Luz Boyero
email: luz.boyero@ebd.csic.es

Richard G Pearson

David Dudgeon

Verónica Ferreira

Manuel A S Graça

Mark O Gessner

Andrew J Boulton

Eric Chauvet

Catherine M Yule

Ricardo J Albariño

Mark O And Gessner

Andrew J And Chauvet

Ricardo J And Ramírez

Alonso Helson

Muthukumarasamy Marcos Arunachalam

Julián Figueroa

Ricardo Mathooko

Jude M Gonçalves

José F Moretti

Ana Marcela

Judy N Davies

Andrea And Encalada

Lamothe

Sylvain

Alonso Ramírez

Julie E Helson

Marcos Callisto

Muthukumarasamy Arunachalam

Julián Chará

Ricardo Figueroa

Jude M Mathooko

José F Gonçalves

Marcelos M Oretti

Ana Marcela Chará-Serna

Andrea Encalada

Sylvain Lamothe

Leonardo M Buria

José Castela

Aydeé Cornejo

Aggie O Y Li

Charles M'erimba

Verónica Díaz Villanueva

María Del

Carmen Zúñiga

Christopher M Swan

Leon A Barmuta

Global patterns of distribution in stream detritivores: implications for biodiversity loss in changing climates

Keywords: Detritus, diversity, guild, latitudinal gradient, leaf litter, shredders, species richness, stream ecosystems, trophic diversity

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

INTRODUCTION

Ecologists have long been interested in global patterns of biodiversity because they seek to explain the general increase in species richness from the poles to the tropics. Numerous explanations for this gradient have been proposed (e.g. [START_REF] Willig | Latitudinal gradients of biodiversity: pattern, process, scale, and synthesis[END_REF][START_REF] Mittelbach | Evolution and the latitudinal diversity gradient: speciation, extinction and biogeography[END_REF], and it has been demonstrated that such explanations need to consider the relationship between local and regional diversity. This relationship is not necessarily linear [START_REF] Caley | The relationships between local and regional diversity[END_REF], as there may be a limit to the number of species that can be supported at a particular site (saturation), but different species assemblages may be found at different sites, thereby leading to higher regional diversity (e.g. [START_REF] Sale | Maintenance of high species diversity in coral reef fish communities[END_REF]. [START_REF] Hillebrand | On the generality of the latitudinal diversity gradient[END_REF] showed that diversity gradients are consistent across most taxa, habitats and spatial scales. However, his meta-analysis was based on species presence-absence data, which are insufficient for investigating ecological processes in which relative abundance of species play a major role [START_REF] Dangles | Species richnessdecomposition relationships depend on species dominance[END_REF]. Also of great ecological significance can be the number of species within particular guilds or trophic levels [START_REF] Gessner | Diversity meets decomposition[END_REF]. When species richness within a given trophic level is low, losing one or more species is likely to have particularly severe consequences at the ecosystem level [START_REF] Duffy | Why biodiversity is important to the functioning of real-world ecosystems[END_REF][START_REF] Dudgeon | Biodiversity and ecosystem functioning in a species-poor guild: a test using tropical stream detritivores[END_REF]. This is because the chances of different species being functionally redundant (i.e. having similar effects on ecosystem processes) are lower with low diversity, and thus the loss of key species [START_REF] Mills | The keystonespecies concept in ecology and conservation[END_REF]) is more likely. Moreover, the risk of losing an entire trophic level increases with decreasing species richness, potentially leading to a major reduction in trophic diversity [START_REF] Hillebrand | Biodiversity in a complex world: consolidation and progress in functional biodiversity research[END_REF]. Reducing the number of trophic levels within an ecosystem strongly affects ecosystem functioning by constraining ecosystem processes (e.g. organic matter decomposition or primary production) and changing the magnitude and efficiency of trophic transfer [START_REF] Duffy | The functional role of biodiversity in ecosystems: incorporating trophic complexity[END_REF].

Gradients of diversity within guilds or trophic levels are, however, virtually unknown. Here we explore global diversity patterns in stream shredders, a key detritivore guild in forest streams, where terrestrially derived detritus is the major energy and carbon source [START_REF] Wallace | Multiple trophic levels of a forest stream linked to terrestrial litter inputs[END_REF]. Shredders are able to assimilate carbon and other nutrients from this dead organic matter and associated microbes, and to convert a portion of it to animal tissue; they increase the rate at which coarse detritus is transformed into fine detritus; promote food availability for collectors and filter feeders; and thus play a fundamental role in organic matter decomposition and nutrient cycling [START_REF] Cummins | The utilization of leaf litter by stream detritivores[END_REF][START_REF] Short | Processing of leaf litter by a stream detritivore: effect on nutrient availability to collectors[END_REF][START_REF] Wallace | Stream detritus dynamics: regulation by invertebrate consumers[END_REF][START_REF] Wallace | The role of macroinvertebrates in stream ecosystem function[END_REF][START_REF] Graça | The role of invertebrates on leaf litter decomposition in streams-areview[END_REF][START_REF] Hieber | Contribution of stream detrivores, fungi, and bacteria to leaf breakdown based on biomass estimates[END_REF]. Although shredders belong to the same trophic level as other detritivores, they occupy a different position in the detritus processing chain, as they specialize in the primary processing of whole leaves rather than depending on processed, fragmented detritus [START_REF] Heard | Processing chain ecology: resource condition and interspecific interactions[END_REF].

Various local studies suggest that shredder diversity may be greater in temperate regions (see [START_REF] Boyero | Are tropical streams really different?[END_REF]. This would imply that tropical streams might be more vulnerable to the loss of key species, or of the entire shredder guild to which shredders importantly contribute, with important consequences for ecosystem functioning. Furthermore, climate warming might be expected to exacerbate this effect, as most shredders belong to cool-adapted taxa and are possibly at the margin of their upper temperature tolerance in the tropics [START_REF] Dillon | Global metabolic impacts of recent climate warming[END_REF]. Studies of shredder diversity over broad spatial scales are, however, lacking, and global studies have shown that different stream taxa can exhibit different diversity patterns at both the local and regional scales [START_REF] Vinson | Broad-scale geographical patterns in local stream insect genera richness[END_REF]Pearson & Boyero, 2009). Strong relationships between regional and local species richness have been demonstrated in Finland [START_REF] Heino | Determinants of macroinvertebrate diversity in headwater streams: regional and local influences[END_REF] and Australia [START_REF] Marchant | Regional and local species diversity for lotic invertebrates across multiple drainage basins in Victoria[END_REF], suggesting that assemblages are unsaturated and indicating the importance of large-scale processes, but not denying the possible influence of local factors (e.g. water chemistry) on the regional diversity.

We examined shredder diversity across latitudes at a global scale (156 sites from 17 regions located in all inhabited continents at latitudes ranging from 67°N to 41°S). Given the scale dependence of estimates of diversity [START_REF] Gaston | Global patterns in biodiversity[END_REF][START_REF] Rahbek | The role of spatial scale and the perception of large-scale species-richness patterns[END_REF], and bearing in mind that local processes and relationships can be of great importance in determining species richness [START_REF] Heino | Biodiversity of aquatic insects: spatial gradients and environmental correlates of assemblage-level measures at large scales[END_REF], we examined shredder species richness at both the local and regional scales (aand g-diversity, respectively), as well as the change in assemblage composition among sites within regions (b-diversity). We hypothesized that shredder diversity would increase with latitude, on the basis of local studies reporting low numbers of shredder species in tropical streams [START_REF] Boyero | Are tropical streams really different?[END_REF]. We also explored the dependence of a-diversity on the regional species pool (i.e. g-diversity) across latitudes, hypothesizing that the relationship would be positive, although we had no a priori expectation regarding the shape of such a relationship. Finally, given that in a global study of this type local factors might mask any general relationships, we examined the influence of local environmental factors on shredder diversity.

MATERIALS AND METHODS

Field and laboratory work

We sampled shredders and their food resources (leaf litter) at 117 sites from a total of 13 regions, in Africa (one region), Asia (three regions), Australia (one region), Central America (two regions), Europe (two regions) and South America (four regions) (Table 1, Fig. 1), using the same methodology. The surveys were conducted between 2006 and 2007, during periods when leaf litter was present in the stream, and within a short period of time in each region to minimize intra-regional seasonal effects. In each region we sampled nine sites, each located in a different headwater stream with no notable human impact. Stream width was Յ 10 m and site length was approximately 10 times the stream width (50-100 m).

At each site, we generally took 10 leaf litter samples, half from pools and half from riffles, from within areas of 20 ¥ 20 cm in a litter layer of no more than 4 cm, using a net with a 0.5-mm mesh, and transferred them to labelled Ziplock plastic bags. Samples were kept cool and rapidly transported to the laboratory, where they were rinsed and carefully inspected. All macroinvertebrates retained on a 250-mm screen were removed and preserved in 70% ethanol. The number of plant species in leaf litter samples was estimated by visually distinguishing morphospecies (local botanists were consulted when necessary), and leaf litter was then dried to constant weight (60-80 °C for at least 48 h) and weighed. Invertebrates were separated into morphospecies (identified to species when possible), counted and classified as shredders or non-shredders based on gut content analysis following [START_REF] Cheshire | Food webs in tropical Australian streams: shredders are not scarce[END_REF]. We assumed that congeneric species found in different regions belonged to different species.

At each site, we recorded the latitude (degrees from the equator) and altitude (m a.s.l.) with a GPS. When possible, we measured water temperature (°C), conductivity (mScm -1 ), dissolved oxygen saturation (%), pH, alkalinity (mg CaCO 3 l -1 ), total nitrogen (mg l -1 ), total phosphorus (mg l -1 ), wetted stream width (mean derived from six cross sections) and water depth (cm; measured every 0.5 m across the cross sections). We also visually estimated the percentage of substrate covered by leaf litter, the percentage of pool habitat, the percentage of canopy cover and the number of riparian tree species. Finally, we used 1:50,000 maps to estimate catchment area (km 2 ) and the percentage of native forest in the catchments.

Table 1 Study regions (including acronyms), range of latitude and altitude of sites, observed and estimated (first-order jackknife estimator; [START_REF] Palmer | The estimation of species richness by extrapolation[END_REF] regional diversity (g), and efficiency of sampling in estimated proportion of species collected. 1 for details).

Because of the relatively small number of high-latitude sites surveyed, we compiled four additional data sets from temperate regions, to check for consistency with the patterns observed in our survey. Two of these regions conformed to the present global study (sampling methods described above) but were not included in the main data set because of the small number of sites surveyed: Chile (five sites) and New South Wales (Australia; six sites). Data from Maryland (USA) were taken from nine sites randomly selected from 84 described by [START_REF] Swan | Identifying the relative importance of leaf versus shredder species loss on litter decomposition in streams[END_REF] and data from Sweden were taken from nine sites randomly selected from 23 described by [START_REF] Jonsson | Leaf litter breakdown rates in boreal streams: does shredder species richness matter?[END_REF].

Statistical analyses

We evaluated shredder diversity as the number of species at each site (a), the total number of species in each region (g) and the change in assemblage composition among sites within regions (b = g/am, am being the mean a for each region; [START_REF] Baselga | Partitioning the turnover and nestedness components of beta diversity[END_REF]. Gamma diversity was estimated using jackknife resampling procedures [first-order jackknife estimator = go + am (n -1)/n,w h e r ego is the observed number of species in each region and n is the number of sites sampled in each region; [START_REF] Palmer | The estimation of species richness by extrapolation[END_REF] in the pc-ord package [START_REF] Mccune | PC-ORD[END_REF], to be used in further analysis and to assess the efficiency of our survey.

Variation in shredder diversity (a-, g-and b-diversity) with latitude was explored by linear regression. As altitude was variable among regions, we removed its effect by using the residuals of the regression altitude versus latitude in the analyses, rather than latitude itself. We also examined the relationship between g-and a-diversity by linear regression. The mean a for each region (a m) was used in this analysis to avoid pseudoreplication [START_REF] Soininen | Local-regional diversity relationship varies with spatial scale in lotic diatoms[END_REF]. We examined the data for curvilinearity or a decreasing slope by including a quadratic term in the regression, as an indication of am approaching some limit that would suggest species saturation (see [START_REF] Shurin | Local and regional zooplankton species richness: a scaleindependent test for saturation[END_REF]. Akaike's information criterion (AIC) was used to select the model that best fitted the data; it was calculated using the formula AIC = n ¥ ln (RSS/n) + 2K,wher en is sample size, RSS is the residual sum of squares and K is the number of parameters in the model. We sought differences in species saturation between temperate and tropical zones (defined here as > 23°N or S and Յ 23°N or S, respectively) by exploring this relationship separately for the two zones, including the four additional temperate regions (see Field and laboratory work and Table 1). We used the AIC to assess whether the data better conformed to a linear or a quadratic relationship in each case.

Correlation analysis was used to explore the relationship between environmental factors and shredder diversity, as several gaps in the environmental data set precluded multiple regression analysis. Relationships with a-diversity were explored at the site scale (the range of n was 54 to 112, depending on availability of environmental factors), while relationships with g-and b-diversity were explored at the region scale (range of n was 6 to 13).

RESULTS

We found a total of 122 shredder morphospecies in the 13 main regions, with 0-10 species per site (a = 4.61 Ϯ 0.26 SE) and 2-22 species per region (g = 9.38 Ϯ 1.71 SE). The four additional temperate regions had 44 morphospecies in total, with 0-9 species per site (a = 4.66 Ϯ 0.49 SE) and 3-18 species per region (g = 11.00 Ϯ 3.14 SE). Jackknife estimates suggested that we recorded on average 90% (Ϯ 3% SE) of the species present in each region at the time of sampling, or 86% (Ϯ 3% SE) when additional sites were included (Table 1).

Linear regression showed that a-diversity increased with latitude (a = 4.6 + 0.091 ¥ latitude; r 2 = 0.22, P < 0.0001; Fig. 2a). When the four additional temperate sites were included in the analysis, the relationship was similar (a = 4.8 + 0.072 ¥ latitude; r 2 = 0.22, P < 0.0001). Gamma diversity showed no latitudinal pattern (g = 9.5 + 0.029 ¥ latitude; r 2 < 0.01, P = 0.83; Fig. 2b), with a similar outcome when the four additional temperate sites were included (g = 11.5 + 0.127 ¥ latitude; r 2 = 0.09, P = 0.23). The relationship between b-diversity and latitude was not significant (b = 2.4-0.032 ¥ latitude; r 2 = 0.16, P = 0.17; Fig. 2c); variability of b-diversity was higher at lower latitudes, but this apparent pattern disappeared when the four additional temperate sites were included in the analysis (b = 2.8 -0.0005 ¥ latitude; r 2 < 0.01, P = 0.98).

Gamma and a-diversity were directly related [linear relationship: am = 1.81 + 0.28 ¥ g; quadratic relationship: am = 2.66 + 0.35 ¥ g -0.34 ¥ (g -10.7) 2 ]. Both relationships were significant (linear: P = 0.007; quadratic: P = 0.0001), but the quadratic model explained more of the total variance (linear: 54%; quadratic: 89%) and had a smaller AIC (linear: 20.9; quadratic: 10.3). When analysed separately, tropical and temperate zones showed distinct tendencies. For temperate regions, the quadratic model explained slightly more of the variance (linear: 58%; quadratic: 69%), but the linear model had a slightly smaller AIC (linear: 12.5; quadratic: 14.6) (Fig. 3a). For tropical regions, the quadratic model explained more variance (linear: 54%; quadratic: 87%) and had a smaller AIC (linear: 15.2; quadratic: 7.9) (Fig. 3b).

Several local habitat variables were correlated with a-diversity: water temperature (r =-0.53, P < 0.0001), water depth (r =-0.45, P < 0.0001), stream width (r =-0.33, P = 0.0003) and percentage of substrate covered by leaf litter (r =-0.27, P = 0.034). Gamma and b-diversity showed no relationship with any of the environmental variables.

DISCUSSION

Our results suggest that global patterns of shredder diversity are complex and depend on spatial scale, as demonstrated for other organisms [START_REF] Rahbek | The role of spatial scale and the perception of large-scale species-richness patterns[END_REF]. However, we can draw several conclusions that have important ecological implications. Firstly, we have shown that the number of shredder species present at a given site (a-diversity) increases with latitude, confirming previous suggestions [START_REF] Boyero | Are tropical streams really different?[END_REF]. This implies that tropical streams have a higher risk of losing key species or the whole shredder guild, which may have serious consequences for stream ecosystem functioning, including slowed leaf litter decomposition [START_REF] Jonsson | Ecosystem process rate increases with animal species richness: evidence from leafeating, aquatic insects[END_REF][START_REF] Boyero | How biological diversity influences ecosystem function: a test with a tropical stream detritivore guild[END_REF][START_REF] Boyero | A global experiment suggests climate warming will not accelerate litter decomposition in streams but might reduce carbon sequestration[END_REF][START_REF] Dudgeon | Biodiversity and ecosystem functioning in a species-poor guild: a test using tropical stream detritivores[END_REF], poor trophic transfer from the main basal resource (leaf litter) to higher trophic levels [START_REF] Duffy | The functional role of biodiversity in ecosystems: incorporating trophic complexity[END_REF] or disruption of the processing chain (sensu [START_REF] Heard | Processing chain ecology: resource condition and interspecific interactions[END_REF].

Secondly, we found that the relation between regional and local diversity differed for temperate and tropical regions. For the tropical assemblages only, we found an upper limit to a-diversity, regardless of g-diversity. This indicates species saturation, which could explain why the latitudinal gradient in a-diversity that we observed was not accompanied by a gradient in g-diversity. Shredder a-diversity seems to be limited at tropical sites by local factors such as environmental constraints or competitive species interactions [START_REF] Caley | The relationships between local and regional diversity[END_REF][START_REF] Heino | Biodiversity of aquatic insects: spatial gradients and environmental correlates of assemblage-level measures at large scales[END_REF]. Alpha diversity correlated with several local habitat variables (water depth, channel width, water temperature) that (linear: 12.5; quadratic: 14.6). For tropical regions, quadratic model explained more variance and had a smaller AIC (linear: 15.2; quadratic: 7.9). relate to position in river networks and reflect the expected distributional pattern, with shredders being most prevalent in small streams [START_REF] Vannote | The river continuum concept[END_REF]. High temperatures might limit the presence of certain shredder taxa at tropical lowland sites [START_REF] Camacho | Local variation in shredder distribution can explain their oversight in tropical streams[END_REF][START_REF] Yule | Shredders in Malaysia: abundance and richness are greater in cool highland tropical streams[END_REF] because many of them have evolved in cool waters [START_REF] Fochetti | Global diversity of stoneflies (Plecoptera; Insecta) in freshwater[END_REF][START_REF] De Moor | Global diversity of caddisflies (Trichoptera: Insecta) in freshwater[END_REF]. However, the lack of a clear relationship between shredder diversity and most environmental factors is likely to reflect the importance of multiple factors operating simultaneously at local scales and that are difficult to pinpoint given the broad spatial extent of the present study.

A potential local limiting factor of a-diversity at tropical sites is the existence of strong competitive interactions. This is possible, for example, if resources are limited in terms of the amount, quality and timing of leaf litter inputs. Even though seasonality exists in the tropics, the temporal pattern of leaf fall is much more even than in the temperate zone, lacking the highly pulsed and temporally predictable inputs typical of temperate streams [START_REF] Cummins | Structure and function of stream ecosystems[END_REF]. As a result, leaf litter tends to be more abundant in temperate streams at a particular time of the year, and thus may allow a greater number of shredder species to coexist. Moreover, the leaves of many tropical plants contain high levels of deterrents [START_REF] Coley | Herbivory and plant defenses in tropical forests[END_REF][START_REF] Coq | Interspecific variation in leaf litter tannins drives decomposition in a tropical rain forest of French Guiana[END_REF][START_REF] Graça | Leaf quality of some tropical and temperate tree species as food resource for stream shredders[END_REF], so palatable leaves are often a scarce resource, notwithstanding that some tropical trees produce high-quality leaves as well [START_REF] Graça | Food quality, feeding preferences, sur-vival and growth of shredders from temperate and tropical streams[END_REF]. Thus, tropical streams tend to have less leaf litter of good quality available at any particular time than temperate streams, exacerbating competitive interactions among shredder species [START_REF] Bastian | Effects of diversity loss on ecosystem function across trophic levels and ecosystems: a test in a detritus-based tropical food web[END_REF]. Different shredder species show preferences for leaves of the same plant species [START_REF] Graça | Food quality, feeding preferences, sur-vival and growth of shredders from temperate and tropical streams[END_REF][START_REF] Bastian | Leaf preferences by shredders in tropical streams[END_REF], and competition is an important mechanism regulating the consumption of leaf litter by shredders [START_REF] Bastian | Effects of diversity loss on ecosystem function across trophic levels and ecosystems: a test in a detritus-based tropical food web[END_REF]. Competitively dominant species feed on the preferred leaves, while other species are forced to feed on other, less palatable, leaves, which may affect their growth and reproductive success [START_REF] Bastian | Effects of diversity loss on ecosystem function across trophic levels and ecosystems: a test in a detritus-based tropical food web[END_REF][START_REF] Gessner | Diversity meets decomposition[END_REF]. Competition for a scarce resource could then limit the number of shredder species coexisting at tropical sites.

Another potential explanation for the curvilinear relationship between regional and local species richness in the tropics is limitation for dispersal among sites. This could be due to the existence of more effective geographical barriers (which is unlikely) or to a lower dispersal ability of tropical shredders. Most temperate shredders are larvae of insect taxa (e.g. caddisflies, stoneflies) with flying adult stages. Although the dispersal ability of adult caddisflies and stoneflies is often limited [START_REF] Kovats | Inland dispersal of adult aquatic insects[END_REF][START_REF] Griffith | Lateral dispersal of adult aquatic insects (Plecoptera, Trichoptera) following emergence from headwater streams in forested Appalachian catchments[END_REF], it is higher than that of other shredder taxa such as crustaceans and molluscs, which lack flying stages altogether. The latter taxa are better represented in the tropics, where they comprised 15% of all shredder species collected in our survey, compared with only 6% in temperate regions. Consequently, although the effect is unlikely to be large, dispersal limitation might have contributed to the greater regional saturation tendency we observed for shredders in the tropics.

Our global-scale study indicates that loss of shredder species might be more critical at tropical sites, where fewer shredder species are present and the loss of key species or the whole shredder guild is therefore more likely. The lack of a latitudinal trend in g-diversity that we observed suggests that, counter to common perceptions, diversity of regional shredder species pools is similar across latitudes. Local extinctions of shredder taxa, for example in response to climate warming, might therefore be compensated by colonization of other species from regional species pools that were not locally present before. This would be more likely if the colonizers were previously absent because they were competitively inferior to the species that went locally extinct. However, limited dispersal ability of shredders lacking an adult flying stage, including some taxa typical of tropical streams, suggests that colonization from adjacent sites following local extinctions may not be the norm. Furthermore, many shredder taxa belong to mostly cool-adapted taxa, and may be close to their thermal maxima in the tropics, where predicted extinctions from climate warming may have disproportionately greater effects [START_REF] Dillon | Global metabolic impacts of recent climate warming[END_REF]. Given their limited local diversity, tropical shredder assemblages would thus merit special scientific attention and conservation effort, to determine or create refugia to prevent species losses and consequent alteration of stream ecosystem functioning.

Figure 2 Figure 3

 23 Figure 2 Linear regressions showing latitudinal variation in (a) alpha (b) gamma and (c) beta diversity (b = g/am, am being the mean a-diversity for each region) of shredders. To normalize for altitudinal effects, the residuals of the regression altitude versus latitude were used as predictor variable instead of latitude. Dashed regression lines: P > 0.05.

ACKNOWLEDGEMENTS

The study was supported by a grant from the National Geographic Society's Committee for Research and Exploration (grant number 7980-06 to Luz Boyero) and various national funding sources. C. Canhoto, Z. Dewson, G. Cabarcas, M. Dunfee, B. Gao, Y. González, M. Hirose, P. Lisle, N. Mochizuki, D. Nawa, L. C. Y. Ng, P. Rosa, R. Sánchez-Argüello and K. Schmidt assisted with field work. J. Hortal provided statistical advice. We thank M. Jonsson, who provided latitudes for the Swedish sites, and the Maryland Department of Natural Resources Monitoring and Non-tidal Assessment Division for the provision of data.

BIOSKETCH


B Hou
email: bo.hou@telecom-bretagne.eu

) P Grosso

Z Y Wu

J L De Bougrenet De La Tocnaye

A turbidi-meter based on a refractometer using a Charge-Coupled Device

Keywords: Charge-Coupled Device, turbidity, turbidi-meter, formazin, refractometer

Salinity and turbidity are two important sea water properties in oceanography. We have studied the use of a high resolution refractometer to measure the salinity of sea water. The requirement of a multifunctional sensor makes the turbidity measurement based on our refractometer valuable. In this paper, we measure turbidity according to the attenuation of the laser beam caused by the scattering. With the configuration of our refractometer, several issues impact the laser beam attenuation measurement, while the measurement of salinity is impacted by the scattering as well. All these issues make light distribution non-sensitive sensors such as PSD unsuitable for building the refracto-turbidi-meters. To overcome these issues, a CCD combined with a new location algorithm is used to measure both the refractive index and the attenuation.

Several simulations and experiments are carried out to evaluate this new method.

According to the results, the way to improve the resolution is discussed as well. The validation of our method is proved by comparing to the nephelometer specified by the NTU standard.

I. INTRODUCTION

The turbidity of water is mostly due to the existence of suspended undissolved solid particles. When light is incident on a particle, several processes occur, including reflection, refraction, diffraction and absorption. For particles that are of the order of the wavelength in size or smaller, these processes are referred to as "scattering". [START_REF] Jones | Light scattering for particle characterization[END_REF] Usually, the measurement of turbidity is not a direct measurement of these suspended particles, but rather a measurement of the scattering caused by these particles. International standard ISO 7027 [START_REF]Water quality -determination of turbidity[END_REF] provides two different methods to measure the turbidity by computing the diffuse radiation and the attenuation of a radian flux. Respectively, two different turbidity units, namely FNU (Formazin Nephelometric Unit) and FAU (Formazin Attenuation Unit), are used for both methods. Another turbidity unit, Nephelometric Turbidity Unit (NTU), defined by EPA method 180.1 3 measures the light diffused at an angle of 90 ± 30 degrees to the incident light beam with a tungsten lamp.

Since the measurement of turbidity is a measurement of the scattering effect caused by particles, the light scattering and its application have been investigated for many years.

In 1907, Gustav Mie [START_REF] Mie | Beiträge zur optik trüber medien, speziell kolloidaler metallösungen, leipzig[END_REF] gave an analytical solution of Maxwell's equations for the scattering of electromagnetic radiation by a single spherical particle, which is called Mie theory. To reduce the complexity of Mie theory, several approximations have been proposed. [START_REF] Henyey | Diffuse radiation in the galaxy[END_REF][START_REF] Cornette | Physically reasonable analytic expression for the singlescattering phase function[END_REF][START_REF] Irvine | Multiple scattering by large particles[END_REF] The study of oceanography requires different high-resolution measurement equipment to measure different physical quantities of the sea water, e.g. turbidity, salinity, temperature, and pressure, etc. [START_REF] Marc Le Menn | Instrumentation et métrologie en océanographie[END_REF] A set of these quantities at different geographical positions is most valuable for oceanography. This makes the research of in situ multi-sensors valuable.

Our previous work involved developing an optical refractometer to measure the salinity of seawater based on laser beam deviation measurement with a 1-D Position Sensitive Device (PSD) [START_REF] Malardé | Highresolution and compact refractormeter for salinity measurements[END_REF][START_REF] Le Menn | Advances in measuring ocean salinity with an optical sensor[END_REF] . The resolution for measuring salinity reaches 0.002g/kg with the measurement range from 0g/kg to 40g/kg. Further researching to replace PSD with Charge-Coupled Device (CCD) gives us an improvement of resolution of nearly 1.5 times compared to PSDbased refractometer. [START_REF] Hou | Charge-coupled devices combined with centroid algorithm for laser beam deviation measurements compared to a position-sensitive device[END_REF] The CCD records the location, shape, and intensity distribution of the laser spot. This provides the possibility to measure physical quantities other than refraction index.

In this paper, we demonstrate how our refractometer can be used to measure turbidity. A brief summary of our optical refractometer is given in the next section. In section III, the problems of measuring turbidity with our optical refractometer are discussed according to the scattering theory. Solutions are also introduced in this section. The simulations and experiments are firstly carried out in a parallel slab to operate at normal incidence and then with our optical refractometer, which can be found in section V and VI. Finally, the performance in highly turbid case and calibrated water samples are given by a series of experiments.

II. PRINCIPLE OF OPTICAL REFRACTOMETER

Our optical refractometer used for salinity measurement is depicted in Fig. 1. The refractometer consists of two prisms with different refractive indices. The laser beam first illuminates the left hand side prism and reaches a mirror AB. After the reflection at AB, the laser beam is redirected to the surface between the medium and the prism, CD. It is then refracted and propagates a distance d in the medium. The laser beam is then refracted at surface DE and enters the right hand side prism. The mirror FG finally reflects the laser beam to the top of the prism, where a laser beam position detection device is used to detect the position of the laser spot x p . With this configuration, the refractive index of the water can be calculated very accurately from the position of the laser spot. [START_REF] Malardé | Highresolution and compact refractormeter for salinity measurements[END_REF] With a CCD instead of a PSD, the position of the laser spot can be calculated with different location algorithms, and it is shown that the resolution is comparable to the system that uses a PSD. [START_REF] Hou | Charge-coupled devices combined with centroid algorithm for laser beam deviation measurements compared to a position-sensitive device[END_REF] By using a CCD, the distribution of the light intensity changed by the scattering of the particles in the medium is also recorded, giving us the possibility to retrieve the turbidity of the medium.

III. PRINCIPLE OF TURBIDITY MEASUREMENT

A. Theoretical aspects

The incident light is diffused in all directions when it meets the particle. The portion of light flux diffused in different directions is defined by the phase function, denoted as p(ŝ ′ , ŝ), which represents the portion of light flux diffused from direction ŝ to direction ŝ′ .

The phase function is related to the wavelength of the incident light and the size of the particles, a normalized radius R = 2πr λ is introduced to define the size of the particle, in which r is the radius of the particle and λ is the wavelength of the incident light. Besides the flux diffused, another portion of light flux is absorbed by the particle, represented as σ a I 0 , where I 0 is the flux intensity of incident light. Similarly, the portion of light diffused out of the light propagation direction, which is related to the normalized radius R of the particle is denoted as σ d I 0 . Here σ a and σ d are called absorption cross section and diffusion cross section, respectively, which are the functions of the incident light wavelength λ. These two coefficients associated with the phase function describe the optical properties of a single particle. For a volume of water, the density of particles should also be considered. The more particles in the medium, the more light is absorbed and scattered out of the propagation direction.

Fig. 2 shows the absorption and diffusion of an incident light with flux intensity I 0 , upon a volume of turbid water with unit cross section, particle density ρ and length of dl. The flux that is absorbed by ρdl particles is calculated by the equation:

I a = ρσ a (λ)dlI 0 (1)
The portion of light diffused out of the propagation direction by these particles can be expressed by:

I d = ρσ d (λ)dlI 0 (2)
According to Eq.1 and Eq.2, the decrease in the incident flux intensity for the volume dl

dI dl = - (I a + I d ) dl = -ρ(σ a (λ) + σ d (λ))I (3)
This partial differential equation can be easily solved as:

I = I 0 e -ρ(σa(λ)+σ d (λ))l , (4)
in which the part ρ(σ a (λ) + σ d (λ)) that causes the attenuation of the incident beam, is a good candidate to describe the optical properties of the volume of medium. To simplify the formula, ρ(σ a (λ) + σ d (λ)) is expressed as T , attenuation coefficient. Therefore, the attenuation coefficient T can be calculated from:

T = - ln(I m ) -ln(I 0 ) l , (5)
Another part of multi-scattering light that increases the transmission radiation is caused by the reflection between the two refraction surfaces. Besides the refraction, a part of the laser beam is reflected in the second refraction surface, the reflected light is diffused by the particles in the medium and reflected again in the first refraction surface. This process continues between the two surfaces. As a result, part of the reflected light is scattered into the transmission direction as well.

The flux intensity of multi-scattered light in propagation direction is related to the density of the particles and the length of the light path. The higher the density of the particles, the more multi-scattering occurs. A longer light path gives more light scattered into the propagation direction too. In this paper, the impacts caused by the multi-scattered light are evaluated in the analysis of the experiment results.

B. The resolution of turbidity measurement

The resolution of the turbidity measurement can be estimated from the Eq 6. The multi-scattering part is ignored here and will be discussed later from the experiment results.

Since the incident light intensity I 0 can be measured with non-turbid water in advance, the equation can be modified as:

T = -( ln(I m ) l -C) (7)
The derivative of T can be expressed as:

T ′ = dT dI m = - 1 l × I m (8)
Thus, the sensitivity of the measurement of turbidity S t is

S t = k t × dT = - dI m l × I m , (9)
where k t is a constant coefficient to convert the attenuation coefficient into other turbidity units, for example, NTU. From this equation, it is obvious that the resolution of turbidity measurement is proportional to the resolution of the light intensity sensor dI m , but inversely proportional to the length of the light path l in the turbid medium. A longer light path can provide better turbidity measurement resolution. Another interesting phenomenon resulting from this equation is the resolution depending on the measurement range. With the same sensitivity of the light intensity sensor and the same light path length, the larger the measured intensity, the better the resolution obtained. Considering that the measured light intensity decreases as the turbidity increases, it is easy to conclude that the resolution is better in low turbid medium than in the high turbid medium when light path and sensor sensitivity are the same.

C. Issues in measuring turbidity with refractometer

As discussed in section III, the attenuation coefficient T can be calculated from the attenuation of the incident laser beam according to Eq. 6. When applying this theory to the refractometer demonstrated in section II, several issues arise. The first one is, according to the theory, the intensity I m is measured by the sensor located far away from the medium, where the light in propagation direction is well separated from the scattered light, however, with the refractometer, the height L shown in Furthermore, since our method measures the attenuation of propagated light as shown in Eq. 6, it is easy to find out that the light intensity I m decreases when the turbidity increases, which can be found by comparing the Fig. 10 (a) and (b). This results in another issue, the light intensity becomes so weak that it can't be measured in a highly turbid case.

Another problem raised by the refractometer is that the light path changes as the refraction index of the medium changes. In With Eq. 10, the relative length of the light path compared to the length of the light path in pure water is calculated and used as the length in Eq. 6 to obtain the attenuation coefficient.

In practice, the laser beam width cannot be ignored. This leads to another problem, the width of the collimated beam causes that the different parts inside the beam propagate through the medium with different lengths. As shown in Fig. 6, for a wide beam shown as the red, the upper parts of the beam have shorter light paths OM than the bottom of the beam O ′ M ′ , and this difference varies as the refractive index of the medium changes.

A solution to this problem is to use the maximum of the intensity, instead of the entire intensity, to calculate the attenuation coefficient T .

The above problems raised by the configuration of the refractometer impact the resolution of the measurement of turbidity. Meanwhile, the measurement of turbidity itself impacts the accuracy of the refractometer, which needs to be addressed in the design of the turbidi-meter.

The first problem related to the resolution of the refractive index measurement is caused by the light path difference as shown in Fig. 6. According to Eq. 6, in a turbid case, this difference of light path leads to different attenuation inside the laser spot, which further causes the change of the laser beam position when applying the mass-center-related laser spot location methods, for example, using PSD or CCD combined the centroid algorithm.

Another problem that leads to the asymmetric laser spot is the divergence of the laser beam. Both the refraction surface and the sensor surface are not perpendicular to the laser beam. When a Gaussian beam projected to the sensor surface at a non-normal angle, the Gaussian spot becomes asymmetric, while different refractive index changes the size of the laser spot. Fig. 7 is generated by the simulation in ZEMAX with the configuration of our refractometer. It presents four laser spots with different laser beam divergences, but with the same refractive index of the medium. It is easy to observe that the width of the laser spot increases as the divergence of laser spot increases. The asymmetry of the laser beam can be noticed from the center of these laser spots calculated by the centroid algorithm, which is depicted in Fig. 8 (The solid line with mark 'x'). The center of the laser spots moves more than 1 pixel from the divergence of 0.5 mrad to 2 mrad.

Similarly with the divergence of the laser beam, the turbidity of the medium diffused the laser beam out of its propagation direction and makes the divergence of the laser beam much larger. Fig. 9 is the result of the simulation in ZEMAX with the collimated laser beam (no divergence) and different densities of particle. The scattering model used in the simulation is the Mie scattering. It is noticed that the position calculated by the centroid algorithm has a deviation of 2.5 pixels with the particle density from 0/cm 2 to 8 × 10 6 /cm 2 .

D. Using CCD to measure the turbidity with a refractometer

One of our previous work used a PSD to measure the deviation of the laser beam. PSD has a single active area formed by a P-N junction. The two parts that originated from the laser spot to the two electrodes form two lateral resistances for the photo-currents running towards the electrodes. The photo currents are collected through the resistances by the output electrodes, which are inversely proportional to the distance between the electrode and the center of the incoming light beam. This relationship is expressed as follows:

12 x = L 2 I 2 -I 1 I 2 + I 1 , (11)
where I 1 and I 2 are the electrode photo-currents, L is the length of the PSD active area and

x stands for the laser spot position. From the principle of PSD, the light intensity can be calculated from I 1 + I 2 . However, since PSD is placed not far from the medium due to the dimension limitation of the prisms, the intensity it measures mixes the scattered radiation so that it cannot give an accurate result. From the principle of PSD, the center is the mass center of the incident light. Since the divergence and turbidity make the laser spot asymmetric, the mass center cannot be used to indicate the laser beam position. What is more, when the light intensity is very weak in a highly turbid medium, I 1 and I 2 will be so small that they cannot be retrieved. These problems, which exist for all the light intensity distribution insensitive sensors make the PSD a poor candidate to measure turbidity with the refractometer.

To solve these problems, PSD will be substituted to a CCD. The resolution of measuring the deviation of laser beam with CCD combined with a centroid algorithm has been proved to be better than the configuration with PSD. [START_REF] Hou | Charge-coupled devices combined with centroid algorithm for laser beam deviation measurements compared to a position-sensitive device[END_REF] Since CCD can be controlled to operate with different exposure times, the transmitted radiation in a high turbid medium can be measured with high exposure time. The attenuation coefficient T can be represented by calculating with the transmitted radiation in a unit time period, which can be expressed as:

T = - ln( Im t ) -ln( I 0 t 0 ) l(x p ) , (12)
in which t is the exposure time and t 0 stands for the exposure time used to measure the incident light intensity. As the length of light path l changes with the deviation of the laser beam, it is noted as l(x p ) according to Eq. 10.

To separate the transmitted radiation with the scattered radiation, the Fourier transformation of the laser spot in different turbidities has been studied, depicted in Fig. 11, and

gives us the profile of the laser spot Fourier transformation in pure water and turbid water 444.4 NTU. Since a laser is used in the refractometer, the ideal Fourier transformation of the laser spot should be Gaussian too, which can be found in the low frequency (between the spatial frequency -20 and 20 approximately). By comparing the Fourier transformation for different turbidities in Fig. 11, a low pass filter can be used to remove the scattered radiation. The result of a low pass filter can be found in Fig. 10 (c) and (d). For pure water, the resulting image does not differ much from the original image, which can be foreseen since there is no scattering in this case. The image (d) shows that this method correctly retrieves the original Gaussian spot from the original image that mixed the transmitted radiation, the scattered radiation and the speckles caused by interference. For the wide beam, the maximum value of the spot is used to avoid the asymmetric spot caused by the different light paths inside the beam. By applying all these settings to Eq. 12, the attenuation coefficient is:

T = - ln( I f c t ) -ln( I 0 t 0 ) l(x p ) , (13)
where I f c is the maximum value of the filtered image. In practice, N images will be captured As discussed in the section III C, the measurement of turbidity and the divergence of the laser beam can cause the laser spot shape to be asymmetric, which leads to the centroid algorithm inaccuracy in showing the position of the laser spot. To solve this problem, a new algorithm is proposed, which is insensitive to the distribution of the laser spot. Fig 12 describes this algorithm, which tracks the peak of the Gaussian source shown as the dash line. This dash line divides the divergent laser beam into two parts, named left part and right part, respectively. Since the source laser beam can be considered as a perfect Gaussian beam, the mass of the left part M lef t is equal to the right one M right and this relationship holds after the refraction of the beam, even though the shape is asymmetric. This beam is quantized into pixels, which is shown as the bars in Fig 12, by a CCD. The mass in the left part M ′ lef t can be expressed as:

M ′ lef t = i 0 P i + M ∆x , (14)
where M ∆x is the mass shown as the shadow area, P i is the value of ith pixel. Similarly, the right part M ′ right can be written as:

x i i -1 i -2 j j + 1 j + 2 ∆x FIG.
12. The principle of new laser spot location algorithm

M ′ right = width-1 j P j -M ∆x (15)
With Eq. 14 and 15, the area in the shadow is obtained by

M ∆x = width-1 j P j -i 0 P i 2 (16)
And the sub-pixel position is calculated as:

x p = M ∆x P j + i (17)
In a turbid medium, the attenuation is not uniform inside the beam. For a standard

Gaussian beam f (x) = I 0 e -(x-xp) 2 2σ 2
, after the attenuation, the beam changes to:

I = I 0 e -(x-xp) 2 2σ 2 e -T u (x-xp)-T l = e -(x-xp+ T σ 2 u ) 2 2σ 2 I 0 e T 2 σ 2 2u 2 -T l , (18)
in which T is the attenuation coefficient, l is the light path of the center, u is a coefficient which describes the different attenuation inside the beam, x p is the original peak position, and σ is the laser beam size. From this equation, it is easy to conclude that the new laser spot is still a Gaussian spot but with a peak shift of -T σ 2 u compared to the original spot. The peak value of the Gaussian spot attenuates to e T 2 σ 2 2u 2 -T l of the original one.

Thus, the mass of the left part and the right part of peak can be calculated from the following equations:

M ′′ lef t = I 0 xp-T σ 2 u -∞ e -(x-xp+ T σ 2 u ) 2 2σ 2 e T 2 σ 2 2u 2 -T l dx = M ′′ right = I 0 +∞ xp-T σ 2 u e -(x-xp+ T σ 2 u ) 2 2σ 2 e T 2 σ 2 2u 2 -T l dx (19)
As in the divergence case, the center calculated by Eq. 17 is x p -T σ 2 u . To obtain the laser spot position x p , the deviation part -T σ 2 u needs to be calculated first. To simplify the discussion, the coefficient σ 2 2u 2 is noted as v, thus the maximum value measured is I 0 e vT 2 -T l . According to the principle discussed in chapter III, we obtain the following equation:

vT 2 -T l = ln(I m ) -ln(I 0 ) (20)
By solving this equation, the attenuation coefficient T is expressed as:

T = l -l 2 + 4v(ln(I m ) -ln(I 0 )) 2v (21)
Combined with Eq. 17, 19, and 21, the laser spot position x p in turbid medium is calculated by:

x p = w( M ∆x P j + i) + k(l -l 2 + 4v(ln(I m ) -ln(I 0 ))), ( 22
)
where w is the size of the pixel.

IV. NEW ALGORITHM FOR TURBIDITY MEASUREMENT WITH CCD

A. Simulation

To evaluate the performance of the new algorithm, two simulations: divergence simulation and turbidity simulation, are carried out in ZEMAX, in which the configuration of the refractometer is simulated, while the scattering model chosen for the simulation of turbidity is the Mie scattering. The divergence simulation takes 4 images with 4 different laser beam divergences from 0.5 mrad to 2 mrad. The new algorithm is applied to both the original image and the filtered image. The calculated center can be found in Fig. 8. To simplify the comparison, the reference center used here is the center calculated for 0.5 mrad, which labeled as position 0. From Fig. 8, it is clear that the new algorithm obtains better stability linear fitting. Centroid algorithm obtains a maximum error of 0.1 pixel with the standard deviation of 0.0784 pixel, while the new algorithm with and without the filter get a maximum error about 0.06 pixel (the standard deviations are 0.0348 and 0.0352 pixel respectively).

For an image with M × N pixels, the two algorithms have the same time complexity of O(M N ). All the results above make the new algorithm a good alternative to the centroid algorithm even in non-turbid case. Besides, according to the simulation results and the algorithm analysis, the new algorithm is insensitive to the divergence and can be applied to the turbid medium.

V. SIMULATION & EXPERIMENT IN A PARALLEL SLAB

A. Simulation

To test the principle of turbidity measurement, the simulation in parallel slab are carried out, firstly in ZEMAX. The turbidity of the medium is changed by adjusting the density of the particles from 1 × 10 6 /cm 3 to 1 × 10 7 /cm 3 . The scattering model used in the simulation is the Mie scattering. The dimension of the parallel slab follows the size of the parallel slab used in the real experiment. A CCD is placed 10 cm from the parallel slab along the laser beam propagation direction. Table III depicts the attenuation coefficient T calculated by Eq 6. By doing a linear fitting, the attenuation coefficient given by the method correctly describes the density of the particles, which is theoretically proportional to the turbidity in the simulation. The error standard deviation of the calculated attenuation coefficient T according to the line is 8.2 × 10 -4 . This result means the multi-scattered light I ms can be ignored in Eq 6 due to the short light path in the turbid water.

B. Experiments in high turbid medium

Besides the simulation, an experiment was carried out in the parallel slab. Fig. 14 shows the setup of the experiment. A red diode laser at 635 nm is mounted perpendicularly to the horizontal plane. A 45 degree mirror redirects the laser beam to a parallel slab with a width of 16 mm. Another 45 degree mirror is used to redirect the propagating beam into a DALSA CCD camera [START_REF]Genie m1280 datasheet[END_REF] , with a 1280 × 960 resolution and a small 3.75 × 3.75µm pixel size. The turbidity reference used in the experiment is the 4000 NTU Formazin standard.

Since the scattering is sensitive to the size of the formazin particles, which change according to temperature, the setup was established in the presence of a thermostat to keep the temperature stable. To obtain different turbidity, 1 ml 4000 NTU Formazin standard was added N times to the parallel slab, which contained 40 ml pure water at the beginning. The turbidity of diluted turbid water can be calculated by:

t i = t i-1 × V i-1 + ∆V × 4000 V i-1 + ∆V , (t 0 = 0, V 0 = 40) ( 23
)
where ∆V is the added volume of 4000 NTU Formazin standard each time, t i and V i is the turbidity and the total volume after adding the ∆V of 4000 NTU Formazin for ith time. 10 images are captured for each turbidity with a sufficient exposure time to make sure the peak of the spot reaches more than 100 (maximum 255 for the CCD). Since the diluted formazin is not stable for long time storage, all experiments are carried out in a dark room and in less than 1 hour to obtain the best performance. coefficients are calculated by using the power of the image, the max value of the image, and the pixel value in the position obtained from the new algorithm as I m , respectively. All these three curves show linearity to the turbidity which is in the range from 0 NTU to about 234.1 NTU as expected. The average error of these three methods is estimated by a linear fitting, which gives three similiar slopes of -0.0085, -0.0084, -0.0086, respectively. By using the max value of the image, the standard deviation of error is the largest of the three, which reaches ±4.87 NTU, while the standard deviation of error obtained by using the power of the image is ±3.17 NTU. The standard deviation of error given by the new algorithm is the smallest: ±2.82 NTU. From Eq 6, it is easy to conclude that the resolution of the turbidmeter is proportional to the sensitivity of the light sensor and inversely proportional to the light path length. It is believed that the resolution in the experiment can be improved by simply extending the width of the slab.

C. Experiments in low turbid medium

As discussed in section III B, the resolution of the turbid-meter is better in the low turbid medium than in the high turbid one with the same light path and light sensor sensitivity.

To demonstrate that, another experiment was carried out with the same parallel slab. All the configurations in this experiment are the same as the one for the high turbid medium discussed in the last section. 40 ml pure water is poured into the slab as the base volume of water. 1 ml diluted turbid water with the turbidity of 78.43 NTU is added to the slab 9 times. For each time, 24 images are captured within 1 second. According to Eq 23, the range of the turbidity for the 9 media varies from 1.91 NTU to 14.41 NTU. Fig. 16 expresses the attenuation coefficient calculated by using the power of the image, the maximum of the image and the pixel value given by the new algorithm, respectively. All of them show a linearity with respect to the turbidity. Even in this small range of turbidity, it is clear that the higher turbid medium gives larger error than the low turbid medium. For these three methods, the maximum value gives a large deviation in higher turbidity medium than the other two. The standard deviation of error for the three methods can be estimated by a linear fitting, which shows that the standard deviation of error of using the power of the image is about ±0.5 NTU, while the new algorithm provides a standard deviation of ±0.6 NTU. Compared with the standard deviation of error obtained in the last section, the resolution of the turbidity is better in a low turbid medium than in a high turbid one. as the measured intensity provides an error with standard deviation of ±8.09 NTU, while the standard deviation of error for the method using the new algorithm is about ±7.96 NTU. As we have discussed in Section III B, the sensitivity of the measurement of turbidity is inversely proportional to the light path in the medium. Compared to the error obtained in the parallel slab with 15.91 mm, the error obtained with the refractometer fits this analysis.

From the Eq. 10, the light path distance can be calculated as about 6.36 mm. The ratio of the errors between parallel slab and refractometer is about 2.7, while the ratio between the light path in parallel slab and the one in refractometer is about 2.5. It is believed that the difference between both ratios is caused by the set-up error of the laser source, which makes the laser beam not exactly perpendicular to the horizontal plane. This set-up error makes the actual light path distance shorter than the theoretical one.

C. Experiments in low turbid medium

The performance of the turbidity measurement with the refractometer in a low turbid medium is tested with another experiment. The experiment set up is the same as the experiment in high turbid medium discussed in last section. 100 ml pure water is used as the base medium, while diluted formazin of 190 NTU is added into the base medium 11 times to generate different turbid water from 0 NTU to about 19 NTU. The attenuation coefficients calculated from the power of the image and the pixel value obtained by the new algorithm are plotted in Fig. 19. The power of the image shows a better linearity than the new algorithm. The reason is that in a low turbid case, the attenuation of the light is very small so that the non-uniqueness of the attenuation inside the beam is not significant. Thus, the more pixels of the spot used as the measured intensity I m , the more accurate the result is. However, the new algorithm only tracks the intensity in one location, which divides the the mass of the spot into two identical parts. Therefore, it highly depends on the sensitivity of the light intensity sensor. In a low turbid case, the attenuation of the light intensity for one pixel is so small that the CCD cannot detect it, this explains that in the low turbid case shown in Fig. 19, the attenuation coefficient calculated from the new algorithm does not hold a linearity, especially in ultra low turbid mediums. The experimental results with parallel slab prove this as well, in which the standard deviation of new algorithm (±0.6 NTU) is larger than the standard deviation of using the image power (±0.5 NTU). With the refractometer, the standard deviation of using the power of the image is obtained from a linear fitting, which is about ±1.15 NTU. The ratio between this error and the error obtained in the parallel slab (±0.5 NTU) is 2.3, which fits the ratio between the light paths (about 2.5).

VII. COMPARE TO THE NEPHELOMETER

Nephelometer, which measures the diffusion of the light at 90 degree from the light propagation direction, is a stationary or portable instrument for measuring suspended particulates in a liquid or gas colloid. It has been proved to be an accurate and reliable method to measure turbidity from scattering. To test the performance of our method mentioned in this paper, the experimental result is compared to the result obtained from a nephelometer. The The experiment setup is the same in section VI B. The turbidi-meter is firstly calibrated by adding 1ml 4000 NTU formazin turbidity solution into 100 ml pure water for 3 times. For each time, 24 images are captured by the CCD within 1 second. Since the test sample is not in low turbid range, the new algorithm is used to calculate the attenuation coefficient. The attenuation coefficients calculated for the calibration are shown in Fig. 20. A linear fitting is made from the calibration results, which has a slope of -0.0055. With this calibrated configuration, the experiment with test sample is carried out as well. The attenuation coefficient obtained by the new algorithm is -0.6054. According to the slope of the fitting line, the turbidity of the test sample can be calculated as t = T k = -0.6054 -0.0055 = 110.07 NTU, which fits the result obtained from the nephelometer.

VIII. CONCLUSION

Salinity and turbidity are two important properties of sea water for oceanography. Our previous work has studied a high resolution optical refractometer to measure salinity. The integration of the salinity and turbidity measurement into one compact sensor is a very interesting topic in oceanography. Based on our refractometer, the attenuation of the light intensity caused by the scattering is measured by using a CCD. The attenuation coefficient, which is proportional to the absorption, diffusion, and particle density of the medium, is chosen as the description of the turbidity. According to the analysis of the attenuation With the configuration of our refractometer, the measurement of turbidity has to face several issues. The interference of the laser is observed in turbid medium, which forms speckles that lead to unexpected result. In our configuration of the refractometer, different refractive index will result in a different light paths. The width of the laser beam and the refraction result in the non-uniform attenuation inside the beam, which disturbs measurement of the attenuation from the laser spot power. In contrast to refractive index measurement, the attenuation measurement requires that the laser intensity is stable during the measurement as a reference intensity. Besides the laser beam, the light diffused out of the beam is received by the light intensity sensor as well, which disturbs the power of the spot. Furthermore, attenuation makes the light intensity too weak to measure, which causes bad performance in high turbid medium. All these problems determine that a simple light instensity sensor such as PSD cannot afford to measure the turbidity in a refractometer. To overcome these problems, a CCD is used to deal with these issues. With recording the light intensity distribution, an image captured by CCD can be treated with a low pass filter to eliminate speckle, and the diffused light can be eliminated by applying a proper threshold. The laser intensity is automatically controlled to keep it stable during all the measurement. By playing with a longer exposure time, weak light can be captured as well. To avoid the non-uniform light path inside the laser beam, only one ray of light is traced and used to calculate turbidity.

In addition to the issues of measuring the turbidity with a refractometer, the turbid medium impacts the measurement of the refractive index as well. Due to the convergence of the laser beam, the laser spot becomes asymmetric, when it is captured by a CCD that is non-perpendicular to the laser beam. What is more, turbidity makes this phenomenon much more obvious. Besides the asymmetric of the laser spot, the turbidity results in a shift of the laser spot peak, which is proportional to the attenuation coefficient. This shift needs to be corrected when applying mass-center-based algorithm to locate the laser spot. A CCD records all the distribution information of the laser spot, which makes it possible to retrieve the position information more accurately. A new algorithm, which tracks the location that divides the mass of the spot into two equal parts, is introduced in this paper, and is proved to be more accurate than the centroid algorithm in both the non-turbid environment and turbid environment.

Through the simulations and various experiments, the average accuracy of our method based on the current refractometer reaches 8 NTU in a range from 0 NTU to 200 NTU and 1.15 NTU in a range from 0 NTU to 20 NTU. We compared our method with the nephelometer specified by the NTU standard. The result computed by our method well fits the result obtained from a nephelometer. The sensitivity can be improved by increasing the length of the light path in the medium, which is very useful to guide the design of new refracto-turbidi-meter.

2

 2

FIG. 1 .

 1 FIG. 1. Principle of the refractometer. Dotted line shows the laser path according to two different refraction indices of water

I 0 I 0 -ρσ a dlI 0 dlFIG. 2 .

 0002 FIG. 2. The light absorption and diffusion in a unit volume of turbid water. The sub-diagram (a) shows the light with power of ρσ a dlI 0 is absorbed. The sub-diagram (b) shows that the light with power of ρσ d dlI 0 is diffused out of the propagation direction

0 dlFIG. 3 .

 03 FIG. 3. The light scattered from other parts of the medium to the incident light propagation direction

FIG. 4 .

 4 FIG. 4. The difference of light intensity measurement by locating the light intensity sensor at different distances of the medium

Fig. 1 ,

 1 OM and ON are two different light paths according to different refraction indices of the medium. This makes the measured flux intensity quite different when measuring two different medium samples, which have the same turbidity but different refractive indices. According to the configuration of the refractometer, the light path length in the medium named l in Eq.6 can be expressed as a function of the laser spot position, which is shown in Fig.5. The laser spot position is counted from the H point shown in Fig.1. A quadratic fitting gives us an approximate equation to calculate the length of light path according to the laser spot position, which is expressed in Eq. 10. l = f (x p ) = 6.338340 -0.000284 x p + 0.000185 x 2 p(10)

FIG. 6 .

 6 FIG.5. The relationship between the length of the light path in the medium and the laser spot position. The laser spot position is the distance from the H to p x in Fig.1

  FIG. 7. The laser spots for different laser beams with different divergence. The image is obtained from the ZEMAX simulation.

FIG. 8 .FIG. 9 .

 89 FIG. 8. The positions obtained by the different algorithms for different divergence of laser beam.(simulated in ZEMAX)

  FIG. 10. (a) the original image with pure water (b) the original image with turbid water of 444.4 NTU (c) the resulting image with pure water after passing through the low pass filter (d) the resulting image with turbid water of 444.4 NTU after passing through the low pass filter

FIG. 11 .

 11 FIG. 11. The Fourier transformation profile of the laser spot with different turbidities. The upper diagram shows the profiles with pure water (shown in red) and turbid water of 444.4 NTU (shown in blue); the bottom diagram is the zoom of the profiles from -200 spatial frequency to 200 spatial frequency

FIG. 13 .

 13 FIG.13. The calculated center provided by the centroid algorithm, new algorithm with and without filter.

Fig

  Fig 15 shows the experimental result. The light intensity I 0 is pre-measured with pure water as the reference light intensity. For each turbidity, according to Eq 6, three attenuation

  FIG.16. Experimental results for the parallel slab for low turbid medium.

2 -

 2 FIG. 17. Experiment setup for the experiments carried out with the refractometer

  FIG. 19. Experimental results with the refractometer in low turbid medium

FIG. 20 .

 20 FIG. 20. Experimental results with the refractometer

ACKNOWLEDGMENTS

Thanks to Marc Le Menn of SHOM (Service Hydrographique et Océanographique de la Marine) for providing the calibrated formazin sample, and fruitful discussion about the application.

than the centroid algorithm when applying different divergences. Table I gives more detail of the center calculated by the new algorithm, which shows a maximum error of 0.028 pixel. The turbidity of the medium is simulated by changing the density of the particles. The reference image is the image simulated in non-turbid case here. 4 different particle densities (2×10 6 /cm 3 , 4×10 6 /cm 3 , 6×10 6 /cm 3 , 8×10 6 /cm 3 ) are simulated and the result is depicted in Fig. 9. Since the turbid medium diffuses the light out of the beam, a threshold is used to eliminate those light intensities that are diffused out of the laser spot but captured by the CCD. Combined with the threshold, the new algorithm provides a much more accurate result than the centroid algorithm, which gives a deviation of 2.4 pixels. In Table . II, the error of the new algorithm can be found as about 0.069 pixel.

B. Experiments

In our last paper [START_REF] Hou | Charge-coupled devices combined with centroid algorithm for laser beam deviation measurements compared to a position-sensitive device[END_REF] , several experiments were carried out to evaluate the performance of the centroid algorithm with a mirco-positioner, which can move with a step of 0.1 µm.

To compare the performance of the centroid algorithm with the new algorithm, the same image set is chosen, and the two algorithms are applied. The centers calculated by these two algorithms are depicted in Fig. 13. Furthermore, the result for the new algorithm with the filter is included in this figure too. It is obvious that the curve of the new algorithm is much smoother than the centroid algorithm. The error of these methods can be calculated by a

VI. SIMULATION & EXPERIMENT WITH A REFRACTOMETER

A. Simulation

The simulation of measuring the turbidity with our refractometer was carried out in ZEMAX. The turbidity of the medium was changed by modifying the particle density of the medium from 1 × 10 6 /cm 3 to 1 × 10 7 /cm 3 . The divergence of the laser beam is set to 1 mrad, the same as the source used in the experiment. A CCD of 1280 × 960 pixels is simulated by a rectangular detector. Table . IV expresses the attenuation coefficient calculated from the simulation. Similarly to the parallel slab case, the attenuation coefficient given by the algorithm discussed in this paper shows a good linearity to the density of the particles in the medium, which is theoretically proportional to the turbidity of the medium.

B. Experiments in high turbid medium

Fig. 17 shows the set up of the experiment with the refractometer. The refractometer is used instead of the parallel slab. The diode laser and CCD used in this experiment are the same as those used in the parallel slab experiment. The refractometer is set-up in a small tank, in which 100 ml pure water is used as the base water. 0.5 ml 4000 NTU formazin solution was added to the small tank 11 times and is diluted to different turbid water levels.

The turbidity can be calculated according to the Eq. 23. All the experiments are carried out in the presence of a thermostat to make sure the temperature of the turbid medium does not change.

The experimental results are shown in Fig. 18. The attenuation coefficients are calculated by two different quantities, the power of the image and the pixel value given by the new algorithm, as the measured intensity I m in Eq. 21. The reference light intensity I 0 is pre-measured in pure water with the same configuration. As the turbidity increases, both methods give a trend of decrease for the attenuation coefficient. The average error of these two methods can be evaluated by a linear fitting. The method using the power of the image


Franziska Schmidt

Klaus-Peter Glaeser

Pierre Hornych

Jean-Michel Piau

Bernard Jacob

Impacts from truck traffic on road infrastructure

Economic constraints nowadays require transporting greater volumes of freight at lower cost.

Yet the physical profiles of trucks do not all generate the same effects on road infrastructure for a given tonnage hauled. The objective then lies in finding an optimal service level that reduces the damage (wear) caused to infrastructure. Results derived for the impact of trucks on pavements relate specifically to rutting as well as the potential for evaluating the aggressiveness with which axle configurations induce fatigue on asphalt pavements. The impact of truck traffic trends on road bridges will also be discussed herein.

IMPACTS ON ROAD PAVEMENTS

Pavement wear is a process involving various deterioration phenomena either acting on their own or with one another. Among the factors influencing this type of wear is the actual traffic load (i.e. the focus of this paper), which takes into close consideration the following elements: the number of axles, axle configurations (single, tandem or tridem), wheel assemblies (single or twinned), wheel loads, and tire characteristics (dimensions, pressure).

Case of rutting

Road pavement rutting as a function of the physical specifications (profile) of trucks was the topic of a European project (COST 334, 2001), during which a method was specifically proposed to calculate the level of distress (or aggressiveness) caused to pavements based on the following set of formulae: where:

is the axle load ( ) equivalency factor, as measured with respect to a 10-ton axle;

is the tire equivalency factor of the considered tire, designed with width and diameter , expressed in millimeters;

is the equivalent axle wear factor;

is the equivalent vehicle wear factor, derived by summing the equivalent wear factors of all axles on the vehicle.

Table 1 lists the results for a European-type semitrailer (40 tons, 5 axles). The axles the most prone to causing rutting are the powered axles and steering axles, whose loads are quite high for relatively narrow tires.

The aggressiveness directed at the pavement per ton transported is used as a benchmark to compare various vehicle types and may be calculated using the PER ratio, i.e.:

where is the load being transported (or payload). These calculations also indicate that a vehicle carrying a 38-ton load distributed on 4 axles, which amounts to 2 tons over the 36 presently authorized, would cause 20% more pavement distress per ton transported compared to the standard 40-ton, 5-axle truck.

Case of asphalt pavement wear and the effects of adjacent axles

The French pavement design method characterizes the aggressiveness of a given truck (by virtue of the overall fatigue imposed upon the layers of a road sub-base) via a set of coefficients that allow calculating the basic damage induced in these particular layers.

As a convention, the so-called coefficient of aggressiveness on the reference axle, i.e. a twin configuration allocated a 13-ton load, is equal to 1. For axle i with a different geometry and/or load, this coefficient of aggressiveness is defined by: where:

is the allowable number of reference axle passages that yields a cumulative wear equal to 1 at the most heavily loaded point of the road structure;

is the number of passages producing this same effect for test axle i .

The values of are calculated based on a multilayer elastic model of the pavement subjected to the action of this test axle (according to Burmister's model). These results then serve to calculate the loadings caused by maximum extension (i.e. strains, stresses), depending on the material fatigue laws used to correlate these quantities with the number of cycles to failure.

For multiple axle configurations, it is assumed that the level of aggressiveness can be deduced from the aggressiveness of a single axle, by summing over the total number of axles in the configuration, followed by weighting with a coefficient of equivalence that takes into account the full extent of interactions between adjacent axles. For an asphalt pavement, the coefficient of aggressiveness for a given axle configuration is expressed as:

where:

is the number of loads at failure for the multiple axle configuration, ref t

is the maximum tensile strain at the base of the asphalt layers for the reference axle, i t is the maximum tensile strain at the base of the asphalt layers for a single axle supporting the same wheel load as the multiple axle configuration, is the total number of axles contained in the studied axle configuration, b / 1 characterizes the material fatigue law (the value of is on the order of 5).

Table 2 provides the coefficient of equivalence values for tandem and tridem axles with respect to the asphalt pavement design, along with the output from a sample calculation of multi-axle aggressiveness. The current method used to calculate values does however present several limitations.

A study of the impact of various truck profiles raises, above all, a question over including the "multi-peak" loadings observed in the sub-base layer during the passage of multiple axles, whether tandem or tridem (Fig. 2), as well as their equivalence expressed in terms of number of standard axle passages (see Table 2).

Recent research findings have led to proposing an extension to the typical fatigue law for asphalt materials, so as to better incorporate the actual curves showing strain evolution in road pavements as multiple axle configurations travel over the test section. This extended law was established from laboratory fatigue tests that simulate real-world axle configurations.

Instead of including just the maximum strain, this law introduces 4 independent parameters related to the in situ signal form (Fig. 2).

This law, when combined with the data in Figure 2, illustrates the aggressiveness calculation results of two EMS-type truck profiles for two pavement structures built on a platform with a load-bearing capacity of 120 MPa, one designed for moderate traffic levels (6-cm layer of semi-coarse asphalt concrete + an 18-cm GB3 layer of bitumen-coated macadam), the other for very heavy traffic (8 cm of semi-coarse asphalt concrete + 31 cm of the GB3 macadam).

These results are expressed in terms of total allowable cumulative load (weight of both the vehicles and their cargo) over the entire pavement life cycle. According to this criterion, the 8-axle EMS2 is less aggressive for both pavements than the 7-axle EMS1. With the EMS1 model, the isolated powered axle is a tremendous hindrance (i.e. a coefficient of aggressiveness = 2.35), whereas the addition of a second powered axle on the EMS2 model serves to reduce aggressiveness by a wide margin, despite a higher total load.

IMPACTS ON ENGINEERING STRUCTURES

The most recent civil works on road infrastructure were designed based on Eurocodes, although the vast majority had nonetheless been calculated using prior rules, which were calibrated with lower-density traffic and lighter vehicles than what is being observed on today's roads. It is thus necessary to recalculate the effects on structures operating under current traffic conditions.

Impact of traffic trends

Typical traffic densities and truck profiles have evolved over time. Figure 4 shows the hourly truck traffic flows by time of day in both 1986 and today, in specifying the composition of traffic flows from both periods.

The calculations of extreme traffic effects from 1986 and 2010 reveal (Fig. 5a) that the Eurocode load model has always remained on the safe side relative to current traffic patterns. Figure 5b indicates that 1986 traffic effects surpass those generated by present traffic levels, hence the safety margin has been reduced due to increased traffic.

An evaluation of the long-term effects on engineering structures however is quite complex, as the diversity of extrapolation methods leads to variable results. It is essential to increase the number of traffic observations over long periods on the European road network.

Impact of various truck configurations

European studies on the potential effects of EMS systems have been undertaken, in drawing comparisons with effects induced by currently authorized configurations. We have also compared the maximum effect (bending of an isostatic bridge span) of measured traffic with the effect caused by this same traffic level, yet modified by replacing three current trucks with two EMS. Up to span lengths of 50 m, the level of aggressiveness stays similar, but as these lengths expand the effect becomes more pronounced (Fig. 6).

These various studies have demonstrated that the impact of traffic on bridges depends to a large extent on: truck configurations (both weight and dimensions), traffic density, travel conditions (specifically the spacing between trucks), and initial bridge design and type. One approach to easily verifying and comparing the aggressiveness of any truck configuration on road bridges and then confirming acceptability consists of implementing a bridge formula, like the one applied in the United States and several other countries, but not yet common practice in Europe.

CONCLUSION

The increase in total weight and flows of freight vehicles has led road facility managers to periodically verify that the infrastructure is still capable of withstanding traffic under acceptable safety and cost conditions. More refined methods are being developed in order to evaluate the effects of new truck configurations on pavements, the surface layer (rutting) and the overall structure (fatigue cracking).

As for bridges, which represent critical nodes on the road network, the forecast of increasingly intense extreme traffic effects now warrants sophisticated extrapolation methods. To implement such methods, it is necessary to produce reliable load measurements spanning the long term, along with periodic monitoring of vehicle configuration modifications and changes in traffic conditions. The safety and sustainability of currently operational facilities, in addition to maintenance and repair costs, depend heavily on not only the freight tonnage being transported by road, but also the new truck configurations resulting from revised regulations. The future challenge thus consists of reconciling the optimization of road freight transport plus its environmental costs and impacts (promoting heavier and bigger vehicles) with an optimized road facility management strategy. Political tradeoffs, relying on accurate scientific and technical studies, must be made and a suitable fare schedule adopted in order for the benefits of some to cover the expenses of others. "Portée" = "Span"

Figure 1

 1 Figure 1 compares these ratios for 10 vehicles or vehicle combinations, of which 9 are traveling (or capable of traveling) in Europe while the tenth is on Australian roads. The level of pavement wear does not always increase with the size of the load hauled, especially when the load is well distributed over all axles, as is the case for vehicle combinations currently being experimented in various European countries, i.e. European Modular Systems (EMS).

Figure 1 :Figure 2 :

 12 Figure 1: Ratio of pavement impact to load transported for various vehicle combinations.Single axles shown in white, twin wheel assemblies in black[START_REF] Glaeser | Comparison of the performance of heavy vehicles -Results of the OECD Study "Moving Freight with Better Trucks[END_REF]

Figure 3 :

 3 Figure 3: EMS profiles used to calculate the aggressiveness on structures 1 and 2 -

Figure 4 :Figure 5 :

 45 Figure 4: Evolution in hourly traffic flows and breakdown of truck traffic(Auxerre-1986 and A9 Motorway-2010)

Table 1 :

 1 Impact on road pavement by a 5-axle, 40-ton semitrailer(26-ton payload)

	Tire spec	295/80R22.5 295/80R22.5 385/65R22.5 385/65R22.5 385/65R22.5
	Twin vs. Single	Single	Twin	Single	Single	Single
	Axle load (tons)	6.5	11.5	7.33	7.33	7.33
	TCF	3.14	1.00	2.25	2.25	2.25
	AWF	1.33	1.32	1.21	1.21	1.21
	VWF			6.28
	PER			26 (tons) = 0.24

Table 2 :

 2 Tandem and tridem trailer equivalence relative to single wheel assemblies, and equivalent number of standard axles for asphalt pavement fatigue Axles have been allocated a 10.5-ton load, with asphalt materials (exponent 5 in fatigue, use of the French design method)

	Type of trailer	Coefficient of equivalence	Equivalent number of axles
	Tandem trailer with single wheels	0.75	0.52
	Tridem trailer with single wheels	1.10	1.14