Bouilhol Emmanuel
email: emmanuel.bouilhol@u-bordeaux.fr

Edgar Lefevre

Thierno Barry

Florian Levet

Anne Beghin

Virgile Viasnoff

Xareni Galindo

Rémi Galland

Jean-Baptiste Sibarita

Macha Nikolski
email: macha.nikolski@u-bordeaux.fr

SalienceNet: an unsupervised Image-to-Image translation method for nuclei saliency enhancement in microscopy images

Keywords: Bioimaging, Deep Learning, Microscopy, Image Processing, Nuclei

Automatic segmentation of nuclei in low-light microscopy images remains a difficult task, especially for highthroughput experiments where need for automation is strong. Low saliency of nuclei with respect to the background, variability of their intensity together with low signal-to-noise ratio in these images constitute a major challenge for mainstream algorithms of nuclei segmentation. In this work we introduce SalienceNet, an unsupervised deep learning-based method that uses the style transfer properties of cycleGAN to transform low saliency images into high saliency images, thus enabling accurate segmentation by downstream analysis methods, and that without need for any parameter tuning. We have acquired a novel dataset of organoid images with soSPIM, a microscopy technique that enables the acquisition of images in low-light conditions. Our experiments show that SalienceNet increased the saliency of these images up to the desired level. Moreover, we evaluated the impact of SalienceNet on segmentation for both Otsu thresholding and StarDist and have shown that enhancing nuclei with SalienceNet improved segmentation results using Otsu thresholding by 30% and using StarDist by 26% in terms of IOU when compared to segmentation of non-enhanced images. Together these results show that SalienceNet can be used as a common preprocessing step to automate nuclei segmentation pipelines for low-light microscopy images. 64 filters, 7x7, s = 1 128 filters, 3x3, s = 2 256 filters, 3x3, s = 2 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 256 filters, 3x3, s = 1 128 filters, 3x3, s = 2 64 filters, 3x3, s = 2 1 filters, 7x7, s = 1 64 filters, 4x4, s = 2 128 filters, 4x4, s = 2 256 filters, 4x4, s = 2 512 filters, 4x4, s = 2 1 filters, 4x4, s = 2

INTRODUCTION

Segmentation of cell nuclei is of particular interest for a number of applications such as cell detection, counting or tracking, morphology analysis and quantification of molecular expression. Being able to automatically segment cell nuclei with high precision is particularly important in the case of high-throughput microscopy imaging, where it is often the first step for downstream quantitative data analysis workflows. Indeed, the quality of downstream quantitative analyses is heavily dependent on the accuracy of segmentation, making precise nuclei segmentation essential for drawing meaningful biological conclusions.

Many solutions have been developed, as exemplified by computational competitions such as reported in [START_REF] Caicedo | Nucleus segmentation across imaging experiments: the 2018 data science bowl[END_REF]. Among popular classical image analysis methods used for nuclei segmentation are thresholding and watershed algorithm [START_REF] Malpica | Applying watershed algorithms to the segmentation of clustered nuclei[END_REF] as well as active contour [START_REF] Li | 3d cell nuclei segmentation based on gradient flow tracking[END_REF].

Challenges for automatizing this process are due to a number of image characteristics that can strongly vary between biological and image acquisition conditions. Among them, we can cite such aspects as morphological differences between nuclei from different tissues, heterogeneity of intensity and texture, variation in spatial organization such as the presence of both sparse or dense images with touching nuclei, as well as imaging artifacts (e.g., low signal-to-noise ratio or out-of-focus signal) [START_REF] Zhou | Cia-net: nuclei instance segmentation with contour-aware information aggregation[END_REF]. This results in the necessity to fine-tune numerous parameters between different image acquisitions, or even between individual images.

Recent deep-learning based tools such as Cellpose [START_REF] Stringer | Cellpose: a generalist algorithm for cellular segmentation[END_REF] and StardDist [START_REF] Schmidt | Cell detection with star-convex polygons[END_REF] have greatly reduced the necessity to choose specific parameters. However, despite these important methodological advances, no single combination of methods and parameters can be adopted to automatically perform nuclei segmentation in all images, due to the aforementioned heterogeneity of biological samples and technical artifacts [START_REF] Hollandi | Nucleus segmentation: towards automated solutions[END_REF]. In particular, live-cell imaging represents a stumbling block for these techniques, since these images are often acquired with low light levels and thus have very low SNR and artifacts. Moreover, current supervised Deep Learning models for nuclei segmentation follow the supervised paradigm and thus require well annotated datasets, which (i) engenders bias due to inaccuracy and incompleteness of available segmentation, where nuclei are improperly annotated and unevenly distributed across images [START_REF] He | Cyclegan with an improved loss function for cell detection using partly labeled images[END_REF] and (ii) limits application to datasets with different image characteristics.

In this paper, instead of focusing on the segmentation itself, we propose to tackle this problem by enhancing the nuclei prior to segmentation step, making the task easy for classical nuclei segmentation tools. Specifically, we take advantage of recent advances in the field of unsupervised generative adversarial networks, aiming to translate images from the source domain to the target domain and alleviating the image annotation requirement. For nuclei enhancement task, the target domain corresponds to images with highly salient nuclei, where strong signal difference between the nuclei and background make segmentation straightforward.

In this work, we introduce SalienceNet, a novel unsupervised Deep Learning-based approach for nuclei saliency enhancement in microscopy images that does not require image annotation when there is need to train the network on new data with different characteristics. We showcase how this can be achieved for translating organoid images acquired with low light into contrasted output images, by training the SalienceNet without providing the network with prior annotation of newly acquired low contrast images. SalienceNet gives a new twist to automatic nuclei segmentation by adapting the domain style transfer framework to this specific task, and thus does not require extensive annotation. We trained a ResNetbased CycleGAN with a custom loss function dedicated to the task of nuclei enhancement, where the intensity of the nuclei and in particular their borders, are made more salient regardless of the contrast, intensity, textures, or shapes of the nuclei in the input data. Furthermore, we evaluated the impact of the obtained nuclei enhancement on the downstream nuclei segmentation by performing segmentation using conventional methods on the enhanced images and have shown that such a pipeline achieves better performance than segmenting the nuclei directly on the original images. We demonstrate here that incorporating SalienceNet in a standard segmentation pipeline, makes it possible to avoid the manual parameter fine-tuning steps.

RELATED WORK

Nuclei segmentation

Nucleus segmentation methods can be partitioned in two major groups: those that rely on classical image processing approaches and those that propose Deep Learning models. For a thorough review, we refer the reader to [START_REF] Hollandi | Nucleus segmentation: towards automated solutions[END_REF].

Image processing pipelines usually contain a number of filtering and thresholding steps combined, if needed, with basic morphological operators to differentiate nuclei [START_REF] Malpica | Applying watershed algorithms to the segmentation of clustered nuclei[END_REF][START_REF] Li | 3d cell nuclei segmentation based on gradient flow tracking[END_REF]. A number of such methods are available as plugins of the main biological analyses open-source software tools such as Fiji [START_REF] Schindelin | Fiji: an opensource platform for biological-image analysis[END_REF], ICY [START_REF] De Chaumont | Icy: an open bioimage informatics platform for extended reproducible research[END_REF], QuPath [START_REF] Bankhead | Qupath: Open source software for digital pathology image analysis[END_REF] or CellProfiler [START_REF] Mcquin | Cellprofiler 3.0: Next-generation image processing for biology[END_REF]. The development of classical image processing methods for nuclei segmentation is still an active field. For example, in a recent publication [START_REF] Haase | Clij: Gpuaccelerated image processing for everyone[END_REF] the authors propose first to denoise the images with Gaussian blur, second to separate regions using Voronoï tessellation, and to finally obtain a binary mask by applying an Otsu thresholding to obtain the segmentation. However, time-consuming parameter finetuning is required from the user at different steps of such classical image processing pipelines, making processing large amount of data impractical [START_REF] Hollandi | Nucleus segmentation: towards automated solutions[END_REF].

The need for an automatized solution capable to segment the nuclei in images with different characteristics, pushed for the adoption of methods based on Deep Learning. The U-Net architecture [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] is used as part of recent Deep Learning nucleus/cell segmentation methods, such as Cellpose [START_REF] Stringer | Cellpose: a generalist algorithm for cellular segmentation[END_REF] and StarDist [START_REF] Schmidt | Cell detection with star-convex polygons[END_REF]. Another successful architecture is Mask R-CNN, that has been recently adapted for nuclei segmentation by the authors of nucleAIzer [START_REF] Hollandi | nucleaizer: a parameter-free deep learning framework for nucleus segmentation using image style transfer[END_REF]. ImageJ has recently proposed Deep Learning-based segmentation plugins, and pre-trained models are available through DeepImageJ (Gómez-de [START_REF] Gómez-De Mariscal | Deepimagej: A user-friendly environment to run deep learning models in imagej[END_REF].

The success of the aforementioned Deep Learning methods for nuclei segmentation is particularly due to the use of large and relatively varied training datasets, with images acquired using different microscopy modalities. Nevertheless, establishing a general solution is still an unmet need, especially for images acquired with novel microscopy techniques, such as for example the live-cell imaging [START_REF] Ettinger | Fluorescence live cell imaging[END_REF] that reduces the intensity of the light sources of the microscope to a minimum in order to limit the photo-damage to the cells thus be able to observe them over long periods of time. Resulting images have a reduced signal intensity and low SNR. Importantly, having both (i) not been part of the training and evaluation datasets of the aforementioned methods and (ii) having different characteristics, such images represent a yet unsolved challenge for nuclei segmentation.

Moreover, the performance of the existing supervised deep-learning methods depends on the amount of high-quality annotated data available for training. Despite the large effort that was put to produce publicly available labels for nuclei segmentation, such as the 2018 Data Science Bowl competition, such data is often partially or even incorrectly labeled [START_REF] He | Cyclegan with an improved loss function for cell detection using partly labeled images[END_REF].

Image preprocessing

A frequently used approach to overcome the difficulty of segmentation is to preprocess the images to improve their quality. In the case of nuclei, such enhancement mainly concerns the contrast between the nuclei and the background. Most traditional image enhancement techniques rely on filtering (low pass, high pass) or on naive noise removal such as Gaussian blur. Other methods are based on normalization of image intensity, such as e.g., histogram equalization or contrast stretching (see for review [START_REF] Qi | A comprehensive overview of image enhancement techniques[END_REF]). However, in the same way as the segmentation methods themselves, these image preprocessing techniques lack the generalization ability. For example, filtering or signal normalization is not applicable to images with low SNR, as it cannot distinguish well enough the signal from the background.

Deep Learning has been also applied at the preprocessing step, in particular to estimate the trans-formation function between sets of acquired images and their enhanced counterparts through supervised learning. One of the first and most successful methods was introduced with the CARE network [START_REF] Weigert | Content-aware image restoration: pushing the limits of fluorescence microscopy[END_REF], designed to restore fluorescence microscopy data without the need to generate manual training data. The authors showed that it is possible to learn the mapping between low-intensity and high-intensity image pairs using a U-Net based neural network. In the case of live-cell imaging, this makes possible to restore the image quality. However, two characteristics of this network limit the generalization capacity of CARE to new types of images. First, CARE network follows the supervised training paradigm and thus requires matching pairs of the same image and the corresponding nuclei masks, which is time-consuming. Second, CARE comports 5 separately trained networks and uses a disagreement score between the individual network predictions to eliminate unreliable results, which implies that images with characteristics that strongly differ from those in the training set will not be well restored [START_REF] Weigert | Content-aware image restoration: pushing the limits of fluorescence microscopy[END_REF].

Image to Image translation

Image quality enhancement has also been approached through image to image translation deep learning methods. The goal is to transform an image having a particular style (source style) into a desired target style. The most efficient models are based on GANs [START_REF] Pang | Image-toimage translation: Methods and applications[END_REF][START_REF] Wang | A state-of-the-art review on image synthesis with generative adversarial networks[END_REF]. Authors of pix2pix [START_REF] Isola | Image-to-image translation with conditional adversarial networks[END_REF] were the first to apply a GAN-based architecture to perform the image to image translation. It is a fully supervised method that requires large paired image datasets to train the translation model that transforms the source images to the desired target images. In the context of nuclei segmentation, pix2pix has been used by the authors of nucleAIzer for data augmentation of their training nuclei datasets. Specialized image enhancement models have been since proposed, such as Cycle-CBAM [START_REF] You | Fundus image enhancement method based on cyclegan[END_REF] for retinal image enhancement and UW-CycleGAN [START_REF] Du | Unpaired underwater image enhancement based on cyclegan[END_REF] for underwater image enhancement, both based on the CycleGAN architecture. Moreover, enhancement of objects of interest has been proposed by the authors of DE-CycleGAN [START_REF] Gao | Decyclegan: An object enhancement network for weak vehicle detection in satellite images[END_REF] to enhance the weak targets for the purpose of accurate vehicle detection.

PROPOSED METHOD

In this section, we present the SalienceNet nuclei saliency enhancement network in detail. We first overview the network's architecture, and then we discuss the custom generator loss function that drives the saliency enhancement.

Network architecture

SalienceNet implements the image style transfer for nuclei microscopy images with CycleGAN architecture [START_REF] Zhu | Unpaired image-to-image translation using cycleconsistent adversarial networks[END_REF] where the network is composed of two Generative Adversarial Network (GAN) blocks that exchange information during training as shown in figure 1. Let X be the domain of acquired nuclei images and Y the style domain of images with enhanced nuclei saliency. Images do not have to be paired. SalienceNet translates an image from domain X to the target domain Y by learning a mapping G : X → Y such that the distribution of images from G(X) is indistinguishable from Y by an adversarial loss.

The architecture is based on the simultaneous training of two generator models and two discriminator models (see figure 1). First, generator G takes input from the domain X and outputs images for the target style domain Y , and second, generator F takes input from the domain Y and generates images for the domain X. Adversarial discriminator models are used to drive the training by estimating how well the generated images fit the domain: D Y distinguishes the outputs of G(X) from domain Y ; in the same manner, D X distinguishes the outputs of F(Y ) from domain X.

In our model the discriminators D X and D Y are implemented as PatchGAN classifiers, composed of 4 convolution blocks (see figure 2), each containing a convolution layer, an instance normalization layer and an activation layer (LeakyReLU). The generators G and F are implemented as ResNets having the same structure with 3 down convolutions, followed by 9 residual blocks, before applying 2 transpose convolutions and one last convolution layer with a Tanh activation (see figure 2).

The discriminator is implemented as a PatchGAN model that outputs a square feature map of values, each value encoding the probability that the corresponding patch in the input image is real. These values are further averaged to generate the global likelihood.

Since the mapping G : X → Y is highly underconstrained, CycleGAN couples it with an inverse mapping F : Y → X: the output "fake Y " from the X → Y generator is used as input to the Y → X generator, whose output "cycle X" should match the original input image X (and vice versa). This is en- forced though the cycle consistency loss to obtain

F(G(X)) ≈ X and F(G(Y )) ≈ Y .

Generator loss function

An additional generator loss is used to enforce the cycle consistency and to measure the difference between the generated output "cycle X" and X as well as between the "cycle Y " and Y . This regularization makes possible to constrain the generation process to image translation.

For SalienceNet we defined the generator loss function as a combination of three terms: (i) the Mean Squared Error (MSE), (ii) the Mean Gradient Error (MGE) and (iii) the Mean Structural SIMilarity index (MSSIM).

The Mean Squared Error (MSE) computes the mean of the squared differences between true and pre-

dicted values L MSE = 1 N ∑ N i=1 ((x i ) -( xi )) 2 .
This term ensures that the generator does not produce outliers too far from the target domain. However, MSE used alone is known to lead to blurring due to the averaging between possible outputs, which in image-to-image translation can lead to low-quality blurred results.

In the case of nuclei segmentation, blurring can yield images where nuclei boundaries are particularly difficult to accurately segment. To solve this gradient problem, we added the Mean Gradient Error (Lu and Chen, 2022) term L MGE that measures the differences in edges of objects between two images, with the aim to learn sharp edges. It is based on vertical and horizontal Sobel operators [START_REF] Kanopoulos | Design of an image edge detection filter using the sobel operator[END_REF], G v and G h :

G v = Y *   -1 -2 -1 0 0 0 1 2 1   G h = Y *   -1 0 1 -2 0 2 -1 0 1   .
where * is the convolution operator. These gradients are combined to define a global pixel-wise gradient map

G = G v 2 + G h 2 .
The gradient map for predicted images Ĝ is computed in the same way. The L MGE is the defined as:

L MGE = 1 n 1 m n ∑ i=1 m ∑ j=1 G(i, j) -Ĝ(i, j) 2
Finally, to drive the network to produce images with a structure similar to the input structure, we added L MSSIM the Mean Structural SIMilarity index (MSSIM) [START_REF] Wang | Image quality assessment: from error visibility to structural similarity[END_REF] as the last term. This loss function compares two images based on luminance l, contrast c and structural information s:

l(x, y) = 2µ x µ y + c 1 µ 2 x + µ 2 y + c 1 c(x, y) = 2σ x σ y + c 2 σ 2 x + σ 2 y + c 2 s(x, y) = σ xy + c 3 σ x σ y + c 3
where µ x and µ y denote the mean intensity for the input and generated image respectively; σ x and σ y are standard deviation for the original and generated images; c 1 , c 2 and c 3 are constants used to avoid instability when the denominators are close to 0. The mean SSIM can be obtained over the entire image using a local window as follows:

L MSSIM (x, y) = 1 M M ∑ i=1 l(x i , y i ) • c(x i , y i ) • s(x i , y i )
where x and y denote the input and the generated image, respectively, while x i and x j are the images at the i-th window when the local window slides over the original and generated images, and M is the number of local windows in the image.

In the case of SalienceNet the intuition for the MSSIM loss for the X → Y generator is to enforce the luminance enhancement, while for the Y → X generator to preserve the structure. The total loss function is defined as the weighted sum of the three terms:

L total = αL MSE + βL MGE + γL MSSIM
where α, β and γ are the weights of each corresponding term so that the sum α + β + γ = 1.

DATASETS

To train and evaluate our SalienceNet enhancement method, we have collected different datasets (see figure 3). First, two experimentally acquired and expertly segmented datasets (see section 4.2), which have been previously extensively used for training segmentation models. Second, we have acquired a dataset of organoid images with low-light conditions that specifically represents the segmentation challenge that we want to address, as well as generated the corresponding synthetic datasets (see sections 4.1 and 4.2). These images belong to one of the two styles:

1. Source style with low saliency of nuclei (organoid and synthetic low saliency datasets), 2. Target style with high saliency of nuclei (two experimental datasets and the synthetic high saliency dataset).

Source style datasets

To evaluate whether SalienceNet enables precise nuclei segmentation, we acquired a 3D cell culture dataset with the soSPIM technique. soSPIM is a single objective light-sheet microscopy approach capa-ble of streamlining 3D cell cultures with fast 3D liveimaging at speeds up to 300 3D cultures per hour [START_REF] Galland | 3d high-and superresolution imaging using single-objective spim[END_REF][START_REF] Beghin | Automated high-speed 3d imaging of organoid cultures with multi-scale phenotypic quantification[END_REF]. We selected 11 neuroectoderm organoids exhibiting a wide variety of shapes and densities. These organoids have been differentiated from hESCs, fixed at day 8, immunostained with DAPI and imaged using soSPIM, yielding 1056 2D slices. These 2D image slices are composing the DS org dataset.

To augment the source style dataset, in addition to the experimental 1056 2D image slices, we generated synthetic images. First, we performed an expert segmentation of nuclei on each individual 2D slice. Second, images paired with their annotated masks were used to train a simple CycleGAN. Finally, this Cy-cleGAN model was applied to transform randomly placed elliptical shapes (roughly approximating nuclei shapes) into organoid look-alike images. The elliptical shapes provide "nuclei" masks in a trivial way. We generated 1500 synthetic low-saliency images, denoted by DS synth .

Target style datasets

The goal of our network is to learn to transform an image i into e(i), where saliency [START_REF] Kim | Saliency-guided enhancement for volume visualization[END_REF] at nuclei location is enhanced. To provide the target style dataset for training the SalienceNet network, we have collected two experimental datasets where the nuclei saliency was already satisfactory for segmentation by classical pipelines and for which the nuclei segmentation masks are available. We complemented them by a synthetic high-saliency dataset.

In 2018, a Data Science Bowl competition orga- nized by Kaggle released a dataset for a challenge of "Identification and Segmentation of Nuclei in Cells" of images acquired under different conditions and of different cell types and that vary in size, magnification, and imaging method (brightfield and fluorescence). Nuclei masks have been manually created by specialists and are provided with the dataset. For the purpose of this paper, only grayscale cell culture images were kept, yielding the TS DB with 551 images. Experimentally acquired nuclei images from human cell lines [START_REF] Chouaib | A dual protein-mrna localization screen reveals compartmentalized translation and widespread co-translational rna targeting[END_REF] were used to define the TS LS dataset. It is composed of 568 images from 57 different acquisition conditions of 32 gene expression measured in the study for the purpose of performing a localization screen. Nuclei masks have been acquired with NucleAIzer.

The synthetic high-saliency dataset, TS synth , was generated following the same procedure as DS synth (see section 4.1) with 2000 images, but with enhanced saliency. Nuclei masks are provided by the input generation procedure (elliptical shapes).

Taking these 3 datasets together (summarized in table 1), the target style dataset contains 3119 images.

RESULTS

To train the SalienceNet models, we split each of the two source datasets as well as the two experimental target datasets (see figure 3) into train and test subsets, in 90% and 10% proportions. The test datasets are denoted DS t org , DS t synth , TS t DB and TS t LS , respectfully. We then performed the hyperparameter search by exploring all possible combinations of α, β, and γ (weights of the loss components, see section 3.2) with step of 0.1 in order to estimate which combination of parameters yielded the best model. This resulted in 42 models, denoted by (α, β, γ) combinations in figure 5. Moreover, for comparison purposes we have trained a vanilla CycleGAN model, without any modification with respect to the original CycleGAN network.

All the 42 SalienceNet models and the vanilla Cy-cleGAN were applied to the 4 test datasets DS t org , DS t synth , TS t DB and TS t LS to perform saliency enhancement. The original images and their enhanced coun-terparts were then segmented, without any parameter tuning, using two widely used segmentation methods:

1. the non-parametric version of the classical segmentation Otsu thresholding method with an adaptive threshold, 2. StarDist, a deep-learning based segmentation, with the 2D fluo versatile model as provided by [START_REF] Schmidt | Cell detection with star-convex polygons[END_REF], without re-training on our data or supplementary fine-tuning.

The resulting masks were then compared with ground truth. For this purpose, expert ground truth annotation was performed on the DS t org test dataset; nuclei masks (ground truth) were already available for the 3 other test datasets (see sections 4.1 and 4.2).

To measure the quality of the resulting segmentation, we computed the intersection over union (IOU) for each image to quantify the overlap (in pixel count) between the segmentation and the ground truth: IOU = |S∩G| |S∪G| , where S is the mask resulting from segmentation and G is the ground truth mask.

SalienceNet enables accurate nuclei segmentation

First, we determined the most performant model with respect to our goal of segmenting low SNR images from live-cell imaging by looking at the enhancement performance on organoid images. Figure 5 shows the IOU scores for segmentation by StarDist of both enhanced (by 42 models) and non-enhanced images, and that for each image of the experimental organoid test dataset DS t org . Individual model results for Otsu segmentation being very similar (albeit slightly worse), are not shown in this figure.

The IOU is shown in figure 5 for each image with respect to the ground truth. The geometric mean of all non-enhanced image's IOU was 0.49 for StarDist segmentation and 0.45 for Otsu segmentation, while the geometric mean for IOU after saliency enhancement ranged from 0.54 to 0.75 for StarDist and from 0.48 to 0.75 for Otsu segmentation. Best results were obtained for segmentation after enhancement by the SalienceNet model with α = 0.2, β = 0.2, and γ = 0.6, with a geometric mean of IOU of 0.75 for both StarDist and Otsu. We denote this model by M.

The impact of this model M on the quality of the downstream segmentation was computed as the ratio of IOU for images enhanced with M over the IOU of non-enhanced images. Impact values range between 1.08 and 2.57 for Otsu segmentation and between 1.09 and 10.73 for StarDist segmentation; notice that the lower bound is > 1 in both cases.

An illustration of StarDist segmentation results for non-enhanced images and for those enhanced by M for low saliency organoid images is provided in figure 4.

Table 2 shows the IOU values for the best model M of SalienceNet applied to the 4 test datasets before and after enhancement by SalienceNet. On one hand, we observed that SalienceNet indeed improved the accuracy of nuclei segmentation in low-light source datasets. On the other hand, this table shows that for the already salient images, SalienceNet did not degrade the quality of segmentation.

Together, these results show that saliency enhancement by SalienceNet enables accurate downstream nuclei segmentation by widely used methods without need for parameter tuning.

SalienceNet enhances nuclei saliency To evaluate whether SalienceNet improved saliency, we computed its indirect measure -the Signal to Noise Ratio (SNR) as SNR = (mµ B )/σ , where m is the maximum pixel intensity within the nuclei masks in an image, µ B is the mean value of the background and σ is the standard deviation of the background. The SNR was computed for the source style datasets DS org and DS synth , and the target style datasets TS synth , TS LS and TS DB . We also measured the SNR of the test datasets DS t org and DS t synth after enhancement by SalienceNet. We observed (see figure 6) that SalienceNet enhanced SNR in low-light images of DS t org and DS t synth close to the level of SNR of the already salient experimental target style images TS LS and TS DB , and up to the SNR level of the synthetic salient dataset TS synth .

SUMMARY

In this work, we introduced SalienceNet, a CycleGAN-based network specifically designed to enhance nuclei's saliency in low SNR images that does not require annotation for training on new data. We used the soSPIM light-sheet microscopy, a technique that allows to illuminate the biological sample with little light compared to other methods, to acquire organoid images. The result is that the illumi- nation and the SNR are lower in these images and the nuclei are less salient. We used these organoid images as source style for training our network and further for testing. To implement SalienceNet we combined three loss functions with different properties and have shown that our adaptation of CycleGan improved segmentation results after enhancement relative to both segmentation of non-enhanced images and of those enhanced with the vanilla CycleGan. We compared the segmentation results of widely used non-parametric Otsu thresholding and StarDist on both raw images and images enhanced with SalienceNet of our novel organoid live-cell imaging dataset. We have shown that using SalienceNet improved the segmentation quality of both classical and deep learning based nuclei segmentation algorithms in low SNR nuclei images. It should be noted that adding the SalienceNet enhancement step prior to nuclei segmentation did not degrade the quality of results for the already salient datasets.

Taken together, these results show that SalienceNet is a useful new step for nuclei segmentation workflows.

CODE AVAILABILITY

SalienceNet network's code for training and testing nuclei enhancement is fully open source and available on GitHub at https://github.com/cbib/SalienceNet. Our best pre-trained model M used in this study is also available from the same GitHub page.

Figure 1 :

 1 Figure 1: Architecture of SalienceNet. The network is composed by 2 GANs, each GAN having a Generator G and a Discriminator D. The main element of the Generator is a residual network, while the discriminator is a PatchGAN whose output is a feature map. The generator loss is computed based in this feature map. Cycle consistency loss is computed between the original image X and it's reconstructed image F(G(X)) and between Y and it's reconstructed image G(F(Y )).

Figure 3 :

 3 Figure 3: Training and evaluation of SaliencyNet. 90% of source style datasets and of the experimental target style datasets were used to train the network. It was then applied to the remaining 10% of the source style datasets to obtain enhanced images. Nuclei in the images enhanced by SalienceNet were segmented using classical methods with fixed parameters.

Figure 4 :Figure 5 :

 45 Figure 4: Examples of segmentation results by StarDist obtained without enhancement and after enhancement by SalienceNet M model. Sample images come from two low saliency test datasets: DS t org for the two upper rows, and DS t synth for the two lower rows. Rows 2 and 4 show a zoom-in of the respective rows right above.

Figure 6 :

 6 Figure 6: Signal to Noise Ratio (SNR) distributions. Boxplots represent the distribution of SNR for the source style images DS t org and DS t synth and the target style images TS LS TS DB , TS synth . SNR distributions of the test images after enhancement with SalienceNet M model are shown for the low-light DS t org and DS t synth datasets.

  Composition of the networks constituting SalienceNet. Generators embed a residual network composed of 9 residual blocks, each block being itself composed of 2 convolution layers. Convolution blocks are composed of a convolution layer, an instance normalization layer and an activation layer which is ReLU for the generator and LeakyReLU for the discriminator.

		Generator	Discriminator
			Residual block
			Conv2D, 256, 3x3, s = 1
			Instance normalization Activation (ReLu) Conv2D, 256, 3x3, s = 1	Shortcut
			Instance normalization
			F(𝒙)
		Convolution block
	Legend	Residual block	F(𝒙) + 𝒙
		Transpose Convolution

𝒙

Figure 2:

Table 1 :

 1 Number of images and nuclei in each dataset (DS column) used for the training and testing of SalienceNet.

	DS	#Images	#Nuclei	Style
	DS org	1056	43633	Source
	DS synth	1500	128962	Source
	TS LS	568	20754	Target
	TS DB	551	23121	Target
	TS synth	2000	171915	Target

Table 2 :

 2 IOU values for segmentation with Otsu or StarDist of non-enhanced and enhanced with M SalienceNet model images in 4 test datasets. All reported values are the geometric mean, per dataset, of the IOU of individual images.

	DS	IOU	Otsu	SN + Otsu	StarDist	SN + StarDist
	DS t org DS t synth TS t LS TS t DB	0.45 0.62 0.82 0.69	0.75 0.90 0.86 0.78	0.49 0.62 0.90 0.83	0.75 0.86 0.90 0.83


Jean-Baptiste Besnard

Pascal Dupont

Ahmed Ould

El Moctar

Alexandre Valance
email: alexandre.valance@univ-rennes1.fr

J-B Besnard

Aeolian erosion thresholds for cohesive sand

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

Abstract

Moisture is known to affect sand cohesion and therefore transport threshold and rate of aeolian sand transport. Aeolian sand transport has been widely documented for dry sand beds, but much more sparsely in the context of moist sand beds. One major challenge in the collection of reliable field or laboratory data for moist sand is to have an accurate control of the moisture level within the sand bed, which is prone to strongly vary over time and space due to evaporation. To suppress the variability of moisture content due to evaporation, we devised a new approach based on the use of a non-volatile liquid (namely silicon oil instead of water) which ensures a proper control of the liquid content. We thus conducted wind-tunnel experiments employing this approach and observed that the aerodynamic threshold friction velocity increases linearly with liquid content, while the dynamic threshold is found to be unchanged in the range of cohesion strength investigated in this study. These outcomes indicate that the difference between the static and dynamic threshold increases with increasing cohesion. This may have strong implications on aeolian transport of moist sand, and in particular on hysteretic behaviors.

Plain Language Summary

Moisture has a significant influence on the initiation of motion of sand by wind and also on the resulting sand transport rate. While the moisture level is usually very low in sandy desert areas and thus irrelevant there, the aeolian sand transport on sandy beaches or in the context of coastal dune morphodynamics is expected to be crucially dependent on the moisture content within the sand. The literature regarding the impact of the moisture on wind blown sand is sparse, and available data exhibit considerable discrepancies regarding the magnitude of the moisture effects. These discrepancies highlight that it is experimentally difficult to control the moisture levels within the sand because of evaporation. To circumvent this difficulty, we carried wind-tunnel experiments with sand-oil mixtures instead of sand-water mixtures. Oil plays the same role as water in generating cohesion but has the significant advantage to have a very low evaporation rate in the standard conditions of temperature and pressure. With these sandoil mixtures, we were able to assess with an unprecedented accuracy the magnitude of the cohesion effects on the aerodynamic erosion threshold and also on the threshold characterizing the cessation of transport, known as the dynamic threshold.

Introduction

Aeolian processes that involve the entrainment, transport, and deposition of sediment by the wind are important geomorphic processes operating in arid regions but also along sandy shores. They are responsible in particular for the formation and migration of sand dunes. Understanding these processes in complex environments (e.g., in the presence of vegetation or in the context of cohesive soils) demands further investigations.

Wind blown sand involves a myriad of physical mechanisms, including particle-particle, bed-particle and fluid-particle interactions. A comprehensive quantification of these interactions in the context of cohesive particulate beds remains a scientific challenge. Aeolian sand transport with non-cohesive particles can be regarded as one of the simplest air-particulate flows, while the transport of moist sand or snow exhibits a much greater complexity.

The complexity of the aforementioned real cohesive systems arises from the fact that the strength of the cohesion may strongly evolve in time and space. Monitoring these variations in situ at the relevant temporal and spatial scales is beyond of the classical instrumental capabilities. Promising instruments based on capacitance measurements [START_REF] Louge | Seepage-induced penetration of water vapor and dust beneath ripples and dunes[END_REF][START_REF] Louge | Temperature and humidity within a mobile barchan sand dune, implications for microbial survival[END_REF][START_REF] Louge | Water vapor transport across an arid sand surfacenon-linear thermal coupling, wind-driven pore advection, subsurface waves, and exchange with the atmospheric boundary layer[END_REF] are however, capable of monitoring tiny variations of moisture content at the surface of a sand bed and within the bed with a centimetric spatial resolution and should be further deployed on the field or in wind tunnel experiments to better document the coupling between sand transport and cohesion. This capacitance technique has already proven to be effective to probe the temporal evolution of the water content within a barchan dune [START_REF] Louge | Temperature and humidity within a mobile barchan sand dune, implications for microbial survival[END_REF][START_REF] Louge | Water vapor transport across an arid sand surfacenon-linear thermal coupling, wind-driven pore advection, subsurface waves, and exchange with the atmospheric boundary layer[END_REF]. Also, the potential effects of inter-particle cohesion on the transfer of mass, momentum and energy between the moving particles and the static bed remain poorly documented [START_REF] Namikas | A review of the effects of surface moisture content on aeolian sand transport[END_REF]. Thus, predicting mass transport rates for these complex systems is very uncertain.

An important issue in wind-blown sand concerns the critical air flow velocity at which transport starts and ceases. These thresholds are referred to as the aerodynamic and dynamic thresholds, respectively [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF][START_REF] Kok | A comprehensive numerical model of steady state saltation[END_REF][START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al., 2015;Pähtz et al., 2020). Different physical interpretations of the dynamic threshold can be found in the literature. Some authors (Pähtz et al., 2020[START_REF] Pähtz | Unified model of sediment transport threshold and rate across weak and intense subaqueous bedload, windblown sand, and windblown snow[END_REF] interpret the latter as the rebound threshold, describing the smallest wind friction velocity to sustain a continuous saltation motion of a single grain along the bed. This hypothesis is independent of the ejection process, but related to the properties of the rebound. Other ones [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF][START_REF] Jenkins | Periodic trajectories in aeolian sand transport[END_REF]Valance et al., 2015) define the dynamic threshold to be the minimum wind speed to sustain a non-zero saturated flux. In the latter perspective (as detailed further below), the dynamic threshold is related to the splash process and the replacement capacity.

For dry aeolian sand of 200 µm size, the dynamic threshold is significantly smaller (20% less [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF][START_REF] Ho | Experimental study of saltating particles in a turbulent boundary layer[END_REF]) than the aerodynamic one and this is due to the fact that once transport has been initiated, erosion induced by the impact of grains onto the bed is a very efficient mechanism to sustain the saltation transport [START_REF] Beladjine | Collision process between an incident bead and a three-dimensional granular packing[END_REF][START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF]. This hysteretic effect between initiation and cessation is expected to be drastically modified for cohesive beds as suggested by the recent numerical work from [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF] which showed in the context of snow transport that saltation over cohesive beds sustains itself at wind speeds 1 order of magnitude smaller than those necessary to initiate it. We shall also mention a recent experimental work in a closed-loop wind-tunnel by [START_REF] Andreotti | A lower-than-expected saltation threshold at martian pressure and below[END_REF] which questions the existence of two distinct thresholds. They did not observe any difference between the aerodynamic and dynamic thresholds when increasing or decreasing the wind strength and ascribe this outcome to the essential role of the turbulent flow velocity fluctuations, which are probably strongly enhanced by the closed-loop wind-tunnel.

Most of the studies dedicated to transport of moist sand focused on the modification of the aerodynamic threshold with the moisture level [START_REF] Chepil | Influence of moisture on erodibility of soil by wind[END_REF][START_REF] Belly | Sand movement by wind, united states army corps of engineers[END_REF][START_REF] Bisal | Influence of moisture on erodibility of soil by wind[END_REF][START_REF] Hotta | Sand transport by wind on a wet sand surface[END_REF][START_REF] Mckenna-Neuman | A theoritical and wind tunnel investigation of the effect of capillary water on the entrainment of sediment by wind[END_REF]Cornelis et al., 2004a;[START_REF] Han | Wind tunnel investigation of the influence of surface moisture content on the entrainment and erosion of beach sand by wind using sands from tropical humid coastal southern china[END_REF]. The presence of moisture in sand is known to create cohesive forces between grains and has thus a strong influence on the initiation of sand transport which requires higher wind strengths. The aerodynamic threshold, also referred to as the static threshold, is defined as the minimum wind friction velocity to set grains into motion from a resting situation [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF]. For a cohesionless sand bed, the transport is initiated when the friction velocity overpasses a critical value u * s given by

u * s = A (ρ p -ρ f ) ρ f gD , ( 1
)
where D is the mean grain diameter, ρ p and ρ f are the particle and fluid density, respectively, and A is an empirical coefficient of order of 0.1 [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF]. This relationship can be inferred from a simple force balance between the aerodynamic force and the weight exerted on a grain at the sand bed surface. A typical value of the aerodynamic threshold for dry sand obtained in wind-tunnel is u * s = 0.21 m/s for sand grains with a mean diameter D = 0.2 mm [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF]. It is worth mentioning that the aerodynamic threshold is experimentally difficult to assess because the latter is sensitive to additional parameters that are not easy to properly control or characterize, like the level of the turbulent fluctuations of the air flow or the disorder at the surface of the bed [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]. As an example, [START_REF] Pähtz | The critical role of the boundary layer thickness for the initiation of aeolian sediment transport[END_REF] emphasize that the thickness of the turbulent boundary layer plays an important role in the initiation of sand transport and consequently, the aerodynamic threshold measured in natural conditions is often smaller than that measured in wind-tunnel experiments.

For moist sand, the aerodynamic threshold is an increasing function of the water content, but the literature presents a wide spectrum of results regarding the magnitude of moisture effects on the aerodynamic threshold. From wind-tunnel experiments with 0.44 mm sand grains, [START_REF] Belly | Sand movement by wind, united states army corps of engineers[END_REF] reported a logarithmic evolution of the static threshold friction velocity with the water content ω (expressed in percent) from ω ≈ 0.046% to ω = 4%:

u * sw = u * s 1.8 + 0.6 log ω . (2)
In contrast, [START_REF] Hotta | Sand transport by wind on a wet sand surface[END_REF] proposed a linear relationship also on the basis of wind-tunnel experiments which is verified up to ω = 8%:

u * sw = u * s (1 + a H ω) . (3)
The authors found that the slope a H decreases with increasing grain diameter D: a H ≈ 0.94, 0.30 and 0.22 for D = 0.2, 0.5 and 0.8 mm, respectively. As highlighted by [START_REF] Hotta | Sand transport by wind on a wet sand surface[END_REF], the great diversity in the experimental data regarding the effect of the moisture on the aerodynamic threshold illustrates the difficulty of controlling the moisture levels within the bed due to evaporation. To mitigate the evaporation process, some of the wind-tunnel experiments were conducted with a saturated air flow, as done by [START_REF] Belly | Sand movement by wind, united states army corps of engineers[END_REF], [START_REF] Mckenna-Neuman | A theoritical and wind tunnel investigation of the effect of capillary water on the entrainment of sediment by wind[END_REF] and V. J.-L. Ralaiarisoa (2020). However, it is quite difficult to maintain an air flow at saturation (i.e., RH = 100%). As a consequence, the water content of the sand bed and in particular within the first layers of the surface is rapidly varying in space and time either through evaporation (under-saturated air) or condensation (over-saturated air), resulting in an erroneous estimation of the actual water content of the sand surface at the precise instant when sand transport is triggered. Recent experiments (V. J.-L. Ralaiarisoa, 2020) reported an intermittent transport regime completely controlled by cyclic evaporation of the superficial layers of the sand bed.

Some theoretical models were developed to predict the modification of the static threshold due to cohesion. [START_REF] Mckenna-Neuman | A theoritical and wind tunnel investigation of the effect of capillary water on the entrainment of sediment by wind[END_REF] derived an expression for the critical shear velocity using a force balance between the grain weight P g , the cohesive force F c and the wind shear stress:

u * sw = u * s √ 1 + α Co , (4)
where Co = F c /P g is the dimensionless cohesion number and α is a constant geometrical parameter (α ≈ 3). This relationship is similar to that proposed by [START_REF] Shao | A simple expression for wind erosion threshold friction velocity[END_REF]. To take benefit of the above relationship, the knowledge of the cohesive force F c at the grain scale and its dependence on the water content is required, which is an experimental challenge with grains of submillimeter size. More elaborated expressions can be found in the literature [START_REF] Cornelis | A conceptual model to predict the deflation threshold shear velocity as affected by near-surface soil water[END_REF][START_REF] Claudin | A scaling law for aeolian dunes on mars, venus, earth, and for subaqueous ripples[END_REF]. Eq. 4 is however useful to infer the strength of the cohesion from the assessment of the static threshold friction velocity u * sw .

The other important threshold in wind-blown sand is the dynamic threshold, also referred to as the impact threshold. According to [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al. (2015), we define it as the minimal friction speed u * d for which a non-zero saturated flux can be sustained.

A practical method to determine it is to extrapolate to zero the curve relating the sediment flux to the shear velocity (cf Eq. 5). It is thus defined in a much more accurate manner than the static threshold, for which a somewhat arbitrary criterion for the onset of particle motion has to be chosen. The key point explaining this dynamic threshold is the ability of grains in saltation to eject other grains, the so-called splash process [START_REF] Kok | A comprehensive numerical model of steady state saltation[END_REF][START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al., 2015). This process is a statistical process, with a wide distribution of velocities and angles. In a steady state of transport, the distribution of grain velocities is stationary and on average, each saltating grain produces a single saltating grain after a collision with the bed, either by rebound or by ejection: the capture by the bed of low energy grains that have a probability to stop is balanced by the ejection of new grains by high energy impacts. One can formally define the replacement capacity as the average number of saltating grains produced per collision. At equilibrium, the replacement capacity is exactly 1. In this perspective, the dynamic threshold is crucially dependent on the splash process. The sand transport model developed in [START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF] that incorporates explicitly the key features of the splash process indicates that the dynamic threshold is intimately linked to the critical impact velocity to trigger the ejection process. As mentioned previously, an alternative interpretation of the dynamic threshold based on the rebound threshold was proposed (Pähtz et al., 2020[START_REF] Pähtz | Unified model of sediment transport threshold and rate across weak and intense subaqueous bedload, windblown sand, and windblown snow[END_REF] and is still unclear which is the more relevant to describe the satured transport state at vanishing flux. The dynamic threshold is smaller than the static one and is about 80% of the latter [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF][START_REF] Ho | Experimental study of saltating particles in a turbulent boundary layer[END_REF] in the context of aeolian sand transport on earth with 200 µm grain size.

The difference between the static and dynamic threshold is in particular crucially dependent on the grain to fluid density ratio as mentioned by [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]. This difference leads to bi-stability and hysteric behaviors when the wind friction velocity lies between the dynamic and static threshold [START_REF] Martin | Distinct thresholds for the initiation and cessation of aeolian saltation from field measurements[END_REF]Comola, Kok, et al., 2019). Indeed, two stable states can coexist: a state with no transport and another one with a finite mass flux. The latter state can be only obtained with specific boundary or initial conditions (e.g, with a finite upwind mass flux or starting from a transport state with u * > u * s and decreasing the friction

speed below u * s ).
Importantly, the dynamic threshold is a key parameter of the transport law [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al., 2015). The transport law quantifies the transport capacity of the turbulent air flow as a function of the wind shear stress in the equilibrium state, i.e., when erosion is exactly balanced by deposition. The mass flow rate at equilibrium is usually referred to as the equilibrium or saturated flux [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al., 2015). For cohesionless sand beds, it scales linearly with the Shields number S * = ρ f u * 2 /(ρ p -ρ f )gD [START_REF] Duran | On aeolian transport: Grain-scale interactions, dynamical mechanism and scaling laws[END_REF]Valance et al., 2015)

Q sat = A Q ρ p Du * d S * -S * d , (5)
where S * d is the critical Shields numbers corresponding to the dynamic friction threshold u * d and A Q is a numerical constant. This linear scaling holds in the saltation regime, but breaks down for very strong winds (i.e., S * > 10S * d ) (J.-L. Ralaiarisoa et al., 2020).

Two important unresolved issues then arise: how the dynamic threshold is altered in the presence of cohesion and how the transport law is modified? In contrast to the static threshold, the modification of the dynamic threshold in the presence of cohesion has not received a lot of attention. There are very few studies on this issue. We are not aware of experimental studies aiming at determining the dynamic transport threshold as a function of the level of moisture. We can however mention two recent related numerical studies: the work by [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF] which investigates the splash process in the context of snow transport and the one by V. [START_REF] Ralaiarisoa | Particle impact on a cohesive granular media[END_REF] dedicated to the numerical study of the impact process on cohesive granular packings in the context of aeolian transport for moist sand. The main difference between these two studies is the nature of the cohesion. In the former one, the cohesion is ensured by solid (ice) bonds and the bond breakage is irreversible. In contrast, in the latter study, bonds are water capillary bridges and the breakage is reversible. One of the salient results in (V. [START_REF] Ralaiarisoa | Particle impact on a cohesive granular media[END_REF] is that the critical impact velocity to trigger the ejection process and its efficiency (i.e., the number of ejected particles per impact) are modified when the cohesion number exceeds a critical value of order 5. Numerical simulations from [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF] confirm that for high cohesion, the efficiency of the ejection process is substantially decreased. These numerical findings thus suggest that for strong cohesion, the dynamic transport threshold should be enhanced. Experimental evidences are however lacking. Concerning the modification of the equilibrium mass flux in the context of cohesive beds, there is no definite answer [START_REF] Mckenna-Neuman | A wind tunnel study of the influence of pore water on aeolian sediment transport[END_REF][START_REF] Davidson-Arnott | The effects of surface moisture on aeolian sediment transport threshold and mass flux on a beach[END_REF] due again to the difficulty to conduct experiments with an accurate control of the cohesion within the bed. The limit case corresponding to infinite cohesion (i.e., a rigid bed) is well documented.

The experimental study from [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF] reported that the transport capacity over a rigid bed is much greater than over an equivalent erodible bed because the rebound is less dissipative. This was confirmed and explained through a simple two-phase transport model based on periodic trajectories [START_REF] Jenkins | Periodic trajectories in aeolian sand transport[END_REF]. The last important issue concerns the equilibrium length (resp. time) needed to reach the equilibrium state from a rest state. For the cohesionless case, several studies were devoted to this complex issue [START_REF] Andreotti | Measurements of the aeolian sand transport saturation length[END_REF][START_REF] Selmani | Aeolian sand transport in out-of-equilibrium regimes[END_REF]. The general belief is that the equilibrium length increases with increasing the cohesion strength, but there are very few experimental quantitative studies on this question (Davidson-Arnott et al., 2008; V. J.-L. Ralaiarisoa, 2020). This belief was however confirmed recently by the numerical simulations from [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF]. The increase of the equilibrium length with increasing cohesion can be explained by the lower efficiency of the splash process (i.e., production of ejected particles) with cohesive beds as argued by [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF].

We propose here an original experimental approach to determine both the static and dynamic threshold in the context of cohesive sand beds in an unprecedented controlled manner.

This approach allows getting rid of the evaporation process and to control with accuracy the cohesion strength of the sand bed. The use of silicon oil instead of water offers the great advantage of suppressing evaporation. We conducted wind-tunnel experiments based on this approach and quantified how the aerodynamic and dynamic thresholds vary with the liquid content.

The article is organized as follows. Section 2 describes the experimental facility and the approach employed to determine both the aerodynamic and impact erosion rates from which we deduce the aerodynamic and dynamic transport thresholds. In section 3 and 4 we present the results on aerodynamic and impact erosion rates and discuss the influence of the cohesion strength of the sand bed on the respective erosion thresholds. Section 5 summarizes the outcome results and presents outlooks.

2 Experimental setup

Wind-tunnel facility

The experiments were carried out in a wind tunnel with a 6.6 m length working section and a 0.245 m×0.27 m cross-section (see Figure 1). We used as a cohesive sand bed a mixture of 0.2 mm sand and silicone oil (AR 20) with a surface tension Γ = 20.6 10 -3 N/m. The sand bed is reduced to a box with a square section of dimensions 0.15 m×0.15 m and a 0.02 m depth. We chose a small bed sample to get a local evaluation of the erosion rate. The requirement is that the length of the sample be much smaller than the saturation length but not too small for statistical representative measurements. We will come back to the influence of the bed length on the experimental outcomes in sections 4 and 5.

The sand bed sample is placed 5.4 m downstream the entrance of the wind tunnel and its surface is at the same level as the wind-tunnel floor so that there is no discontinuity. The floor of the wind tunnel (i.e., upstream and downstream of the sand bed) was made rough by gluing sand particles of the same nature as the sand bed. The sand bed is weighed continuously during the experiment by means of a scale with a milligram accuracy. This allows to record the erosion rate in the course of time (see further details in section 3).

The air flow velocity profile upstream the sand bed was characterized with Pitot tubes displayed at 10, 15, 20, 25, 30 and 40 mm above the tunnel floor. The profile obeys a classical logarithmic law and the aerodynamic roughness length z 0 is roughly constant and equal to z 0 ≈ 4.10 -6 m ≈ D/50.

U(z) = u * κ ln z z 0 , (6)

Sand-oil mixture elaboration

Several sand-oil mixtures of about 1 kg were elaborated with various liquid content ranging from w = 0.025% to w = 0.4%. Each mixture was prepared in a large container and homogenized manually using a metal rod. The mixture is then poured layer by layer in the dedicated box. Each layer is about 5 mm height and is smoothed out by a level rake before pouring the next layer. The particle volume fraction of the obtained packing slightly decreases with increasing liquid content (see Table 1). However, the decrease is relatively weak except for the two largest liquid contents (ω = 0.3% and 0.4%). For ω = 0, we obtained a volume fraction of φ = 0.558 while for ω = 0.2%, we get φ = 0.545.

Upstream conditions

We used two different protocols to determine the static and dynamic threshold described below. For the assessment of the static threshold, the upstream air flow is free of particles and the air flow velocity is increased by successive incremental steps. A prescribed air flow velocity is set for a duration of 10 minutes and the mass of the packing is recorded in real time during the run. If the run led to a finite erosion of the sand bed, the packing is rebuilt entirely for the next run. If not, the air flow velocity is incremented using the same packing. When a packing is newly built, the first process is to raise the wind speed above the transport threshold for a short time in order to remove the unstable grains lying at the surface of the packing [START_REF] Mckenna-Neuman | A theoritical and wind tunnel investigation of the effect of capillary water on the entrainment of sediment by wind[END_REF].

For assessing the dynamic threshold, similar experiments were conducted but a given incoming particle flux at the entrance of the wind-tunnel. To do this, a hopper filled with dry sand was placed on the roof of the tunnel at 0.5 m downstream the entrance. The hopper was designed to feed the air flow with a constant and small incoming sand flux Q in ≈ 48 g/s. We used a sufficient small incoming flux which can be transported by weak winds, that is with speeds lower than the dynamic threshold obtained with a cohesionless erodible bed. The sand bed is then subject to a finite impacting flux Φ that depends both on Q in and the air flow velocity. This procedure allows assessing the erosion rate by impact and to infer the dynamic transport threshold as explained in further details in Section 4.

3 Aerodynamic erosion

Temporal variation of the erosion rate

The continuous recording of the mass M of the sand bed allows determining the temporal evolution of the erosion rate during a given experiment, achieved with a prescribed wind speed. The erosion rate E is defined as

E = - 1 S dM dt ( 8
)
where S is the surface area of the sand bed. Our measurements reveal that is constant during the first stage of the erosion process. In a second stage, the erosion rate decreases with time, corresponding to the moment where the bed surface is no longer flat due to scouring effects at the downwind of the bed. The second stage occurs when the cumulative mass loss exceeds approximately ∆M ≈ 4 g (Note that a single layer of grains is a bit less than 1 g). In the following, we disregard the second stage of the erosion and infer the erosion rate only from measurements taken in the first stage of the erosion process. The erosion rate is thus calculated via the slope of the curve M(t) in the linear regime.

Erosion rate versus Wind speed

We have measured the erosion rate as a function of the wind strength for sand beds with various liquid contents, ω ranging from 0.025% to 0.2%. For higher liquid contents (i.e., ω = 0.3 and 0.4) we were not able to reach the transport threshold which was beyond the maximum wind speed we can reach in our wind-tunnel (i.e., U ∞ ≈ 25 m/s corresponding to a friction velocity u * ≈ 1 m/s). The data presented in Fig. 2.a indicate that for a given liquid content, the erosion rate follows an exponential growth with the wind friction speed u * :

E = A e exp u * u * e , (9)
where u * e is the characteristic friction velocity of the exponential growth (see Fig. 2.b).

The exponential behavior suggests that transport could be initiated at a vanishing friction velocity if one waits for an infinite time. The origin of the exponential trend is not clear to us, but could be possibly ascribed to the turbulent fluctuations of the air flow. This result then leaves us with the unresolved issue of how to determine a static threshold with a relevant criterion in the experiments. [START_REF] Stout | The wolfforth field experiment: A wind erosion study[END_REF] indeed, emphasized that the determination of a threshold is dependent on the time of the measure. They also indicate that although the threshold is sensitive to the time of the measure, it remains finite. These arguments suggest that the experimental assessment of the aerodynamic threshold of transport may depend on the set-up and experimental procedure.

Here, we define the aerodynamic threshold as the erosion rate E overcomes a definite critical value E c . We chose a critical value E c = 4.10 -3 g/m 2 s, that corresponds roughly to a mass loss ∆M ≈ 5.410 -2 g within 10 mn (which is the typical experiment duration). We selected this value because it is just above the accuracy of the weigh scale. A different choice for the critical value E c would of course affect the assessment of the transport threshold but in the range of less than 10% variation. Using the above criterion, we determine the aerodynamic threshold for our various cohesive sand beds (see Fig. 3). We find that the static threshold friction velocity increases linearly with the liquid content: with a ω ≈ 7 ± 0.5. The static threshold for cohesionless sand (i.e., ω = 0) is rather large (u * s = 0.3 m/s) in comparison with the values of the literature (u * s ≈ 0.21 m/s [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF]). This discrepancy is so important that it can not be ascribed to the uncertainty of the measurements. We strongly believe that this is due to the finite size of the sand bed. Indeed, the length of the sand bed is expected to play a significant role in the initiation of the transport since the latter is triggered by events of low probability. A long bed will thus make the occurrence of such events more likely than for a short bed. It is hard to tell what would be the relevant bed length to get size-independent results. This issue is of significant importance and would deserve a specific study which is out of the scope of this article. Besides this, our results are in line with those from [START_REF] Hotta | Sand transport by wind on a wet sand surface[END_REF] concerning the linear increase with ω.

u * sw = u * s (1 + a ω ω) , (10)
However, the coefficient a ω is about 10 times greater than that found by [START_REF] Hotta | Sand transport by wind on a wet sand surface[END_REF] for a sand bed with similar grain size (i.e., D = 0.2 mm) but mixed with water and subsequent potential evaporation phenomena. These results thus suggest that the oil modifies quantitatively the cohesion strength but not qualitatively.

Interestingly, we can take advantage of the relationship from McKenna-Neuman and Nickling (1989) (cf Eq. 4) to get an estimation of the strength of the cohesion force in terms of the cohesion number. Plugging Eq. 10 in Eq. 4 yields: sw as a function of the liquid content ω. The dash line corresponds to a linear fit to the data (see Eq. 10). Inset: The cohesion number Co as a function of the liquid content. The cohesion number Co is obtained from Eq. 4. The dash line corresponds to the predicted cohesion strength computed from the linear relationship between the threshold friction velocity and the liquid content:

Co ≈ a ω ω 3 (2 + a ω ω) (
Co = (a ω ω/3)(2 + a ω ω).
The cohesion number varies between 0.01 to 2 (see the inset of Fig. 3). The magnitude of the cohesive strength can be compared with that produced by the capillary force: Co cap = πDΓ/mgD ≈ 120 (with D = 0.2 mm, ρ p = 2650 kg/m 3 and Γ = 20.610 -3 N/m). The estimated cohesion strength of the investigated sand beds is thus two order of magnitude less than the capillary force, which indicates that cohesion is probably driven by very thin films adsorbed on the grains rather than liquid capillary bridges.

Impact erosion

Upstream mass flux

To investigate the erosion by impact, we modified the upstream condition by prescribing a small but finite incoming mass flow rate Q in = 0.48 g/s at the entrance of the windtunnel. With this prescribed incoming flux, experiments should be operated at a friction velocity equal or greater than 0.15 m/s. Below this value, the air flow is not able to transport the prescribed mass flux and deposition occurs, resulting in a decreasing mass flow rate with downstream distance.

The grains released at the entrance of the wind tunnel experience a saltation motion over a rigid and rough bed and are expected to be quickly in equilibrium with the flow. Their equilibrium downstream velocity, as well as their mean saltation height and length, are governed by the strength of the flow. It is necessary to characterize the properties of the saltating grains when they impact the sand. Two important properties should be determined: the vertical flux Φ (i.e., the number of particles impacting per unit area) and the mean velocity u p of the impacting particles. The impact erosion rate E depends on both quantities and can be expressed as

E = Φ × N E (u p , Co . . .) , (12)
where N E is the average number of ejected grains per impact produced by impacting particles having a mean velocity u p . N E is expected to depend as well on the cohesion number Co. We should emphasize here that N E is of course closely related to the number of ejected grains per impact determined in splash experiments [START_REF] Beladjine | Collision process between an incident bead and a three-dimensional granular packing[END_REF] but it is different. Indeed, in splash experiments, the number of ejected grains per impact, N e j (ξ), is assessed for a well-controlled impact velocity ξ. This is not the case in the present experiment where the impacting particles can exhibit a quite significant dispersion around the mean value u p . We can infer N E (u p ) from N e j (ξ) if the distribution of the particle velocity is known. The calculation is done in Appendix A where a Gaussian velocity distribution is assumed. The mean velocity of the impacting particles can be estimated from the measurements made by [START_REF] Ho | Experimental study of saltating particles in a turbulent boundary layer[END_REF]. He reported that the equilibrium velocity of saltating particles over a rigid bed is completely determined by the flow strength and proposed the following empirical relationship for 0.2 mm sand grains,

u p gd ≈ 80 u * /u * reb -1 , (13)
where u * reb is the critical shear velocity to sustain a steady saltation motion of a single grain on a rigid and rough bed with u * reb ≈ 0.128 m/s. This critical friction velocity can be interpreted as the rebound threshold on a rigid bed (Pähtz et al., 2020[START_REF] Pähtz | Unified model of sediment transport threshold and rate across weak and intense subaqueous bedload, windblown sand, and windblown snow[END_REF]. The relation holds as long as the flow is far from being saturated, that is, when the saltation layer is so dilute that the sand grains do not have any feed-back effect on the flow.

The impact flux Φ was directly measured by trapping the impacting grains at the location of the sand bed. To do so, we replaced the sand bed by an equivalent surface acting as a sand trap. The container used for the sand bed was filled instead with a viscous liquid (sunflower oil). Doing so, we avoid both evaporation of the liquid and ensure an efficient trapping.

The flux is assessed by the same system of weighing used to determine the erosion rate. Fig. 4 presents the variation of the vertical flux Φ as a function of the shear velocity u * for a prescribed incoming mass flux Q in = 0.48 g/s. As expected, the latter decreases with increasing shear velocity and the decreasing trend is well captured by

Φ ∝ Q in (u * /u * reb -1) 2 . ( 14
)
This is in agreement with the findings from [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF]. In a steady and fully developed state of transport, the impact flux is given by Φ = Q/l salt where l salt is the mean saltation length and Q the mass flow rate. [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF] showed that over a rigid and rough bed, the mean saltation length scales as (u * /u * reb -1) 2 , which is fully compatible with our results on Φ.

manuscript submitted to JGR: Earth Surface

Experimental results

As the impacting flux is varying in our experiments, the impact erosion rate E is rescaled by the impacting flux Φ and can be interpreted as the mean number of particles ejected by a single impact. The experimental data are reported in Fig. 5 where we display the rescaled erosion rate E/Φ as a function of the friction velocity for 4 different cohesion strengths. We can clearly identify a critical friction velocity u * d for impact erosion. We interpret this critical velocity as the dynamic transport threshold. The first salient result is that the dynamic transport threshold is insensitive to the level of cohesion of the bed: u * d ≈ 0.16 m/s. This threshold value is consistent with those found in the literature in the context of cohesionless sand beds. For example, [START_REF] Ho | Scaling laws in aeolian sand transport[END_REF] reported a dynamic threshold u * d ≈ 0.17 m/s for 0.2 mm cohesionless sand, consistent with our value. In contrast to what found for the aerodynamic threshold, this agreement suggests that the outcomes concerning impact erosion are not much sensitive to the size of the sand bed sample. Interestingly, the value of the dynamic threshold corresponds to a critical mean particle velocity u p,0 ≈ 20 gd. According to [START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF] and as shown in appendix A, we can infer from u p,0 the critical impact velocity ξ 0 to trigger the erosion process: ξ 0 ≈ 2 u p,0 ≈ 40 gd. The obtained value for ξ 0 is in agreement with that found from model collision experiments with 6 mm plastic beads [START_REF] Beladjine | Collision process between an incident bead and a three-dimensional granular packing[END_REF].

The second salient result is that close to the threshold, the rescaled impact erosion rate E/Φ obeys an linear law

E Φ ≈ N E 0 (ω) u * u * d -1 , (15)
where N E 0 is a fitting parameter (see Fig. 5.b). Two important comments follow. Using the relationship between the mean particle velocity and the air friction velocity (cf Eq. 13), the rescaled impact erosion rate E/Φ can be expressed in terms of the mean particle velocity of the impacting grains:

E Φ ≈ N E 0 (ω) 5 u p u p,0 -1 . ( 16
)
To derive this relationship, we used that u * d /u * reb ≈ 5/4. The critical velocity u p,0 can be interpreted as the mean particle velocity at which the replacement capacity is equal to 1. We found that the critical mean particle velocity u p,0 is not modified by the cohesion strength of the packing. Only, the efficiency of the impact erosion rate encoded through the quantity N E 0 is altered by the cohesion. N E 0 decreases significantly for liquid contents ω equal or greater than 0.3% (i.e., Co ≥ 3). We can note that for ω = 0.2, the coefficient N E 0 is a bit greater than for cohesionless beds (see Table 1). This may be probably explained by the fact that the packing fraction of the cohesive packing is slightly smaller than the cohesionless one. The bed is therefore looser and may enhance the erosion by impact.

The second important point to mention is that the linear behavior of the impact erosion rate E with the air friction velocity or mean particle velocity is observed only close to the dynamic threshold (i.e., 0.16 m/s < u * < 0.22 m/s). Far above the threshold, the increase becomes non-linear with a power-law greater than 1. Several plausible additional physical mechanisms may act in concert to increase the efficiency of the measured erosion rate at high friction velocity. An additional contribution may result from the direct aerodynamic erosion but also from a chain reaction process. Indeed, as the bed has a finite size, the ejected grains may rebound several times before leaving the bed. If the latter are sufficiently accelerated by the wind, they can trigger other ejection events as they hit the bed as in a chain reaction process.

We believe that this process is responsible for the non-linear behavior of the erosion rate at high friction velocity.

Discussion and conclusion

With our original experimental set-up, we were able to assess the aerodynamic and impact thresholds in the context of the cohesive sand beds. Importantly, we used oil silicone instead of water to make the sand bed cohesive. This allows to get rid of the issue of water evaporation which makes difficult to control the cohesion properties of the bed in the course of time.

The first major experiment outcome is that the aerodynamic threshold friction velocity increases linearly with the liquid content, while the dynamic threshold remains unchanged with increasing cohesion strength, in the range of cohesion investigated so far (i.e., up to cohesion number Co ≈ 4.5). We ascribe the invariance of the dynamic transport threshold with cohesion to the splash process and in particular to the fact that the critical impact velocity ξ 0 to trigger the ejection process is unaffected by cohesion in this range. A similar result was reported in numerical simulations of the impact process on cohesive granular packings by V. [START_REF] Ralaiarisoa | Particle impact on a cohesive granular media[END_REF]. The numerical outcomes indicate that the critical impact velocity is unchanged as long as the cohesion number is less than 5. According to that prediction, an effect is expected to appear for liquid content ω equal or greater than 0.45%, which was not reached in our experiments. There are alternative explanations for the invariance of the dynamical threshold as proposed by [START_REF] Pähtz | Unified model of sediment transport threshold and rate across weak and intense subaqueous bedload, windblown sand, and windblown snow[END_REF]. They relate the dynamic threshold to the rebound threshold, which is indeed weakly dependent on the level of cohesion as reported in the numerical simulations by [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF].

The second feature is that the erosion by impact becomes less efficient for cohesion number equal or larger than 3 (N E 0 decreases when Co ≥ 3) although the dynamic threshold re-mains unchanged. According to the numerical outcomes by V. [START_REF] Ralaiarisoa | Particle impact on a cohesive granular media[END_REF], the splash process and its efficiency are not affected for cohesion number Co ≤ 5, indicating a possible discrepancy between the experimental and numerical outcomes. However, as shown in Appendix A, the impact erosion rate E depends of course on the efficiency of the splash process but also on the nature of the velocity distribution of the impact particles. Increasing the air flow velocity may affect the velocity distribution. As an example, an increase of the vertical impact velocity fluctuation (i.e., T y ) results in the reduction of the erosion rate (see Eq.A10). We can not therefore conclude definitively about the cause of the decrease of N E 0 for cohesion number between 0.3 and 0.5. A decreasing efficiency of impact erosion rate should have important consequences on the equilibrium length to reach the equilibrium mass flux. In particular, this would lead to an augmentation of the equilibrium length.

The third important result is that aerodynamic erosion rate shows an exponential increase with the friction velocity both for cohesionless and cohesive beds. This raises the question of setting an appropriate criterion to define a meaningful aerodynamic threshold. To circumvent this difficulty, we used a criterion based on a critical value of the erosion rate in compliance with the weigh scale accuracy. In contrast, the impact erosion rate obeys a linear law with the friction velocity. Here we conjectured that the mass transport law at equilibrium is unchanged for cohesive granular beds (see Eq. 5).

The most impressive effect of the cohesion is to increase the difference between the static and dynamic threshold (see Fig. 6.a). A practical consequence of this outcome is the development of strong hysteretic behaviors due to bi-stability if the wind friction velocity lies between the static and dynamic threshold. Indeed, for increasing cohesion strength, the range of the bi-stable domain strongly increases (see Fig. 6b). As a consequence, the experimental assessment of the mass flow rate in this bi-stable regime could lead to a large bias because the measurements may aggregate transport states of different nature according to the upstream boundary conditions.

An important issue to be addressed in the future is the determination of the maximum transport capacity of the wind in the context of cohesive sand beds [START_REF] Mckenna-Neuman | A wind tunnel study of the influence of pore water on aeolian sediment transport[END_REF][START_REF] Davidson-Arnott | The effect of wind gusts, moisture content and fetch length on sand transport on a beach[END_REF]. For cohesionless sand bed, the intensity of the saturated mass flux depends on the distance of the Shields number S * from the dynamic threshold Shields number S * d multiplied by the dynamic threshold friction velocity u * d (see Eq. 5).

As the dynamic threshold is insensitive to cohesion at least in a definite range of cohesion strength (i.e., Co < 2), our expectation is that the saturated flux should remain independent of the bed

The result of the integration yields [START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF]:

E e j ≈ mc 0 N 0 π T x T y T 3 x u p (ξ 0 -u p ) 2 e -(ξ 0 -u p ) 2 /2T x ×         1 -A 2 + AB 2πT x ξ 0 u p         , (A7)
E loss ≈ 74 mc 0 π T x T y ξ 3 c e -u 2 p /(2T x ) .

(A8)

The impact erosion rate vanishes when E e j balances exactly E loss . Assuming that u p √ T x , the balance reduces to [START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF]:

u p ≈ ξ 0 2 (A9)
This means that the erosion rate vanishes when the mean particle velocity of the impacting particle equals the critical velocity u p,0 ≈ ξ 0 /2. The critical mean particle velocity is thus completely linked to the critical impact velocity ξ 0 to trigger the ejection process. A linear expansion around u p,0 provides a approximate for the erosion rate which yields to first order:

E ≈ φ N 0         1 -A 2 + AB

  Consequently, as suggested by[START_REF] Davidson-Arnott | The effects of surface moisture on aeolian sediment transport threshold and mass flux on a beach[END_REF], we may expect that for large cohesion strength, the saturated flux should overpass the one corresponding to the cohesionless case. The numerical simulations from[START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF] achieved in the context of snow transport provide some indications about the equilibrium mass flux for cohesive beds. Their results indicate that the equilibrium (i.e., saturated) mass flux increases with increasing but rather moderately: for very strong cohesion (i.e., Co ≈ 10 4 ), the flux is found to increase only by a factor 1.25 in comparison with the cohesionless case.

Figure 1 .

 1 Figure 1. Wind-tunnel facility

Figure 2 .

 2 Figure 2. (a) Erosion rate E as a function of the friction speed u * for different liquid content w. The dashdoted lines represent exponential fits to the data. The horizontal dash line stands for the critical value of the erosion rate E c used to define the threshold friction velocity to initiate transport. (b) Characteristic friction velocity u * e (see Eq. 9) as a function of ω. Inset: Amplitude A e of the exponential growth as a function ω.

Figure 3 .

 3 Figure 3. Static threshold u * sw as a function of the liquid content ω. The dash line corresponds to a linear fit to the data (see Eq. 10). Inset: The cohesion number Co as a function of the liquid content. The

Figure 4 .

 4 Figure 4. Impact flux Φ as a function of the shear velocity u * for a given incoming flux Q in = 0.48 g/s.

Figure 5 .

 5 Figure 5. (a) Rescaled impact erosion rate E/Φ as a function of the friction velocity for different cohesion strengths. Inset: Magnification of the region close to the threshold, underlining the linear trends of the impact erosion rate. (b) N E 0 as a function of the liquid content ω (see Eq. 15).

Figure 6 .

 6 Figure 6. (a) Aerodynamic and Impact thresholds as a function of the liquid content. (b) Conjectured mass transport rate at equilibrium and bi-stable domain for various liquid content: This graph illustrates the increase of the range of the bi-stable domain (i.e., u * d < u * < u * sw ) with increasing cohesion.Here we conjectured that the mass transport law at equilibrium is unchanged for cohesive granular beds (see Eq. 5).

  φ = mc 0 T y is the vertical impacting mass flux. If we take a typical value of T for saltation transport on a rigid and rough bed[START_REF] Ho | Experimental study of saltating particles in a turbulent boundary layer[END_REF] (T x ≈ T y ≈ 200 gd), we get: E ≈ 0.5 φ (u p /u p,0 -1) which is of the same order of magnitude as what found in the experiments for cohesionless sand bed (E(ω = 0) ≈ φ (u p /u p,0 -1); see Eq. 16).Soil Science, 161 (9), 616-632.Valance, A.,Rasmussen, K. R., Ould El Moctar, A., & Dupont, P. (2015). The physics of aeolian sand transport. Comptes Rendus Physique, 16(1), 105-117.

Table 1 .

 1 Mixtures used in the experiments and corresponding volume fractions of the sand packings.

	ω(%)	0	0.025	0.05 0.075	0.1	0.2	0.3	0.4
	φ	0.558 0.559 0.556 0.551 0.551 0.545 0.520 0.500

Acknowledgments

We acknowledge the support of the French Research National Agency through the project ANR-17-CE01-0014.

Data Availability Statement

The data set corresponding to Figures 2, 3, 4 and 5 are available as Supporting Information at "https://doi.org/10.5281/zenodo.7100605" [START_REF] Besnard | Aeolian erosion thresholds for cohesive sand[END_REF]. The file ReadMe indicates how the data are displayed.

manuscript submitted to JGR: Earth Surface cohesion as illustrated in Fig. 6.b and suggested by the numerical simulations from [START_REF] Comola | Cohesion-induced enhancement of aeolian saltation[END_REF]. Experimental verifications of this conjecture are currently under investigation.

Appendix A Calculation of the impact erosion rate

We derive here the expression of the impact erosion rate assuming that the velocity distribution of the impact particles as well as the features of the ejection process are prescribed.

Based on the numerical simulations and experiments [START_REF] Oger | Discrete element method to study the collision of one rapid sphere on 2d and 3d packings[END_REF][START_REF] Beladjine | Collision process between an incident bead and a three-dimensional granular packing[END_REF], we assume that the number of particles, including the rebound, resulting from a impact at velocity ξ is given by:

with

ξ 0 is the critical velocity below which there is no ejection and N e j is the number of ejected grains per impact when ξ ≤ ξ 0 . θ is the impact angle measured from the horizontal and The measurements for a cohesionless granular packing give N 0 = 13, A = 0.86, B = 0.72, and ξ 0 = 40 gd [START_REF] Beladjine | Collision process between an incident bead and a three-dimensional granular packing[END_REF]. This relation indicates that the number of ejected particles is the product of a function that depends only on the impact angle and a linear function of the impact velocity above a threshold value ξ 0 . If the velocity of the impacting particle is less than ξ c , the impacting particle is captured by the bed (ξ c ≈ gd),

As done in [START_REF] Creyssels | Saltating particles in a turbulent boundary layer : experiment and theory[END_REF], it is reasonable to assume that the velocity of the impacting grains obeys a half-Gaussian distribution (i.e., ξ y < 0):

where ξ x and ξ y are the horizontal and vertical components of the impact velocity ξ (ξ y is negative for impacting particle), c 0 is the concentration of the impacting particle at the bed, u p is the mean horizontal velocity of the impacting particles, T x = ξ 2 x and T y = ξ 2 y .

With these assumptions, the impact erosion rate reads: