A Avumadi
email: havumadi@gmail.com

K Gnandi

J L Probst

Trace Element Distribution and Enrichment in the Stream Sediments of the Lake Togo Watersheds (South of Togo)

Keywords: Trace metals, stream sediments, enrichment factor, labile fraction, natural and anthropogenic contributions

To evaluate the level of sediment contamination in watershed of lake Togo (south of Togo), the concentrations of twelve trace elements, TE (As, Sn, Cr, Co, Ni, Cu, Zn, Zr, Cd, Pb, Th, U) are analyzed using inductively coupled plasma-mass spectrometry (ICP-MS) in eighteen stream sediment samples from Zio and Haho rivers draining into the lake Togo and from lake Togo itself. The results obtained allow to characterize each sediment sample by its TE geochemical distribution pattern. Average TE concentration in the finest fractions (< 63 µm) is ranked from the hightest to the lowest content: Cr>Ni>Zn>Cu>Co>Pb> Th> Sn>U>As>Cd. The degree of contamination of these stream sediments is evaluated by calculating sediment quality parameters such as enrichment factors (EF), anthropogenic and naturel contribution. Globally, 70% of TE have an EF lower than 1.5, particularly for As, Sn, Co, Cu, Zn, Pb, Th and U. However, 30% of the samples are more contaminated (1.5<EF<6), particularly for Ni, Cr, Cd from one sampling point to another. Nevertheless, the anthropogenic contribution could represent only 18% of the total content, 82% originating from natural rock weathering processes.

A single chemical extraction by EDTA allows to assess the non-residual (labile) fractions for Zio and Haho river sediments. For Co, Cu, Cd and Pb, the EDTA extracted fractions represent respectively 38%, 32%, 25% and 24% of the total concentration. The EF values are subjected to multivariate statistical analysis in order to evaluate the origins of TE in the study area. Most of TE are controlled by clay, oxi-hydroxide minerals and organic matter.

Introduction

Trace element (TE) are natural constituents of stream sediments, whose concentrations depend on different factors such as lithology, geomorphology and structural setting of the catchment area. It also depends on the climate, which controls the rate of weathering, hydrologic characteristics, vegetation type and density [START_REF] Salomons | Metals in the hydrocycle[END_REF]. These elements can also be introduced into the river channels by anthropogenic effluents, which are the products of human activities, like for instance domestic, industrial and agricultural wastewaters, fossil fuel combustion and atmospheric pollutant deposition [START_REF] Mantei | Heavy metals in stream sediments: effect of human activities[END_REF]Foster 1991, Benamar et al., 1999). Most of the metals released into aquatic systems are generally bound to particulate matter, which eventually settles and becomes incorporated into sediment.

Sediment acts as a potential scavenger and after becomes a source of contamination in an aquatic system. This is affecting the water quality, and therefore is bring up the question of the effects of human activities in the pollution of lakes (Salomons and Forstner, 1984) and rivers (Helios-Rybicka, 1992). In fact, metals are not permanently stored in sediments, they could be released as a response to the environmental condition changes [START_REF] James | Effects of Heavy Metals on Aquatic Life[END_REF][START_REF] Wen | Mobilization of heavy metals from Le in River sediment[END_REF]. Different factors, such as pH, clay fractions, iron and manganese oxides, organic matter etc. can influence the sorption of trace elements onto the particles [START_REF] Serpaud | Adsorption des métaux lourds (Cu, Zn, Cd et Pb) par les sédiments superficiels d'un cours d'eau: rôle du pH, de la température et de la composition du sédiment[END_REF][START_REF] Alloway | Chemical Principles of Environmental Pollution. Blackie Academic and Professional[END_REF] Ayres 1997; USEPA, 2005).

Aquatic ecosystems in farming areas like the Lake Togo Basin are subjected to disturbance of trace elements due to the use of fertilizers and pesticides. Indeed, farming activities like for example the use of the mineral and organic fertilizers (mainly phosphates), which are added to soil to improve plant growth and yield, add a considerable amounts of trace metals into the soils, depending on the rates and types of fertilizers applied. The streams of Lake Togo basin contain a huge amount of nutrients from anthropogenic wastes including domestic wastes, non-rational use of fertilizers, which are in turn leached to the waters of lagoon areas whose banks are already heavily polluted [START_REF] Bruce | Identification of Environmental Changes and Land Use in the Lagoon Ecosystems of Togo Southeastern[END_REF]. Beside these inputs, the outlets of the Zio and Haho rivers are confronted with a permanent contamination in trace elements from the sea, coming from Aneho and the mining of trace metal rich phosphorite in Kpogame and Hahotoe, located in the northern side of the lake. The pollutants come from industrial effluents and phosphate washing residues coming from the South of the lagoon system [START_REF] Gnandi | The pollution of marine sediments by trace elements in the coastal region of Togo caused by the dumping of Cd rich phosphorite tailings into the sea[END_REF][START_REF] Gnandi | l'impact de l'exploitation des phosphates sedimentaires et de Hahotoee-Kpogame sur la pollution chimique des sediments du fleuve Haho et du Lac (Sud Togo)[END_REF].

The work in this paper focuses on the pollution status and distribution of trace metals in the suspended matters and streambed sediments of Zio and Haho rivers, which are the main rivers (85% of the total water supply) draining into the Lake Togo. To evaluate the ecological risk of trace metal in the environment, it is today, widely admitted that determination of their total concentration is not sufficient. Chemical speciation, distribution, partitioning of trace metals between dissolved phases, suspended particulate matters and bottom sediments, are essential to better understand their availability and potential ecotoxicity [START_REF] Förstner | Metal speciation-general concepts and applications[END_REF][START_REF] N'guessan | Trace elements in stream bed sediments from agricultural catchments (Gascogne region, S-W France): Where do they come from?[END_REF]. Unfortunately, for river sediments in Togo, little information is available for these processes and the controlling parameters. Then, the objectives of this study are to:

 Determine the level of trace metal contamination of Zio and Haho river sediments and to evaluate the enrichment factor (EF).

 Determine the respective contribution of anthropogenic and natural sources to the total concentration.  Evaluate the non-residual (labile) fractions for each ET using an EDTA chemical extraction;

Materials and Methods

Study Area

The Lake Togo watershed (Figure 1) covers an area of 8000 km 2 (14% of the country land area), with approximately 50% of the Togolese population against 20% living in the capital Lome and it has a complex coastal lagoon system and a fragile marine environment. It contains on one hand, perennial surface water resources but limited and highly variable and the other hand abundant (coastal sedimentary) or limited (base) groundwater resources. Located in southern Togo, the watershed of Lake Togo is drained by a complex hydrosystem consisting of the Zio, Haho and Boko rivers and the lagoon system which is located in a depression of the coastal sedimentary basin. The entire lagoon system communicates with the sea through the Aneho channel opening portion, which has been opened continuously since 1989 because of the coastal erosion. Except for the direct runoff of the banks, the Lake Togo itself, is fed by its two major tributaries, the Haho and the Zio rivers. These two rivers basins drain on 85% of their surface, ferralitic and ferruginous soils coming from the alteration of the crystalline basement, where dominate gneisses and migmatites accompanied to the north-west by quartzite, amphibolite and marble dolomitic as well as of numerous micaschists [START_REF] Millet | Hydrologie et hydrochimie d'un milieu lagunaire tropical : le lac Togo[END_REF]). The climate is subtropical, warm and humid with an annual average rainfall which varies between 800 and 1000 mm. Four climatic seasons can be observed : two dry seasons (from December to March and from August to September) and two rainy seasons (from April to July and from October to November). The average air temperature varies between 24°C and 29°C. The area has been continuously used to grow corn, beans, cassava, rice, yam, sugar cane, cotton and coffee, cocoa being grown in upstream. Following anthropic pressures, protected forests have been turned into farms. All these environmental characteristics make the Lake Togo basin area vulnerable to surface runoff and physical erosion processes, which might contribute to supply rivers with pollutions.

Figure 1 : Map of the study area, the Lake Togo and its drainage basin, and sampling sites in the lake and on the two main rivers, Zio and Haho, flowing into the Lake Togo.

Sampling and Pre-treatment of the Samples

Sediments from the bottom of the stream were collected from nine different sampling points (Figure 1), in February (low flows) and October (high flows) 2015. Sediment samples are placed in plastic bags and registered. Samples were collected in the first centimeters of the bottom sediments using plastic tube of 1000 ml then, they were air-dried in laboratory for two weeks. After the two weeks, samples are carefully homogenized in an agate mortar, quartered, and separated by sieving into four fractions (< 63 µm; 63 µm-200µm; 200 µm -2mm; > 2mm). A micro-granulometry analysis is then performed with a Horiba LA 950 laser micro-granulometry at EcoLab Laboratory, Toulouse France.

Chemical Treatments and Analysis

1"3a!TE

Mineralization is performed on the fine fraction (<63 µm) of sediments because trace elements are known to be preferentially associated to fine fractions [START_REF] Probst | Fluvial transports of mercury pollution in the Ill river basin (Northeastern France): Partitioning into aqueous phases, suspended matter and bottom sediments[END_REF]. Alkaline fusion has been selected as the digestion method for the determination of the total concentration of trace and major

Enrichment Level Assessment

Trace elements in stream bottom sediments come mainly from soil/bedrock weathering and anthropogenic sources. To evaluate the level of contamination in the environment, the enrichment factor (EF) and the TE anthropogenic contribution in the stream sediments are evaluated by comparing their average abundance in reference materials, such as the widely used "shale PAAS" ( , 2005). In our case study, scandium (Sc) was chosen as the normalizing element for the determination of the EF because of its attributes of high immobility in an oxidizing surface environment, low occurrence variability and frequent usage as reference element [START_REF] Hernandez | Dynamique des éléments traces métalliques dans les sols de différents écosystèmes forestiers Français: origine, distribution physique et chimique et facteurs de contrôle[END_REF][START_REF] Hissler | Impact of mercury atmospheric deposition on soils and streams in a mountainous catchment (Vosges, france) polluted by chlor-alkali industrial activity: the important trapping role of the organic matter[END_REF]. Moreover, Sc presents a better correlation with the majority of the studied trace elements than Cs, Al and Fe.

The following equation was applied to calculate EF and the % of anthropogenic contribution (AC), taking Sc as a reference element : The residual fraction results from the difference between the total sample and the labile fractions (NR).

EF = ([X]/[Sc] ) sample ⁄ ([X]/[Sc]) ref mat Equation 1 % AC = ([X] sed -[Sc] sed * [X/Sc] ref mat ) / [X]

Results and Discussions

Physical Characteristics of Sediments

TE contamination in sediments is often related to the distribution of particle sizes. In streams, clay fraction, colloidal oxides and some insoluble organic compounds that are characterized by high electrically-charged surface areas have the high capacity to adsorb and to co-precipitate soluble TE [START_REF] Probst | Fluvial transports of mercury pollution in the Ill river basin (Northeastern France): Partitioning into aqueous phases, suspended matter and bottom sediments[END_REF]. TE associated to abundant clays and silts travel long distances adsorbed onto suspended sediments. The investigated sediments are very fine in general and the less than 63 µm fraction represents on average 90% of the bulk sediment. The distribution patterns of the relevant fractions that compose the sieved sediments are illustrated in Figure 2 for the different sediment samples. Except for Z4 and Z5, the sediment samples are principally composed by clay (<2µm) and silt particles (2-63µm), which represent favorable conditions for TE adsorption. Indeed, the grading distlibution of sediments shows globally a vaiiation from 34% to 94% of clays and silts. Contra1y to the sediment samples of Z4 and Z5 where the sand dominate with respectively 65 % and 56 % of the total sediment, silt is tl1e major granulometric fraction with up from 33% to 67%. The highest proportions of silts are obse1ved in the mouths of rivers Zio (Zl: silt = 67%; day = 13%) and Hal10 (Hl: silt = 61 %; clay=18%) with the lake Togo. The percentage of clay is below 20 % in the samples of rivers, except for station Z2 (47%) and for the lake (L3 = 28%). The reactivity of the sediment towards the processes of surface being bound to the total specific smface area of the paiticles (Salomons and Forstner, 1980;[START_REF] Probst | Fluvial transports of mercury pollution in the Ill river basin (Northeastern France): Partitioning into aqueous phases, suspended matter and bottom sediments[END_REF], which is inversely proportional to the average diameter of the particles; brings us to say that the TE contents in our sampled sediments will be higher in the stations where the silt and clay fractions are dominating.

Geochemish)' of Maj or and Trace Elements

Average Concentrations

Concerning major elements, the results of sediment chemical composition on the Table 1 shows that among oxides, silica, aluminum, iron and manganese are more concent::1•ated in 1iver sediments as well as in lake ones. These high contents are due to the erosion of the fenuginous soil materials recove1ing the basin and the sub-sequent sedimentation in the rivers and in the lake. The concentrations of major cations (Ca, Mg, Na, K) are very weakly represented in the whole of the pond (3 % -9 %). For TE analyses in our basin, Cd, As, Sn and U present the lowest mean concentrations (0.06 µg.g -1 -2.53 µg.g -1 ) while the highest contents are for Zr (188.8-1285 µg.g -1 ) follow by Cr (143.70-280.32) and Ni (42.73 µg.g -1 -280.32 µg.g -1 ). For other elements, concentrations vary between 8.53 µg.g -1 (Th) and 105.20 µg.g -1 (Zn).

As a whole, the order of TE abundance is Zr>Cr>Ni>Zn> Cu>Co>Pb>Th>Sn>U>As>Cd. By comparing the sum of the average TE concentrations, we notice that the fluvial sediments of the Haho basin are more concentrated in the Haho river (ΣTE = 1258 μg.g -1 ) than in the creek (921 μg.g -1 ) considered as the local reference sediment, but they are also more concentrated than in the Zio (ΣTE = 1093 μg.g -1 ) and in the Lake Togo (ΣTE = 1081 μg.g -1 ). The high contents in the Haho river might result from the geographic localization of this river. Indeed, the TE concentration in the reference creek sediment, situated upstream and considered as non-polluted sediment, is 1.4 times (but 1.8 for Sn, 3 for Cr and 3.7 for Ni) less concentrated than sediments of the main course of the Haho river which is situated in the area of phosphate exploitation and which is more exposed to contamination by this industrial mining activity.

These high contents in the Haho can also result from the agriculture which uses fertilizers and pesticides.

In addition, most of the mean TE contents in studied sediments are higher than the corresponding literature values of the reference materials (UCC and PAAS from [START_REF] Taylor | The continental crust: its composition and evolution[END_REF]), except for Cu, Zn, Pb, Th, U. Also, the contents of TE such as Cr, Ni, Cu and Pb seems more important in sediments of Haho and Lake Togo analyzed by [START_REF] Gnandi | l'impact de l'exploitation des phosphates sedimentaires et de Hahotoee-Kpogame sur la pollution chimique des sediments du fleuve Haho et du Lac (Sud Togo)[END_REF] while the values of the major elements are more important in this present study.

Spatial and Temporal Distribution Patterns

The distribution graphs plotted for each TE in the different sediments of the study area are presented in Figure 3. Excepted As, Sn and Cd, the variation of TE concentrations between the two campaigns of sampling (February and October) is low for each station. In addition, TE study are rather widely distributed in the area. The concentrations of TE, except Cd and Sn, are generally slightly higher during the period of the high-water (October) than in low-water (February). Indeed, the streamflow being very low during August and September 2015, it favorites on one hand, the deposit of fine particles to supply bottom sediments, and on the other hand, the adsorption of TE in solution onto particles, so pulling higher concentrations of TE in thorough sediments. However, the insignificant duration between these deposits and the beginning of the high-water of October which also corresponds to the small rainy season with the increase of the flow favors the re-suspension and the transfer of TE associated to the finest particles towards the downstream. This could be at the origin of these higher TE concentrations in the sediments in October 2015.

3 Enrichment Factor

The Emi chment Factor (EF) is a potent tool for TE contamination evaluation. Elements which are natmally derived have an EF value of nearly unity, while elements of anthropogenic 01igin have EF values of several orders of magnitude . It is generally accepted that EF < 2 reflects narural variability of the regional geochemical background and of the mineralogical composition of the bedrocks (Sutherland, 2000; Concerning EF values, the average results obtained in figure 5 show that among the twelve TE analyzed, only Zr and Cd present a moderate emichment with the P AAS normalization for Haho and Zio sediments.

To these, must be added As and Sn for lakeside sediments with P AAS and Creek nonnalization. In With regard to this previous analysis, the EF spatial distribution (Figure 6) based on the local pristine Creek sediment normalization indicates a significant variability among the samples for all elements.

Globally, the spatial distribution of EF data reveals that 70% of TE in sampling stations have EF values lower than 1. • EF > 4.00

Anthropogenic Contribution

The average anthropogenic contribution (AC) in the stream bed sediments of lake Togo basin, calculated using equation 2 and the local creek sediment as reference material, is greatly variable according to TE. AC is very high for Ni (54%) and Cr (53%), high for Cd (36%) and Sn (25%), low for Co (12%); As (8%) and ; Zn (6%) and very low for Cu (2%) and Pb (2%). For the other TE (Th, U and Zr), there is no AC. For Ni, Cr and Cd spatial distribution, the anthopogenic contamination of Zio and Haho stream sediments is obvious at Z3, Z4, Z5, H1, H2, H3 with regard to the intensity of the enrichments observed. In the case of As, Sn, Ni and Cr, the anthropogenic signature increases from upstream to downstream in the Haho basin while it is variable in Zio basin where the stations impacted by the anthropogenic signature depend on the TE. Indeed, Z3 station in Zio basin exhibits the highest AC for As, Sn and Pb. In the lake Togo (station L3), the AC shows high to very high levels whatever the TE, except Pb.

- AC_ Ni C]NC_Ni () - AC Pb C] NC_ Pb
Based on the Pearson correlation coefficients, displayed in Table 2, there is a positive significant correlation between EF and AC of each TE. The enrichment increases in run away as the AC becomes important. Moreover, the correlations between EF values of Sn, Co, and Pb, and the anthropogenic contribution of Cd allow to make the hypothesis that those metals may be derived from the same pollution source in the area. All the value have a significant level of 0.05

EDTA extractable fraction of metal

The total concentration of metals in soils and sediments is not a good indicator of their availability, due to their different and complex distribution patterns among various chemical species or solid phases.

Indeed, sorbed elements onto particles are potentially available, as they may be extracted due to changes in the physico-chemical properties of the aquatic environment such as salinity, pH, redox potential, and concentration of chelators [START_REF] Abollino | Distribution and mobility of metals in contaminated sites, Chemometric investigation of polluant profiles[END_REF][START_REF] Bourg | Metals in aquatic and terrestrial systems: sorption, speciation and mobilization[END_REF][START_REF] Bourg | Speciation of heavy metals in soils and groundwater and implications for their natural and provoked mobility[END_REF][START_REF] Calmano | Binding and mobilization of heavy metals in contaminated sediments affected by pH and redox potential[END_REF][START_REF] Chuan | Solubility of heavy metals in a contaminated soil: Effects of redox potential and pH[END_REF][START_REF] Ernst | Bioavailability of heavy metals and decontamination of soils by plants[END_REF][START_REF] Calmano | Binding and mobilization of heavy metals in contaminated sediments affected by pH and redox potential[END_REF][START_REF] Forstner | Assessment of metal mobility in dredged material and mine waste by pore water chemistry and solid speciaton[END_REF][START_REF] Forstner | Mobility of heavy metals in dredged harbor sediments[END_REF][START_REF] Gambrell | The influence of redox potential on the environmental chemistry of contaminants in soils and sediments[END_REF]. The objective consists to determine in the particulate fractions, the distribution of the element between the residual phases and the non-residual phases (labile fractions), and consequently its potential mobility toward the dissolved fractions as well as its potential bioavailability and then, its capacity to contaminate water resources and to infiltrate the food chain.

The figure 8 reports for each ET, the percentage of non-residual fractions (NR = non-residual or labile fraction) which have been extracted using an EDTA single extraction and the percentage of residual fractions (R), for the various studied samples. The relative ordering of elements, in terms of their environmental mobility or bioavailability, is observed from the most mobile to the least as follows:

Co>Cu>Cd>Pb>Ni> As>Zn> Th> Sn> U>Cr>Zr.

Comparing the R and NR fractions of TE, the Co, Cu, Pb and Cd are associated more than 24 % to the NR fractions, except Co in sediments of the lake. The percentage of As and Ni in the NR of is between 10% to 16% (Figure 8). Zn, Th, Sn, U, Cr and Zr are rather associated to the residual fraction, which represents on average 91 to 96 % of total particulate fraction for Zn and Th, and 99 to 100% for Sn, U, Cr and Zr.

These results show that Cu, Co, Pb, Cd, are potentially more available and mobile with regard to the variations of the physico-chemical conditions of the aquatic systems than the rest of TE. Among them, Co is although into the available fonn in the sediments of Zio and Haho rivers with respectively 40% and 36% of NR fractions. Co could be logically considered like the element possessing the highest potential of mobility and toxicity, except in the Lake Togo, followed by Cu (30-33%), Cd (24-25%) and Pb (24-25%) for Hal10 and Zio, but 39% for the Lake. According to Salomons and Forstner (1980), the mobility and the toxicity of TE aie bound to their propmtion of non-residual fractions. More an element has a strong proportion of non-residual fraction, more its capacity of mobility and availability for the environment and for the living organisms is high, and vice versa if the residual fraction is dominant.

Origins of Trace Elements in the Sediment Using Multivariate Statistical Analyses

In the absence of sequential extraction analyses which allows to determine the different TE bearing minerals [START_REF] Leleyter | A new sequential extraction procedure for the speciation of particulate trace elements in river sediments[END_REF], multivariate statistical analyses can provide meaningful information for the identification of the most important bearing geochemical phases [START_REF] Santos | Heavy metal contamination in coastal sediments and soils near the Brazilian Antarctic Station, King George Island[END_REF]. Principal component analysis (PCA) (Table 3 andFigure This association shows that the P controlling factor mostly originates from agricultural sources and domestic wastes. 3.

In the stream sediments of the watersheds draining into the Lac Togo, all TE contents are mainly linked to the geological and lithological nature of the rocks and to the soils. Nevertheless for the Zio riverbed sediments, two groups of elements can be distinguished according to their anthropogenic sources:

 As, Cr, Cu, Zn, Pb, Th and U are enriched by the contributions of atmospheric deposition, domestic effluents, solid waste and traffic in the environment. The exogenic Pb coming from the accumulation

A)

Biplot Comp 1 and 3: 56.00 %) B) Biplot (Comp 1 and 3: 52.00 %)  Cd, except the agriculture impact, also comes from apatite of phosphate mining. Sediment Quality Guidelines for sediments (SQGs): TEL-Threshold Effect Level [START_REF] Smith | A preliminary evaluation of sediment quality assessment values for freshwater ecosystems[END_REF], ERL-Effects Range Low [START_REF] Long | The potential for biological effects of sediment-sorbed contaminants tested in the National Status and Trends Program[END_REF], LEL-Lowest Effect Level [START_REF] Persaud | Guidelines for the protection and management of aquatic sediment quality in Ontario[END_REF], MEL-Minimum Effect Level (MENVIQ/EC,1992), PEL-Probable Effect Level [START_REF] Smith | A preliminary evaluation of sediment quality assessment values for freshwater ecosystems[END_REF], ERM-Effect Range Median [START_REF] Long | The potential for biological effects of sediment-sorbed contaminants tested in the National Status and Trends Program[END_REF], SEL-Severe Effect Level [START_REF] Persaud | Guidelines for the protection and management of aquatic sediment quality in Ontario[END_REF], TET-Toxic Effect Threshold (MENVIQ/EC,1992), CB PEC-Consensus-Based for Probable Effect Concentrations (MacDonnald et al., 2000).

6 5 4 3 2 'iF 'iF .. •••••••••••••.\ 0 "' 25

Comparison with

Moreover, the issue of bioavailability is not well addressed by the empirical SQGs since they are based on total sediment concentrations [START_REF] Burton | Sediment quality criteria in use around the world[END_REF]. As seen in the previous section, the non-residual fractions which correspond more or less to the bioavailable fractions which represent a real threat to aquatic ecosystems present lower values (see Figure 8), particularly for Ni for which the NR fractions represent only 12-13% of the total concentrations and for Cr for which there is no NR, Cr being only in the residual fractions of the sediments. Then, the total TE concentrations could be divived by 2.5 to 3 for Pb and Cu, until 10 for As to get the TE concentrations which indeed represent a real threat for the organisms.

Consequently, the non-residual TE concentrations are largely under the SQGs, even for Cr and Ni for which the total concentrations are over the SQGs, mainly because they are mainly associated to residual fractions and then, not at all bioavailable.

Conclusions

A study of the occurrence, distribution and enrichment of TE like As, Sn, Cr, Co, Ni, Cu, Zn, Cd, Pb, Th and U in the stream sediments of the watersheds draining into the Lac Togo, reveals the following important results. The levels of total concentrations of trace metals in the study area, in general, do not constitute any serious environmental risk except for Ni, Cr and specially Cd which need to be monitored at the outlet of both rivers, Zio (Z1) and Haho (H1) and also at Togblekope (Z3) and Hahotoe (H2) sites.

Nevertheless when compared the TE labile fractions with the Sediment Quality Guideline values, all the TE labile concentrations remain largely under the ecotoxicological limits. Knowing that most of the studies on trace elements more dealt with the coastal zone especially on the discharge of the mining effluents in the sea, the concentration ranges for the different trace metals in the Zio and Haho can serve as baseline environmental data against which the degree of pollution of these trace metals can be evaluated in the future.

  ......_,,, Ma in rivers Q Cap ital-Lame • Lake Togo : : : ~ Lake Togo bas in . . -.....

  TE are usually included in two large sets of geochemical phases. The residual phase (crystalline structure of the minerals) of the particles, where the elements are considered inert, released in the very long term by the processes of alteration, and the non-residual phase or labile fractions where the elements can interact with their environment because they are potentially available for the environment and living organisms. The non-residual (NR) concentration was determined by single chemical extraction with EDTA. The percentage of this fraction is calculated for a given element X as follows: % NR=([X] extraction ) / ([X] total ) * 100 Equation 3

Figme 2 :

 2 Figme 2 : Abm1dances (% of bulk sediment) of the different granulometric fractions in the stream sediments: Zl to Z5 for the Zio, HI to H3 for Haho and L3 for Lake Togo.

For 50 -Figme 3 :

 503 Figme 3 : Spatial and temporal distributions of trace element contents in the finest fractions ( <63 ~nn) of the bottom sediments: Zl to 25 for Zio river, H I to H3 for Hal10 river and L3 for Lake Togo.

5 (Figure 4 :

 54 Figure 4: Normalization of TE in Zio and Hal10 stream bed sediments with the local pristine material (Sed/Creek), UCC (Sed/UCC) and PAAS (Sed!PAAS). Data for PAAS and UCC are from Taylor and McLennan, 1985.

0As 2 0Figure. 5 :

 25 Figure. 5 : TE enrichment factors in the finest sediment fractions (<6311m). Mean values of trace elements in Zio, Hal10 and Lake were normalized using the P AAS and local creek sediment as natural references. TI1e dashed lines represent the natural variability thresholds respectively for P AAS (EF = 2) and local creek sediment (EF = 1.5) normalization.

  [START_REF] Benamar | Assessment of the state of pollution by heavy metals in the surfacial sediments of Algeris Bay[END_REF]. A moderate enrichment is observed for Ni and Cr at all stations; for As at Z3, L3 ; for Sn at Z1, Z3, H1, H3 and for Cd at H1, H3, Z3. However significant enrichments in Cd and Sn are respectively observed at L3, Z4, H2 and at L3. Generally Cd and Sn are from the agriculture practices, especially from seasonal agriculture which are practiced in the minor and major river beds of Haho and Zio. The enrichment of Cd and Sn can also be result of the various domestic practices such as the clothes, cars and motorcycles washing with highly concentrated detergents in the bed of the rivers.However, there is no significant enrichment of trace elements like As, Sn (except L3), Co, Cu, Zn, Pb, Th and U. Nevertheles, it is useful to determine the relative contribution of natural and anthropogenic sources to each TE content in the sediments.

Figure 6 :

 6 Figure 6 : Maps showing the spatial distribution of the most relevant TE enrichment factors.

Figure 7 :

 7 Figure 7 : Maps showing the spatial distribution of anthropogenic (AC) and natural (NC) contributions in percentage of the total concentration for each of the most relevant TE.

Figure 8 :

 8 Figure 8 : Proportion of the various fractions (NR = non-residual; R= residual) outcome from the single chemical extraction using EDTA in the sediments ofZio and Haho rivers and of the Lake Togo.

  9 A and B) were carried out to identify the origins of the different TE and their relationships with the various bearing phases in the sediment samples. The input data were enrichment factors (EF) for TE and the major element concentrations to represent the main bearing phases. Three principal components (Comp 1, Comp 2 and Comp 3) have been identified, explaining 80.8% and 76.94% of the total variance for Zio and Haho respectively.In the Zio basin, component 1 distinguished between the metals that are least anthropogenically influenced (As, Sn, Ni, Cu, Zn, Pb, Th) and which are linked to Al and Fe oxides[START_REF] Filgueiras | Evaluation of distribution,mobility and binding behaviour of heavy metals in surficial sediments of Louro River (Galicia, Spain) using chemometric analysis: a case study[END_REF] and clay-silt minerals[START_REF] Suresh | Assessment of spatial distribution and potential ecological risk of the heavy metals in relation to granulometric contents of Veeranam lake sediments, India[END_REF]. The opposite correlation for Ni, demonstrates that there is no affinity for Ni to Al and Fe oxides[START_REF] Chaillou | The behaviour of arsenic in muddy sediments of the Bay of Biscay (France)[END_REF]. Component 2 and 3 isolated the most anthropogenically influenced metals and indicated that Sn, Co and Cd were linked to phosphate minerals (P) and organic matter (C, N). It was proposed that Cd and Sn mostly originated from agricultural sources due to fertilizer or pesticide inputs, particularly associated with organic matter during the erosion. This association is illustrated by the enrichment of Cd, Sn and Cu in Zio sediments at Z3 and Z1 in October (Figure9-A) after the leaching of soil surface during the small rainy season. The opposite correlation about Pb, Cr, Th, and U with the component 2 reflects that those elements are associated to other sources of pollution. Indeed, contribution of Pb would be due to the accumulation of the old atmospheric pollutions from leaded gasolines and the activities of cleaning and draining of big trucks in the bed of the Zio river especially at Togblekope (Z3).In the Haho basin, component 1 indicates that Cu and Ni are linked to Al and Fe oxides and also to clay-silt minerals. The anti-correlation to fine minerals for TE like Cd, Th and U, which are highly concentrated in the phosphates of exploited mines, confirms the study of[START_REF] Gnandi | l'impact de l'exploitation des phosphates sedimentaires et de Hahotoee-Kpogame sur la pollution chimique des sediments du fleuve Haho et du Lac (Sud Togo)[END_REF] which showed that the Cd concentrations in the Haho sediments increase when the size grading increases. This is one of characteristics of phosphates from mining activities in the basin. Component 2 indicated that Ni, Pb and U were linked to P and organic matter (C, N). The component 3 shows that Pb, Cu and Cr are linked to P.

  According to the hydrological periods (F-low flows of February or O-high flows of October) and to the origine of metal contamination, the PCA of major and trace elements compared to sampling stations for component 1 and 3 (Figure9-A) showed that As, Sn, Co and Zn which are more enriched in sediments of H1 during the period of February, are controlled by hydroclimatic factors. Yet during the low water period (February),[START_REF] Julien | Use of EGNOS in the management of water resources in a lagoon system in West Africa[END_REF] showed the hydrological effect of the lake Togo on the outlets of rivers Zio (Z1) and Haho (H1). TE like As, Sn, Co and Zn may result from the intrusion of the sea water in the lake.Besides, the group of Cd, Th and U in sediments of stations H2 in october (H2-O) and H3 in february (H3-F), both periods in the course of which the grain-size of sand and coarse silt is more important in those stations (50% and 51% of coarse silt and sand for H2-O and H3-F respectively) confirm the results of[START_REF] Gnandi | l'impact de l'exploitation des phosphates sedimentaires et de Hahotoee-Kpogame sur la pollution chimique des sediments du fleuve Haho et du Lac (Sud Togo)[END_REF]. Contrary to the other TE which increase when the clayey fine fraction increases, the Cd contents increase rather when the size of the grain increases. It is one of the characteristics of the cadmium stemming from the old abandoned exploitation areas. The Cd from this area is preferentially bound to apatite mineral.

Figure 9 :

 9 Figure 9 : Loading plots (components 1 and 3) from a PCA of major (C, N, P, Fe, Al), % Clay+Fine Silt (CFS) and TE compared to sampling stations of Zio (A) and Haho (B) stream bed sediments during the period of low flows in February (Z1-F to Z5-F and H1-F to H3-F) and high flows in October (Z1-O to Z5-O and H1-O to H3-O). The variance percentage of each component is mentionned in Table3.

  Comp1 (29.59 %) of the old atmospheric pollutions from car gasoline and also from the activities of cleaning and draining of big trucks in the river bed of the Zio;  Sn, Co and Cd are enriched by fertilizer inputs and are associated to phosphorus. Fertilizers are known to be significantly enriched in Cd associated to phosphates (Avril, 1992; Micó et al., 2006; N'Guessan et al., 2009). Their high concentrations in sediments of the station Z3 in October confirmed the result of soil leaching during rainy seasons in the cultivated areas. With regard to Haho sediments, one can distinguish three groups of TE:  Pb, Cr, Ni, Cu, Th, U are enriched by contributions of atmospheric deposition, domestic waste in the environment and the phosphate exploitation area;  The contents of As, Co, Zn and Sn are influenced by the rise of brackish water of the lake into the rivers under the influence of the sea ;

  Sediment Quality Guidelines (SQGs) for Some TE Sediment quality issues are important focus in the assessment, protection and management of aquatic ecosystems. Then numerous SQGs have been developped during the last decades to assist regulators in dealing with contaminated sediments. The original SQGs which were compared with a reference or with geochemical background, like EF, provided little insight into the potential ecological or ecotoxicological impacts of sediment TE. The new generation of SQGs was developped relying on field sediment chemistry paired with field or laboratory biological effects data. If we compared the TE concentrations in the river bed sediments with different SQGs, particularly for Cr, Ni, Cu, Zn, As, Cd and Pb for which SQGs exist in the literature (see the references in

Table 1 :

 1 Concentrations of major (%) and trace elements (µg.g -1 ) in the bottom sediments of Zio (n=9) and Haho (n=6) rivers and in the creek taken as a reference, in the Lake Togo (n=2), compared with UCC and PAAS(Taylor and MacLennan, 1985); Gnandi's results in 2002 for Haho (n=13) and Lake Togo (n=21) sediments.

		Zio stream sed.	Haho stream sed.	Lake sed.	Creek sed.	UCC PAAS Gnandi, 2002
		Min	Max	Mean	Min	Max	Mean	Mean	Mean	Mean Mean	Mean	Mean
												Lake	Haho
	Major elements (%)
	SiO 2	45.67	70.29	57.72	52.16	64.11	58.23	48.96	59.22 28.80	62.80	-	-
	Al 2 O 3	11.23	21.37	15.55	13.28	16.18	14.66	14.52	13.47	7.96	18.90	8.53 15.96
	Fe 2 O 3	4.79	8.03	6.74	5.77	8.17	7.06	9.15	5.38	4.32	6.50 13.85	7.02
	MnO	0.03	0.25	0.11	0.12	0.24	0.17	0.23	0.20	0.07	0.11	1.30	0.11
	MgO	0.58	1.82	1.10	1.35	1.77	1.59	1.81	0.99	2.20	2.20	0.30	1.26
	CaO	0.56	2.79	1.32	0.95	1.67	1.29	2.49	1.81	3.85	1.30	1.66	1.23
	Na 2 O	0.29	1.72	1.04	0.75	1.16	0.99	1.66	0.79	2.36	1.20	0.83	0.67
	K 2 O	0.59	1.02	0.82	1.12	1.38	1.26	0.95	1.73	2.14	3.70	1.47	0.70
	TiO 2	0.98	2.89	1.53	1.18	1.26	1.23	1.26	1.12	0.40	1.00	1.21	1.41
	P 2 O 5	0.10	0.18	0.14	0.10	0.21	0.16	0.31	0.18	0.08	0.16	0.12	0.20
	Traces elements (µg.g -1 )
	As	1.15	4.23	2.06	1.69	2.64	2.05	3.50	1.60	1.50	-
	Sn	1.97	9.02	4.23	2.49	6.75	3.96	9.35	2.20	2.70	4.00
	Cr	143.70 277.62	180.53 184.30 280.32	228.44	145.22	75.26 35.00 110.00	177	232
	Co	16.28	33.22	23.19	26.44	36.45	31.00	25.98	21.00 10.00	23.00
	Ni	42.73 110.72	78.05 100.20 170.69	126.76	93.51	34.40 20.00	55.00	114	142
	Cu	22.09	62.05	39.55	27.36	40.31	34.09	32.70	35.81 25.00	50.00	42	42
	Zn	49.77 105.20	76.80	62.54	77.64	70.19	79.23	58.97 71.00	85.00	55	49
	Zr	188.8 1285.0	658.2	427.1 1079.0	725.4	659.0	650.6	190	210	126	175
	Cd	0.06	0.73	0.30	0.14	0.87	0.43	0.57	0.14	0.09	-	0,02	0,06
	Pb	13.52	25.36	17.40	16.16	24.38	19.66	19.00	21.28 20.00	20.00	69	56
	Th	8.53	11.61	10.25	12.13	15.90	13.87	10.93	16.65 10.70	14.60
	U	2.07	3.01	2.46	2.53	3.48	3.00	2.94	3.49	2.80	3.10

Table 2 :

 2 Pearson correlation coefficients between the percentages of AC and EF values for all the stations (n=17 values), including Zio (Z1 to Z5), Haho (H1 to H3) et Lake Togo (L3).

	TE	As	Sn	Cr	Co	Ni	Cu	Zn	Cd	Pb
	R 2	0.83	0.78	0.97	0.81	0.92	0.67	0.92	0.85	0.62

Table 3 :

 3 Loadings of experimental variables on significant principal components.

			ZIO			HAHO
	Variables		Component		Component
		1	2	3	1	2	3
	As	0.86 0.13 -0.23 -0.35 -0.13 0.74
	Sn	0.46 -0.51 0.62 0.41 0.29 0.58
	Cr	-0.24 0.74 0.37 -0.42	0.4 -0.68
	Co	0.19 0.35 0.88 -0.31 0.32 0.84
	Ni	-0.48 0.01 0.36 -0.78 0.55 -0.13
	Cu	0.76 -0.17 -0.55 -0.77 -0.33 -0.47
	Zn	0.95 0.12 -0.24 0.03 0.44 0.76
	Cd	0.2 0.36 0.66 0.87 0.29 0.11
	Pb	0.84 0.51 0.01 0.12 0.81 -0.48
	Th	0.51 0.66 0.43 0.76 0.48 -0.22
	U	0.44 0.79 0.36 0.71 0.58 -0.25
	Al	0.83 -0.39 -0.11 -0.71 0.47 -0.36
	Fe	0.76 -0.16 0.16 -0.54 0.44 0.32
	P	0.06 -0.66 0.51 -0.05 0.46 -0.45
	C	0.09 -0.76 0.56 -0.34 0.83 0.29
	N	0.21 -0.70 0.58 0.07 0.81 0.12
	CFS	0.83 -0.28 -0.11 -0.72 0.04 0.26
	Eigen value	5.97 4.22 3.55 5.03 4.24 3.81
	% total variance	35.1 24.8 20.9 29.59 24.94 22.41
	Cumulative % variance	35.1 59.9 80.8 29.59 54.53 76.94
	Bold values indicate strong and moderate loadings. (CFS =% clay + fine silt)

Table 4 )

 4 , one can see that, except Cr and Ni, our total TE concentrations are lower (Cu, Zn, As, Cd, Pb) than most of the SQG values.

Table 4 :

 4 TE average concentrations in the sediments (fractions <63μm) of the Zio and Haho rivers and of Lake Togo, compared to SQGs concentrations.

	TE (µg.g -1 )	Zio	Sediments (<63μm) Haho Lake Togo	SQGs for TE (µg.g -1 ) TEL ERL LEL MEL PEL ERM	SEL	TET CB PEC
	Cr	180.53 228.44 145.22 37.3	80	26	55	90	145	110	100	111
	Ni	78.05 126.76 93.51	18	30	16	35	36	50	75	61	48.6
	Cu	39.55 34.09	32.70	35.7	70	16	28	197	390	110	86	149
	Zn	76.80 70.19	79.23	123	120	120	150	315	270	820	540	459
	As	2.06	2.05	3.50	5.9	33	6	7	17	85	33	17	33
	Cd	0.30	0.43	0.57	0.6	5	0.6	0.9	3.53	9	10	3	4.98
	Pb	17.40 19.66	19.00	35	35	31	42	91.3	110	250	170	128

Acknowledgment

This work is part of the cotutelle PhD (Toulouse INP-University of Lome) research of A. Avumadi on the river transports of dissolved and particulate matters into the lake Togo (South Togo). The French Embassy in Lome which attributed to A. AVUMADI a financial support via a Campus France fellowship for her PhD stays in France at EcoLab is gratefully acknowledged. We greatly acknowledge also the technical staff of EcoLab and of the different analytical platforms. The thanks also go to the MAGNIFIC European project to whom the financing of the missions of ground were realized and to EcoLab which financially supported all the chemical analyses.


Romy Ratolojanahary
email: romy-alinoro.ratolojanahary@enit.fr

Raymond Houé Ngouna

Kamal Medjaher

Jean Junca-Bourié

Fabien Dauriac

Mathieu Sebilo

Model selection to improve multiple imputation for handling high rate missingness in a water quality dataset

Keywords:

a b s t r a c t

In the current era of "information everywhere", extracting knowledge from a great amount of data is increasingly acknowledged as a promising channel for providing relevant insights to decision makers. One key issue encountered may be the poor quality of the raw data, particularly due to the high missingness, that may affect the quality and the relevance of the results' interpretation. Automating the exploration of the underlying data with powerful methods, allowing to handle missingness and then perform a learning process to discover relevant knowledge, can then be considered as a successful strategy for systems' monitoring. Within the context of water quality analysis, the aim of the present study is to propose a robust method for selecting the best algorithm to combine with MICE (Multivariate Imputations by Chained Equations) in order to handle multiple relationships between a high amount of features of interest (more than 200) concerned with a high rate of missingness (more than 80%). The main contribution is to improve MICE, taking advantage of the ability of Machine Learning algorithms to address complex relationships among a large number of parameters. The competing methods that are implemented are Random Forest (RF), Boosted Regression Trees (BRT), K-Nearest Neighbors (KNN) and Support Vector Regression (SVR). The obtained results show that the hybridization of MICE with SVR, KNN, RF and BRT performs better than the original MICE taken alone. Furthermore, MICE-SVR gives a good trade-off in terms of performance and computing time.

Introduction

The proliferation of sensing devices has increased the ability of organizations to acquire various and great amount of data, allowing them to implement real-time monitoring of their systems. This is generally based on the analyses of complex relationships between several factors of interest, such as in water quality analysis. Online monitoring has indeed offered the development of decision systems that are able to accelerate decision-making and anticipate actions to prevent undesired events or to eradicate critical issues. To achieve such a goal, it is required to pre-process the raw data, especially when some values are missing on a certain level.

Missing data is a recurring phenomenon in real-world applications [START_REF] Sterne | Multiple imputation for missing data in epidemiological and clinical research: Potential and pitfalls[END_REF][START_REF] Yang | Real-time condition monitoring and fault detection of components based on machine-learning reconstruction model[END_REF]. It may occur due to sensor failures, bad or non-existing strategy for data acquisition, budget issues, lack of response from a participant in the case of survey or various other reasons. If the complete data are representative of the studied phenomenon, this missing information is negligible, otherwise the results may be incorrect and may lead to wrong interpretations. For example, anomalies could go undetected if they happen during a non-monitored period of time.

There are two ways of dealing with missing data: deletion or imputation [START_REF] Buhi | Out of sight, not out of mind: Strategies for handling missing data[END_REF]. Deletion means discarding the observations or the variables with missing data, which is called completecase analysis, while imputation consists in reconstructing the missing values. Because of its simplicity, deletion is usually the default method used in practice. However, there are many cases in various fields in which this method showed some limitations. Indeed, it decreases the sample size and may lead to a loss of substantial information. In [START_REF] Clark | Developing a prognostic model in the presence of missing data[END_REF] for instance, the number of observations dropped from 1189 to 518 (43% of the original data) in an ovarian cancer dataset, which led to biased interpretation.

Another deletion method is pairwise deletion through which only non-missing values are used for analyses, for instance in correlations scores calculation where the method fails when the two correlated variables are not filled at the same time. Instead of discarding an observation or a variable concerned with missing value, it is preferable to estimate accurately those missing values in order to provide relevant interpretations.

Quoting White and co-authors, "awareness has grown of the need to go beyond complete-analysis" and some major improvements of the simplistic methods have been proposed in the literature, since Rubin's innovative proposal for approaching missingness [START_REF] White | Multiple imputation using chained equations: Issues and guidance for practice[END_REF]. Among others, Rubin, who is the author of Multiple Imputation (MI), defined a conceptual framework for characterizing missing data that allows to distinguish various types and to determine when missing data can be ignored [START_REF] Little | Multiple imputation for nonresponse in surveys[END_REF][START_REF] Rubin | Inference and missing data[END_REF]. The major insight of the proposed imputation method is that it addresses uncertainty and complexity of the data structure, allowing to go beyond deleting or discarding data.

Following Rubin, van Buuren introduced the Multiple Imputations by Chained Equations (MICE), a MI technique that requires fewer assumptions on missingness and also handles relationships between variables ( van Buuren & Groothuis-Oudshoorn, 2011 ). However, original MICE considers only linear relationships and has been successfully applied to dataset with at most 70% of missingness. It may therefore fail in other cases such as in water quality data as considered in the present study, which are characterized by a high rate of missingness and a great amount of factors of interest that are not necessarily linearly related. This suggests the need of an alternative method to improve the imputation mechanism in order to provide relevant interpretation of the results, which is the purpose of this work.

The rest of the paper is organized as follows: the main imputation methods available in the literature are reviewed in Section 2 , followed by the presentation of a method to improve MICE for multiple data imputation in Section 3 . An application of the proposed method on experimental dataset, along with associated results, are described in Section 4 while the last section contains the conclusion and perspectives of the present work.

Related work

In order to choose an appropriate method for handling missing data, the underlying cause of the missingness has to be investigated. Indeed, as mentionned in [START_REF] Buhi | Out of sight, not out of mind: Strategies for handling missing data[END_REF] , each method only works under certain assumptions, namely complete randomness, conditional randomness or systematic reasons.

Missingness patterns

The conceptual framework allowing to take into account certain assumptions, as noted above, has been defined by [START_REF] Rubin | Inference and missing data[END_REF] . There are three types of missing data, depending on the missing mechanism : (1) Missing completely at Random (MCAR), (2) Missing at Random (MAR) and (3) Missing Not at Random (MNAR).

Let R be the locations of the missing data in a dataset X = (X obs , X miss ) , and ψ the parameters of the missing data model;

where X obs and X miss are respectively the observed and the missing values. MCAR, MAR and MNAR patterns are formally defined as follows ( van Buuren, 2018 ):

• Data are MCAR if the probability of missingness is independent of both the observed variables and the variables with missing values. This is the case, for example, when people forget to answer a question in a survey. Formally,

P (R = 0 | X obs , X miss , ψ ) = P (R = 0 | ψ ) (1)
• Data are MAR if the probability of missingness is due entirely to the observed variables and is independent of the unseen data.

In other words, the missingness is a function of some other observed variables in the dataset (for example, people of one sex are less likely to disclose their weight):

P (R = 0 | X obs , X miss , ψ ) = P (R = 0 | X obs , ψ ) (2)
Therefore, MAR data are a good candidate for data imputation based on observed variables [START_REF] Buhi | Out of sight, not out of mind: Strategies for handling missing data[END_REF].

• Data are MNAR if the missing value is related to the actual values (for example, people who weigh more are most likely to not disclose their weight):

P (R = 0 | X obs , X miss , ψ ) (3)
depends on all three elements.

When data are MNAR, the missingness process is called nonignorable , meaning that the cause of the missingness must be included in the model, whereas MAR and MCAR data missingness processes are called ignorable . Following the assumptions behind these three patterns, several methods have been provided in the literature for solving appropriately the missingness.

Single imputation methods

Methods that compute one single value per missing data are referred as single imputation methods. The most common single imputation methods are mean, median or mode imputation, consisting in replacing the missing value with the mean, median or mode of the associated variable [START_REF] Buhi | Out of sight, not out of mind: Strategies for handling missing data[END_REF]. In this case, the missing value is easy to compute, but the method ignores the correlation among the variables and underestimates the standard deviation. If the variable containing missing values is categorical, a simple option is to create a new category for the missing values. This method is suitable for MNAR data, i.e. when the missingness is correlated to the values of the missing data. When a variable of the incomplete dataset is a periodic time series, a more elaborated single imputation technique is to apply a linear interpolation or an Autoregressive Integrated Moving Average (ARIMA) model to fill in the missing values [START_REF] Shao | Evaluation of missing value imputation methods for wireless soil datasets[END_REF]. Although those two techniques are simple, the first one is not efficient when the missing gap is large, and the second one requires a periodic time series. Another technique involves predicting the values from the observed variables. For example, K-nearest neighbors (KNN) replaces the missing value with a linear combination of the K nearest non-missing observations [START_REF] Jordanov | Classifiers accuracy improvement based on missing data imputation[END_REF][START_REF] Tutz | Improved methods for the imputation of missing data by nearest neighbor methods[END_REF]. To use this algorithm, it is necessary to choose the optimal K and define a distance measurement between two observations. A local similarity imputation based on Fast Clustering was proposed in [START_REF] Zhao | Local similarity imputation based on fast clustering for incomplete data in cyber-physical systems[END_REF] . The authors partition the incomplete data with a fast clustering method (Stacked Autoencoder-based), then fill the missing data within each cluster using a KNN algorithm. The obtained results showed that the proposed method outperformed other local similarity-based methods. Shao and co-authors applied two Single Layer Feed Forward Neural Networks (Extreme Learning Machine and Radial Basis Function Network) on a periodic soil moisture time series [START_REF] Shao | Evaluation of missing value imputation methods for wireless soil datasets[END_REF]. This method performed better predictions than a linear interpolation and ARIMA in infilling missing segments. However, it requires parameter tuning in order to be performing. A brief summary of these implementations of single imputation methods is presented in Table 1 that provides the main drawbacks and advantages. A well-known limitation that they have in common is that once a missing value is imputed, it is treated as a non-missing value.

Multiple imputation methods

In order to solve the limitations of single imputation, some authors have proposed to take into account the uncertainty of the imputed values [START_REF] Little | Multiple imputation for nonresponse in surveys[END_REF][START_REF] Neter | The effect of mismatching on the measurement of response errors[END_REF]. In that purpose, Rubin has developed the Multiple Imputation (MI) method, which combines several single imputations [START_REF] Little | Multiple imputation for nonresponse in surveys[END_REF], as described in the following.

Principles of multiple imputation

The principles of MI are illustrated in Fig. 1 , based on the following main steps: (1) imputation phase where m datasets are produced by drawing them from a distribution, which can be different for each variable ( van Buuren, 2018 ), (2) analysis phase in which the m datasets are analyzed, and (3) pooling phase that combines the m datasets to produce a final result, for example by calculating the mean of the imputed values for each missing value. The m datasets can be generated in parallel using parametric statistical theory and assuming a joint model for all the variables [START_REF] Van Buuren | Multiple imputation of discrete and continuous data by fully conditional specification[END_REF][START_REF] Rubin | Efficiently creating multiple imputations for incomplete multivariate normal data[END_REF], such as in Multiple imputAtions of incoMplEte muLtIvariate dAta (AMELIA), which uses expectation-maximization with a bootstrapping algorithm [START_REF] Honaker | Ameliaii: A program for missing data[END_REF]. Such approach lacks flexibility and may lead to bias [START_REF] Van Buuren | Multiple imputation of discrete and continuous data by fully conditional specification[END_REF]. The other alternative is to generate the m datasets until a stop criterion is met: in [START_REF] Hong | Mining rules from an incomplete dataset with a high missing rate[END_REF] for instance, the authors iteratively used association rules to successfully estimate the missing values. Although the studied dataset had a high missing rate, it was relatively small (there were only three variables). Some other examples of the sequential methods are Sequential Imputation for Missing Value (IMPSEQ) [START_REF] Betrie | On the issue of incomplete and missing water-quality data in mine site databases: Comparing three imputation methods[END_REF], a covariance-based imputation method and MICE, a series of linear regressions that consider a different distribution for each variable [START_REF] Van Buuren | Multiple imputation of discrete and continuous data by fully conditional specification[END_REF][START_REF] Raghunathan | A multivariate technique for multiply imputing missing values using a sequence of regression models[END_REF]. Betrie and co-authors have found that the two sequential methods outperform AMELIA [START_REF] Betrie | On the issue of incomplete and missing water-quality data in mine site databases: Comparing three imputation methods[END_REF]. In [START_REF] Stekhoven | MissForest-non-parametric missing value imputation for mixed-type data[END_REF] , the authors introduced a MI method called MissForest, which is similar to MICE, except that it uses Random Forest instead of Linear Regression in the imputation step. As MissForest yielded a better performance than MICE, that result is encouraging towards tweaking the MICE algorithm, which is the object of the present work. A brief summary of ,---------------------- r--------------------- the advantages and drawbacks of the methods presented above is given in Table 2 , while the original MICE principles are described in the following.

Main principles of MICE

The main steps of MICE are summarized in Fig. 2 and detailed in Algorithm 1 . MICE algorithm implementation was based on a method described in [START_REF] Azur | Multiple imputation by chained equations: What is it and how does it work[END_REF] . It assumes that missing data are of MAR type. The first step is to initialize the missing values to the mean of each column. Then the missing values of the first variable are reset to "missing". After that, a regression model is fitted on the subset of the dataset where the value of this variable is present. Finally, the obtained model is used to fill in the value and update the dataset. This process is repeated for each variable until all the missing data are estimated. The whole process, first step excluded, is reiterated n _ cycles times until the estimated data converge. In the literature, it is advised to increase the number of cycles in function of the size of the dataset and the missingness ratio [START_REF] Graham | How many imputations are really needed? some practical clarifications of multiple imputation theory[END_REF]. Although MICE has been proved efficient in the literature, the trade-off between computational cost and performance becomes imbalanced when dealing with large datasets and/or datasets with a high missingness rate. Indeed, the number of imputed datasets has to be increased, and so does the computational time. Furthermore, a high missingness rate implies high uncertainty. Another key issue is that this form of the algorithm is based on linear regression, which may not reflect the actual relationships between the variables of the current study. To address these issues, an improved version of MICE is proposed and described in the following.

The proposed method to improve MICE

As noted above, the dataset concerned with water quality considered in this study has a very high missing rate (82%). Besides, there is a great amount of variables (more than 200) in which each is concerned with at least one missing value. The methods mentioned above, including the most performing, have been applied in a less constrained context and therefore, can fail to provide good results in the specific case of the dataset considered in this paper. It is then proposed to take advantage of the ability of Machine Learning algorithms for handling such issues in order to improve MICE. The two main ideas are: (1) define a set of competing methods, and then (2) replace the Linear Regression in the original MICE by each of these methods in order to select the most performing that fits the context of the present study.

The competing methods have been chosen among the most performing supervised learning algorithms in the literature, namely Random Forest(RF), Boosted Regression Trees (BRT), and Support Vector Regression (SVR). Besides, K-Nearest Neighbors (KNN), which is commonly used to solve missingness, has also been selected.

The main steps of the proposed method are illustrated in Fig. 3 .

1. The first phase of the original MICE is initialized (step 1). 2. A competing method is then chosen, followed by a mechanism for optimally setting its hyperparameters (step 2).

Next, phase (II) of the original MICE is modified by replacing

Linear Regression with the chosen method, and then launched in a loop that goes a number of times corresponding to the predefined number of cycles (step 3). -

+~: -+ y v, • -e- • • v, -•- (i) V21 -•- • v, ... v, v, ... m 2 ... • m2 .. . -•--•• •• •-V, ~(V2, ... ) (i) V21 • ... m 2 ... linear • m 2 .. . regression • ... • • .. . v, ... v, v, ... -e--•••- • (i) v,2
... Algorithm 1 MICE. Input:

• ... V2 ~(V1 , ... ) (i) V21 • ... -e--•-linear • (i) ... regression V32 • ... • • .. . ... I ... I ~---------------------------------------- ---------------------------------------------- (
• X incomplete data matrix of size n _ obs × n _ f eatures • n _ cycles number of cycles
Output:

• Completed data matrix of size n _ obsn _ f eatures X f ull := mean_impute( X) for i := 1 to n _ cycles do for j := 1 to n _ f eatures do y j := X j /* the jth column */

X ( j) := X \ X j m ⊂ { 1 , n } = { i | X j ! =
NaN} /* m denotes the indices where X j is not missing */ regressor := linear_regressor() regressor.fit( X m ( j) , y m j ) /* the model is fitted on the subset of the dataset where X j is not missing */ y ¬ m ( j) := regressor.predict( X ¬ m ( j) ) /* ¬ m denotes the indices where X j is missing */ end for end for return X f ull 4. After convergence, performance indicators for the current method are computed (step 4). 5. When all the competing methods have been processed according to the four previous steps, a selection mechanism takes place by comparing their performance indicators (step 5). 6. Finally, the best method is applied to solve the missingness (step 6).

Due to the high missingness rate, the optimal choice of the hyperparameters (as considered in step 2) is based on a modified version of the studied dataset constructed according to the following procedure:

• For each variable, a triangular distribution is simulated with different parameters (min, mode, max). If a variable always has the same value, then that value is replicated in each observation. The triangular distribution has been used because it pro-vides a simple representation of the real distribution of the dataset and allows more flexibility by taking into account the uncertainty of the values. • The data are scaled so that the units of the variables do not play any role. • The observations are shuffled and the missingness distribution of the real dataset is reproduced in order to mimic the real problem as accurately as possible.

Two main performance indicators have been used for the comparison (as realized in step 5), namely processing time and Mean Squared Error (MSE).

Theoretical background of the competing methods

Random Forest

Random Forest is an ensemble method based on fully grown regression trees. The objective is to build several weak learners (the regression trees) in parallel in order to produce a strong regressor. The main steps are as follows:

1. The observations are sampled with replacement (bootstrap aggregating). 2. A set of variables is selected randomly. 3. The tree is built upon the observations from step (1) and the variables from step (2). 4. The final prediction is made by averaging over the predictions of all decision trees.

In this algorithm, one of the most relevant hyperparameters to set in order to make the model perform well is the number of trees.

Boosted Regression Trees

Similarly to the Random Forest algorithm, BRT is an ensemble method based on regression trees. Gradient boosting is used to train the weak learners (shallow regression trees) sequentially. In this algorithm, a higher focus is set on observations that have higher errors on the previous tree and a gradient descent is used to minimize the loss function (least squared errors) at each step.

Let y i be the target value and f ( x i ) its predictor. The objective function is given as in Eq. ( 4) : where l(y i , f

L (y, f ) = n i =1 l(y i , f (x i )) (4)
(x i )) := (y i -f (x i )) 2 .
The algoritm goes as follows: f 0 is the trivial tree, it returns the mean value of Y .

For k := 1 to m :

• Calculate the negative gradientl(y i , f (x i )) , which corresponds to the residual for i = 1 to n . • Fit a regression tree h k for the residuals.

• Create a model f k = f k -1 + νγ k h k , where γ is the step magnitude, found by searching arg min γ n i =1 l(y i , ( f k -1 (x i )) + νγ h k (x i ) , and ν is the learning rate.

Return f m . For this algorithm, the number of trees m , as well as the learning rate ν, are the hyperparameters that need to be set by the user in order for the method to perform well.

K-Nearest Neighbors

Let X and y be the training data, X * a new observation and y * the associated value to predict. The KNN algorithm goes through the following steps:

1. Calculate the distance between X * and each of the observations of the training set; 2. Take the y values of the K closest observations y i 1 , y i 2 , . . . , y ik ; 3. Assign to y * a linear combination of these values (usually the mean).

Three hyperparameters have to be defined properly so that the algorithm performs well: the distance, the number of neighbors K and the type of aggregation of the neighbors values.

Support Vector Regression

Let X, y be a training data. The objective of SVR is to find a function f such that the deviation of f (.) from the real values y is at most ε [START_REF] Smola | A tutorial on support vector regression[END_REF]. If the problem has no solution, slack variables ξ i , ξ i * are introduced to tolerate part of the error. First, let's consider the case where f is linear, i.e. f (x ) = w.x + b. f is then the solution of the following optimization problem ( Eq. ( 5) ):

Minimize 1 2

|| w || 2 + C n i =1 (ξ i + ξ * i ) s.t. y i -< w, x i > -b ≤ ε + ξ i < w, x i > + b -y i ≤ ε + ξ * i ξ i , ξ * i ≥ 0 (5)
where C > 0 is the trade-off between the flatness of f and the amount of tolerated deviations larger than ε, and < , > is a scalar product. By using the dual representation of the problem based on Lagrange multipliers, we finally get:

f (x ) = sum n i =1 (α i + α * i ) < x i , x > + b
where α i are the Lagrangian multipliers. If the adequate f is not linear, we can map the data into a high dimensional space where the function f becomes linear ( Fig. 4 ). Instead of searching for the expression of φ, a function k called a kernel function, which satisfies k (x, x ) = < φ(x ) , φ(x ) > is used. The existence of such a function is proved by the Mercer's theorem. ε, C and the kernel functions are the Support Vector Regression (SVR) hyperparameters that need to be selected properly for the performance of the algorithm.

Application and results

The context of the study

The incomplete dataset used in this paper is taken from a water sample analysis made at Oursbelille, in the Adour plain, South-West of France, from 1991 to 2017. The operational principle of this drinking water collection point is described in Fig. 5 . First, the water is pumped, its nitrate rate is measured and is conveyed to large aerial tanks in order to be treated by active charcoal. Then, the treated water is stored in a water tank. In a third step, some sensing devices are then used to monitor some quality indicators, such as the pH. In a fourth step, on demand, the stored water is chlorinated, before being dragged to another underground well, few kilometers away from the pumping well. From this second storage tank, water is distributed to the citizens of the Adour region. The region benefits of an oceanic climate, with a rainy winter and an average temperature ranging from 4 to 19 • C.

The acquired data contain 148 observations of 411 water quality indicators, with an overall missingness of 82%. Fig. 6 a is an overview of the dataset, where some of the measured water quality indicators are displayed, while Fig. 6 b summarizes the missingness distribution per variable in the dataset.

Only the variables that are measured at least 5 times are considered, which reduces the dataset to 257 variables (52% of the 411 variables). It is noted that the removed variables do not restrict the analysis since they are not among the common hyperparameters for water quality assessment found in the literature.

Settings and assumptions of the implementation

Based on the presentation of the three missingness patterns, and the nature of the studied dataset (as described in the previous subsection), we can assume that our study is within the MAR pattern.

Moreover, the proposed method depends on several factors: (a) the number of cycles to perform the imputations, (b) the num- The implementation of the proposed method was performed by using Python programming language, on a computer with the following main features:

• Operating System: Windows 10;

• RAM: Intel(R) Core(TM) i5-7200U CPU @ 2.50GHz 2.70 GHz;

• Processor: 8.00 Go.

The corresponding results are described and discussed in the following.

Implementation of the proposed method

The main steps of the proposed method have been implemented according to the following explanations.

• Step 1. The first phase of the original MICE, that is mean imputation, is launched (initialization step). • Step 2. The next step concerns the hyperparameter tuning of the Machine Learning algorithms. There is no analytical solution that allows to find the optimal values. Therefore, to do so, a cross-validation is performed using the modified dataset, and a mean squared error (MSE) is measured. Step 5. The method that performed best in terms of MSE, and with a reasonable computing time, is then selected. • Step 6. Finally, the winning method is used to solve the missingness. The main results of this implementation are presented and discussed in the next subsection.

Results and discussion

In the following, only steps 2, 4 and 5, which contain the main results of the implementation, are presented.

• Step 2: Hyperparameter tuning.

Random Forest . In this algorithm, the performance increases proportionally to the number of trees. However, it becomes rapidly time consuming. The objective is to find the smallest value for which the performance is good enough. Although it is not the optimal value, the number of trees is set to 15 in order to reduce the K-Nearest Neighbors . For this algorithm, the hyperparameters to tune are the number of neighbors K , the distance d and the linear combination method of the neighbors value y * . In this study, the euclidean distance is chosen, K = 4 , and y * is the weighted mean of the KNN. Their choice is illustrated in Fig. 8 . Indeed, MSE score is lower for these values.

Support Vector Regression . For this algorithm, ε, C , the kernel function and the parameter γ associated to the kernel function need to be tuned. In Fig. 9 , it is seen that the MSE is generally lowest for the polynomial kernel, and for ε = 0 . 1 . The lowest MSE score is obtained with ε = 0 . 01 , C = 1 , kernel = poly and the associated γ = 0 . 01 . . rt,f 0.5 MICE-SVR performed best in both criteria, it is therefore the best performing competing method in this particular case.

The proposed methodology can handle datasets with a high missingness rate, and is also suitable for high-dimensional data. It is a flexible method that can take into account complex nonlinear relationships between variables (if the competing methods are non-linear). It makes it possible to automate the selection of the best method to solve missingness, which reduces the amount of work of the data analyst, who can focus on tasks with higher added value, aiming at extracting knowledge. However, a few limitations are worth noting, particularly concerning the number of cycles preset to 10, and the relatively low number of potential hyperparameters values (that does not allow a rigorous sensitivity analysis of these hyperparameters). Furthermore, these parameters are tuned using an artificial dataset which has been constructed by modifying the real one. All these limitations are mainly due to algorithmic complexity, which constitutes by itself a challenge as well as a great scientific issue.

Conclusion and perspectives

It is widely acknowledged that data-driven methods provide powerful algorithms to analyze any issue that is of interest for decision-makers. However, performing such analyses with incomplete data may not be helpful to take reliable decisions. In this paper, a methodology for selecting the best algorithms to address the issue of data imputation, in the context of water quality assessment, has been proposed. A benchmark of four of the most powerful and commonly used ML algorithms has been performed for that purpose (Random Forest, Booted Regression Trees, K-Nearest Neighbors, Support Vector Regression). The results showed that MICE-SVR is the best in that it converges faster than the three others, and provides the best performance (notably in terms of prediction average error). It can then be applied to high missingness dataset, including data for water quality assessment that are often incomplete, as in the case of Adour (south-west of France) considered in the present study.

Based on the weaknesses of the proposed method, as mentioned in the discussion of the results, the following improvements are planned for further studies: (1) deeper automate the mechanism of the model selection by setting fuzzy rules in an inference engine that will aggregate all the performance indicators in a single indicator; (2) improve, for each competing method, the optimal choice of the hyperparameters using evolutionary algorithms in order to speed up the computing time and increase the number of values for each hyperparameter; (3) automate the choice of the number of cycles needed for the convergence of the imputations by taking into account the size of the data and its missingness rate; (4) introduce the temporal dimension within the imputation process.

Fig. 1 .

 1 Fig. 1. Overview of the multiple imputation method.

Fig. 2 .

 2 Fig. 2. Overview of the MICE algorithm.

Fig. 3 .

 3 Fig. 3. The proposed method for model selection to improve MICE.

Fig. 4 .

 4 Fig. 4. Mapping to the feature space in SVR.

Fig. 5 .

 5 Fig. 5. Operational principle of the drinking water well of Oursbelille.

  :' . ~• . . . :-. •~•-.' "' <: .... ~• • ~. ,-., .... l}:I~\}f. : : ~I:' .-~"". . . . 1. __ .J. __ _L_~*+~~;;;;;;,~ \. -~ : .:• • ~••:._.. ' 1"-.:, .:• /(;!?~t/\' : , ' .

  . . : . .. .,, ~ • :, • • .:,--~•• . .. active charcoa Overview of the dataset. (b) Number of missing values per variable.

Fig. 6 .

 6 Fig. 6. Description of the dataset.

Fig. 7 .

 7 Fig. 7. Variation of MSE to choose the hyperparameters in BRT.

  Choice of K and the linear combination. (b) Choice of K and the distance.

Fig. 8 .

 8 Fig. 8. Variation of MSE to choose the hyperparameters in KNN.

  (a) Choice of ε and the kernel function. (b) Choice of C and ε.

Fig. 9 .

 9 Fig. 9. Variation of MSE to choose the hyperparameters in SVR.

Fig. 7

 7 Fig.7represents MSE in function of the learning rate ν, where the labels represent the number of trees. According to these results, the optimal hyperparameters for this study are ν = 0 . 01 and m = 150 . For computational time sake, hyperparameters with a slightly higher mean squared error (only a difference of 0.001) are chosen: ν = 0 . 1 and m = 30 .

Table 1

 1 Advantages and Drawbacks of the reported single imputation methods.

	Method	Advantages	Drawbacks
	Mean	Easy to implement	-Underestimates standard deviation
			-Ignores relationships between variables
	Add a category	Easy to implement	Only works with categorical and MNAR data
	Linear Interpolation	Takes time into account	Does not work when the missing gap is large
	ARIMA	Takes time into account	Requires a periodic time series
	Linear Regression	Takes into account relationships between variables	-Underestimates the variance
			-Ignores non linear relationships between variables
	Stochastic linear regression	Takes into account relationships between variables	Ignores non linear relationships between variables
	KNN	Takes into account relationships between variables	Requires parameter tuning
	ANN	Takes into account the time factor	Requires parameter tuning

Table 2

 2 Advantages and Drawbacks of the reported MI methods.

	Method	Advantages	Drawbacks

AMELIA Can be applied to categorical, ordinal or continuous data Assumes a joint model for all the variables MI using decision rules Works well when the missing-value rate is high Not adapted to data with a large number of variables IMPSEQ Time complexity -Lack of robustness toward outliers -Does not take into account nonlinear relationships between variables MICE Flexibility -Does not take into account non-linear relationships between variables -Theoretical justification needed MissForest -Adapted to high dimensional datasets Computation time issue -Takes into account linear relationships between variables

  The performance indicators, namely MSE and processing time, are computed for each algorithm.

	The optimal hyper-
	parameters are therefore those that have the lowest MSE. Note
	that only a limited number of candidate values have been taken
	into account because adding more would drastically affect the
	algorithmic complexity.
	The competing methods are MICE, MICE combined with RF
	(MICE-RF), MICE combined with BRT (MICE-BRT), KNN (MICE-
	KNN) and MICE combined with SVR (MICE-SVR).
	The candidate values for the hyperparameters of the four Ma-
	chine Learning algorithms (KNN, RF, BRT, SVR) are detailed in
	Table 3 . For KNN, let us notice that since the studied dataset
	contains variables with only five non missing values, the num-
	ber of neighbors is at most 4.
	• Step 3. Phase (II) of the original MICE is modified by replacing
	Linear Regression with one of the competing algorithms, each
	with its optimal hyperparameters (as obtained in step 2).

• Step 4.

Table 3

 3 Candidate values of the hyperparameters for each Machine Learning method.

	Algorithm	Hyperparameter	Candidate values
	RF	n_trees	{10, 15, 20, 50, 100}
	BRT	m	{30, 50, 100, 150}
		ν	{0.01, 0.1, 0.5}
	KNN	K	{2, 3, 4}
		d	{euclidean, manhattan}
		y *	{uniform, weighted}
	SVR	ε	{0.01, 0.1}
		C	{0.01, 0.1, 1, 10, 100}
		kernel	{rbf, poly, sigmoid}
		γ	{1e-3, 0.01, 0.1, 1}

Table 4

 4 Performance indicator (MSE) of the main RF hyperparameter.Boosted Regression Trees. Similarly to the previous algorithm, the best trade-off between computing time and performance is sought. It is noted that the number of trees is higher, because shallow trees are built in BRT instead of fully grown ones in RF.

	n_trees	MSE
	10	0.5159
	15	0.4943
	20	0.4850
	50	0.4691
	100	0.4653
	computation time. Furthermore, the error does not decrease a lot
	between 15 and 100 estimators (see Table 4 ).

Table 5

 5 Performance indicator scores.

		MICE	MICE-SVR	MICE-4NN	MICE-RF	MICE-BRT
	Processing time	6.87	5.29	8.25	65.18	32.59
	MSE	1.09e24	0.44	0.58	0.55	0.54

4: Computing the performance indicators

	The results summarized in Table 5 show that MICE-SVR is the
	most performing method regarding both processing time (5.29
	seconds) and MSE (0.44).
	The processing time was significantly high while combining
	MICE with RF and BRT. Indeed, all three methods, MICE, RF, and
	BRT are already computationally expensive by themselves. With
	a number of estimators set to 15 for Random Forest, a number
	of cycles set to 10 for MICE and 251 variables to fill, MICE-RF
	computes 15 × 10 × 251 = 37651 fully grown regression trees.
	Similarly, MICE-BRT computes 43500 shallow regression trees.
	MICE performed the worst because in terms of MSE in the cur-
	rent implementation of the algorithm. Indeed, all the variables
	were used as predictors in the regression, whereas an interme-
	diate variable selection step would have been appropriate. It
	also proves that the relationship between the variables are not
	linear.

•

Step MICE-KNN is a little less performing than the other combinations of MICE with Machine Learning algorithms. This is due to the fact that the closest resembling observations are logically those that are closer in time. However, these values are not

5: Selection of the most performing method.

  •systematically filled and the closest neighbors are only searched among non-missing observations for a given variable.

					• poly . . sigmoid	• •					•
	0.4					0.4
	0.0	0.2	0.4	0.6	0.8	LO	0.0	0.2	0.4	0.6	0.8	LO
			Eps						Eps

• Step

raymond.houe-ngouna@enit.fr (R. Houé Ngouna), kamal.medjaher@enit.fr (K. Medjaher), jean.junca-bourie@eau-adour-garonne.fr (J. Junca-Bourié), fdauriac@hautespyrenees.chambagri.fr (F. Dauriac), mathieu.sebilo@upmc.fr (M. Sebilo).

Conflict of interest

There is no conflict of interest.

Credit authorship contribution statement

Romy Ratolojanahary: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing -original draft.

Raymond Houé Ngouna: Conceptualization, Methodology, Investigation, Writing -original draft, Writing -review & editing, Supervision. Kamal Medjaher: Conceptualization, Methodology, Investigation, Writing -original draft, Writing -review & editing, Supervision, Funding acquisition. Jean Junca-Bourié: Investigation, Resources, Supervision, Funding acquisition. Fabien Dauriac: Investigation, Resources, Funding acquisition. Mathieu Sebilo: Investigation, Writing -review & editing, Supervision.