dataesr/scientific-paragraphs-categorization huggingface dataset:
Post-processing of SAFRAN-Crocus data and comparison with MODIS-retrieved data To compare the SSA values simulated by SAFRAN-Crocus with those retrieved from MODIS data, we computed a ver- tical average of the SSA of the surface layers using Crocus outputs relevant to the the first centimeters of the snowpack. This average was performed to a single and appropriate surface SSA value to be compared to MODIS retrieved data. This was done considering an exponential decay to accomodate the attenuation of the solar radiation through the snowpack  (Warren, 1982)  as SSA surf = s 0 SSA(z) e -z d dz s 0 e -z d dz , ( 2 ) where s is a truncation of the penetration depth, and d denotes the e-folding depth. The latter varies with SSA, density, and wavelength  (Warren, 1982). In order to simplify the processing steps of SAFRAN-Crocus outputs, we used a single value of d = 2 cm and s = 4 cm for the whole study.
Indeed, the sensitivity study conducted by  Kokhanovsky et al. (2011)  revealed that NIR wavelengths are only sensitive to the optical radius on the very first centimeters of the snowpack. 3  gives an illustration of the variation of the e-folding depth for two extreme cases (fresh light snow and aged dense snow) and for each of the MODIS bands used in this study. These values have been calculated with DISORT and assuming that grains are disconnected spheres. Note that, as noticed in  Sergent et al. (1987) , the e-folding depth computed using this assumption may be higher than for real snow. Following typical extremes values for these two cases, SAFRAN-Crocus SSA data were processed for the six studied dates using an e-folding depth of 1 mm and 40 mm. The root mean square deviation between all SSA values obtained in the two cases range from 0.
7 to 8. 0 m 2  kg - 1  depending on the date (mean 4. 24 m 2 kg -1 ). These variations are sufficiently small to justify the use of a single value for d in this study. Further developments may consider using wavelength and perhaps even SSA and density specific d values for an even more detailed computation of a representative surface SSA value corresponding to the remotely-sensed variable. According to the minimum and maximum values presented in Table  3 , the surface SSA was processed for the six studied dates from the outputs of SAFRAN-Crocus using an e-folding depth of 1 mm and 40 mm respectively. The standard deviation of the SSA processed in these two cases is small (3. 53 m 2 kg -1 ). This shows that a single value of the penetration depth can be used throughout the study to compute a relevant value for surface snow SSA from Crocus outputs to be compared to MODIS-derived data regardless the spectral bands upon which the retrieved values are computed.
Field measurements To complement the comparison between MODIS-retrieved data and SAFRAN-Crocus outputs and introduce a slight dose of ground truthing in our analysis, field measurements of SSA were performed in winter 2012. Two field sites featuring a maximum homogeneity in terms of slope, aspect, absence of shading over a characteristic horizontal scale on the order of MODIS pixel sizes were selected for this purpose within the Belledonne massif. One of them is a flat terrain at 2000 m. a. s. l. and the second one is a south-westerly facing slope tilted around 15 • , at 2100 m a. s. l. Near-surface vertical profiles of snow SSA and density were measured using the optical instrument DUFISSS  (Gallet et al. , 2009). The estimated accuracy of each SSA measurement is ±10 %. Repeated measurements within the same areas were performed with the intent to quantify the in situ variability of surface snow SSA.
From reflectance to SSA Maps of ground reflectance were obtained with MODImLab from MOD02 data (corrected for topographic effects, and corrected or not for anisotropic reflectance effects), or readily available from MOD09 data products. Two general classes of methods were then employed to convert spectral reflectances into surface SSA values. In one case, the spectral signature of snow was converted based on a look-up table built from a wide range of DISORT runs. Alternatively, the ART theory was employed. The two methods are described in detail below. An overview of the methods and options is provided in Table  4.
Comparison to field measurements Table  5  shows an overview of the comparison between simultaneous estimates the SSA of surface snow using in-situ measurements, MODIS-derived estimates and SAFRAN-Crocus simulated values. It shows that MODIS DTA SSA retrievals and SAFRAN-Crocus data are the closest to field measurements. SSA MODIS data retrieved without topographic corrections (DA and DR) exhibits significant biases compared to field measurements. The measured intrapixel variability is up to 5. 1 m 2 kg -1. This underlines the need for making numerous field measurements inside the pixel area to be as representative as possible of the snow properties within each MODIS pixel. For the two dates considered, the standard deviation of MODIS-derived data within a topographic class is low (2. 4 and 1.
Although SAFRAN-Crocus outputs can by no means be considered ground truth for the evaluation of the different retrieval methods employed, it was used here as a common benchmark to compare the different methods. It was considered that the overall realism of the meteorological driving data along with the detailed numerical simulations of the physical properties of the snowpack, evaluated independently in several previous studies, provides a physically consistent view of the general features of surface snow SSA in the domain and the time span considered. Whether the output of a given retrieval method is in agreement with the general features of the SAFRAN-Crocus output is hypothesized here to mean that the large scale features of the physical properties of the uppermost snow layers are well represented in the MODIS-derived surface snow SSA estimate.
With this threshold, the method using four bands provides data for about 87% of the pixels; in this case, the RMSD between the MODIS-derived and SAFRAN-Crocus values were approximately the same whether four or one band were used, with 14. 0 and 14. 8 m 2 kg -1 , respectively. The overall SSA mean difference on the subset was reduced from 1. 7 m 2 kg -1 when using band 5 alone to -0. 1 m 2 kg -1 with four bands. Using four bands generally yields smaller SSA values: this result is consistent with  Li et al. (2001)  who reported the fact that the SSA usually decreases with depth in the first centimeters, consistent with the generally observed decrease of SSA with time  (Domine et al. , 2008) , and the fact that band 2 (860 nm) penetrates deeper in the snowpack, as shown in Table 3. In the following, due to the fact that the obtained results are not significantly different, only computations using only Table  5.
Intraclass SSA variability Figure  9  shows the standard deviations of SSA values from SAFRAN-Crocus and MODIS data on the six dates. The standard deviation is systematically higher for satelliteretrieved data. Maps of SSA illustrated in Fig. 6  also illustrate the greater dispersion of DTA values. Both data sources have very different signal entropy, i. e. even on the same number of pixels, the two datasets feature different degrees of freedom. Indeed, while SAFRAN-Crocus provides estimates based on a discrete subset of topographic parameters (classes defined by massif, elevation, aspect and slope) representing 891 different classes altogether (cf. Table  2 ), each MODIS pixel is considered independant from each other. In fact, the mean standard deviation for DTA within classes represented by at least 10 pixels is 10.
Interclass SSA variability We analyse here the variability of SAFRAN-Crocus and DTA retrievals by means of a multiple linear regression of log(SSA) over topographic parameters and date. We used log(SSA) rather than SSA to overcome limitations of the linear regression technique due to the asymmetry of SSA distributions between the two datasets compared. The predictors used are date, elevation, slope, aspect, and massif. We also took into account predictor interactions, because topog- raphy effects tend to depend strongly on the date. In addition, effects related to the position of the sun are related to a combination of slope and aspect. For DTA, standard regression techniques (not shown here) show the significance of all predictors, as well as of the interactions between date and massif, and date, slope and aspect.
This is the only predictor considered where the retrievals and the model disagree on the trends of variability. This behaviour needs a larger dataset to be analyzed in detail. These results strengthen our confidence in MODIS data retrievals, as the technique show physically consistent behaviours of retrieved SSA. The relative differences between retrievals and SAFRAN-Crocus -mainly, gradient intensity or massifs heterogeneities -calls for further in-depth comparisons. A larger set of data over a whole snowy season, and validation against field measurements of SSA, are required to further analyze these results, buiding on the methodology outlined in the present study.
Conclusions In this work, we assessed the effect of accounting for (1) the local topography and multiple reflections, (2) the anisotropy of snow and ice reflection, (3) the shape of snow grains, in snow grain size retrievals from MODIS data in mountainous areas. We compared different methods (with combinations of these effects) on six clear sky dates representative of the different states of the winter snowpack, in the French Alps. In terms of SSA, the method using a topographic correction on absolute reflectance (though assuming Lambertian surface and spherical disconnected particles) is the most consistent with the SSA provided by the estimates of SAFRAN-Crocus and with field measurements. In this case, the overall RMSD is 9. 4 m 2 kg -1 and the mean difference is 0. 1 m 2 kg -1. The differences with the other methods are larger on date with high mean SSA values (high reflectance), where the other methods (including band ratioing) tend to give higher SSA than SAFRAN-Crocus.
Furthermore, the presence of mixed pixels could not be excluded and surface roughness is not taken into account. These two facts can partly explain that the anisotropy corrections, not adequate to mixed pixels and roughness, does not benefit to the retrieval. In future work, these problems should be addressed in order to reduce the uncertainties of retrieval implied by these features. The mean variability of SSA within the topographic classes of SAFRAN-Crocus estimated using MODIS data varies from 8 to 6 m 2 kg -1 when the number of classes increases from roughly 300 to 400. Along with the results of the field measurements, this seems to indicate that semidistributed snowpack modelling with a sufficient number of classes gives a satisfying representation of the snowpack variability for these dates in the French Alps at the scale of the MODIS 500 m pixels.
This is consistent with the results of  Fiddes and Gruber (2012) , who demonstrated that lumped land surface simulations could match the performance of fully distributed simulations provided that a minimum number of adequately chosen classes are considered. This study opens the way to the assimilation of MODIS-derived information over wide geographical areas in the detailed snowpack model Crocus. Our findings indicate that such an assimilation may be appropriate in the fixed altitude/slope/aspect/massif framework of the SAFRAN-Crocus-MEPRA chain used operationally for avalanche warning activities in France  (Durand et al. , 1999) , and even potentially surpass direct assimilation in a fully distributed simulation where inter-pixel variability ("noise") from MODIS data could be detrimental to the model overall performance.
Acknowledgements. The authors are grateful to  J. Gardelle ,  Q. Libois  and  M. Harter  for their help and useful discussions. A. Mary  thanks the  Ecole Nationale de la Méteorologie  for the opportunity to work on this subject, and  C. Fischer  for allowing time for writing this paper. A. Kokhanovsky acknowledges the support of  BMBF   CLIMSLIP  Project. We thank the scientific editor  M. Schneebeli  and the reviewers  A. W. Nolin ,  T. H. Painter ,  R. Essery  and  H. Löwe  for their insightful and relevant reviews which allowed to greatly improve this paper. Edited by: M. Schneebeli The publication of this article is financed by  CNRS-INSU.
The present study provides an extensive overview of red and near infra-red (NIR) spectral relationships found in the literature and used to constrain red or NIR-modeling schemes in current atmospheric correction (AC) algorithms with the aim to improve water-leaving reflectance retrievals, ρ w (λ ), in turbid waters. However, most of these spectral relationships have been developed with restricted datasets and, subsequently, may not be globally valid, explaining the need of an accurate validation exercise. Spectral relationships are validated here with turbid in situ data for ρ w (λ ). Functions estimating ρ w (λ ) in the red were only valid for moderately turbid waters (ρ w (λ NIR ) < 3. 10 -3 ). In contrast, bounding equations used to limit ρ w (667) retrievals according to the water signal at 555 nm, appeared to be valid for all turbidity ranges presented in the in situ dataset.
Similarly, several studies investigated the spectral dependence of the marine reflectance in the NIR region of the spectrum to model ρ w (λ NIR ) for the AC of second generation ocean color satellite images (hereafter referred to as the NIR spectral relationships)  [18] [19] [20]. Lee et al. [21]  also suggested to correct remote sensing ρ w (667) estimations (due, for instance, to imperfect AC) for the Quasi-Analytical Algorithm by means of spectral relationships between ρ w (667) and ρ w (555). Most of these spectral relationships have been developed with restricted datasets and have not been confirmed theoretically nor validated with independent in situ datasets. An overview and validation of these different red and NIR marine spectral relationships are thus essential to verify if these relationships are globally valid and if they can be used to improve AC for past, present and future ocean color sensors.
g. , the iterative scheme suggested by Stumpf et al. [4]  and Bailey et al. [5]  modeling ρ w (λ NIR ) according to ρ w (λ red )). With the arrival of SWIR ocean color bands, a similar exercise could be performed to evaluate spectral relationships allowing to estimate ρ w (λ ) in the NIR from ρ w (λ ) in the SWIR spectral domain, and inversely. However, the present study is limited by the spectral range of the in situ reflectance measurements, notably, from 400 to 900 nm, and is thus valuable for sensors with visible and NIR spectral bands (e. g. , SeaWiFS, MODIS and MERIS sensors, the SEVIRI instrument on MSG, the Geostationary Ocean Color Imager (GOCI) and possibly the future GOCI-2 carried by COMS) as well as for studies covering decadal time scales including data from past and current sensors.
In situ data Above-water reflectance measurements were made using TriOS-RAMSES hyperspectral radiometers during 63 sea campaigns undertaken between 2001 and 2012 (860 stations). Data were collected in coastal waters located in the southern North Sea and English Channel  [32] , the Celtic the Ligurian Sea, the Adriatic Sea and in the Atlantic Ocean along the coasts of Portugal and French Guyana  [33, 34]. This dataset is particularly suitable for the validation of the spectral relationships as it includes measurements over contrasted and optically complex coastal waters. In situ data processing, averaging and selection are described in Ruddick et al. [19]. Out of the 860 stations, 105 in situ reflectance spectra satisfy the selection criteria and were not used by Ruddick et al. [19]  for the calibration of the NIR similarity spectrum.
3(a)-3(c)]. Accordingly, α(λ 1 , λ 2 ) has a wider validity range when λ 1 is taken at longer wavelengths (> 750 nm). However, the constant α(λ 1 , λ 2 ) values are not valid for ρ w (λ NIR ) above 3. 10 -2. ρ w (λ NIR ) is systematically underestimated for these water masses [Figs. 3(a)-3(c)]. This suggests that one or more assumptions made by Ruddick et al. [18, 19]  are not verified with the present dataset and result in variations of the reflectance ratio α(λ 1 , λ 2 ) with turbidity. Indeed, Ruddick et al. [18, 19]   [36] , who showed a flattening of the reflectance ratios ρ w (850)/ρ w (550) and ρ w (850)/ρ w (650) with increasing TSM concentrations, and with the conclusions of Shi and Wang  [29] , who observed a maxima in ρ w (675) for ρ w (859) values greater than 0. 03. Our results also confirm the observations of Doron et al.
Conclusion The present study aimed to review spectral relationships in order to select appropriate functions which could be used as constraints to improve red or NIR-modeling schemes in current AC processes. Spectral relationships found in the literature were developed with restricted or regional datasets explaining the need of an accurate validation. Sixteen published spectral relationships, estimating ρ w (λ ) in the visible or NIR spectral region, were validated using 105 highly accurate in situ above-water reflectance measurements taken in diverse coastal water types. Functions used to model ρ w (λ ) at 670 nm for CZCS AC processes  [10] [11] [12] 15] , systematically underestimated the water signal for very turbid waters. Similarly, the function suggested by Lee et al. [21]  to estimate ρ w (667) from the water signal in the green and the blue-green reflectance ratio, tends to underestimate higher ρ w (667) values.
In contrast, the bounding equations used in the latest version of the QAA, to evaluate maximum and minimum ρ w (667) estimations according to the water signal in the green, appear to be valid for the entire range of turbidity encountered in the in situ dataset. In the NIR spectral region, the constant reflectance ratio α(λ 1 , λ 2 ), suggested by Ruddick et al. [18, 19]  to extend the GW94 AC algorithm to turbid waters, was valid for moderately to very turbid waters with ρ w (865 -869) values below 10 -2 , while the polynomial function of Wang et al. [20]  was also valid for extremely turbid water masses. However, the latter slightly underestimated ρ w (869) for water masses with ρ w (λ NIR ) exceeding 0. 05. From this study we can conclude that the red spectral relationships are not appropriate for the entire range of coastal turbidity encountered in our in situ dataset suggesting that either the red spectral functions need to be updated or that the functions should differ according to the optical water type and/or the turbidity range.
Acknowledgments Most of the in situ measurements used here were collected in the framework of the BELCOLOUR-1 and BELCOLOUR-2 projects funded by the  Belgian Science Policy Office STEREO programme. Griet Neukermans  and  Barbara Van Mol  are acknowledged for data acquisition. This work has been supported by the  French Spatial Agency (CNES)  through the  TOSCA program  and the " Ministère de l'Enseignement et de la Recherche Francaise " which provided a PhD scholarship.
Moreover, to test the robustness of our analytical results that assume equal dispersal rates for the prey and the predator, we explored cases with contrasting dispersal rates of the prey and of the predator (d P = 100 d N and d P = 0. 01 d N ). The stability of the dynamics of the metacommunity was investigated using two methods. First, we studied the stability in the neighborhood of the equilibrium of the metacommunity. Equilibrium densities were derived analytically when possible or computed numerically using the function fsolve in Matlab 7. 6 (Levenberg-Marquardt algorithm). We retained equilibriums with positive densities. The stability was assessed checking the eigenvalues of the Jacobian matrix of the system (1). When the real parts of all eigenvalues are negative, the equilibrium is stable; when at least one eigenvalue has a positive real part, the equilibrium is unstable.
This measurement of the stability of population dynamics gives binary information: it indicates whether the population dynamics converge to the equilibrium or not. To complete this information, we used a second measurement to characterize the stability of population dynamics that do not reach equilibrium. We simulated the population dynamics in the landscape by numerically integrating equations (1) over a period of 30000 time units using the function ode15s in Matlab 7. 6 (adaptive step size and variable order integrator based on the numerical differentiation formulas). According to the simulations, asymptotic regime (stable equilibrium or a stable limit cycle) was reached after 20000 units of time and we performed measurements on time series between 20000 and 30000 units of time. The stability of the population dynamics was quantified by the amplitude of the fluctuations of population densities over time and by the minimal densities reached in the time series.
The inter-and seasonal patterns of water vapor and canopy carbon fluxes were compared for four forest ecosystems in two contrasting climatic zones in Europe. The eddy covariance and ancillary data were taken from the Carboeurope and FLUXNET databases and a linear modeling statistical analysis was made. The four sites were a high-density poplar (Populus spp. ) short rotation coppice plantation (in Lochristi, Belgium) and a mature Scots pine (Pinus sylvestris) forest (in Brasschaat, Belgium) in the Temperate climate versus a fast-growing Eucalypt (Eucalyptus) plantation (in Espirra, Portugal) and a Holm oak (Quercus ilex) forest (in Puechabon, France) in the Mediterranean climate. • The Eucalypt stand showed an efficient stomatal control in response to changes in vapor pressure deficit (VPD), suggesting an ideal adaptation of this species to the severe Mediterranean climate.
For this study we used eddy covariance data in combination with ancillary data which were gathered at each site. The four sites were a high-density poplar (Populus spp. ) short rotation coppice plantation (in Lochristi, Belgium) and a mature Scots pine (P. sylvestris) forest (in Brasschaat, Belgium) in the temperate climate versus a fast-growing Eucalypt (Eucalyptus) plantation coppiced for pulp production (in Espirra, Portugal) and a Holm oak (Q. ilex) forest (in Puechabon, France) in the Mediterranean climate. The time periods analyzed for each site were constrained by available data serie, which were 2010-2011for the poplar site, 1999-2010 for the Scots pine site, 2001-2006 for the Holm oak site and 2002-2006 for the Eucalypt site. The latter period concerned the last six years of a 12-year rotation cycle with a clear cut in November 2006.
Experimental sites Four experimental forest sites were selected for this comparative study. Two sites with a temperate maritime climate -"Lochristi   1. The four forest stands had a very different vegetation type, stand structure, phenology and management. A statistical analysis with weekly data based on linear models with analysis of variance, multiple linear regressions and correlation analysis, was performed on the entire data series of the four sites and separately on the years with higher and lower precipitation. These 2 years (Table  2 ) were selected with the aim to study the role of water availability related factors as drivers for GPP at each site. As the inter-annual pattern of rainfall presented a very high variability at the Mediterranean sites we selected the year with the least precipitation in combination with a clear summer drought.