables a visual comparative assessment of the different precipitation products quantifying the degree of correspondence between the estimated and observed precipitation in terms of three statistics: the Pearson correlation coefficient, the root-mean-square error (RMSE), and the standard deviation. Correlation scores are plotted as the radial lines, and the linear distance of a point to the Observed point indicates the RMSE from in situ measurements. For instance, the GPCC point for Benin site is close to the 0.4 radial line (R=0.42 in Table3) and close to the "7" dotted circle (RMSE=6.8 mm/days). Graphically, the best products are those closest to the "Observed" point and to the dashed curve which indicates the same amplitude of the variations. In Benin (2015), those best products are the two IMERG products and the PrISM product. For Niger (2015), PrISM and TRMM-Adj perform better than the other ones.

Figure 4 :

 4 Figure 4: Taylor diagrams for the Benin (left) and Niger (right) 0.25° sites for the year 2015 for the 11 precipitation products. Color dots refer to the different products (blue=CMORPH, red=TRMM, purple=IMERG, green=TAMSAT_025, cyan=SM2RAIN, orange=CHIRPS, dark green=GPCC and black=PrISM). Statistical scores are given in Table3.

Figure 5 :

 5 Figure 5: Taylor diagrams for the Benin (left) and Niger (right) 0.25° sites and the 2010-2016 period (except for IMERG, 2015-2016) and the 11 precipitation products. Color dots refer to the different products (blue=CMORPH, red=TRMM, purple=IMERG, green=TAMSAT_025, cyan=SM2RAIN, orange=GPCC and black=PrISM).

Figure 6 :

 6 Figure 6: Statistical scores (R, RMSE and bias) for the five regions (Benin, Niger, Burkina-Faso, Central Africa and East Africa) and for the 11 precipitation products. The temporal period depends on the satellite product and in situ availabilities.

©

  2019 by the authors. Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Figure S1 :

 S1 Figure S1: Example of comparison between in situ precipitation measurements (Niger 0.25° site, 2015, in grey) and the ten precipitation products (PrISM, SM2RAIN, CMORPH (Raw and Adj), TRMM (Raw and Adj), IMERG (Early and Final), CHIRPS-025 and TAMSAT-025). Statistical scores are reported in Table3.

Table 1 .

 1 Observed rainfall data sets used for evaluation.

	Data set	Nb stations	Period	Time scale
	Niger	12	2010-2016	3h
	Benin	10	2010-2016	3h
	Burkina Faso	20	2010-2015	Daily
	Central Africa	42	2010-2016	Daily
	East Africa	78	2010-2013	Daily

Table 2 .

 2 The dataset is currently available for Africa and South Inventory of all satellite rainfall products data sets used in the study. To enable fair comparison of all products, each product was regridded to the 0.25° spatial resolution and daily time-scale.

	America (2015-2018), Europe, India, Contiguous United States and Australia (2015-2017) and can be
	downloaded at https://doi.org/10.5281/zenodo.3345323.
	Data set	Spatial Resolution	Time-scale	Period	Latency	Ground calibration
	PrISM	0.25°	3-hourly	2010-present	~5 day	no
	CMORPH-Raw	0.25°	3-hourly	1998-present	18 h	no
	TRMM-RT	0.25°	3-hourly	1998-present	~6 h	no
	IMERG-Early	0.1°	30 min	present 03/2015-	~12 h	no
	TAMSAT-v3.0	0.0375°	Daily	1983-present	~2 days	no
	SM2RAIN	0.25°	Daily	2015-2018	~5 days	no
	CHIRPS-v2.0	0.25°	Daily	1981-present	~3 weeks	yes
	GPCC	1°	Daily	2009-present	15-45 days	yes
	CMORPH-Adj	0.25°	3-hourly	1998-present	>1 month	yes
	TRMM-3B42	0.25°	3-hourly	1998-present	>1 month	yes
	IMERG-Final	0.1°	30 min	present 03/2015-	>1 month	yes
	2.3 The SMOS soil moisture dataset

The Soil Moisture and Ocean Salinity

[START_REF] Kerr | Soil moisture retrieval from space: The Soil Moisture and Ocean Salinity (SMOS) mission[END_REF][START_REF] Kerr | Overview of SMOS performance in terms of global soil moisture monitoring after six years in operation[END_REF]

satellite was launched in November 2009 and started delivering data on January 2010. The primary goals of this Earth Explorer mission are to measure globally and frequently surface soil moisture over land and sea surface salinity over the oceans. The SMOS data used in the study as the main input to the PrISM algorithm corresponds to the CATDS level-3 soil moisture data obtained through https://www.catds.fr site. The SMOS-L3SM

Table 3 )

 3 . Best performances in term of correlation are obtained by PrIMS (R=0.81), CMORPH-Adj,

IMERG-Final (R=0.80), IMERG-Early (R=0.78) and CHIRPS (R=0.77). Regarding RMSE, best performances are obtained by CMORPH-Adj, PrISM, IMERG-Final and SM2RAIN and IMERG-Early with RMSE values equal to 4.3, 4.4, 4.5 and 4.6 mm/day respectively. Lowest performances are obtained by TRMM-Raw and GPCC with 6.8 mm/day. Regarding bias score, four products obtained annual cumulative precipitation values very close to the observation (1150 mm): TRMM-Raw (1138 mm, -1%), PrISM (1124 mm, -2.3%), CHIRPS (1110 mm, -4.3%) and SM2RAIN (1216 mm, +5.7%

Table 3 .

 3 Similarly, the CMORPH-Adj and PrISM products obtain good performances in term of correlation (R=0.82 and R=0.81 respectively) and GPCC obtains the lower score (R=0.33) probably due to the low density of gauges in the Niger region and its original spatial resolution of 1°. Regarding the RMSE scores, best

	performances are obtained by PrISM, TAMSAT-025, CHIRPS, TRMM-Adj, SM2RAIN, CMORPH-Adj
	and IMERG-Final (from 3.7 mm/day to 4.6 mm/day). Conversely, CMORPH-Raw and TRMM-Raw
	products obtain lower RMSE scores (6.7 and 6.9 mm/day). In term of annual bias, four products
	obtained annual cumulative precipitation values quite close to the observation (601 mm): TRMM-Adj
	(602 mm), IMERG-Final (547 mm, -9%), PrISM (669 mm, +11%) and IMERG-Early (687 mm, +14%).
	On the contrary, CMORPH-Raw and TRMM-Raw strongly overestimate annual precipitation (1052
	mm, +75% and 1090 mm, +81% respectively). Other products obtain intermediate annual bias (see
	Table 3). Regarding the number of rainy days in Niger (43 days from in situ measurements), best
	performances were obtained by SM2RAIN, TAMSAT_025 and CMORPH-Adj (48, 50 and 51 days
	respectively) whereas GPCC still provides an overestimated number of rainy days (71 days). Other
	products, PrISM included, provide a slight overestimation of the number of rainy days compared to
	observations (from 52 to 57 days).

Table 3 .

 3 Statistical scores (R, RMSE, annual bias and nb of rainy days) between in situ precipitations measurements (Benin and Niger, 2015) and the eleven precipitation products. Bold values indicate the best performances. There are 103 rainy days in Benin and 43 rainy days in Niger in 2015.

	2015	Benin 0.25° (1150 mm, 103 rainy days)	Niger 0.25° (601 mm, 43 rainy days)

Acknowledgments:

The authors would like to thank University of Douala, University of Bangui, University Omar-Bongo in Libreville, University of Liège, CIRAD Montpellier for providing precipitation data in Central Africa, and National Meteorological Department of Burkina Faso.

Funding: This research was funded by ESA, grant number ESA/AO/1-7875/14/I-NC (4000114738/15/I-SBO). This research also benefits from TOSCA (CNES, Centre national d'études spatiales, France).

(medium vegetation), and the PrISM performances in Central Africa are better than in East Africa (in term of correlation and bias correction).

Summary and next step

This study presents the PrISM algorithm and its evaluation over 5 regions in Africa. PrISM algorithm uses knowledge of soil water content (provided by SMOS soil moisture measurements) to adjust the precipitation rate of an existing satellite product (CMORPH-raw in this study). To assess the benefit of the proposed methodology, PrISM was compared against ten state-of-the-art satellite and ground-based rainfall products for five rain gauge networks located in semi-arid to wet areas in Africa.

PrISM was found to generally outperform all real-time products (CMORPH-Raw, TRMM-Raw, IMERG-Early, TAMSAT_025 and SM2RAIN), especially when considering areas where there exists a dense network of rain gauge stations as a reference data set. It showed same or even better performances than adjusted or post-processed products. The main contribution of PrISM is that it greatly decreases RMSE values and reduces the bias values compared with the original CMORPH-Raw product. Results in term of correlations are more modest. This result is quite important for many applications that require real-time information on precipitation such as crop yield estimates, flood nowcasting, dam management, ground-water recharge estimates and irrigation demand over large areas.

Future studies will be designed to apply PrISM algorithm to other satellite soil moisture dataset such as SMAP, ASCAT or SMOS-IC. At the moment, PrISM product is available on the ftp site: