Gabriele A Pedroza

Lucia H G M C Macedo

Ricardo De Oliveira Bordonal

Natalia N Silveira

Renato P Orenha

Renato L T Parreira

Raquel A Dos Santos

Yann Molard

Maria Amela-Cortes

Eduardo F Molina
email: eduardo.molina@unifran.edu.br

Ricardo De Oliveira

Natália S Nascimento

Cost-efficient polyurea carrier for precise control of an anti-inflammatory drug loading and release

Keywords: sol-gel, polyetheramine, isocyanate crosslink, microphases, small angle X-ray scattering

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

Introduction

Polymer derivated materials are usually applied as carrier for delivery and control release of drugs [START_REF] Moorkoth | Star-Shaped Polylactide Dipyridamole Conjugated to 5-Fluorouracil and 4-Piperidinopiperidine Nanocarriers for Bioimaging and Dual Drug Delivery in Cancer Cells[END_REF], proteins [START_REF] Guo | Charged Poly(N-isopropylacrylamide) Nanogels for the Stabilization of High Isoelectric Point Proteins[END_REF], therapeutic compounds [START_REF] Xu | Temperature-Responsive Multilayer Films of Micelle-Based Composites for Controlled Release of a Third-Generation EGFR Inhibitor[END_REF], inorganic particles [START_REF] Karimi-Maleh | Effects of silver nanoparticles added into polyurea coating on sulfate-reducing bacteria activity and electrochemical properties; an environmental nano-biotechnology investigation[END_REF] showing advanced functions such as imaging agents for analytics and diagnostics [START_REF] Chang | Highly Stable Conjugated Polymer Dots as Multifunctional Agents for Photoacoustic Imaging-Guided Photothermal Therapy[END_REF], targeted delivery [START_REF] Babikova | Multifunctional Polymer Nanocarrier for Efficient Targeted Cellular and Subcellular Anticancer Drug Delivery[END_REF], controlled encapsulation [START_REF] Hamilton | Hyaluronic Acid Hydrogel Microspheres for Slow Release Stem Cell Delivery[END_REF], and more. However, the methodology used to produce these materials are often not economically viable and do not meet the requirements for production on an industrial scale.

Therefore, many efforts have been made aiming to develop such carrier technologies by using, for example, electrospinning [START_REF] Cleeton | Electrospun Nanofibers for Drug Delivery and Biosensing[END_REF] or microfluidic [START_REF] Wang | Functional Polymeric Microparticles Engineered from Controllable Microfluidic Emulsions[END_REF] methods that allow a fine control over their monodispersity, structures, and compositions.

Polyurea is an elastomer polymer obtained from the reaction of polyamines and polyisocyanates resulting in the formation of urea linkages (-NH-CO-NH-) [START_REF] Jandaghian | Performance of polyurea formulations against impact loads: A molecular dynamics and mechanical simulation approach[END_REF]. This class of polymer receives continuous attention from the scientific community, in particular, due to i) the absence of a catalyst during the reactions [START_REF] Soccio | Urea and Polyurea Production: An Innovative Solvent-and Catalyst-Free Approach through Catechol Carbonate[END_REF], ii) its high thermal/chemical stability [START_REF] Zhang | Thin-film composite nanofiltration membrane based on polyurea for extreme pH condition[END_REF][START_REF] Reed | Synthesis and characterization of elastomeric polyurea foam[END_REF], ii) its facile processability and iv) its resistance to UV radiation [START_REF] Zhang | Phoxim Microcapsules Prepared with Polyurea and Urea-Formaldehyde Resins Differ in Photostability and Insecticidal Activity[END_REF]. Polyurea elastic network shows microphase separation of two immiscible, covalently connected components, known as "hard" and "soft" domains. The "hard" domains act as physical cross-linker to reinforce the elastomer, while the "soft" domains form the continuous phase provide elasticity [START_REF] Holden | Thermoplastic Elastomers[END_REF]. Furthermore, polyurea networks exploiting the hydrogen-bonding directionality (i.e. well-defined secondary structures) are of particular interest as supramolecular polymers [START_REF] Feula | Thermoreversible Supramolecular Polyurethane with Excellent Healing Ability at 45 °C[END_REF][START_REF] Kieltyka | Mesoscale Modulation of Supramolecular Ureidopyrimidinone-Based Poly(ethylene glycol) Transient Networks in Water[END_REF][START_REF] Wisse | Multicomponent Supramolecular Thermoplastic Elastomer with Peptide-Modified Nanofibers[END_REF].

Zhang et. al [START_REF] Zhang | Thin-film composite nanofiltration membrane based on polyurea for extreme pH condition[END_REF] produced new polyurea thin-film membranes for extreme pH nanofiltration. The fabricated membranes, based on branched polyethyleneimine, piperazine, and multi-isocyanate monomers, showed excellent acid/alkali resistance after exposure to HCl, H2SO4 and NaOH solutions (20 wt/v%) and are suitable for the treatment of industrial wastewater. By using commercially available reagents, Paraskevopoulou et al. [START_REF] Paraskevopoulou | Polyurea-crosslinked biopolymer aerogel beads[END_REF] obtained polyurea-crosslinked calcium alginate beads (X-Ca-alg). The authors reported that X-Ca-alg biopolymers are robust materials compared to conventional Ca-alginate aerogels that are mechanically weak, and have J o u r n a l P r e -p r o o f pratical applications including environmental remediation. In another work, polyurea was used as microcapsule to incorporate phexim pesticide for agriculture purposes. The phoxim-loaded polyurea showed high UV-resistance ability and can prolonge the effective duration of pesticide. It may be also applied as microcapsule for others pesticides [START_REF] Zhang | Phoxim Microcapsules Prepared with Polyurea and Urea-Formaldehyde Resins Differ in Photostability and Insecticidal Activity[END_REF].

Reports of polyurea as carrier for drug delivery systems are scarce [START_REF] John | Phospholipid End-Capped Bioreducible Polyurea Micelles as a Potential Platform for Intracellular Drug Delivery of Doxorubicin in Tumor Cells[END_REF][START_REF] Cuscó | Multisensitive drug-loaded polyurethane/polyurea nanocapsules with pH-synchronized shell cationization and redox-triggered release[END_REF][START_REF] Gajbhiye | Stimuli-responsive biodegradable polyurethane nano-constructs as a potential triggered drug delivery vehicle for cancer therapy[END_REF][START_REF] De Resende | Design of polyurea networks containing anticancer and antiinflammatory drugs for dual drug delivery purposes[END_REF]. In this work, we present a facile preparation of a polyurea xerogel with capacity to incorpotate high amounts (up to 30 wt%) of an anti-inflamatory drug. Diclofenac sodium (DCF) was chosen for this study. It has both analgesic and antipyretic properties and is classicaly used for the treatment of degenerative joint diseases such as rheumatoid arthritis, osteoarthritis. Administrated by ocular route, it is used in the management of ocular pathologies treated by surgery. Its low biological half-life (1 or 2 hours) implies multiple dosing to keep its therapeutic blood level, which often leads to adverse side effects in a long-term administration such as gastrointestinal bleeding, disturbances or peptic ulceration.

Therefore, its controled release should provide extended therapeutic benefits with minimal local irritation.

The polyurea obtained in this work is a low-cost material that contains flexible polyetheramine blocks connected to an isocyanate trimer to form urea linkages. It is produced by a facile one-pot sol-gel reaction, which is a scalable, powerful and economically viable method, offering fine control over structure and loaded amount of drugs. The objectives of this work are to investigate in depth the i) visual polyurea gelation time as a function of monomers contact time with a solvent, ii) the biocompatibility of the matrix through citotoxicity studies, iii) the influence of the drug content on the structure of polyurea, iv) the release profile and kinetic mechanisms as a function of drug load. In particular, we show that the diclofenac drug release profile can be modulated by the interactions between DFC drug and the polyurea matrix as well as by the loaded drug amount.

J o u r n a l P r e -p r o o f

Experimetal and characterizations

2.1 Materials: Diclofenac sodium salt DCF (C14H10Cl2NNaO2) and acetone (ACS reagent, ≥99.5%) were purchased from Sigma-Aldrich. O,O'-bis-(2-aminopropyl)polypropylene glycol-blockpolyethylene glycol-block-polypropylene (Jeffamine ED2003 -PEO block with a molecular weight of 1900 g mol -1 ) and the hexamethylene diisocyanate trimer-HDI (Desmodur N3300 with a molecular weight of ~ 504 g mol -1 ) were donated by Huntsman Performance Products (Brazil) and Bayer Corporation, respectively. The Jeffamine ED2003 and Desmodur N3300 are reagents commercially avaliable from Huntsman and Bayer. All reagents were used without further purification.

Synthesis of polyurea gels:

The polyurea xerogel was obtained by organic polycondensation reaction (sol-gel process) as reported in literature [START_REF] Sánchez-Ferrer | Synthesis and Characterization of New Polyurea Elastomers by Sol/Gel Chemistry[END_REF][START_REF] Sánchez-Ferrer | Polyurea Networks from Moisture-Cure, Reaction-Setting, Aliphatic Polyisocyanates with Tunable Mechanical and Thermal Properties[END_REF][START_REF] De Jesus | Facile and scalable design of light-emitting and ROS-generating hybrid materials made of polyurea gels embedding a molybdenum cluster-based salt[END_REF]. In brief, tridentate ligand HDI was covalently bonded to the PEO (Jeffamine ED-2003) by reaction of the isocyanate groups of HDI and the primary amino groups attached to the end of the polyether backbone of PEO (Scheme 1). In brief, 4 g of PEO macromer (2.10 x 10 -3 mol) and 1 g of HDI cross-linker (1.98 x 10 -3 mol) were completely dissolved using acetone in two separated beakers. These were sealed and stirred for 2h, at room temperature (~25°C), to form a homogenous solutions. The HDI solution was added dropwise to the PEO solution, while stirring at room temperature, until complete dissolution. The resulting solution was poured into Teflon ® mold and kept at 25°C for 24 h for gelation.

Synthesis of polyurea gels containing diclofenac drug:

Polyurea samples containing DCF were prepared via one-step sol-gel process. The desired drug amount (from 1 to 30 wt% with respect to the mass of PEO) was dissolved in acetone and then mixed with PEO to obtain a homogeneous solution. The HDI solution was dissolved in a separated beaker and added as cited above to form DCF-loaded polyurea samples. The resulting mixture was poured into Teflon ® mold and gelled using the same conditions (temperature and time) than for the pure polyurea. The final materials were named PolyU (polyurea xerogel), PolyU-DCFx (loaded polyurea containing diclofenac DCF J o u r n a l P r e -p r o o f and x for the wt% of drug loaded). Regardless of the polyurea sample (loaded and unloaded) the obtained membranes were transparent and flexible. Formulations of the polyurea samples without and containing diclofenac drug percentage from 1 to 30 wt% are presented in Table S1. SCHEME 1

Characterization:

Fourier Transform Infrared Spectroscopy FTIR spectra was recorded at 3100-700 cm -1 J o u r n a l P r e -p r o o f by ATR mode using a Perkin Elmer Frontier spectrometer, with a resolution of 4 cm -1 and average of 12 scans.

Small angle X-ray scattering SAXS experiments were conducted using a Nano-InXider (Xenocs). X-rays of wavelength λ = 1.54 Å was used, and the measurements was performed at sample-to-detector distance of 938 mm to cover a q-range of 0.009 < q < 0.45 Å -1 , where q = (4 π/λ) sin (θ/2) corresponding to the magnitude of the scaterring vector, and θ is the scaterring angle.

Beam size on sample: 400 μm (0.4 mm), typical flux:60 Mph/s, and Qmin: 0.0044 Å -1 . All the measurements were recorded at room temperature (~25 °C) using a cell window under vacuum. To collect the SAXS pattern, samples with 1.8 mm ± 0.10 (thickness) and 20 mm 2 (area) were used.

Visual determination of gel time:

In order to evaluate the reactivity (gelation time) of the polyetheramine-PEO and isocyanate HDI, acetone was used as solvent for capping the amines of the polymer chains. In this sense, after the total solubilization of PEO and HDI (separately) the influence of polymer/isocyanate solution contact time with acetone before condensation reaction was studied. The volume of acetone to solubilize PEO and HDI was 7 and 5 mL, respectively. Gelation was considered when the particles present in the initial sol rigidifies the whole wet sol medium. Specifically, condensation reaction was induced by HDI solution added dropwise to the PEO solution. Shortly thereafter, the mixed PEO-HDI solution was spread in an acrylic plate covered by Teflon® using a film extensor. A glass slide was placed on the film without pressure.

The gel time was considered when the sol sharply decreased its viscosity converting a viscous liquid state to a gel. The visual experiments were performed on two independent samples, and the results are presented as the data average. Differential scanning calorimetry DSC was used to evaluate the influence of drug content on the glass transition temperature and fusion temperature of crystalline PEO domains. DSC measurements were made using a TA25 DSC. Disk shape of approximately 10 mg were cut off from the polyurea membranes and placed in 40-μL aluminium containers. Each sample was heated from -80 to 250 °C at rate of 10 °C min -1 using argon as the purge gas.

J o u r n a l P r e -p r o o f

Computational methods: the geometry optimization of all compounds was performed without constraints and the vibrational frequencies were calculated using the B97D3, [START_REF] Becke | Density-Functional Thermochemistry. V. Systematic Optimization of Exchange-Correlation Functionals[END_REF][START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF] functional and the 6-31+G(2d,p) basis set (Table S2) [START_REF] Hariharan | The influence of polarization functions on molecular orbital hydrogenation energies[END_REF][START_REF] Francl | Self-Consistent Molecular Orbital Methods. XXIII. A Polarization-Type Basis Set for Second-Row Elements[END_REF][START_REF] Frisch | Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets[END_REF]. The 6-31+G(2d,p) basis set provides a good accuracy/efficiency relationship for organic complex systems [START_REF] Molina | Ureasil-Poly(ethylene oxide) Hybrid Matrix for Selective Adsorption and Separation of Dyes from Water[END_REF]. Vibrational analyses for all optimized geometries confirm that they are all energy minima at the computational model applied here. Importantly, the molecular electrostatic potential (MEP) [START_REF] Ford | Role of Electrostatic Potential in the in Silico Prediction of Molecular Bioactivation and Mutagenesis[END_REF] surfaces of the: i) isolated drug (diclofenac); and ii) structures derived from polymer polyurea (I-III), were calculated for aid in the choice of the conformations of the complexes investigated (Figure S1). These calculations were made using the Gaussian 16 (Revision A.03) software [34]. The bonding mechanism was elucidated through the energy decomposition analysis (EDA) [START_REF] Bickelhaupt | Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry[END_REF] using the BLYP [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF] functional and Grimmes D3 dispersion correction with Becke-Johnson damping function (D3(BJ)) [38] combined with the TZ2P [START_REF] Guerra | Towards an order-N DFT method[END_REF] basis set. These calculations were realized with the ADF2019 package [START_REF] Molina | Fine-tuning of a nanostructure, swelling, and drug delivery profile by blending ureasil-PEO and ureasil-PPO hybrids[END_REF]. (P4) cell plates with cell growth area of 9.5 cm 2 , 3.8 cm 2 , 1.9 cm 2 and 0.95 cm 2 , respectively. After 24 h cell cultures were exposed to a polyurea piece (0,04 cm 2 ) during 48 h, when cell viability was assessed using the Cell Proliferation Assay Kit (Roche) according to manufacture instructions.

Cytotoxicity assay (XTT

Percentage of viable cells was calculated considering the negative control as 100% viable after three experimental repetitions. Differences between negative control and experimental groups were evaluated using Analysis of Variance followed by Dunnet's test considering 95% of confidence.

Cell media and doxorubicine (1 µM) were used as negative control NC and positive control, respectively.

In vitro drug release assays: temporal release of DCF was evaluated in distilled water (100 J o u r n a l P r e -p r o o f mL, pH 6) using ~ 0.3 g of loaded PolyU containing different amounts of DCF drug. The release assays were carried out at a controlled temperature of 37 °C, under constant stirring (100 rpm). In vitro studies were performed by UV-Vis spectroscopy, using a Cary60 dual-beam spectrophotometer (Agilent Technologies) connected to an immersion probe (optical path length of 2 mm). Quantitative determination of the cumulative DCF release were performed using a calibration curve constructed using the maximum absorbance values at λmax= 275 nm of drug solutions at different concentrations. All the in vitro citotoxicity and release experiments were performed with three independent samples, and the results are presented as data average.

Results and Discussion

Visual gel time

Gel formation from polyureas occurs as the condensation reaction proceeds. Several parameters can affect the rate of this reaction. Indeed, amines are highly reactive in presence of isocyanates, thus acetone was used to capp the amine groups of polyetheramine-PEO and to evaluate the time of the gelation. Figure 1 shows gelation time of the polyurea samples as a function of contact time of PEO and HDI with acetone before their mixing (i.e. condensation reactions). We observed that the contact time of the solutions (polyetheramine and HDI) with acetone clearly reduces the reactivity of the polyether. Depending on their applications, e.g. coating or spray processes, the combination of acetone solvent with fast gelation time is an important issue to eliminate energy consumming baking ovens or dryers.

Structural characterization and theoretical studies

FTIR studies were performed to evaluate the possible interactions between polyurea matrix and DCF as a function of drug content (1-30 wt%). Figure 2 shows the FTIR spectra of unloaded and loaded PolyU with the DCF drug from 1750 -1400 cm -1 (Figure 2a) and 1300 -700 cm -1 (Figure 2b). Regardless of the polyurea matrix (unloaded and loaded), the presence of bands centered at 1636 cm -1 (C=O amide I) and 1560 cm -1 (CO-N-H amide II) evidences the formation of urea groups (Figure 2a). It is important to note the absence of the peak at 2262 cm -1 (characteristic of the free isocyanate reactive group from HDI) and the presence of a band at ~3346 cm -1 (N-H ν, hydrogen-bond) [START_REF] Sánchez-Ferrer | Polyurea Networks from Moisture-Cure, Reaction-Setting, Aliphatic Polyisocyanates with Tunable Mechanical and Thermal Properties[END_REF] (see Figure S2 for full FTIR spectra). These results indicate the sucessful completion of the reaction between isocyanate and amino groups, after gelation process and curing at room temperature, and thus the formation of the polyurea network.

The polyether region (from 1300 -700 cm -1 , Figure 2b) shows the characteristic bands at 1142, 1102, 948 and 846 cm -1 , attributed to the ethylene rocking vibrations (CH2 r) and stretching To evaluate the interactions between the DCF and the polyurea, we performed computational studies using an energy decomposition analysis (EDA) looking at three representative structures of the polymer network (See compounds I-III in Figure S4). The main results are presented in Table 1. According to the EDA formalism [34], the interaction energy, ΔEint, is the summation of several terms corresponding to electrostatic, ΔVelstat, Pauli repulsions, ΔEPauli, orbital interactions, ΔEoi, and dispersion ΔEdisp, components. The term ΔVelstat represents the quasi-classical electrostatic interaction between unperturbed charge densities and nuclei of the geometrically deformed fragments. The Pauli-repulsion ΔEPauli contains the destabilizing interactions between the occupied orbitals and is accountable for the steric repulsion. The orbital interaction ΔEoi reflects the charge transfer (donor-acceptor interactions between occupied orbitals on one fragment with the empty orbitals of another fragment) and polarization (unoccupied/occupied orbital mixing on one moiety due to the presence of the other). The term ΔEdisp is the dispersion correction contributions [38]. the DCF content (Figure 5a). Table 2 presents the glass transition and melting temperatures as well as the degree of crystallization (Dc) deduced from the DSC thermograms. The Tg was characterized by step changes in the heat capacity, and Tm can be obtained from the onset of the endothermic peak, while the crystallinity degree Dc (eqn ( 1)) is calculated using the ratio between the melting enthalpy of semi-crystalline PEO in the polyurea sample and the melting enthalpy of 100% crystalline PEO:

(

) 1
where ΔHm is the melting enthalpy per gram of PEO in the PolyU sample, and ΔH°m is the melting enthalpy for 100% crystalline PEO (188.9 J g -1 ) [START_REF] Mya | Crystallization behavior of star-shaped poly(ethylene oxide) with cubic silsesquioxane (CSSQ) core[END_REF].

Upon DCF incorporation (1 -30 wt%), significant changes are observed in the DSC thermograms and the Tg/Tm values (Figure 5a, Table 2). The presence of the drug through the polyurea network generates three main effects: (i) a significant increase in the glass transition Tg

Citotoxicity evaluation

The evaluation of medical devices follows the International Organization for Standardization (ISO) rules that recommend : "in vitro test methods, which are appropriately validated, reasonably and practically available, reliable and reproducible shall be considered for use in preference to in vivo tests" [START_REF]Biological evaluation of medical devices -Part 1: Evaluation and testing within a risk management process[END_REF]. The polyurea sample was exposure to cells by direct contact with culture medium according to ISO (2003) [START_REF]Biological evaluation of medical devices. Part 1: Evaluation and testing[END_REF]. Thus, it mimics the physiological conditions by a zone of diffusion in which could affects cellular trauma in accordance with the density of materials [START_REF] Baek | Evaluation of the extraction method for the cytotoxic testeing of latex gloves[END_REF][START_REF] Ratner | Testing biomaterials[END_REF]. According to J o u r n a l P r e -p r o o f

In vitro diclofenac release assays

The cumulative release of DCF incorporated into polyurea xerogel as a function of drug loading (1 -30 wt%) are shown in Figure 7. The release rate of DCF is low for polyurea samples containing 1 and 5 wt% of DCF, with only a 13 and 36% release after 1440 min, respectively (Figure 7 red and blue squares). For the polyurea matrices loaded with 10 -30 wt% of DCF (Figure 7 green, cyan and purple squares), the release rate was higher compared to samples with lower amounts of drug incorporated (1 -5 wt%).

The release rate of DCF may be described by simultaneous swelling front (water uptake)

and DCF release. To explain such a facile solvation (solubilization) of the drug through the polymer backbone, we hypothesized interactions between PEO chains and diclofenac DCF. By increasing the DCF amount loaded in polyurea xerogel a consequent augmentation of drug molecules present on the surface (physisorbed) leads to a high cumulative release of the DCF until ~80% (Figure 7 purple squares). These results are in line with FTIR, theoretical, SAXS and DSC studies which demonstrate i) interactions between DCF and the host matrix with the shift of the drug characteristic bands in the FTIR spectrum, ii) favorable interactions with the polymer depending on the bonding site, iii) evident decrease of the peak intensity in the SAXS pattern of the host and iv) clear changes in glass transition temperature (Tg) followed by the inhibition of the polymer-PEO crystalline moities as a function of drug load. Here, the tuning of the cumulative release profiles (low or high DCF amount released) have proven valuable in drug delivery applications, due to the ability to easily encapsulate DCF molecules into polyurea by direct dissolving the drug in the PEO polymer. The release mechanism of the diclofenac from the loaded PolyU xerogel (1 -30 wt%) was evaluated by Korsmeyer-Peppas equation [START_REF] Korsmeyer | Mechanisms of Solute Release from Porous Hydrophilic Polymers[END_REF] (eq. 2), where Mt is the solute mass released at time t, M∞ is the initial solute mass, Mt/M∞ is a fraction of the drug released at time t, k is the released rate constant and n is the released exponent which gives information regarding the drug transport mechanism [START_REF] Korsmeyer | Mechanisms of Solute Release from Porous Hydrophilic Polymers[END_REF]. Depending on the n value, different mehanisms can be envisioned: a Fickian diffusion (n value of ≤ 0.50), a case II transport indicated by a zero-order drug release (n value of ≥ 1), while an anomalous non-Fickian transport mechanism (swelling as well diffusion) is indicated by a n value of 0.50 < n < 1.0. showing a coefficient of determination (R 2 ) for all samples of about 0.99. For the PolyU samples containing between 5 and 30 wt% of diclofenac drug the experimental n values (see details in Table S3) indicate an anomalous transport followed by diffusion/zero-order rate of drug controlled by the penetration of the water-swollen front. For PolyU-DCF1, the calculated n value being close to 1, it suggests a Case II transport mechanism for which DCF drug release is mainly controlled by the swelling effect of the polyurea matrix. The cumulative drug released by PolyU-DCF1 sample, suggests that the amount of DCF molecules available near the monolithic surface is low and that entrapped DCF molecules begin to release by water uptake, at slow rate due to the DCF-PEO chains interactions.

𝑀 𝑡 𝑀 ∞ = 𝑘 𝑡 𝑛 (2)
Recently, we demonstrated the possibility to incorporate simultaneously an anti-inflamatory and an anticancer drug into a polyurea xerogel for dual delivery purposes [START_REF] De Resende | Design of polyurea networks containing anticancer and antiinflammatory drugs for dual drug delivery purposes[END_REF]. A low loading of amount of drugs (1 wt%) was used to evaluate the potential applications of polyurea as drug delivery system. Herein, we highlight a facile and reproducible control over the amount of drug encapsulated into polyurea xerogel in which 30 wt% of drug load can be easily reached and its release profile can be modulated by the interactions with the host matrix. Moreover, the influence of the drug amount loaded into structural/thermal polyurea properties was in depth correlated.

A cost estimation to produce polyurea PolyU using the synthesis conditions of this work was evaluated. By using the identifiable components values at the laboratory scale prices to obtain three polyurea membranes, the estimated cost (the summation of individual cost elements) was approximately US$ 2.00 (see Table S4 and Figure S5). Due to their physico-chemical properties, biocompatibility, easy-shaping, high capacity of drug loading, and low-cost production these polyurea materials could be fabricated as contact lenses, films, microcapsules, bulky materials and more, with broad implications for many fields. This work has clearly opened up highly interesting prospects for the polyurea as biomaterials. Several aspects derived from the results reported here J o u r n a l P r e -p r o o f need to be investigated in the future, such as in vivo assays. [a] ΔEint = ΔVelstat + ΔEPauli + ΔEoi + ΔEdisp; [b] Values in parentheses correspond to the percentage of each stabilizing contribution (ΔVelstat + ΔEoi + ΔEdisp = 100%).

  ): CHO-K1 cells were cultured in complete medium containing DMEM+HAM F10 (1:1, v/v) (Sigma, St Louis, USA), 10 % fetal calf serum (Sigma, St Louis, USA) and 1% of antibiotics penicillin/streptomycin stabilized solution (Sigma, St Louis, USA) in cell culture flasks of 25 mm 2 (TPP, Swizerland). Cells were seeded in 6 (P1), 12 (P2), 24 (P3) or 48

Figure 1

 1 Figure 1

Figure 2 J

 2 Figure 2

Figure 3

 3 Figure3displays the form of interactions between the selected three polyurea derivates (I-

Figure 3 J 4 .Figure 4 J o u r n a l P r e -p r o o f 3 . 3

 34433 Figure 3

  temperature from -58ºC (PolyU) to -35ºC (PolyU-DCF30); (ii) a shift of the melting peak temperature centered at 21°C (PolyU) followed by a decrease of the crystallinity degree Dc and (iii) the appearance of a cold-crystallization characterized by an additional exothermic event between -50°C and 14°C. The linear and significant increase in Tg values (Figure5b) and the decrease in the Dc , followed by a Tm shift (from 21°C to 29°C) as a function of the drug loading (see details in D C = ∆H 𝑚 ∆H°m x 100% J o u r n a l P r e -p r o o f

Furthermore, by incorporating

  Figure 5 330

Figure 6 ,

 6 Figure 6

Thus, this classFigure 7

 7 Figure 7

Figure 8

 8 Figure8shows the release curves, plotted as log (Mt/M∞) vs. log t, for loaded PolyU

Figure 8 J

 8 Figure 8

Figure Legends Scheme 1 .

 1 Figure LegendsScheme 1. Synthetic route for the preparation of polyurea matrix and schematic network showing hard domains isocyanurate ring (yellow squares) and soft domains polyether chains (blue lines).

Figure 1 .

 1 Figure 1. Gelation time formation of polyurea networks as a function of monomers contact time with acetone solvent.

Figure 2 .

 2 Figure 2. FTIR spectra of the unloaded and loaded polyurea PolyU containing different amount of drug (1-30 wt%) in the region between (a) 1750 -1400 cm -1 , and (b) 1300 -7000 cm -1 .

Figure 3 :

 3 Figure 3: Equilibrium geometries for the Diclofenac....(I-III) complexes [B97D3/6-31+G(2d,p)]. Distances are given in angstroms.

Figure 4 .

 4 Figure 4. SAXS patterns of the unloaded PolyU and PolyU containing 30 wt% of drug DCF. Inset: schematic representation of the microphases formed between the hard domains and soft domains in the polyurea network and correlation distance between these domais.

Figure 5 .

 5 Figure 5. (a) DSC thermograms of the unloaded and loaded PolyU containing different amount of drug (1-30 wt%), (b) comparison of both Tg and Tm as a function of drug content, and (c) schematic representation of the semi-crystalline PEO chains with decrease of crystallization degree induced by the increase of diclofenac drug content.

Figure 6 .

 6 Figure 6. Percentage of CHO-K1 viable cells obtained by XTT assay after 48 h exposure to PolyU membrane (0.04 cm 2 ). The P1-P4 represents different well plates. NC: negative control (cell media); PC: positive control (doxorubicin 1 µM).

Figure 7 .Figure 8 .

 78 Figure 7. Temporal evolution of cumulative amount released for polyurea PolyU containing different amounts of diclofenac drug (1 -30 wt%)

J o u r

  n a l P r e -p r o o f

Table 2 )

 2 evidence the great solvation of DCF. Due to the presence of functional groups such as urea and ether-type oxygen atoms (from polyether), high drug incorporation capability is achieved by the polyurea network. These results are in good agreement with the theoretical and FTIR studies.

TABLETable 1 .

 1 Analysis of the bonding situation between the DCF drug and structures derived from polymer polyurea (I-III) through of the EDA method. The energy unit is kcal mol -1 .[a,b]

	Complex	ΔEint	ΔVelstat	ΔEPauli	ΔEoi	ΔEdisp
	Diclofenac .... I	-53.40	-39.92 (47)	30.88	-34.23 (41) -10.12 (12)
	Diclofenac .... II	-36.70	-34.01 (46)	37.05	-19.05 (26) -20.70 (28)
	Diclofenac .... III	-27.61	-19.64 (34)	29.97	-13.10 (23) -24.83 (43)

Table 2 .

 2 Thermal characteristics determined by DSC measurements of the unloaded and loaded Pug containing different amount of DCF drug from 1 to 30 wt%.

	Sample	T g (°C)	T m (°C)	D c (%)
	PolyU	-58	21	30
	PolyU-DCF1	-56	23	28
	PolyU-DCF5	-55	23	27
	PolyU-DCF10	-52	21	18
	PolyU-DCF15	-45	29	15
	PolyU-DCF30	-35	-	-

J o u r n a l P r e -p r o o f

X ray scattering measurements (SAXS -EMU Instituto de Química -Câmpus de Araraquara), thank

J o u r n a l P r e -p r o o f

Huntsman Performance Products and Bayer Group for donating the Jeffamine ® and triisocyanate crosslinker reagents, respectively. The authors are grateful to funding agencies CAPES (Finance Code 001), CNPq (307696/2021-9), and FAPESP grant (n° 2021/06552-1 and SPRINT 2017/50286-9) and CNRS (PRC Clustobrane).

Highlights

Facile control over diclofenac drug release Kinects is described Polyurea provide promising opportunities for scale up fabrication new functional devices Versatile and cost-efficient carrier for drug delivery application High amounts of anti-inflammatory drug loaded into polymer matrix J o u r n a l P r e -p r o o f

Cost-efficient Polyurea Carrier for Precise Control of an antiinflammatory Drug Loading and Release

Gabriele A. Pedroza, 1 Lucia H. G. M. C. Macedo, 1 Ricardo de Oliveira, 1 Natália S.

Nascimento, 1 Renato P. Orenha, 1 Renato L. T. Parreira, 1 Raquel Santos, 1 Yann Molard, 2 Maria Amela-Cortes, 2 Eduardo F. Molina *1 J o u r n a l P r e -p r o o f

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:


Maxime Turko

Marielle Gosset
email: marielle.gosset@ird.fr

Modeste Kacou

Christophe Bouvier

Nanee Chahinian

Aaron Boone

Matias Alcoba

Paul Universite

Sabatier

Rainfall measurement from Commercial microwave links for urban hydrology in Africa: a simulation framework for sensitivity analysis

Urban floods due to intense precipitation are a major problem in many tropical regions as in Africa. Rainfall measurement using microwave links from cellular communication networks has been proposed as a cost effective solution to monitor rainfall in these areas where the gauge network is scarce. The method consists in retrieving rainfall from the attenuation estimated along the commercial microwave links (CMLs) thanks to the power levels provided by an operator. In urban areas where the network is dense, rainfall can be estimated and mapped for hydrological prediction. Rainfall estimation from CMLs is subject to uncertainties. This paper analyzes the advantages and limitations of this rainfall data for a distributed hydrological model applied to an urban area. The case study is in West Africa in Ouagadougou where a hydrological model has been set up. The analysis is based on numerical simulations, using high resolution rain maps from a weather radar to emulate synthetic microwave links. Two sources of uncertainty in the rain estimation and on the simulated discharge are analyzed by simulations: i) the precision of the raw information provided by the operator and ii) the density and geometry of the network. A coarse precision (1 dB) in the signal provided by the operator can lead to substantial underestimation of rainfall and discharge, especially for links operating at low frequency (below 10 GHz) or short (less than 1 km). The density of the current mobile networks in urban areas is appropriate to analyze hydrological impact of tropical convective rainfall.

Main ( < 7500 words)

Introduction

During the last 10 years, rainfall measurement from commercial microwave link (CML) network has gradually emerged as a useful complement to traditional rainfall measurement based on gauges, weather radar or satellites. [START_REF] Uijlenhoet | Opportunistic remote sensing of rainfall using microwave links from cellular communication networks[END_REF] and [START_REF] Chwala | Commercial microwave link networks for rainfall observation: Assessment of the current status and future challenges[END_REF] provide a good review of the state of the art and the research developed since the pioneering work of [START_REF] Messer | Environmental Monitoring by Wireless Communication Networks[END_REF] and Leijnse et al. (2007b)The CML technique is based on the analysis of attenuation induced by rain over the radiofrequency part of the mobile network, i.e. between pairs of telecommunication antennas. The main advantage of this technique is to exploit a network already in place and well maintained by mobile operators. In developing countries where the mobile network is already well developed [START_REF] Noam | Telecommunications in Africa[END_REF]ITU 2004) while hydrometeorological services have limited resources [START_REF] Novella | African Rainfall Climatology Version 2 for Famine Early Warning Systems[END_REF][START_REF] Dieulin | A New 60-year 1940/1999 Monthly-Gridded Rainfall Data Set for Africa[END_REF]) the prospect for operational use of the CML technique is very appealing [START_REF] Hoedjes | A Conceptual Flash Flood Early Warning System for Africa, Based on Terrestrial Microwave Links and Flash Flood Guidance[END_REF][START_REF] Gosset | Improving Rainfall Measurement in Gauge Poor Regions Thanks to Mobile Telecommunication Networks[END_REF]. The telecommunication network density follows population density (i.e. the customers) and most of the antennas lay in urban areas. This means that urban hydrology and urban flood risk monitoring is a subject area that could benefit from the CML technique [START_REF] Fencl | Assessing the potential of using telecommunication microwave links in urban drainage modelling[END_REF][START_REF] Fencl | Commercial microwave links instead of rain gauges: fiction or reality?[END_REF][START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF][START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF][START_REF] Pastorek | Commercial microwave links for urban drainage modelling: The effect of link characteristics and their position on runoff simulations[END_REF]. Cities in developing countries and especially in Africa are suffering from an increase exposure to extreme weather events [START_REF] Bradshaw | Global evidence that deforestation amplifies flood risk and severity in the developing world[END_REF][START_REF] Ebi | Extreme events as sources of health vulnerability: Drought as an example[END_REF][START_REF] Egbinola | Flood management in cities of developing countries: the example of Ibadan, Nigeria: Flood management in developing countries[END_REF][START_REF] Engel | Extreme Precipitation in the West African Cities of Dakar and Ouagadougou: Atmospheric Dynamics and Implications for Flood Risk Assessments[END_REF]. The amount of material damages and casualties due to flooding in West Africa has increased in the last decade under the conjunction of demographical pressure and population flow towards cities on one hand, and an increase of rainfall on the other hand. The mobile communication network could potentially contribute to a better monitoring of these hydrometeorological events. With current network Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1.

Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC monitoring systems (NMS) or dedicated software CML rainfall is typically monitored at time steps of 5 to 15 minutes [START_REF] Uijlenhoet | Opportunistic remote sensing of rainfall using microwave links from cellular communication networks[END_REF][START_REF] Chwala | Commercial microwave link networks for rainfall observation: Assessment of the current status and future challenges[END_REF] which provides an interesting temporal resolution for urban hydrology. Data have been collected at even shorter time steps for some experiments [START_REF] Schleiss | Identification of Dry and Rainy Periods Using Telecommunication Microwave Links[END_REF][START_REF] Fencl | Assessing the potential of using telecommunication microwave links in urban drainage modelling[END_REF]Zinevich et al. 2009;[START_REF] Fencl | Commercial microwave links instead of rain gauges: fiction or reality?[END_REF]Chwala et al. 2016) Most studies on CML estimation of rainfall have been based in European countries [START_REF] Fenicia | Microwave links for rainfall estimation in an urban environment: Insights from an experimental setup in Luxembourg-City[END_REF][START_REF] Fencl | Assessing the potential of using telecommunication microwave links in urban drainage modelling[END_REF][START_REF] Zohidov | Retrieval of rainfall fields in urban areas using attenuation measurements from mobile phone networks: a modeling feasibility study[END_REF][START_REF] D'amico | Use of Operational Microwave Link Measurements for the Tomographic Reconstruction of 2-D Maps of Accumulated Rainfall[END_REF][START_REF] Pastorek | Commercial microwave links for urban drainage modelling: The effect of link characteristics and their position on runoff simulations[END_REF][START_REF] De Vos | Rainfall Estimation Accuracy of a Nationwide Instantaneously Sampling Commercial Microwave Link Network: Error Dependency on Known Characteristics[END_REF][START_REF] Polz | Rain event detection in commercial microwave link attenuation data using convolutional neural networks[END_REF][START_REF] Graf | Rainfall estimation from a Germanwide commercial microwave link network: optimized processing and validation for 1 year of data[END_REF][START_REF] Roversi | Commercial microwave links as a tool for operational rainfall monitoring in Northern Italy[END_REF] and Israel [START_REF] Messer | Environmental Monitoring by Wireless Communication Networks[END_REF][START_REF] Zinevich | Estimation of rainfall fields using commercial microwave communication networks of variable density[END_REF]Zinevich et al. , 2009)). Most have focused on the quality of the estimate from this technique by comparison with rain gauges and/or weather radar. More recently, investigations on CML rainfall estimation have started outside Europe and Mediterranean countries [START_REF] Hoedjes | A Conceptual Flash Flood Early Warning System for Africa, Based on Terrestrial Microwave Links and Flash Flood Guidance[END_REF][START_REF] Rios Gaona | Rainfall retrieval with commercial microwave links in São Paulo, Brazil[END_REF][START_REF] Kim | Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation[END_REF][START_REF] Sohail Afzal | Real time rainfall estimation using microwave signals of cellular communication networks: a case study of Faisalabad, Pakistan[END_REF]. [START_REF] Doumounia | Rainfall monitoring based on microwave links from cellular telecommunication networks: First results from a West African test bed: WIRELESS NETWORKS FOR RAINFALL IN AFRICA[END_REF] presented the first quantitative test of the technique in Africa, based on a single link.

A few studies discussed the interest of the CML rainfall for hydrological applications in Europe [START_REF] Brauer | The effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment: Rainfall Measurement Techniques for Hydrological Simulations[END_REF][START_REF] Smiatek | Potential of commercial microwave link network derived rainfall for river runoff simulations[END_REF] in particular for urban hydrology where the high spatial and temporal resolution of the rain maps is beneficial [START_REF] Fencl | Assessing the potential of using telecommunication microwave links in urban drainage modelling[END_REF][START_REF] Fencl | Commercial microwave links instead of rain gauges: fiction or reality?[END_REF][START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF][START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF][START_REF] Pastorek | Commercial microwave links for urban drainage modelling: The effect of link characteristics and their position on runoff simulations[END_REF]. These studies showed that the density of links in urban areas helps improving the simulation of the discharge dynamics compared to simulations based solely on rain gauges. They also pointed out some biases in CML rainfall estimate and their propagation in the simulated discharge.

In african cities where the flood risk is very high and rainfall is due to intense convective systems, the CML technique seems particularly promising for urban hydrology. This study wishes to contribute to its development by analyzing the expected benefits.

The study by [START_REF] Doumounia | Rainfall monitoring based on microwave links from cellular telecommunication networks: First results from a West African test bed: WIRELESS NETWORKS FOR RAINFALL IN AFRICA[END_REF] in Ouagadougou was part of the MeghaTropiques satellite ground validation (MTGV) program [START_REF] Guilloteau | Stochastic generation of precipitation fraction at high resolution with a multiscale constraint from satellite observations[END_REF][START_REF] Guilloteau | Stochastic generation of precipitation fraction at high resolution with a multiscale constraint from satellite observations[END_REF]. During this experiment a weather radar and a dense network of rain gauges were available. In order to take full Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1.

Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC advantage of the CMLbased rain maps when they will be available, the Institut de Recherche pour le Développement (IRD) started the development of a fully distributed hydrological model compatible with this urban context. [START_REF] Bouvier | Large-Scale GIS-Based Urban Flood Modelling: A Case Study on the City of Ouagadougou[END_REF]Bouvier et al. ( , 2018) ) have adapted their modeling platform ATHYS (ATelier en HYdrologie Spatialisée; [START_REF] Bouvier | Un modèle de ruissellement urbain pour les villes d'Afrique de l'Ouest[END_REF][START_REF] Bouvier | Modélisation hydrologique distribuée -Plate-forme ATHYS[END_REF] Section 2 provides an introduction to rainfall measurement from commercial microwave links (CMLs). Section 3 introduces the study area and the simulation set up, the highresolution radar data used as input for the link simulations, the hydrological model ATHYS and the numerical experiments carried out. Section 4 presents the results from the numerical experiments, analyzing the impact of the precision in attenuation measurement and of the spatial configuration of the network inside the basins. For both topics, the impact is first analyzed on rainfall and then on the simulated discharge.

Section 5 provides conclusions and perspectives.

Rainfall measurement from commercial microwave links: principle and known limitations

The fundamental quantity used for rainfall estimation from CMLs is the specific attenuation k (dB/km) due to the rainfall along the wave propagation path. Because both k and the rainfall intensity R (mm/h) depend on the rain drop size distribution (DSD), they are related, and their relationship can be expressed via a power law:

𝑘 = 𝑎 𝑅 𝑏 (1)
where a and b depend strongly on the frequency, the polarization and more mildly on other factors (DSD; temperature etc.).

### Table 1 around here ####

Table 1 reports values of a, b for several frequencies typical of the range commonly used on operational mobile networks. The values of a and b were computed using the Mie scattering model [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF] and DSDs measured in West Africa [START_REF] Moumouni | Main features of rain drop size distributions observed in Benin, West Africa, with optical disdrometers[END_REF].

Between the two ends of a CML of length L the total (or path integrated) attenuation PIA can be estimated by comparing the transmitted (Tx) and received (Rx) powers. In most cases the transmitted signal Tx is constant and rainfall attenuation is detected through variations (drops in signal) of Rx compared to its baseline level [START_REF] Overeem | Measuring urban rainfall using microwave links from commercial cellular communication networks: MEASURING URBAN RAINFALL USING MICROWAVE LINKS[END_REF]Chwala et al. 2012;[START_REF] Chwala | Commercial microwave link networks for rainfall observation: Assessment of the current status and future challenges[END_REF].

The PIA is the integral of k along the path:

𝑃𝐼𝐴 = ∫ 𝑘(𝑠)𝑑𝑠 𝐿 0 = ∫ 𝑎 𝑅(𝑠) 𝑏 𝑑𝑠 𝐿 0
(2)

For practical purpose Eq. ( 2) is simplified to relate the PIA to the mean rate along the link, <R> :

𝑃𝐼𝐴 =< 𝑘 > 𝐿 = 𝑎′ < 𝑅 > 𝑏′ 𝐿 (3)
Unless rainfall is uniformly distributed along the link, or the exponent b is equal to 1, a′, b′ in Equation

(3) are different from a, b in Equation ( 2) (Leijnse et al. 2008[START_REF] Leijnse | Errors and Uncertainties in Microwave Link Rainfall Estimation Explored Using Drop Size Measurements and High-Resolution Radar Data[END_REF]. For the frequency range 18 to 40

GHz (where b is close to 1, see Table 1) using (a, b) in Eq. ( 3) leads to little error. For short frequencies (below 15 GHz) the parameters need to be adjusted to account for rainfall variability along the link and the nonlinearity of the relation. [START_REF] Doumounia | Rainfall monitoring based on microwave links from cellular telecommunication networks: First results from a West African test bed: WIRELESS NETWORKS FOR RAINFALL IN AFRICA[END_REF] used radar data from Ouagadougou to analyze this effect for a 29 km link operating at 7 Ghz, and found an increase of 25% in the prefactor a' compared to a. Similar calculations for a 5 km link gives an average increase of 3.5 % at 6 GHz and 2% at 12 GHz, and about twice these values for a 10 km link. Our data set based on 1 km radar data is however not best suited to analyze the small scale structure of rainfall.

Based on Eq. ( 3) and assuming that the parameters a' and b' are known, the rainfall estimation (𝑅 ̂) is given by:

𝑅 ̂= [ 𝑃𝐼𝐴 𝑎′𝐿 ⁄ ] 1/𝑏′ (4)
Equation 4 and the values of a and b reported in Table 1 show that the amount of PIA for a given mean rain rate increases with the frequency and with the link length. For a given increment in PIA the equivalent rain rate is lower for higher frequencies and longer links, as illustrated in therefore primary factors to consider in rainfall estimation and to assess the expected errors. As discussed in previous work (Leijnse et al. 2008a(Leijnse et al. ,b, 2010;;[START_REF] Zinevich | Prediction of rainfall intensity measurement errors using commercial microwave communication links[END_REF] there are several other sources of uncertainty in CMLs based rainfall estimation. One difficulty arises from the existence of fluctuations in the received power (Rx) that are not related to rainfall along the path. Attenuation by water vapor and other gas, refraction or reflection of the beam, misalignment of the antennas, can create such fluctuations. Drift in the electronics associated with temperature changes can also cause signal variability. These phenomena complicate the estimation of the baseline level during the dry periods and may cause error in rainfall detection and estimation. During and after rainfall, another source of error is the attenuation caused by antenna wetting (Leijnse et al. 2007a;[START_REF] Overeem | Measuring urban rainfall using microwave links from commercial cellular communication networks: MEASURING URBAN RAINFALL USING MICROWAVE LINKS[END_REF][START_REF] Chwala | Commercial microwave link networks for rainfall observation: Assessment of the current status and future challenges[END_REF][START_REF] Fencl | Rainfall retrieval from E-band commercial microwave links[END_REF] which may lead to overestimating rainfall. There is not a simple analytical formula to relate the attenuation due to antenna wetting (in dB) at a given frequency to the rain rate, and its evolution in time. Experimental [START_REF] Ostrometzky | Empirical Study of the Quantization Induced Bias in Commercial Microwave Links' Min/Max Attenuation Measurements for Rain Monitoring[END_REF][START_REF] Islam | Measurement of wet antenna effect on microwave propagation at 23, 26 and 38 GHz[END_REF][START_REF] Kharadly | Effect of wet antenna attenuation on propagation data statistics[END_REF] or theoretical (Leijnse et al. 2008a) analysis, and discussion with telecommunication engineers reveal that it depends on many factors like the material the antenna cover is made off or local wind effects. Given this complexity antenna wetting is not included in our simulations.

Study area, data and simulation setup a. Study area

The area of Ouagadougou (12.3° N; 1.5°W) in Burkina Faso was selected as an illustrative test bed for the present sensitivity study for several reasons. Ouagadougou is representative of african cities exposed to increased flood risk as illustrated by several recent extreme events [START_REF] Engel | Extreme Precipitation in the West African Cities of Dakar and Ouagadougou: Atmospheric Dynamics and Implications for Flood Risk Assessments[END_REF] The main data as input to the simulations is high resolution rain maps from a weather radar located in Ouagadougou in 2012 and 2013. The radar is an Xband polarimetric radar from which 5 minutes, 1 km 2 rain maps were produced using an algorithm based on the polarimetric specific differential phase shift (RKdp) as in [START_REF] Matrosov | Evaluating Polarimetric X-Band Radar Rainfall Estimators during HMT[END_REF], [START_REF] Kacou | Analyse des précipitations en zone sahélienne à partir d'un radar bande X polarimétrique[END_REF] and [START_REF] Koffi | Evaluation of X-band polarimetric radar estimation of rainfall and rain drop size distribution parameters in West Africa[END_REF].

In Ouagadougou as in most West Africa the rainfall season is associated with organized convective systems characterized by a front of convective cells followed by a stratiform trail [START_REF] Moumouni | Main features of rain drop size distributions observed in Benin, West Africa, with optical disdrometers[END_REF][START_REF] Depraetere | The organization and kinematics of tropical rainfall systems ground tracked at mesoscale with gages: First results from the campaigns 1999-2006 on the Upper Ouémé Valley (Benin)[END_REF][START_REF] Alcoba | Characterization of Hydrometeors in Sahelian Convective Systems with an X-Band Radar and Comparison with In Situ Measurements. Part II: A Simple Brightband Method to Infer the Density of Icy Hydrometeors[END_REF]) and propagating mostly westwards. Figure 2 displays the rain maps over Ouagadougou while a convective system recorded by the radar on 2012 August 4th is crossing the area. The front of heavy rainfall associated with the convection arrives first followed by more widespread and lower rain rates. Altogether three rainfall events that lead to heavy precipitations and were well sampled by the radar are used for the simulations. CMLlike data, mimicking various network configurations are generated from the radar maps. The quality of these syntheticCML rainfall estimates is first compared with the original rainfall maps. Then these rainfall estimates are used as forcing to the hydrological model, and the simulated discharges is compared to the reference (i.e. the model forced by the highresolution rain map).

1) CML SIMULATION FROM RADAR DATA

The CML simulation is based on calculating the interception between the links and the radar maps. The lines in Figure 2 display simulated links with their colors representing the mean rainfall over the link path.

For each radar image, the mean rainfall over each link Rlink is computed as the weighted average of the rain rates over all radar pixels intercepted by the link:

𝑅 𝑙𝑖𝑛𝑘 = ∑ 𝑙 𝑖 𝑅 𝑝𝑖𝑥 𝑖 𝑛 𝑖=1 ∑ 𝑙 𝑖 𝑛 𝑖=1
(5)

with n the number of radar pixels intercepted by the link, li is the length of link intercepted by the pixel, 𝑅 𝑝𝑖𝑥 𝑖 the rain intensity on the radar pixel i, and the link length is 𝐿 = ∑ 𝑙 𝑖 𝑛 𝑖=1 . Similarly, the PIA is calculated based on the specific attenuation of each pixel,

Accepted for publication in

𝑃𝐼𝐴 𝑙𝑖𝑛𝑘 = ∑ 𝑙 𝑖 𝑘 𝑝𝑖𝑥 𝑖 𝑛 𝑖=1 (6)
where 𝑘 𝑝𝑖𝑥 𝑖 is related to 𝑅 𝑝𝑖𝑥 𝑖 through Eq. ( 1) with the parameters (a, b) suited for the frequency of the simulated link. The simulated PIA can be altered by adding a measurement noise or considering other sources of errors. A rounding error of 1 dB or 0.1 dB can be considered as in section 4.1 to account for the coarse precision of the raw data provided by the operator. The rainfall estimated from the link 𝑅 ̂𝑙𝑖𝑛𝑘 is then computed using Eq. 4. A range of values of the coefficients (a, b) can be tested in Eq. 4 to account for the uncertainty in the kR relationship.

From the principle above a variety of CML network configurations can be tested by varying the frequency, length, position and orientation of the links. Several sources of uncertainty can be included in the simulations.

2) HYDROLOGICAL MODEL

A distributed hydrological model is needed to analyze the impact of rainfall spatial variability and to assess the ability of the CML network to reproduce rainfall characteristics that are important for the hydrological response. This work concentrates only on sensitivity analysis, by comparing the simulated response for various rainfall forcing. The purpose is not to evaluate the model output against real discharge data as these were not available when the radar was operating. The model was however setup and compared with real data in some areas of Ouagadougou, using rain gauge data, as described In this study rainfall is provided each 5 minutes, either on the radar grid (1 km resolution) for the reference simulation, or at the position of the links (center of each link) when testing the various network configurations. Inside ATHYS, the rainfall is interpolated at each grid point based on the Thiessen polygons method [START_REF] Thiessen | Climatological data for july, 1911 -District No. 10, Great basin[END_REF].

3) REFERENCE SIMULATION

The reference simulations are based on the model above with the highresolution rainfall maps (1 km resolution; 5 minutes time step) as forcing. A reference simulation is provided for each 3 rainfall events displayed in Fig. 3. The discharge is calculated in 1078 intermediary points within the simulated area.

In the next sections the discharge sensitivity to the rain forcing is analyzed specifically at the outlets of

Analysis of CML Rainfall uncertainty and propagation in discharge simulation

The simulation framework is used in this section to analyze uncertainties in rainfall estimation based on CMLs and its impact on the hydrological simulations. The reference simulation is based on the full resolution (1 km) rain maps. Synthetic CML rainfall estimates are produced using the link simulations introduced in section 3c for several network configuration.

First the impact of the precision of the attenuation data provided by the operator is tested in section 4a. For this experiment the links are positioned and oriented as in Fig. 1 As discussed in section 2 (Table 1) the accuracy of rainfall estimation from Eq. 4 depends on the precision of the PIA measurement itself, on the frequency (through the parameters a and b) and on the link length L. The most recent network monitoring systems (NMS) provide Tx and Rx with 0.1 dB or better, but more basic NMS provide only 1dB precision (Leijnse et al. 2007b;[START_REF] Fencl | Commercial microwave links instead of rain gauges: fiction or reality?[END_REF][START_REF] Kim | Rainfall Detection and Rainfall Rate Estimation Using Microwave Attenuation[END_REF]. The relative effect of PIA precision is stronger for the lowest rain rate and sets the lower limit of rainfall detection. According to Table 1 for instance the theoretical limit of detection for a link of 1km operating at 12 GHz and with a coarse accuracy of 1 dB is 22 mm.h 1 ; rainfall below this threshold cannot be measured with such a link. For the highest end of the rainfall spectra (and specially for intense convective rainfall as in Africa) the relative error due to PIA is low (Leijnse et al. 2008a).

In order to analyze the impact of PIA precision on rainfall and subsequently discharge simulation, synthetic CML networks with precision 1 or 0.1 dB, and a range of frequency and length are simulated.

1) NUMERICAL EXPERIMENT

For this experiment the links' center position and their orientation are those provided by the operator metadata in Ouagadougou for the 75 links shown in Figure 1 but the links' length, operating frequency, and the PIA precision can be changed. Three link lengths: 1, 5 and 10 km; five frequencies: 6, 12, 18, 24 and 30 GHz; and two rounding errors on the PIA: 0.1 and 1 dB, are considered. For each experiment the network is homogenous (same length, frequency and precision for all links).

The values of a and b used to simulate the PIA and the estimated rainfall at each link are those from Table 1. The only source of uncertainty in the simulation is the rounding error of the PIA. of the rain intensity class. The blue line is for a link with perfect precision (where the retrieved rainfall is exactly the mean link rainfall as in Eq.5), the other curves show the degradation as function of precision (0.1 or 1 dB) for the various frequencies. Figure 4 is consistent with the numbers displayed in Table1. A 1 km long link operating at 6 GHz would miss a substantial amount of rainfall, because an intensity above 26 mm/h is needed to create a 0.1 dB shift in attenuation, and 150 mm/h to create a 1 dB shift. Fortunately, short links (common in urban areas) usually operate at higher frequency, and a 10 km long 6 GHz link would have better detection (cf Table 1). As expected from Table 1, the distribution of rain intensity is better reproduced for higher frequencies and for all frequencies the errors are relatively lower for higher rain rates. This last point is important when considering the impact of the highest rain rates on floods. For 1 dB precision the overall bias on the mean event rainfall

is small (about 10 %) from frequency 24 GHz and above. For a precision of 0.1 dB all the frequencies from 12 GHz and above provide a good reproduction of the rain rates, with biases below 5 %. The rendering would be better for longer links (and worse for shorter links) following Eq. ( 4).

It is worth stressing again that our simulations do not account for the wet antenna effect. Antenna wetting would typically increase the measured PIA by about 1dB (this is indicative; the range of values reported in the literature and by engineers is wide), with a risk of overestimating rainfall and creating false alarms. The existence of this positive bias can in practice counterbalance (compensating errors) some of the negative bias due to missing low rain rates with a coarse precision. Other effects such as the nonlinearity of the attenuationrainfall relationship (as discussed in section 2) tend to add a positive bias for long links (above 5 km) and frequency below 15 GHz if they are not accounted for in the retrieval. The strength of this effect depends on the variability of rainfall at small scale. According The dark blue line is the simulation based on the CML (1 km length and position as in Fig. 1) with perfect precision (no error on the rainfall retrieval over the link), and the other colors display the tests with precision 0.1dB (left) or 1 dB (right),and frequencies 6,12,18,24 and 30 GHz as in Fig. 4. The difference between the reference (black) and the links with no error (dark blue) reflects solely the impact of rainfall sampling. This will be discussed further in the next section. The difference between the various colors and the dark blue line is related to the signal precision and its impact on rainfall estimation over the basin. Fig. 5 confirms what was seen in Fig. 4, rain rates below a given threshold are undetected if the precision is coarse, especially for the lower frequencies. With a precision of 0.1 dB except for the unlikely case of 1 km/6GHz link the discharge is well reproduced; a coarse precision of 1 dB has a negative impact on the simulated discharge, especially for frequencies below 24 GHz.

The results are generalized in Figure 6 for all 3 events and several numerical experiments: 5 frequencies; 2 precision levels and 3 link lengths (1, 5 and 10 km). The time series of the discharge simulated at outlets 1060 and 1074 for each network configuration is compared with the discharge simulated with the highresolution radar maps. The average over the three events of the following statistics are displayed as a function of frequency/length/precision : the mean bias on the discharge, the relative error on the peak discharge and Kling-Gupta efficiency (KGE; [START_REF] Gupta | Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling[END_REF]).

Because of the high value of the coefficient a (Eq. 4; Table 1) the frequency 30 GHz is mostly immune to a lack of precision up to 1 dB, even for the shortest link length considered here, 1 km. For this frequency all 3 scores are good. For frequencies in the range 1224 GHz which is very common in current mobile networks in urban areas, a precision better than 1 dB is needed to reproduce rainfall and discharge satisfactorily. For short links (1 km) with coarse precision (1 dB) in this range, the loss of small to medium rain rates means an underestimation of the discharge and its dynamic (also seen in ), impacting all 3 scores. For lower frequencies (6 GHz) a lot of rainfall is undetected leading to a strong underestimation of the discharge, its peak and its dynamic, unless the precision is 0.1 dB or better, and the length above 5 km.

The horizontal lines in Figure 5 show the scores for the links with perfect precision, considering the retrieved rainfall is exactly the weighted average over the radar pixels (Eq. 5). In that case the difference with the reference simulation is due to the difference in spatial sampling. We note that this difference is higher for outlet 1060 than for outlet 1074; this is explained by the position of the links inside the basin as seen in Fig 1 . The network is more homogeneous and denser for the southeastern basin (outlet 1074), though not perfect, while rainfall in the eastern part of the northern basin (outlet 1060) is poorly sampled. For the latter the mean and peak discharge are underestimated. The results are also impacted by the length of the links as expected given the spatial variability of the rain field within squall lines (Fig. 2 and3). The next section analyses further the question of the network spatial layout and its capacity to capture rainfall characteristics within the basin.

######. Fig 6 around here b. Impact of network spatial layout

The network overall geometry, which includes the length, the position and the orientation of the links, determines its ability to capture and quantify rainfall variability inside the basin. As discussed with Figures 2 and3, the convective systems that bring rainfall in West Africa exhibit high spacetime variability.

This section investigates the impact of the network geometry on rainfall QPE (quantitative precipitation estimate) over the basin, then on the simulated discharge. This is based on several numerical experiments, either with varying length, density, and random positions and orientations of the links inside the basins or using the actual network of 75 links (Fig1). In these experiments only the network geometry is investigated, no error is considered in the estimation of the mean rainfall intensity over each link, which is simply calculated as in Eq (5). the KGE for a given density higher for short links, as the rain field structure is better sampled with several small links than a single long one. For instance, the mean KGE is above 0.5 for a density equivalent to ten 1 km link per 100 km 2 (density, 0.1), but five 5 km or two 10 km length 100 km 2 (density 0.25) are needed for the same scores. Fig. 10c provides a similar analysis for the real network configuration of 75 links seen in Fig. 1, with their lengths ranging from 0.3 to 26 km. As for the top figures the rainfall at each link is the weighted average (Eq. 5), no estimation error is considered. In order to compare the relative impacts of the shortest and longest links, the results are also presented, when only the 18 links longer than 5 km or on the contrary the 57 links shorter than 5 km, are kept.

Accepted for publication in

2) RAINFALL ESTIMATION AND VARIABILITY WITHIN THE BASIN

######. Fig 7 around here

For link linear density below 0.5 (km/km 2 ) the spread for a given basin and network configuration (same shape and color) illustrates the variability of the rainfall structure among the 3 rain events. For a given linear density (in km/km 2 ), event and basin there is no significant difference between the tests where we kept only the smallest (below 5km) or on the contrary the longest (above 5km) links. It is noteworthy that because of the Thiessen interpolation method, a link which is partially or entirely outside a subbasin may or not contribute to the rain estimation for this basin and a given configuration, depending on the other links available. The differences between events and the impact of the configuration is marked for outlet Ri3 which is mostly rural and poorly sampled by the real network.

Accepted for publication in

Figure 10 is illustrative. More case studies would be needed to account for the complexity of the problem and all the parameters to be considered like the orientation of the links compared to the anisotropy of the rain field, the spatial decorrelation of the rain field, the size and shape of the basin etc. Figure 10 and the other figures in this section tend to show that a dense (in km/km²) network of short links, if they are evenly spread inside the basin (not clustered), is more suited for hydrology than the same linear density of longer links, because it samples better rainfall variability inside the basin. As noted in section 3c the rain information is spatialized in ATHYS by considering each rainfall estimate as a punctual value at the center of the link and using Thiessen interpolation. Other interpolation methods [START_REF] Zinevich | Estimation of rainfall fields using commercial microwave communication networks of variable density[END_REF](Zinevich et al. , 2009) could be used to exploit the spatial information provided by the links and account for their length and orientation. This a field of research on its own. Capturing the spatial variability of rainfall is however only one aspect of the problem. In most of the basin the simulations based on the CML sampling represent much better the discharge and its variability than the simulations based on a single source of information (spatial average or single gauge). This good results in the urban part of the basin are consistent with previous findings. [START_REF] Fencl | Assessing the potential of using telecommunication microwave links in urban drainage modelling[END_REF][START_REF] Fencl | Commercial microwave links instead of rain gauges: fiction or reality?[END_REF] also found that the density of the network at urban scale is beneficial to reproduce the hydrological dynamics. They also notice that the links, especially when short, may introduce bias in the rainfall and recommend using both gauge and link information [START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF][START_REF] Smiatek | Potential of commercial microwave link network derived rainfall for river runoff simulations[END_REF]. Similar conclusions were drawn by [START_REF] Pastorek | Commercial microwave links for urban drainage modelling: The effect of link characteristics and their position on runoff simulations[END_REF] and [START_REF] Stransky | Runoff prediction using rainfall data from microwave links: Tabor case study[END_REF]. Only at the very East end of the basin, where only two long links are available, the simulation based on the central pixel or the average perform slightly better than the CML. The benefit of the CML sampling for distributed hydrological modeling, even when a coarse precision is considered in the raw signal, is clearly striking in Fig. 12. The results are very similar for the 2 other rainfall events. Table 2 summarizes the results of these experiments for the three events. The statistical scores for the discharge at two discharge are much lower for the links, even with coarse precision, than for the single pixel or spatial mean forcing. The benefit of the CML ability to capture rainfall is also marked on the KGE, confirming the importance of the spatial information on rainfall to reproduce the discharge dynamics. For both subbasins the linear link density (defined in 5b) is above 0.4 km/km 2 and KGE above 0.7, even with coarse precision. The results are even better for outlet 1074, with KGE above 0.9 whatever the precision, because the network covers this basin more homogenously.

### Table 2 around here ####

Conclusion

This work investigates the potential benefits of CMLs rainfall estimation for urban hydrology in West For the majority of numerical experiments, the discharge simulated with the synthetic links data as entry is close to the reference based on the highresolution radar map. The performance is reduced when the raw data from the operator is provided with a coarse precision (1dB), especially if the frequency is low (below 10 GHz) and for short links, because the lower rain rates are undetected. The trend in mobile communication networks is for the operating frequencies to increase in order to match the operational needs (need for increase bandwidth in particular), this will help the detection of rainfall from CMLs. Higher operating frequencies are also expected in the perspective of the next generation networks (5G). As the networks modernize the built in monitoring software are also improved and accessing to the data with a good sampling rate (15 minutes or less) and fine precision (0. accumulation is associated with intense rain rates. These intense rain rates create a strong microwave attenuation which is well detected by the CML network, whatever the length and frequency. The present work and previous studies show indeed that the relative error on rainfall estimation from CML decreases with rainfall intensity (Leijnse et al. 2008a,b). The spatial organization and dynamics of the convective cells influence the spacetime structure of the rain fields. The relevant observational scales to capture these structures are kilometric and subhourly, which is compatible with the current CML networks in populated areas.

This positive outcome encourages to continue promoting CMLs as a source of information on rainfall quantities and spacetime distribution in urban basins, especially in tropical regions where weather radar is not yet routinely available.

The presented simulation setup could be used for further sensitivity studies and for accounting for other sources of uncertainties that were not explicitly considered here (wet antenna; error in the baseline determination; uncertainty in the attenuationrain rate relationship etc.). Here only the errors brought in by the difference in the rain forcing were considered, by comparing the output to a reference simulation based on a highresolution radar map and a given setup of the hydrological model. The radar data is used as a realistic proxy of rain fields for simulations purposes. In reality radar estimation of rainfall is subject to many uncertainties, described at length in the literature [START_REF] Berne | Radar for hydrology: Unfulfilled promise or unrecognized potential?[END_REF][START_REF] Cecinati | Optimal Temporal Resolution of Rainfall for Urban Applications and Uncertainty Propagation[END_REF]. The hydrological brings in its own uncertainties in the discharge prediction system [START_REF] Beven | The future of distributed models: Model calibration and uncertainty prediction[END_REF][START_REF] Ajami | An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction: AN INTEGRATED BAYESIAN MULTIMODEL FRAMEWORK[END_REF]. They come from the simplistic representation of hydrological processes, the equifinality problem in the optimization of parameters and other factors such as the interpolation of the rain information inside the model. These were beyond the scope of this paper but are being investigated.

Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. For each statistics the mean over the 3 events is reported. The scores are reported for the following rainfall forcing as described in section 5c: spatial mean of radar rainfall ; rainfall at central pixel ; rainfall from the 75 links at 13 Ghz network (Fig. 1) with perfect precision, precision 0.1 dB or precision 1 dB.

Accepted for publication in

  with a first validated set up for the city of Ouagadougou. The primary purpose of the present work is to investigate how such a distributed hydrological model can benefit from CML based rain estimation : what is the added value for hydrological prediction of the spatial information on rainfall provided by the CML network ; how does it balance with the uncertainties brought in by CML estimation ; what is the sensitivity of the predicted discharge to the CML network configuration. While CML and hydrological data is being gathered in various African testbeds (Cameroun; Niger), these questions are first investigated based on numerical simulations. The proposed simulation framework is based on three components, i) the distributed hydrological model ATHYS, currently set up for the city of Ouagadougou, ii) high resolution (1 km; 5 minutes) rain maps acquired with a weather radar in Ouagadougou during the MTGV campaign ; these are the reference rain fields used for the reference hydrological simulations and to generate synthetic CML measurements, and iii) the production of pseudoCML data simulated by positioning a virtual network inside the high resolution rain fields. With this set up several aspects of CML based rainfall measurement and uncertainty propagation into the model can be investigated. There are many sources of uncertainty in rainfall estimation from a network of commercial microwave links (see Chwala and Kunstmann 2019 for a recent review). In this paper we primarily focus on two aspects that are directly linked to the network itself : i) the uncertainty in rainfall estimation at each individual link due to the inaccuracy of the raw signal (digitizing step) and the length and frequency of the link, and ii) the network spatial configuration and its capacity to represent rainfall characteristics over the basin. Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

  Figure 3 displays the hyetogram (rain rate versus time) of these events and the frequency distribution of rain intensities. The values are typical of African squall lines, with most of the rainfall accumulation due to the convective front which lasts about one hour, and only 20 to 30% of the event accumulation due to the stratiform trail that lasts several hours. The heavy convective rainfall, with peak intensities well above 50 mm/h is the main driver for the floods and needs to be monitored. The spread in the value of the percentiles in Figure 3 illustrates the spatial variability of rainfall over the domain, especially during the convective front. The ability of the CML network to capture this variability is crucial as discussed in section 4. Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC ######. Fig 2 and Fig 3 around here c. Simulation setup The objective of the simulations is to analyze the capacity of the CML network to reproduce the characteristics of the rain field that are needed to simulate the discharge. The benchmark is the hydrological model forced by the highresolution radar rain maps; they provide the reference simulation.

  Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

in

  Bouvier et al. (2018). The model is based on the open source platform ATHYS ( www.athyssoft.org ;[START_REF] Bouvier | Un modèle de ruissellement urbain pour les villes d'Afrique de l'Ouest[END_REF][START_REF] Bouvier | Modélisation hydrologique distribuée -Plate-forme ATHYS[END_REF]. The model has been used for flood modeling in many areas, especially for small catchments. RecentlyBouvier et al. (2018) proposed a version of the model suited for the analysis of urban floods in African cities. The motivation was to propose a distributed gridded model operating over the whole city, with small computation time allowing real Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC time forecasting. ATHYS distributed eventbased parsimonious model, with Soil Conservation ServiceLagandRoute (SCSLR) formula for runoff production and propagation is well suited for these constraints. As detailed inBouvier et al. (2018) the model was setup over a 1000 km2 domain which includes the city of Ouagadougou as represented in Figure1. The hydrographic network was defined using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) elevation model. This defines the 'natural' network in the rural area while the flux is forced by the street layout provided by the OpenStreetMap (/www.openstreetmap.org) data base for the built areas. The runoff is calculated based on the SCS formulation on elementary grid cells of resolution 10 m, and then propagated through the connected grid cells downstream using a 'lag and route' formula. The velocity of propagation over a given grid cell is parameterized by the slope at this grid point and by the drainage area upstream that grid. This is a simplified version compared toBouvier et al. (2018) who also considered hydraulic propagation (kinematic wave) in some parts of the network. Another simplification is that the SCS parameters are uniform for the whole area (the interception parameter S is equal to 100 mm, in the range used byBouvier et al. 2018) as the purpose here is to analyze the relative impact of various rain products, rather than the discharge simulation itself.

  Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC the two main basins in Fig.1 (1060 and 1074) and their subbasins (Ri1, Ri3 and Sa1). Part of the northern basin (outlet 1060) lays in rural areas which are poorly observed by the telecommunication network (Fig 1), while the southern basin (outlet 1074) is located mostly in the urban area, thus better covered by the mobile network.

  and the impact of the rounding error on attenuation (0.1 or 1 dB) is analyzed considering several frequencies and link lengths. The impact is first analyzed on the retrieved rainfall distribution and then on the simulated discharge over the 2 main outlets 1060 and 1074. Section 4b concentrates on the spatial configuration of the network and its ability to sample rainfall variability within the basin. As above the analysis is first focused on the uncertainty on rainfall estimation over the basins and then on the simulated discharge. Several subbasins of various size and shape are used. a. Impact of PIA rounding error Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

Figure 4

 4 Figure4illustrates the error in the frequency distribution of the rainfall rates due to the rounding error,

  Figure5displays the discharge simulated by the model at the outlets 1060 and 1074 (Fig.1), for the

  Figure5), impacting all 3 scores. For lower frequencies (6 GHz) a lot of rainfall is undetected leading to

  Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC 1) NUMERICAL EXPERIMENT The effect of the network geometry is investigated for 3 subbasins of size 74 to 193 km 2 with outlets marked Ri1, Ri3 and Sa1 in Figure 1. The number of links per basin (i.e. a link which center is inside the basin) N varies from 1 to 100. For each value of N, 10 experiments with random positions and orientations of the links are generated. For each of these link positions and orientations, 3 lengths (1, 5 and 10 km) are considered as in section 4. Altogether 410 synthetic network configurations are simulated for each 3 subbasins. For each, the 3 rainfall events are sampled with the link simulator (3.c).

Figure 7 Figure 8 Figure 9

 789 Figure 7 illustrates the spatial variability of rainfall as captured by the link network. The rainfall time

  Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

  Figures 11 and 12 illustrate the spatial variability of rainfall and of the simulated discharge quality.

Figure 11

 11 Figure11show the rainfall accumulation for the 2012/08/04 event as seen by the highresolution radar

  main basins outlets (1060 and 1074) are reported. The error on the mean and on the maximum Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

  Africa. One expected benefit of CMLs for hydrological application is the density of the network, especially in urban, thus populated, areas; on the other hand, as for any indirect measurement, rainfall estimation from CMLs is subject to uncertainties. A pending question for the development of CMLs based hydrological applications is: what is the final balance between the benefits and drawbacks of CMLs rain measurements, and how basin dependent and network dependent are they. A simulation setup based on high resolution radar rain maps and a distributed hydrological model was used for a case study over the city of Ouagadougou. The radar is a research radar that operated in Burkina Faso as part of a satellite validation program in 2012 and 2013. The distributed model (ATHYS) was developed and calibrated for Ouagadougou area in the framework of an urban flood prediction project. Here the radar rain maps were used as a reference rainfall, as forcing to the hydrological model and for generating synthetic CML measurements which can in turn be used as model input. This setup was used to analyze the ability of the microwave link network to i) quantify rainfall over the urban basins, ii) to capture rainfall space and time variability. In this work we primarily focused on two characteristics of the CMLs network that influence rainfall estimates: i) the accuracy of the raw Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC information (digitizing step) provided by the operator and ii) the network configuration that includes the position and orientation, length and operating frequency of the links.

  1 dB) becomes common (personal communications from Orange and Nokia engineers). The number of links inside the basin is important. To quantify this effect, numerical experiments with an increasing number of links randomly distributed within the subbasins were performed. The performance in terms of discharge dynamics (KGE criteria), mean bias and error on the maximum discharge increases quickly with the network density expressed in total length of link in km per km 2 of basin and especially with the number of short (1 km) links. For the present simulations satisfactory results (KGE close to or above 0.5) are obtained from a density of 0.1 km/km 2 for 1 km long links (i.e. 10 links inside a 100 km 2 basin) and 0.3 km/km 2 (3 links of size 10 km for 100 km 2 ). When the positions of a real network are used, with a total of seventyfive links of various lengths for the Ouagadougou area (1000 km 2 ) the simulations with the CML sampling are very close to the reference (KGE above 0.5) for most of the basin. The CML sampling, even when a coarse precision is considered, outperforms the simulation based on idealized satellite pixel or a single gauge situated in the city center. These good results are partly explained by the nature of rainfall systems in the study region. Rainfall in West Africa (and in most of the Tropics) is provided by deep convection, where most of the rain Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

FiguresFigure 1 :

 1 Figures

  Fig 2 :

Figure 2 :

 2 Figure 2 : Evolution of rain intensity maps over the area on the 2012/08/04 event as seen by the

Figure 3 :

 3 Figure 3: Time evolution of radar rainfall over the studied area (from Fig. 1) for the three

Figure 4 :

 4 Figure 4: Cumulated rainfall distribution per rain rate classes as a function of link frequency and attenuation precisionhere for links of length 1 km. The Y axis is the mean amount of

Figure 6 :

 6 Figure 6: Effect of signal precision, link length and frequency on the simulated discharge. The

Figure 8 :Figure 9 Figure 9 :

 899 Figure 8: Rainfall variability between realizations and among simulated links, illustrated for

Figure 11 :

 11 Figure 11 : rainfall accumulation map over the area for the 2012/08/04 event, as measured by

Figure 12 :

 12 Figure 12 : Spatial distribution of KGE for the simulations with various rain forcing

Table 1

 1

	; for short

Accepted for publication in Journal of Hydrometeorology. DOI 10.1175/JHM-D-20-0163.1. Brought to you by UNIVERSITE PAUL SABATIER | Unauthenticated | Downloaded 06/02/21 03:41 PM UTC

Table 2 :

 2 Statistics on the simulated discharge for different rainfall sampling experiments compared to the reference simulation (based on the high-resolution rain map). The following statistics are reported for the two main outlets (1060 and 1074, see text) : the absolute error on the event mean discharge (in %) ; the absolute error on the event maximum discharge (in %) ; the KGE.

Acknowledgments

Maxime Turko's PhD was funded by the French Space Agency CNES and Meteo-France CNRM. The radar experiment in Ouagadougou was financed by the French Space Agency CNES as part of the Megha-Tropiques Ground Validation (MTGV) program. We would like to thank Frédéric Cazenave who installed the radar and supervised its operation. We are very thankful to the technical teams from telecommunication operators who have provided us with meta-data and data from their networks in several african countries, in particular at Telecel and Orange.

Data Availability Statement

The data used for this study is openly available -A specific repository will be created when the paper is accepted.

ATHYS code is freely available here: http://www.athys-soft.org.