Marc Corbeels
email: corbeels@cirad.fr

Rémi Cardinael

Krishna Naudin

Hervé Guibert

Emmanuel Torquebiau

The 4 per 1000 goal and soil carbon storage under agroforestry and conservation agriculture systems in sub-Saharan Africa

Keywords: alley cropping, carbon sequestration, climate change mitigation, crop residues, crop rotation, fallows, no-tillage, parklands, intercropping

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Introduction

The Paris Climate Agreement of the United Nations Climate Conference (COP21, November 30 to December 11, 2015) commits to keeping the increase in global average temperature to well below 2 °C above pre-industrial levels and sets a more aspirational goal to limit warming to 1.5 °C. To achieve this, major greenhouse gas (GHG) reductions are needed together with technologies that result in net removal of CO2 from the atmosphere [START_REF] Meinshausen | Greenhouse-gas emission targets for limiting global warming to 2°C[END_REF][START_REF] Field | Rightsizing carbon dioxide removal[END_REF]. In this context, the "4 per 1000" initiative -"Soils for Food Security and Climate" -(http://4p1000.org) was launched by the French Minister of Agriculture at the COP21, with the aspirational goal to increase soil organic carbon (SOC) stocks globally by 0.4 percent per year, suggesting that this would compensate for the global anthropogenic GHG emissions [START_REF] Lal | Beyond COP 21: Potential and challenges of the "4 per Thousand" initiative[END_REF][START_REF] Chabbi | Aligning agriculture and climate policy[END_REF][START_REF] Dignac | Increasing soil carbon storage: mechanisms, effects of agricultural practices and proxies[END_REF][START_REF] Minasny | Soil carbon 4 per mille[END_REF]. Soils store two to three times more carbon than the atmosphere, and the amount of organic carbon stored in soils is estimated at 2400 Gt C to 2 m depth [START_REF] Batjes | Total carbon and nitrogen in the soils of the world[END_REF]. A slight increase or decrease of this SOC stock has therefore a large impact on atmospheric CO2 concentration [START_REF] Schlesinger | Carbon balance in terrestrial detritus[END_REF]. Besides, the annual GHG emission from fossil carbon combustion is estimated at 9.3 Gt C (Le [START_REF] Quéré | Global Carbon Budget 2016[END_REF]. The 4‰ figure simply originated from the ratio of the global anthropogenic carbon emissions (9.3 Gt C yr -1 ) to the global SOC stock (2400 Gt C) [START_REF] Minasny | Soil carbon 4 per mille[END_REF], and thus implies that increasing global SOC stocks by 4‰ per year would completely offset the anthropogenic CO2 emissions. However, increasing SOC up to 2 m through changes in land management practices is rather impossible, because they are known to principally affect the topsoil SOC content [START_REF] Vandenbygaart | Comments on soil carbon 4 per mille by Minasny et al[END_REF]. Another interpretation of the 4‰ figure considers therefore the global SOC stock to 40 cm soil depth only, arguing that a more correct scientific rationale behind the 4‰ initiative is to counteract the annual rise in atmospheric CO2 [START_REF] De Vries | Soil carbon 4 per mille: a good initiative but let's manage not only the soil but also the expectations[END_REF]. A 4‰ increase of the global 0-40 cm SOC stock, which is estimated at 860 Gt, would result in an annual sink of 3.4 Gt C yr -1 . Combining this with stopping deforestation (that causes an estimated emission of 0.9 Gt C yr -1 , Le [START_REF] Quéré | Global carbon budget 2014[END_REF] would lead to a net CO2 removal of 4.3 Gt C yr -1 from the atmosphere, close to the present annual rise in atmospheric CO2, being estimated at 4.5 Gt C (Le [START_REF] Quéré | Global Carbon Budget 2016[END_REF].

Soil organic carbon stocks of Africa are currently estimated between 133 and 184 Gt for the 0-100 cm soil layer (about 10% of the global SOC stock), with large variations depending on the ecoregion [START_REF] Henry | Soil carbon stocks in ecoregions of Africa[END_REF][START_REF] Scharlemann | Global soil carbon: understanding and managing the largest terrestrial carbon pool[END_REF]. Due to an increasing demographic pressure and associated food demand, many native grassland and forest areas have been converted to croplands, and soils have experienced a massive decline in SOC, mainly as a result of low carbon inputs into soil, and topsoil erosion (Agbenin and Goladi, 1997;[START_REF] Solomon | Soil organic matter dynamics in the subhumid agroecosystems of the Ethiopian highlands: Evidence from natural C-13 abundance and particle-size fractionation[END_REF][START_REF] Lemenih | Soil organic matter dynamics after deforestation along a farm field chronosequence in southern highlands of Ethiopia[END_REF][START_REF] Zingore | Long-term changes in organic matter of woodland soils cleared for arable cropping in Zimbabwe[END_REF][START_REF] Kintché | Carbon losses and primary productivity decline in savannah soils under cotton-cereal rotations in semiarid Togo[END_REF][START_REF] Moebius-Clune | Long-term soil quality degradation along a cultivation chronosequence in western Kenya[END_REF]. For example, from a review of published research it was estimated that SOC in croplands in southern Africa has declined by 25 to 53% [START_REF] Swanepoel | Review and meta-analysis of organic matter in cultivated soils in southern Africa[END_REF]. Other studies (e.g. in Western Kenya) found decreases of up to 85% of the original SOC stocks under forest [START_REF] Solomon | Long-term impacts of anthropogenic perturbations on dynamics and speciation of organic carbon in tropical forest and subtropical grassland ecosystems[END_REF]. These soils, far from their saturation level [START_REF] Six | Stabilization mechanisms of soil organic matter: Implications for C-saturation of soils[END_REF][START_REF] Stewart | Soil carbon saturation: concept, evidence and evaluation[END_REF], are now seen as potentially important carbon sinks. The concept of SOC saturation suggests that the quantity of stable SOC in a given soil is limited since SOC stabilization, i.e. SOC protection from decomposers, is to a great extent determined by the amount of fine soil particles (typically <20 μm) [START_REF] Hassink | The capacity of soils to preserve organic C and N by their association with clay and silt particles[END_REF][START_REF] Six | Stabilization mechanisms of soil organic matter: Implications for C-saturation of soils[END_REF]. The difference between the theoretical SOC saturation value and measured SOC of the fine fraction corresponds to the soil saturation deficit and may represent the potential for SOC sequestration in a stable form [START_REF] Castellano | Integrating Plant Litter Quality, Soil Organic Matter Stabilization and the Carbon Saturation Concept[END_REF], but this concept is now being challenged [START_REF] Barré | Ideas and perspectives: Can we use the soil carbon saturation deficit to quantitatively assess the soil carbon storage potential, or should we explore other strategies?[END_REF]. SOC increase can be achieved through the implementation of restorative land use and recommended management practices on agricultural soils [START_REF] Lal | Soil carbon sequestration impacts on global climate change and food security[END_REF]. Restoring SOC levels is often seen as a win-win strategy to mitigate climate change while improving soil quality, potentially leading to higher crop yields [START_REF] Lal | Enhancing crop yields in the developing countries through restoration of the soil organic carbon pool in agricultural lands[END_REF]. Important effects of increased SOC levels are increased supply of nutrients [START_REF] Vanlauwe | Long-term integrated soil fertility management in South-western Nigeria: Crop performance and impact on the soil fertility status[END_REF][START_REF] Bationo | Soil organic carbon dynamics, functions and management in West African agro-ecosystems[END_REF], and better soil structure resulting in increased infiltration of water and reduced soil crusting, compaction and erosion [START_REF] Blanco-Canqui | Soil structure and organic carbon relationships following 10 years of wheat straw management in no-till[END_REF][START_REF] Nyamadzawo | Improved legume tree fallows and tillage effects on structural stability and infiltration rates of a kaolinitic sandy soil from central Zimbabwe[END_REF]. Higher SOC levels also result in more efficient use of the agricultural inputs in cropping systems [START_REF] Tittonell | Yield gaps, nutrient use efficiencies and response to fertilisers by maize across heterogeneous smallholder farms of western Kenya[END_REF][START_REF] Zingore | Managing soil fertility diversity to enhance resource use efficiencies in smallholder farming systems: A case from Murewa District, Zimbabwe[END_REF]. This in turn may lead to improved climate change adaptation, food security and livelihoods [START_REF] Lal | Soil carbon sequestration impacts on global climate change and food security[END_REF].

Several management practices are recognized to improve SOC contents in croplands, such as organic amendments, cover crops, improved crop rotations with or without temporal grasslands or legumes, biochar, agroforestry, or conservation agriculture [START_REF] Vågen | Soil Carbon Sequestration in Sub-Saharan Africa: a Review[END_REF][START_REF] Lorenz | Soil organic carbon sequestration in agroforestry systems. A review[END_REF][START_REF] Paustian | Climate-smart soils[END_REF].

This study focuses on the impact of agroforestry and conservation agriculture on SOC storage; both practices can increase SOC through increased carbon inputs from higher biomass productivity within a field and do not lead to carbon leakage from one field to another as often the case with recycling of exogenous organic matters [START_REF] Powlson | Soil carbon sequestration to mitigate climate change: A critical re-examination to identify the true and the false[END_REF].

The first aim of this study is to develop evidence for increased SOC stocks under agroforestry and conservation agriculture systems in sub-Saharan Africa based on a systematic review of available data in the literature. We present the results of the review against the 4‰ objective and discuss the extent to which agroforestry and conservation agriculture can enhance SOC storage and contribute to climate change mitigation. Second, we highlight the opportunities and challenges that lay ahead for SOC storage in the context of African smallholder farming systems by virtue of findings from studies on soil fertility gradients on smallholder farms. Finally, we discuss the challenges with the widespread implementation of the 4‰ initiative in the context of African farming systems, leading to concluding commentaries on the overall findings of our study.

Materials and Methods

Literature search

Using the online databases ISI Web of Science (Thomson Reuters, New York, NY, USA) and Scopus (Elsevier, Amsterdam, the Netherlands), a comprehensive search was conducted in May 2017 for peer-reviewed publications that reported SOC storage under agroforestry and conservation agriculture systems in sub-Saharan Africa (excluding South Africa). The literature search was conducted using the terms described in Table S1 (Supplementary Materials).

Agroforestry is defined as the intentional, integrated combination of trees (including shrubs) and agricultural crops simultaneously or sequentially grown on the same piece of land [START_REF] Nair | An introduction to agroforestry[END_REF][START_REF] Torquebiau | A renewed perspective on agroforestry concepts and classification[END_REF]. Simultaneous systems include scattered trees in cropland, often referred to as 'parklands', alley cropping, intercropping and multistrata agroforestry. Sequential systems include improved fallows, relay cropping with trees and rotational woodlot systems where a piece of land is deliberately planted with fast-growing, often nitrogen-fixing trees [START_REF] Nair | Classification of agroforestry systems[END_REF]. Conservation agriculture is defined according to FAO (2015) as a cropping system characterized by three principles, namely 1) continuous minimum mechanical soil disturbance;

2) permanent organic soil cover, and 3) diversification of crop species grown in sequences and/or associations.

Retrieved publications were screened and had to meet the following defined basic selection criteria to be included in our analysis. First, studies are field experiments conducted in sub-Saharan Africa in which SOC measurements were done on a control treatment (i.e. a cropland without an agroforestry or conservation agriculture intervention) and on an agroforestry treatment or a (partial) conservation agriculture treatment where at least the effect of no-or minimum tillage was tested ('space for time' or synchronic approach), or on a agroforestry or conservation agriculture treatment with repeated soil sampling in time (diachronic approach).

Results from chronosequence studies and studies using forests or natural ecosystems as a control were excluded. Second, the same crop was grown in both treatment and control. Third, studies report SOC stocks, which is the quantity of carbon per unit area expressed in kg C m -2 or kg C ha -1 , or SOC stocks could be calculated from the published SOC concentration expressed as proportion of the total soil mass, and soil bulk density. Studies that reported only SOC concentrations without soil bulk density were excluded. In some cases when published data were incomplete to calculate SOC stocks, the authors of the studies were contacted for additional information. In this way, SOC stocks were retrieved from the original datasets provided by the authors for the following studies: [START_REF] Baumert | Soil Organic Carbon Sequestration in Jatropha curcas Systems in Burkina Faso[END_REF], [START_REF] Bright | Long-term Piliostigma reticulatum intercropping in the Sahel: Crop productivity, carbon sequestration, nutrient cycling, and soil quality[END_REF]), Paul et al. (2015) and [START_REF] Rimhanen | Ethiopian agriculture has greater potential for carbon sequestration than previously estimated[END_REF]. Fourth, the treatment duration is reported in the paper.

For each study, we calculated the absolute annual rate of change in SOC stock (kg C ha -1 yr -1 ) and the relative rate (i.e. to the initial or control value of the SOC stock, ‰ yr -1 ) to the maximum soil depth specified in each paper from the initial and final measurements (diachronic approach) or from the SOC stocks under treatment and control (synchronic approach), and the duration of the treatment. When for a study SOC storage rates could be calculated with both the diachronic and synchronic approach, we used the diachronic rate in the further analysis of data because confounding effects of spatial heterogeneity with the synchronic approach may lead to less accurate results compared to the diachronic approach [START_REF] Junior | Assessing soil carbon storage rates under no-tillage: Comparing the synchronic and diachronic approaches[END_REF]. Four studies on agroforestry systems reported SOC contents for soil depths well below 40 cm, i.e. up to 100 or 200 cm soil depth. To account for these potential soil depth effects, we also calculated and analyzed SOC storage rates to a maximum soil depth of 40 cm. If SOC contents to 40 cm depth (or less) were reported in the above four studies, they were included in this additional analysis.

If a site was sampled more than once at different points in time, we used the results of the first and last reported samplings, so to obtain the largest sampling interval. Data from the same study but reported in more than one publication were not repeated to avoid double counting; the publication with the most complete dataset was used. When the study investigated multiple agroforestry or conservation agriculture treatments, each treatment was considered as a single point in the analysis; when multiple controls were reported, the most representative practice for the study area was used as control, and when more than one form of tillage was assessed in a study, we selected the tillage treatment representing the greatest soil disturbance as control.

When a paper presented results from single control and treatment plots (no replicates), the study was not included in the analysis.

The literature search returned 183 publications for agroforestry and 157 for conservation agriculture. With the above selection criteria, 15 and 20 publications were selected in the final dataset for agroforestry and conservation agriculture, respectively. The complete reference list and details of selected publications are given as Supplementary Material (Table S2,S3).

Statistical analyses

All the statistical analyses were performed using R software version 3.1.1 (R Development Core Team, 2013), at a significance level of ≤0.05. Reported data concerning SOC storage rates for the different agroforestry and conservation agriculture systems presented heterogeneous variances, preventing from using classical statistical tests [START_REF] Scheffé | The Analysis of Variance[END_REF][START_REF] Littell | SAS for Mixed Models[END_REF].

We therefore used a weighted least squares regression, using the gls function from the nlme package [START_REF] Galecki | Linear Mixed-Effects Models Using R: A Step-by-Step Approach[END_REF]. Each observation per subsystem i (alley cropping, fallows, multistrata system, parkland; no-tillage, no-tillage + residues, no-tillage + residues + rotation/intercropping) was weighted by

𝑉 𝑖

, where Vi was the variance of a given subsystem.

Weights were normalized so that their sum equaled the total number of observations (n=66 for the agroforestry, n=33 for conservation agriculture). The lsmeans function [START_REF] Lenth | Least-Squares Means: The R Package lsmeans[END_REF] was then used to test whether SOC storage rates for each sub-system were significantly different from 0‰ yr -1 and from 4‰ yr -1 . To compare the different subsystems, pairwise comparisons were also performed with the lsmeans function, using the Tukey's method.

Results

Agroforestry

The total of 15 retrieved publications from peer-reviewed literature resulted in 68 observations with absolute changes in SOC stocks reported. For two observations (Verchot et al., 2011) the relative change of SOC stock could not be calculated since the initial or control SOC levels were not reported (Table S2). This review will concern the 66 observations. The studies were conducted in 12 countries. There were 19 observations from alley cropping and eight from intercropping systems which we regrouped in our analysis. Nineteen observations came from improved fallows, one from natural fallow and five from rotational woodlots which were combined as 'fallows'. Finally, eight observations were from multistrata systems and six from parklands. Only two publications [START_REF] Raddad | Productivity and nutrient cycling in young Acacia senegal farming systems on vertisol in the Blue Nile region, Sudan[END_REF][START_REF] Bright | Long-term Piliostigma reticulatum intercropping in the Sahel: Crop productivity, carbon sequestration, nutrient cycling, and soil quality[END_REF] presented SOC stocks measured at different time periods (diachronic approach); all other publications reported data from paired-site experiments. Since the synchronic approach allowed with the available data from [START_REF] Bright | Long-term Piliostigma reticulatum intercropping in the Sahel: Crop productivity, carbon sequestration, nutrient cycling, and soil quality[END_REF] to calculate SOC storage rates that covered a longer time span (13 years) than the diachronic approach (4 years), we considered the synchronic rates for this study in the further analysis. Maximum soil sampling depth ranged from 12 to 200 cm (Figure 1). A majority of the data (62%) covered only the 20 first centimeters of soil, while 20% of the data reported a maximum sampling depth of 30 to 50 cm. Only 14% of the observations were obtained by sampling at least down to 1 m depth. The time since the introduction of the agroforestry system varied from 2 to 50 years, with 70% of the observations that had trees planted less than 10 years before the final soil sampling (Figure 1). Overall, the absolute rate of SOC change varied from -9.6 (0-40 cm) to 14 Mg C ha -1 yr -1 (0-100 cm) (Table S2). The largest rate of SOC increase was from a study with 11 years of continuous alley cropping with Maesopsis eminii Engl. on a sandy loam soil in Uganda [START_REF] Tumwebaze | Soil organic carbon under a linear simultaneous agroforestry system in Uganda[END_REF]. The largest decrease reported was on a loamy sand site in Burkina Faso under a 2-year alley cropping system with Jatropha curcas L. [START_REF] Baumert | Soil Organic Carbon Sequestration in Jatropha curcas Systems in Burkina Faso[END_REF].

Relative rates of SOC change varied widely from -159 to +194‰ yr -1 (Figure 2, values considering maximum reported soil depths). Eighty percent of the observations had annual relative SOC storage rates higher than 4‰ yr -1 . Fifty percent of the observations had SOC storage rates of 34‰ yr -1 or higher.

The alley cropping, fallows and multistrata systems showed similar median rates of, respectively, 37, 37 and 45‰ yr -1 . Alley cropping systems showed the highest variability, with storage rates ranging from -159 to 149‰ yr -1 (Figure 3). Most negative rates of SOC change were from paired-site comparisons between sorghum cropped alone and alley cropped with Jatropha curcas L. at seven sites in Burkina Faso with the age of the alley cropping system varying between two and four years [START_REF] Baumert | Soil Organic Carbon Sequestration in Jatropha curcas Systems in Burkina Faso[END_REF]. Four observations of this same study showed, however, positive rates of SOC storage of between 15 and 67‰ yr -1 . Two negatives rates were also observed in multistrata systems in Ethiopia [START_REF] Rimhanen | Ethiopian agriculture has greater potential for carbon sequestration than previously estimated[END_REF]). The highest rates of SOC storage under alley cropping (72-149‰ yr -1 ) were from paired-site comparisons where the soils were sampled to, respectively, 1 m and 2 m depth, i.e. the four observations reported by [START_REF] Tumwebaze | Soil organic carbon under a linear simultaneous agroforestry system in Uganda[END_REF] on alley cropping with four different tree species, and the two observations reported by [START_REF] Makumba | Long-term impact of a gliricidia-maize intercropping system on carbon sequestration in southern Malawi[END_REF] on alley cropping with Gliricidia sepium.

We retrieved only one publication on multistrata systems [START_REF] Rimhanen | Ethiopian agriculture has greater potential for carbon sequestration than previously estimated[END_REF]) that reported eight paired-site comparisons (0-15 cm sampling depth) at different sites in Ethiopia. SOC storage rates under these systems ranged widely from -5 to 80‰ yr -1 . For parkland systems, there were six observations from two publications (Abaker et al., 2016, 5 observations;Gelaw et al., 2014, 1 observation). The SOC storage rates varied from -3 to 22‰ yr -1 , mainly depending on the type of grass species in the treatments.

Soil organic carbon storage rates were significantly higher than 4‰ yr -1 (and 0‰ yr -1 ) in the fallows and in the multistrata systems (p-value = 0.0001 and 0.0178, respectively) (Figure 3, values considering maximum reported soil depths). Rates in the fallows were significantly higher than in the parklands (p-value = 0.0003). When we considered reported SOC contents to a maximum soil depth of 40 cm only, SOC rates in the fallows became significantly higher than in the alley cropping systems (p-value = 0.0169) (Fig S1,Supplementary Materials). For the parkland systems, we were left with only one observation. Rates in the fallows and in the multistrata systems remained significantly higher than 4‰ yr -1 (and 0‰ yr -1 ) (p-value = 0.0001 and 0.0144, respectively).

Conservation agriculture

We retrieved 20 publications that resulted in a total of 33 observations, comprising 21 sites in seven countries (Table S3). Maize was by far the most studied crop species (27 observations); the remaining studies related to six other crop species. In several studies, only one or two of the conservation agriculture principles were applied: five observations were from treatments with no-tillage alone and three observations from no-or minimum tillage with intercropping and/or rotations, but without crop residue mulching. They were grouped in the analysis (Figure 3). Ten observations were from treatments with no-or minimum tillage with crop residue mulching, but without rotation or intercropping, and 14 observations referred to treatments with all three principles of conservation agriculture applied. In one study [START_REF] Ojeniyi | Soil conditions and cowpea and maize yield produced by tillage methods in the rainforest zone of Nigeria[END_REF], it was not clear from reading the paper whether crop residues were left on the soil or not. The one observation from this study was therefore not used when differentiating between the varying degrees of application of the conservation agriculture principles (Figure 3). Most conservation agriculture treatments in the dataset involved no-tillage, i.e. manual or mechanized direct seeding (26 observations). The other seven observations were minimum tillage treatments, i.e. ripping (5 observations) or surface scraping of the soil (2 observations). The tillage type to which the conservation agriculture treatment was compared was mainly ploughing (11 observations with ox-ploughing and 9 observations with tractor ploughing,). Hoeing and ridging represented respectively eight and five observations. Fourteen studies measured SOC storage through repeated sampling in time of the conservation agriculture treatment, but at the same time these studies were also paired-site comparisons between a conservation agriculture and conventional tillage treatment; the other six studies were only paired-site comparisons. Soil sampling depth ranged from 5 to 60 cm, but 91% of the observations had a maximum sampling depth of 30 cm (Figure 1). The time since the introduction of the conservation agriculture treatment varied from 1 to 11 years, but 85% of the observations had a maximum treatment age of 5 years (Figure 1).

Overall, the absolute SOC change varied from -10.2 (0-30 cm) to 6.86 (0-15 cm) Mg C ha -1 yr - 1 for observations were SOC storage was calculated using the diachronic approach (Table S3).

The largest decrease reported was from a 2-year experiment on a site in south-eastern Nigeria where sweet potato was cultivated on a loam soil under no-tillage without residues retention [START_REF] Anikwe | Short-term changes in soil properties under tillage systems and their effect on sweet potato (Ipomea batatas L.) growth and yield in an Ultisol in south-eastern Nigeria[END_REF]. This large decrease can probably be explained by the fact that the site was slashed and cleared of fallow vegetation, and thus had an initial high level of relatively labile SOC that decomposed rapidly following cultivation. The data also showed large variability with least significant difference (p = 0.05) values of up to 8.6 Mg C ha -1 . The largest rate of SOC increase (diachronic approach) was from a study in southern Nigeria on sandy loam under 2-year no-tillage without residue retention [START_REF] Agele | Effects of some soil management systems on soil physical properties, microbial biomass and nutrient distribution under rainfed maize production in a humid rainforest Alfisol[END_REF], but this is probably an overestimate due to the small soil sampling depth (0-15 cm); the practice of no-tillage results in stratification of SOC concentration with depth, with surface soil layers having considerably higher SOC concentration than the layers below [START_REF] Baker | Tillage and soil carbon sequestration-What do we really know?[END_REF].

Figure 3. Soil organic carbon storage rates for different agroforestry and conservation agriculture systems. Crosses represent mean SOC storage rate per type of subsystem. For each system, different letters represent significant differences between subsystems. ** represents subsystems with SOC storage rates significantly higher than 0‰ yr -1 and 4‰ yr -1 .

Relative SOC change varied from -142 to 450‰ yr -1 (Figure 2). SOC change under conservation agriculture was negative for nine observations. Sixty-four percent of the studies had annual relative SOC storage rates that were higher than 4‰ yr -1 . Fifty percent of the observations had relative rates that were larger than 34‰ yr -1 . Treatments with no-tillage without residue retention showed the smallest median SOC storage rate, -12‰ yr -1 (Figure 3), and the highest variability, ranging from -142 to 450‰ yr -1 . The reported negative rates of SOC change were from repeated sampling on sites that were cleared from negative vegetation. They became however positive when calculated on the basis of the comparison with the conventional tillage treatment (Figure 4). Rates under no-or minimum tillage with residue retention also varied widely between -98 and 448‰ yr -1 . Again, negative rates were reported from two experiments in Nigeria where the conservation agriculture treatment was installed following clearing of native vegetation [START_REF] Agbede | Nutrient availability and cocoyam yield under different tillage practices[END_REF][START_REF] Lal | Soil quality changes under continuous cropping for seventeen seasons of an Alfisol in western Nigeria[END_REF]. The highest rate (448‰ yr -1 ) was reported in a paired-site study in Malawi [START_REF] Mloza-Banda | Soil properties after change to conservation agriculture from ridge tillage in sandy clay loams of mid-altitude Central Malawi[END_REF] in which manual direct seeding with retention of crop residues was compared with ridging without crop residues on three different fields after four years. The value is an outlier and probably an overestimate.

Apart from the methodological problems with making comparisons of SOC stocks between flat planting and ridge and furrow systems, the data were from three paired-site comparisons on different farmer's fields where great variability between fields is to be expected. Annual SOC rates from treatments with all three principles of conservation agriculture varied less, between -96 and 176‰ yr -1 (Figure 3). The lowest rate (-96‰ yr -1 ) was reported in a 2-year study in Zimbabwe by [START_REF] Nyamadzawo | Soil organic carbon dynamics of improved fallow-maize rotation systems under conventional and no-tillage in Central Zimbabwe[END_REF] in which SOC storage was measured on a sandy clay loam (0-20 cm) under direct seeding of maize, following a fallow period with Sesbania sesban.

The highest value of 176‰ yr -1 was from a sandy loam site in Western Kenya [START_REF] Ngome | Fertility management for maize cultivation in some soils of Western Kenya[END_REF] where the soil (0-15 cm) was sampled after 1 year in a no-tillage treatment with maize grown on a permanent living cover of Arachis pintoï. Two other observations from the same study with the same conservation agriculture treatment on two different sites gave also relatively high rates of 102 (on clay) and 77‰ yr -1 (on clay loam). The values were however derived from small absolute changes in measured SOC concentrations (0.19, 0.16 and 0.15%, respectively). The increase is certainly also the result of SOC redistribution nearer to the soil surface.

Only SOC storage rates in the system with the full set of conservation agriculture principles, i.e. no-tillage, residue retention and intercropping or rotation were significantly higher than 0‰ yr -1 (p-value = 0.0244) and 4‰ yr -1 (p-value = 0.0438). SOC storage rates were not significantly different between the different degrees of application of the conservation agriculture principles (Figure 3). The comparison of studies for which SOC storage rates could be calculated both using the diachronic and the synchronic approach showed that the synchronic rates were in most cases higher than 0‰ yr -1 (two exceptions). They were larger than the diachronic rates, especially in case of negative diachronic rates (Figure 4). All large deviations were from conservation agriculture experiments that were installed following clearance of native vegetation or fallow.

In these cases, initial SOC was relatively high, and probably labile provoking net negative changes in SOC, both for the treatment and control.

Discussion

SOC storage potentials

Agricultural soils in sub-Saharan Africa have a strong carbon sink capacity as a result of previous SOC depletion [START_REF] Lal | Beyond COP 21: Potential and challenges of the "4 per Thousand" initiative[END_REF]. Theoretically, SOC stocks can be restored through soil and crop management practices that have a positive carbon budget (i.e. with carbon inputs from biomass exceeding carbon outputs through decomposition and erosion [START_REF] Stockmann | The knowns, known unknowns and unknowns of sequestration of soil organic carbon[END_REF][START_REF] Dignac | Increasing soil carbon storage: mechanisms, effects of agricultural practices and proxies[END_REF]). We examined the SOC storage potentials of two widely promoted management practices in sub-Saharan Africa, agroforestry and conservation agriculture. In the following sections we discuss the extent to which these practices can increase SOC stocks and contribute to climate change mitigation. Other practices that increase carbon inputs to soil are e.g. the addition of manure or other organic materials to fields. However, adding organic materials to soil does not necessarily lead to a net transfer of carbon from the atmosphere to the soil. Depending on the alternative end use of the materials, it can just constitute a transfer from one location to another, and thus without mitigating climate change [START_REF] Powlson | Soil carbon sequestration to mitigate climate change: A critical re-examination to identify the true and the false[END_REF].

Agroforestry

Overall, our review showed that agroforestry has a potential to store SOC (Figure 2 and 3), especially multistrata systems and fallows. The largest SOC storage rates (> 190‰ yr -1 ) were obtained with rotational woodlots [START_REF] Kimaro | Carbon pools in tree biomass and soils under rotational woodlot systems in eastern Tanzania[END_REF]. These agroforestry systems conflict however with food security goals, since edible crops are not grown in these systems. Parklands showed the lowest potential for storing SOC (Figure 3), probably because of a low tree density per hectare (Takimoto et al., 2008). Besides improving carbon levels in soils, agroforestry systems store also a vast amount of carbon in the tree aboveground and belowground biomass, which considerably increases their interest in a perspective of climate change mitigation [START_REF] Luedeling | Carbon Sequestration Potential of Agroforestry Systems in Africa[END_REF][START_REF] Zomer | Global Tree Cover and Biomass Carbon on Agricultural Land : The contribution of agroforestry to global and national carbon budgets[END_REF][START_REF] Feliciano | Which agroforestry options give the greatest soil and above ground carbon benefits in different world regions?[END_REF].

Trees have an extensive root system that can grow deep into the soil (Cardinael et al., 2015b;[START_REF] Pierret | Understanding deep roots and their functions in ecosystems: an advocacy for more unconventional research[END_REF] and root derived carbon is probably the most important source for SOC storage since it is more likely to be stabilized in the soil by physicochemical processes than shoot derived carbon [START_REF] Balesdent | Major contribution of roots to soil carbon storage inferred from maize cultivated soils[END_REF][START_REF] Menichetti | Contribution of roots and amendments to soil carbon accumulation within the soil profile in a long-term field experiment in Sweden[END_REF]. The highest relative SOC storage rates (72-149‰ yr -1 ) in our database were reported from experiments where soil was sampled to depths of 1 to 2 m, confirming the need to sample deep soil layers to study agroforestry systems [START_REF] Haile | Contribution of trees to carbon storage in soils of silvopastoral systems in Florida, USA[END_REF]Cardinael et al., 2015a). Overall, trees enhance SOC storage because of higher biomass production and carbon inputs to soil [START_REF] Peichl | Carbon sequestration potentials in temperate tree-based intercropping systems, southern Ontario, Canada[END_REF][START_REF] Cardinael | High organic inputs explain shallow and deep SOC storage in a long-term agroforestry system -Combining experimental and modeling approaches[END_REF] caused by increased light, water and nutrient use efficiency at the plot scale compared to monoculture. Trees can also recover nutrients from deeper soil layers and thus improve soil nutrient availability and uptake [START_REF] Nair | Nutrient cycling in tropical agroforestry systems: myths and science[END_REF]. Likewise, agroforestry systems with N-fixing trees may cause higher biomass production and carbon inputs as a result of increased soil nitrogen availability [START_REF] Sileshi | Meta-analysis of maize yield response to woody and herbaceous legumes in sub-Saharan Africa[END_REF]. Effects of agroforestry systems on rates of SOC decomposition are far less understood [START_REF] Lorenz | Soil organic carbon sequestration in agroforestry systems. A review[END_REF]. Changes in litter quality and in the soil microbial and faunal communities involved in SOC decomposition may play a role [START_REF] Gnankambary | Decomposition and nutrient release from mixed plant litters of contrasting quality in an agroforestry parkland in the south-Sudanese zone of West Africa[END_REF][START_REF] Mitchell | The ecological engineering impact of a single tree species on the soil microbial community[END_REF].

Within a type of agroforestry system, published rates of SOC storage varied widely (Figure 3, Table S2). The age of the agroforestry system, tree density, initial SOC stock and soil texture are amongst the most influencing factors that determine SOC storage rates [START_REF] Laganière | Carbon accumulation in agricultural soils after afforestation: A meta-analysis[END_REF] and to a certain extent explain the variability in published data. Rates of SOC change are likely to be smaller for older agroforestry systems since they are expected to gradually decrease as a new SOC equilibrium is reached (Paustian et al, 1997). This also means that a strict interpretation of the 4‰ concept of increasing SOC stocks each year by a slightly larger absolute amount as SOC increases is not reasonable. A significant decrease of SOC storage rate with time was indeed found for agroforestry systems (p-value = 0.0328) (Figure 5). This entails that the capacity for SOC storage is finite and net CO2 removals under a new management system are thus of limited duration [START_REF] Powlson | Soil carbon sequestration to mitigate climate change: A critical re-examination to identify the true and the false[END_REF][START_REF] Paustian | Climate-smart soils[END_REF]. On the other hand, we did not find significant relationships between SOC storage rate and initial SOC stock or tree density (Figure 5), which is probably due to the fact that other factors, such as tree species, type of control treatment and soil and climatic conditions interfered. It is generally known that positive effects on SOC are more likely to occur in finer-textured soils than in sandy soils because of the presence of physical and structural protection of SOC [START_REF] Torn | Mineral control of soil organic carbon storage and turnover[END_REF]), but we were not able to test for this effect due the lack of soil texture data in several of the retrieved publications. In conclusion, our review suggests a high potential for SOC storage under newly established agroforestry systems in soils of sub-Saharan Africa, which represents a genuine option for climate change mitigation. Most of the published values were well above the 4‰ yr -1 . The limited number of observations and the high variability in results ask for more research to better understand the positive effects of different agroforestry systems on SOC and how management could optimize these effects [START_REF] Nair | Solid-fluid-gas: The state of knowledge on carbon-sequestration potential of agroforestry systems in Africa[END_REF][START_REF] Feliciano | Which agroforestry options give the greatest soil and above ground carbon benefits in different world regions?[END_REF].

Conservation agriculture

Conservation agriculture has received much attention as a practice to increase SOC stocks and mitigate climate change [START_REF] Hobbs | How conservation agriculture can contribute to buffering climate change[END_REF][START_REF] Lal | Sequestering carbon and increasing productivity by conservation agriculture[END_REF]. In general, SOC storage under conservation agriculture has been attributed to increased retention of crop residues compared to conventional cropping practices [START_REF] Virto | Carbon input differences as the main factor explaining the variability in soil organic C storage in no-tilled compared to inversion tilled agrosystems[END_REF]. For example, in a global meta-analysis, [START_REF] Luo | Can no-tillage stimulate carbon sequestration in agricultural soils? A meta-analysis of paired experiments[END_REF] found that in most studies no-tillage alone did not increase the overall SOC stocks, except for those with increased biomass production and crop residue retention, especially via double cropping (two crops per year). These findings are corroborated by the results from our review and from a recent review by [START_REF] Powlson | Does conservation agriculture deliver climate change mitigation through soil carbon sequestration in tropical agro-ecosystems?[END_REF]: no-tillage treatments with retention of crop residues and with crop rotation or intercropping resulted in the largest SOC storage rates. Moreover, we found that conservation agriculture produced SOC storage rates compatible with the "4 per 1000" initiative, only when all three principles are implemented (Figure 3).

No-tillage systems with retention of crop residues are also effective in reducing carbon losses through soil erosion [START_REF] Ranaivoson | Agro-ecological functions of crop residues under conservation agriculture[END_REF]. Carbon lost on a field through erosion is, however, not necessarily converted to CO2 as it may be transported and (permanently) stored in soil or sediments in another location [START_REF] Wang | Human-induced erosion has offset one-third of carbon emissions from land cover change[END_REF].

No-or minimum tillage alone can lead to SOC storage if it decreases the rate of SOC decomposition. [START_REF] Six | Aggregate and Soil Organic Matter Dynamics under Conventional and No-Tillage Systems[END_REF] showed that less disruption of macro-aggregates with no-tillage enhances the formation of micro-aggregates that are crucial in the stabilization (lower decomposition rate) and storage of SOC in the long term. The results from our review showed however that there was no positive effect of no-tillage on SOC storage (Figure 3). Besides, it is important to note that conversion from conventional tillage to no-tillage alters the vertical distribution of SOC in the soil profile, resulting in increased SOC in the 0-20 cm soil layers and decreased soil carbon in the 20-40 cm soil layers [START_REF] Baker | Tillage and soil carbon sequestration-What do we really know?[END_REF][START_REF] Angers | Full-Inversion Tillage and Organic Carbon Distribution in Soil Profiles: A Meta-Analysis[END_REF][START_REF] Luo | Can no-tillage stimulate carbon sequestration in agricultural soils? A meta-analysis of paired experiments[END_REF]. This means that there is not necessarily a net increase in SOC stocks with no-tillage and that studies on SOC storage should investigate at least the 0-40 cm soil layer and not only the topsoil.

Our review showed highly variable SOC storage under conservation agriculture, with some reported rates that were anomalously large or low (Figure 2 and 3). A conclusion that was also made by [START_REF] Powlson | Does conservation agriculture deliver climate change mitigation through soil carbon sequestration in tropical agro-ecosystems?[END_REF] in their meta-analysis of SOC stock changes under conservation agriculture practices in the Indo-Gangetic Plains and SSA. We did not find significant relationships between SOC storage rate and initial SOC stock or age of the conservation agriculture systems (Figure 5). The effects of these factors may be confounded with the effects of several other factors that influence SOC storage rates. First, the agro-ecological conditions across the studies are highly heterogeneous. For example, diachronic studies that were established on a land that was cleared from natural vegetation will result in negative SOC storage rates even under conservation agriculture, whilst studies on degraded land may result in build-up of SOC. Second, various forms of conservation agriculture (and conventional tillage practices) were tested in the reported experiments. Third, several methodological approaches are used for measuring SOC storage under conservation agriculture, including diachronic versus paired-site approaches (Figure 4); on station versus on farm experiments; and different depths of soil sampling (Figure 1).

There was a major difference in SOC storage rates estimated by the diachronic versus the synchronic approach, the latter one usually leading to higher rates (Figure 4). This phenomenon can be explained by the land use history of the fields [START_REF] Junior | Assessing soil carbon storage rates under no-tillage: Comparing the synchronic and diachronic approaches[END_REF]. The diachronic approach provides a measure of net SOC changes under a treatment with respect to an initial state. These changes are expected to be negative under any agricultural system that was recently installed on soils that were previously under natural ecosystems (e.g. [START_REF] Solomon | Long-term impacts of anthropogenic perturbations on dynamics and speciation of organic carbon in tropical forest and subtropical grassland ecosystems[END_REF]. In other words, diachronic rates depend to a large extent on the initial levels (and quality) of SOC, and thus on the land-use history. On the other hand, the synchronic approach compares the difference in SOC stocks of a treatment with respect to a control. Besides, spatial variability of soil properties can interfere in the synchronic approach where space is substituted for time [START_REF] Junior | Assessing soil carbon storage rates under no-tillage: Comparing the synchronic and diachronic approaches[END_REF]. As such, positive synchronic SOC rates do not provide evidence of a net SOC storage or a true carbon sink that removes CO2 from the atmosphere. This pleads for long-term diachronic experiments in sub-Saharan Africa.

In conclusion, conservation agriculture with the three principles applied can increase SOC and offer a scope for climate change mitigation, if carbon inputs are increased through higher crop productivity (intercropping and/or crop rotations). The impact will depend on the site conditions, type of cropping system, management and the historical land use. However, conservation agriculture practices, and SOC-restoration practices in general, once established, need to be preserved over time. If the practice of CA that led to increased SOC stocks is reversed, the previously accumulated SOC will be lost as CO2, and usually more rapidly than it was accumulated [START_REF] Vandenbygaart | Persistence of Soil Organic Carbon after Plowing a Long-Term No-Till Field in Southern Ontario, Canada[END_REF].

Soil fertility gradients illustrate potential and challenges with SOC storage

The potential and challenges with SOC storage in the agriculture landscapes of sub-Saharan Africa are probably best illustrated with studies on soil fertility gradients on smallholder farms [START_REF] Tittonell | Soil Heterogeneity and Soil Fertility Gradients in Smallholder Farms of the East African Highlands[END_REF]. Soil fertility gradients are a consequence of the differential allocation of nutrient and labor resources to the various fields of a farm. They are the result of the limited resources that smallholders possess and that they tend to concentrate in the fields close to their homestead. Over time, this leads to soil fertility gradients, including gradients of SOC. Soil fertility typically decreases within a farm at increasing distances from the homestead [START_REF] Prudencio | Ring management of soils and crops in the west African semi-arid tropics: The case of the mossi farming system in Burkina Faso[END_REF][START_REF] Carter | Spatial variability in soil fertility management and crop response in Mutoko Communal Area, Zimbabwe[END_REF][START_REF] Tittonell | Exploring diversity in soil fertility management of smallholder farms in western Kenya[END_REF][START_REF] Zingore | Soil type, management history and current resource allocation: Three dimensions regulating variability in crop productivity on African smallholder farms[END_REF].

Reinforcing the soil fertility gradients, farmers often prioritize nutrient and labor allocation to their most fertile fields, where crop responses to inputs are generally highest.

For example, a case study in Western Kenya [START_REF] Tittonell | Yield gaps, nutrient use efficiencies and response to fertilisers by maize across heterogeneous smallholder farms of western Kenya[END_REF] showed gradients of SOC levels across fields in farms at three different locations (Table 1). On average per location, SOC levels in the outfields were 61, 67 and 83% of those in homestead fields. The midfields had SOC levels that were 60, 73 and 88% of the SOC levels in the homestead fields. These SOC gaps between fields are mainly the results of the higher use of manure or composted household waste and mineral fertilizer on the homestead fields compared to the other fields. Besides, the higher soil fertility combined with better overall management of homestead fields gave rise to higher crop yields (Table 1), which in turn results in higher carbon inputs (via roots and residues, if left on the field). These findings suggest that there is a wide scope for storing SOC in the midfields and outfields; in the presented case study between 10 to 40% of the original SOC levels. On the other hand, SOC storage on those fields is not achieved given the limited production resources of the farmers. Several authors showed that SOC storage can only be achieved with increased nutrient (most importantly, nitrogen) availability in soils [START_REF] Van Groenigen | Element interactions limit soil carbon storage[END_REF][START_REF] Van Groenigen | Sequestering Soil Organic Carbon: A Nitrogen Dilemma[END_REF][START_REF] Kirkby | Carbon-nutrient stoichiometry to increase soil carbon sequestration[END_REF][START_REF] Kirkby | Nutrient availability limits carbon sequestration in arable soils[END_REF][START_REF] De Vries | Nutrients trigger carbon storage[END_REF][START_REF] Richardson | The inorganic nutrient cost of building soil carbon[END_REF].

Table 1: Gradients of soil organic carbon (SOC) levels (0-30 cm soil layer) and maize grain yields on farmers' fields at three locations in Western Kenya (from [START_REF] Tittonell | Yield gaps, nutrient use efficiencies and response to fertilisers by maize across heterogeneous smallholder farms of western Kenya[END_REF].

Location/position within the farm SOC (g kg -1 ) Grain yield (kg ha -1 ) a The above spatial effects of differential allocation of limited resources by farmers are also occurring at the large scale of a village, as for example illustrated in a study in north-east Zimbabwe by [START_REF] Zingore | Managing soil fertility diversity to enhance resource use efficiencies in smallholder farming systems: A case from Murewa District, Zimbabwe[END_REF]. Wealthier farmers with cattle have usually fields with higher SOC levels (especially their homestead fields) as a result of application of manure compared to poorer farmers without cattle who do not have manure. Moreover, crop residues from fields of non-cattle farmers are often grazed by cattle of the wealthier farmers, reducing the carbon inputs in the soils of these fields. As a result, fields of non-cattle owners are SOC depleted. These fields represent an important carbon sink, if farmers' resources would allow to purchase and apply organic manures, alone or in combination with chemical fertilizer. Although the higher SOC storage in the fields of the wealthier cattle-owners are to a large extent the results of a transfer of organic material from the communal grazing areas and fields of non-cattle farmers to their own fields, and does not constitute a net transfer of carbon from atmosphere to soil, the higher SOC levels on fields of the wealthier farmers result in higher nutrient use efficiency and crop yields, thus providing more carbon inputs to the soil, and thus a net transfer of carbon from atmosphere to soil.

Implementation and adoption of SOC restoration practices

Strategies for widespread adoption of SOC-restoration practices are required for the 4‰ initiative to be effective in mitigating climate change. In sub-Saharan Africa, however, the challenge to implement these strategies for agricultural soils is enormous. Many farmers are extremely poor and live below the poverty line, often with the inability to invest in new practices or technologies. It should also be clear that for smallholders, climate change mitigation is no priority [START_REF] Luedeling | Carbon sequestration potential of parkland agroforestry in the Sahel[END_REF]. Farmers' priorities are to get immediate benefits from farming and to ensure their food security [START_REF] Jerneck | Food first! Theorising assets and actors in agroforestry: risk evaders, opportunity seekers and "the food imperative" in sub-Saharan Africa[END_REF]. Therefore, the entry point for promoting SOC-restoration practices should be on the grounds of increasing crop productivity through better soil quality, and not on the basis of climate change mitigation. The majority of the management practices that build SOC represent, however, ''win-win'' options, and strategies to implement these practices can be promoted on a ''no regrets'' basis [START_REF] Smith | Greenhouse gas mitigation in agriculture[END_REF], i.e. they do provide other benefits even if the climate change mitigation potential is not realized. Especially in low-input smallholder farming systems, enhancing SOC storage positively impacts crop productivity (e.g. [START_REF] Tittonell | Yield gaps, nutrient use efficiencies and response to fertilisers by maize across heterogeneous smallholder farms of western Kenya[END_REF], and is expected to contribute to enhanced resilience to climate change.

Despite these co-benefits, adoption of SOC-restoration practices, such as agroforestry and conservation agriculture, by smallholders is low in sub-Saharan Africa [START_REF] Giller | Conservation agriculture and smallholder farming in Africa: The heretics' view[END_REF][START_REF] Jerneck | More than trees! Understanding the agroforestry adoption gap in subsistence agriculture: Insights from narrative walks in Kenya[END_REF]. There are several technical, infrastructural, socio-economic, or policy barriers to adoption. First of all, farm sizes are small (often less than 2 ha) which raise questions about the potential impact of technological interventions on farm income [START_REF] Harris | Is rainfed agriculture really a pathway from poverty?[END_REF]. Small farm sizes make farmers also more risk averse in trying out new technologies.

Second, there is a general lack of effective support for smallholder agriculture in much of sub-Saharan Africa, such that there are actually economic disincentives to investment in agriculture [START_REF] Ehui | Resource degradation, low agricultural productivity, and poverty in sub-Saharan Africa: Pathways out of the spiral[END_REF]. Private sector support is often uncertain, because only a small part of farm produce is marketed. Good markets for sale of extra produce and for input supply are a prerequisite condition for the widespread adoption of new agricultural technologies that aim at productivity increase. Third, failure of efficient extension services in most African countries limit the possibility to scale up best management practices [START_REF] Davis | Strengthening Agricultural Education and Training in sub-Saharan Africa from an Innovation Systems Perspective: A Case Study of Mozambique[END_REF]. Fourth, effective policies, including input subsidies, which incentivize farmers to invest in new technologies are needed [START_REF] Jayne | Input subsidy programs in sub-Saharan Africa: A synthesis of recent evidence[END_REF].

Farming systems and farmers in sub-Saharan Africa being highly diverse, a major challenge with the development and dissemination of practices such as conservation agriculture and agroforestry is the identification of situations where they can offer major benefits [START_REF] Giller | Communicating complexity: Integrated assessment of trade-offs concerning soil fertility management within African farming systems to support innovation and development[END_REF][START_REF] Luedeling | Carbon Sequestration Potential of Agroforestry Systems in Africa[END_REF]. Specific technologies should be adapted and targeted to categories of farmers who are likely to benefit from these technologies, and adapted to the local circumstances and specific farming contexts. Features that need to be considered include farmers' production objectives and constraints, expected costs (requirements in terms of inputs, equipment, labor), benefits (especially in the short term), production and financial risk, input supply and marketing, farmers' perceptions, and technical advice. This can be achieved through an innovation systems approach that fosters dynamic interactions and collaboration among researchers, extension agents, farmers, policy makers and the private sector [START_REF] Schut | Sustainable intensification of agricultural systems in the Central African Highlands: The need for institutional innovation[END_REF].

More generally, an alignment of agriculture and climate policy also appears to be essential [START_REF] Chabbi | Aligning agriculture and climate policy[END_REF].

Recommendations for SOC monitoring in field experiments

Implementing the 4‰ initiative on a large scale will require the capacity to measure and monitor SOC stocks with acceptable accuracy, quantifiable uncertainty and at relatively low cost [START_REF] Paustian | Climate-smart soils[END_REF]. This implies the combination of direct measurements with modeling approaches [START_REF] Post | Monitoring and verifying changes of organic carbon in soil[END_REF]. For example, repeated measurements at a given site are needed to establish relationships between environmental and management factors and SOC dynamics to improve statistical and quantitative models as tools in monitoring, reporting and verification systems for carbon in soils [START_REF] Batjes | Measuring and monitoring soil carbon[END_REF]. Our review clearly highlighted the scarcity of good quality data on SOC stocks under agroforestry and conservation agriculture practices in sub-Saharan Africa.

In general, there is a lack of standardized procedures for studying and reporting SOC sequestration in agroforestry and conservation agricultural systems, making it difficult to evaluate the precise effect of a given management practice. We recommend the use of the diachronic approach to estimate SOC storage rates given the high uncertainty with the synchronic approach because of spatial variability of soil properties that may influence SOC storage rates (e.g. [START_REF] Cerri | Combining soil C and N spatial variability and modeling approaches for measuring and monitoring soil carbon sequestration[END_REF]. A prerequisite for interpretation of reported SOC data is information on the experimental design together with soil sampling methods (including sampling depth), sample size and a measure of variance of SOC stocks. Soil sampling depth was reported for different soil depths across the studies that we analyzed. Although the 2006 IPCC guidelines recommend a reference depth of 30 cm, it is useful to have estimates for SOC stocks of the entire root zone or to a depth of 1 or 2 m, especially in agroforestry systems (Cardinael et al., 2015a[START_REF] Cardinael | High organic inputs explain shallow and deep SOC storage in a long-term agroforestry system -Combining experimental and modeling approaches[END_REF]. Amongst other minimum data to be reported are the exact location of the experiment, climate, soil type and soil texture, soil bulk density, land-use history, date of establishment of the sequestering practice, land management practices (e.g, fertilizer and organic residue applications), tree density and spacing as well as the management of pruning residues in the case of agroforestry systems. Finally, an estimate of the plant productivity in the experiments is helpful for interpretation of measured SOC storage rates as it determines the carbon inputs into soil.

Conclusions

Our systematic review of published literature showed that both agroforestry and conservation agriculture have a large potential to increase SOC stocks above the rate of 4‰ yr -1 in sub-Saharan Africa. Respectively 80 and 64% of the observations in the published studies had rates that were larger than 4‰ yr -1 (Figure 2). The data showed, however, a very large variability.

As a result, we found that only the agroforestry practice of fallows and multistrata systems led to SOC storage rates significantly higher than 4‰ yr -1 (Figure 3). Among the agroforestry systems, parklands showed the lowest SOC storage rates, a median rate of 8‰ yr -1 . Only 'full' conservation agriculture, i.e. with all three principles implemented, resulted in SOC storage rates that were significantly higher than 4‰ yr -1 . The lowest rates were attained with no-tillage without residue retention.

The example of SOC gradients across different fields of individual farms and across farms illustrated the potential and challenges in increasing SOC stocks in the context of African smallholder agriculture. Low SOC levels are to a great extent the result of the limited resources of smallholder farmers in sub-Saharan Africa. Since climate change mitigation is not a priority for these smallholders, the 4‰ initiative has to be implemented on the grounds of the cobenefits that are offered through improved SOC storage. It means that for the African situation SOC-storing management practices should be promoted on the basis of their positive impact on crop productivity. Furthermore, these practices need to be targeted and adapted to the specific bio-physical and socio-economic situations of the farmers. The strategies to implement the 4‰ initiative in sub-Saharan include the promotion of good markets for sale of extra produce and for input supply, effective private support and policy, including credit schemes and subsidies for inputs, and efficient extension services which incentivize farmers to invest in new technologies.

In conclusion, we argue that there is a great potential for SOC storage in agricultural soils of sub-Saharan Africa given the large areas SOC-depleted soils. Practices such as agroforestry

and conservation agriculture have a potential to restore SOC in these soils. The efficiency in doing so will depend on the specific situations and will need economic support to smallholder farmers. Climate change mitigation should be seen as a no-regret option, not as a key driver for promoting best management options. The key driver is increased farm income through higher crop productivity.

Figure 1 .

 1 Figure 1. Number of observations for agroforestry and conservation agriculture as a function of

Figure 2 .

 2 Figure 2. Cumulative distribution function of SOC storage rates in agroforestry and in

Figure 4 .

 4 Figure 4. Comparison of SOC storage rates estimated by the diachronic or synchronic approach

Figure 5 .

 5 Figure 5. Soil organic carbon storage rates as a function of initial SOC stocks, age since the

Table S3 :

 S3 Africa* OR Angola OR Benin OR Botswana OR Burkina OR Burundi OR Cameroon OR Chad OR Congo OR Ivory OR Guinea OR Eritrea OR Ethiopia OR Gabon OR Gambia OR Ghana OR Kenya OR Liberia OR Madagascar OR Malawi OR Mali OR Mauritania OR Mozambique OR Namibia OR Niger OR Nigeria OR Rwanda OR Senegal OR "Sierra Leone" OR Somalia OR Sudan OR Tanzania OR Togo OR Uganda OR Zambia OR Zimbabwe OR Swaziland) AND ("conservation agriculture" OR "zero till*" OR zero-till* OR "no till*" OR no-till* OR "reduced till*" OR reduced-till* OR "minimum till*" OR minimum-till* OR "direct seeding" OR "direct drill*" OR direct-drill* OR mulch*) Reference list and details of the selected publications for the analysis of SOC storage under conservation agriculture systems

	Tumwebaze et al., (2011) Ngome et al., (2011)	Uganda Kenya	0°48'N 32°46'E 34°51'E	1250 0°14'N	1560 1569	21-25 2232	-	21	-	-11	Alley cropping 27 62	NT + residues + 320 intercropping/rotation
	Kaonga and Coleman, (2008) Kaonga and Coleman, (2008) Reference Nyamadzawo et al., (2008) Ojeniyi and Adekayode, Agbede, (2008) (1999) Reference	Zambia Zambia Country 13°39'S 32°34'E 13°39'S 32°34'E Coordinates Zimbabwe 31°14'E 19°35'S 1030 1030 Rotational crop Nigeria 5°12'E 7°12'N Nigeria 5°15'E 7°15'N Crop species species	1000 1000 Altitude (masl) 1474 Number Maximum 23 23 Mean annual precipitation (mm) 750 SOC (kg ha -1 ) 61 13 61 13 Mean annual temperature (°C) -Sampling -2688 26 210 --of years depth (cm) Control. Initial	26 26 Sand/Silt/Clay (%) Improved fallow (coppiced) Improved fallow (coppiced) 71 7 22 SOC storage rate (Mg C ha -1 yr -1 ) 70 13 17 ---Diachronic Synchronic Diachronic Synchronic 10000 CA Type NT + residues + intercropping/rotation SOC storage rate (‰ yr -1 ) 10000 NT + residues NT + ? + rotation
	Agroforestry soil AND ("carbon stock*" OR "carbon pool*" OR "carbon sequestration" OR "carbon concentration") AND (Africa* OR Angola OR Benin OR Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Agbede, (2008) Nigeria 5°12'E 7°12'N -2688 Paul et al., (2015) Kenya 34°24'E 0°06'N 1420 1800 Agbede, (2008) Cocoyam None 2 20 3 343 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Agele et al., (2005) Nigeria 5°10'E 7°5'N -1328 Paul et al., (2015) Kenya 34°24'E 0°06'N 1420 1800 Agbede, (2008) Cocoyam None 2 20 3 343 Agele et al., (2005) Nigeria 5°10'E 7°5'N -1328 Thierfelder and Wall, (2012) Zimbabwe 30°98'E 17°57'S 1136 884 Agele et al., (2005) Maize None 2 15 68 030	61 61	26 -31 -31 18	13 5 630 13 5 630 -	26 70 24 26 18 24 18 77	Improved fallow 13 17 18 58 -0.55 0.59 (coppiced) 25 57 18 58 -0.60 0.54 Improved fallow (coppiced) 25 57 16 7 1.96	10000 NT + rotation NT -98 177 NT + residues NT + residues + rotation -107 162 10000 NT NT + residues -29
	Botswana OR Burkina OR Burundi OR Cameroon OR Chad OR Congo OR Ivory OR Guinea OR Eritrea OR Ethiopia OR Gabon OR Gambia OR Ghana OR Kenya OR Liberia OR Madagascar OR Malawi OR Mali OR Mauritania OR Mozambique OR Namibia OR Niger OR Nigeria OR Rwanda OR Senegal OR "Sierra Leone" OR Somalia OR Sudan OR Tanzania OR Togo OR Uganda OR Zambia OR Zimbabwe)***AND(agroforest* OR parkland* OR "cereal*tree intercrop*" OR silvo*arable OR "rotation* wood*" OR tree*fallow* OR (tree* AND "improve* fallow*") OR (tree* AND relay*crop*) OR (tree* AND alley*crop*)) Kaonga and Coleman, Conservation agriculture (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Ambassa-Kiki and Nill, (1999) Cameroon ---1600 Thierfelder and Wall, (2012) Zimbabwe 30°98'E 17°57'S 1136 884 Agele et al., (2005) Maize None 2 15 48 732 Ambassa-Kiki and Nill, Anikwe and Ubochi, (2007) Nigeria 7°15'E 6°52'N 450 1700-2010 Thierfelder et al., (2012a) Zimbabwe 30°98'E 17°57'S 1136 884 (1999) Maize Groundnuts 2 5 7 865 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Coleman, (2008) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Bayliss-Smith, (2009) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Bayliss-Smith, (2009) Zambia 13°39'S 32°34'E 1030 1000 23 Kaonga and Bayliss-Smith, (2009) Zambia 13°39'S 32°34'E 1030 1000 23 Nyamadzawo et al., (2008) Zimbabwe 19°35'S 31°14'E 1474 750 -Nyamadzawo et al., (2008) Zimbabwe 19°35'S 31°14'E 1474 750 -Diels et al., (2004) Senna siamea Maize, Cowpea (+NPK) 16 12 8 000 Bright et al., (2017) Piliostigma reticulatum Millet, Groundnut (0*NPK) 13 10 3 145 Bright et al., (2017) Piliostigma reticulatum Millet, Groundnut (0.5*NPK) 13 10 3 411 Millet, Nyamadzawo et al., (2008) Acacia angustissima Maize 8 20 16 900 Nyamadzawo et al., (2008) Sesbania sesban Maize 8 20 16 900 Anikwe et al., (2016) Nigeria 7°54'E 6°29'N 450 1700-2010 Thierfelder et al., (2012b) Zambia 32°61'E 13°70'S 1070 748 Anikwe and Ubochi, (2007) Sweet potato None 2 30 43 667 Barthès, et al., (2004) Benin 2°24'E 6°24'N -1200 Anikwe et al., (2016) Thierfelder et al., (2012b) Zambia 32°61'E 13°70'S 1070 748 Groundnut, bambara Lal, (1998) Nigeria ---1250 nut, soybean None 2 30 9 611 Lal, (1998) Nigeria ---1250 Mloza-Banda et al., (2016) Malawi 34°40' -35°30'E 14°30' 15°20'S 625 828 Mloza-Banda et al., (2014) Malawi 33°14' -35°56'E 13°29' 15°20'S 1200 1000 Mujuru et al., (2013) Zimbabwe 31°43'E 17°00'S 1000-1800 750-1000 Mujuru et al., (2013) Zimbabwe 31°44'E 17°42'S 1000-1800 750-1000 Mujuru et al., (2013) Zimbabwe 31°43'E 17°00'S 1000-1800 750-1000 Mujuru et al., (2013) Zimbabwe 31°44'E 17°42'S 1000-1800 750-1000 Gwenzi et al., (2009) Zimbabwe 32°21'E 20°21'S 444 482 Gwenzi et al., (2009) Zimbabwe 32°21'E 20°21'S 444 482 Ngome et al., (2011) Kenya 34°46'E 0°16'N 1534 1978 Thierfelder et al., (2013) Zambia 32°61'E 13°70'S 1070 748 Okeyo, et al., (2016) Kenya 34°25'E 0°08'N 1320 1769 Barthès, et al., (2004) Maize Mucuna pruriens 11 40 24 200 Lal, (1998) Maize None 5 10 12 398 Okeyo, et al., (2016) Kenya 34°25'E 0°08'N 1320 1769 Lal, (1998) Maize None 5 10 12 398 Mloza-Banda et al., (2016) Maize None 5 20 12 740 Mloza-Banda et al., (2014) Maize None 4 20 27 166 Mujuru et al., (2013) Maize None 4 10 5 160 Mujuru et al., (2013) Maize None 4 10 19 130 Mujuru et al., (2013) Maize Cowpea 4 10 5 160 Mujuru et al., (2013) Maize Soybean 4 10 19 130 Gwenzi et al., (2009) Wheat Cotton 4 60 27 800 Gwenzi et al., (2009) Wheat Cotton 5 60 27 800 Ngome et al., (2011) Maize Arachis pintoï 1 15 66 600 Ngome et al., (2011) Maize Arachis pintoï 1 15 21 800 Ngome et al., (2011) Maize Arachis pintoï 1 15 46 900 soil AND carbon AND (4 61 13 26 Improved fallow (coppiced) 10000 61 13 26 -31 26 46 18 77 16 7 NT + residues 44 649 6.86 4.81 154 99 NT + rotation NT + residues + Improved fallow 10000 -44 40 16 NT 18 77 16 7 intercropping/rotation 11 000 -0.19 1.38 -17 175 (coppiced) 61 13 26 Improved fallow (coppiced) 10000 61 13 26 Improved fallow (coppiced) 10000 61 13 26 Improved fallow (non coppiced) 10000 61 13 26 Improved fallow (non coppiced) 10000 61 13 26 Improved fallow (non coppiced) 10000 61 13 26 Improved fallow (non coppiced) 10000 61 13 26 Improved fallow (coppiced) 10000 61 13 26 Improved fallow (coppiced) 10000 61 13 26 Improved fallow (coppiced) 10000 71 7 22 Improved fallow (coppiced) 10000 71 7 22 Improved fallow (non coppiced) 10000 --0.33 -41 --0.16 -51 --0.17 -51 --1.18 -70 --1.06 -63 -44 40 16 19 82 6 12 NT + residues 72 075 -10.22 3.98 -142 91 NT 27 ---NT + residues + NT + residues + 19 82 6 12 intercropping/rotation intercropping/rotation ----NT + residues + 8 208 3.70 2.99 450 312 NT ----NT + residues 23 37-45 20-16 43-38 NT + residues 21 40-70 10-20 20-40 NT + residues -89 7 5 NT + residues -54 20 26 NT + residues -89 7 5 NT + residues + intercropping/rotation -54 20 26 NT + residues + intercropping/rotation 24 78 11 11 NT + residues + intercropping/rotation 24 78 11 11 NT + residues + intercropping/rotation 21 13 34 53 NT + residues + intercropping/rotation 19 82 6 12 intercropping/rotation 23 2 31 67 27 700 1.24 1.56 45 65 NT + residues + 25 364 -1.12 1.50 -44 118 intercropping/rotation 23 2 31 67 NT+ intercropping /rotation 11 23 819 -0.17 2.11 -7 170 --3.73 -292 --12.17 -448 6 384 -0.00 0.30 -0 59 16 080 0.53 -0.23 33 -12 5 453 0.36 0.44 67 85 17 640 0.10 -0.27 5.5 -14 32 800 1.77 3.02 54 109 32 900 1.74 2.76 53 99 66 267 5.13 4.80 77 72 21 594 3.81 3.60 176 165 46 536 4.76 4.40 102 94 Bright et al., (2017) Piliostigma reticulatum Groundnut Ngome et al., (2011) Kenya 34°47'E 0°19'N 1558 1612 21 61 20 19 intercropping/rotation (1*NPK) 13 10 3 131 --0.16 -51 NT + residues + Nyamadzawo et al., (2008) Maize Sesbania sesban 2 20 16 800 25 400 -2.45 1.85 -96 110

Acknowledgements

This work was partly funded by the French Agricultural Research Centre for International Development (CIRAD) and the CGIAR Research Program MAIZE, FP 4: Sustainable Intensification of Maize-based Cropping Systems. The authors are grateful to Philippe Letourmy for his help with the statistical analysis.

Supplementary materials

Table S1: Lists of terms used in the literature search using the engines ISI Web of Science and and Scopus for carrying out the literature search. 13 Figure S1. Comparison of SOC storage rates in the agroforestry systems taking into account all studied maximum soil depths (left) or only soil depths with a maximum of 40 cm. Crosses represent mean SOC storage rate per type of subsystem. For each system, different letters represent significant differences between subsystems. ** represents subsystems with SOC storage rates significantly higher than 0‰ yr -1 and 4‰ yr -1 .


Matthieu Volat

Flavien Vernier

Marie-Pierre Doin

Cecile Lasserre

Emmanuel Trouvé

Erwan Pathier

IMPROVING THE EXECUTION OF WORKFLOWS FOR SAR IMAGE ANALYSIS

INTRODUCTION

While the resolution and repetitivity of SAR data has strongly increased in the last years, the execution of the processing workflows remained mostly the same. Many scientists continue to manage repetitive tasks over many files either with crude scripts or by hand. Moreover, the quantity of available SAR data increases more and more with the satellite generations and the "free and open access" data policy adopted by some space agencies.

In this paper, we propose a task-based framework oriented toward simpler and better workflow execution that deals transparently for the user with multi-core architectures and cluster or grid systems. The workflows are based on two sets of processing tools: the EFIDIR tools [START_REF] Vernier | Fast correlation technique for glacier flow monitoring by digital camera and spaceborne SAR images[END_REF] [START_REF] Yan | Fuzzy uncertainty representations of coseismic displacement measurements issued from SAR imagery[END_REF] developed in collaboration between several French Earth sciences Image processing laboratories and the ISTerre's NSBAS chain [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: the Etna deformation monitoring from 2003 to 2010 using ENVISAT data[END_REF], based on the JPL/Calltech ROI PAC [START_REF] Buckley | Roi pac documentation-repeat orbit interferometry package[END_REF] project. These tools are the implementation ground for our framework. Our usecase is the processing of ascending and descending repeated orbits SAR image time series from raw data to surface displacement with those tools.

GENERAL PURPOSE

First, we investigated the qualities required by such a framework. Speed improvements through distributed computing is one of the main goals, but it is not the only one. Practical usage of both software showed that easiness of workflow construction, errors and interruption handling, resumption/recovery were equivalently important. This is especially true when distributed execution makes the process more complicated.

While the EFIDIR project focused on rigorously defined programs with single purpose, the NSBAS project is a loosely integrated collection of scripts calling either ROI PAC or internal programs. NSBAS has a small, but active, community of developers and end-users that rely on the software to do their work. Implementing a complete workflow solution would have mean a total rewrite that is not acceptable by the team and the users. So we decided to use least intrusive techniques to improve the chain efficiency without changing too much code.

On the other hand, EFIDIR's workflow was to be written from scratch, which left us room for a clean implementation. We decided that a more rigorous approach would be used in EFIDIR, with an emphasis on both efficiency through distributed computing and execution control quality. A NSBAS rewrite is planned later on the basis of the EFIDIR workflow framework.

In both cases, we noticed that the atomic operation would be the execution of a program. We also observed that in both case, we had a strongly input/output oriented workflow were intermediate results had to be kept. This led us to think of our processing as a graph of program execution connected by their inputs and outputs. We did not assume anything about the average program duration, since we observed instances of a few seconds to a few hours. We also wanted it to be easily deployable on the target environments, which would be barebone computer clusters with no available display and little preinstalled libraries.

We analyzed a few existing frameworks proposed by various entities and communities, such as DAGMan1 , ipython task interface2 , and soma-workflows 3 . In each of those tools, we found blocking points, such as specific jobs scheduler dependencies and integration, reliance on frameworks not easily available in the computing environments. So we decided to implement our own solution. That would mean that we provide less features, but enough to cover our needs and that runs our solution in situation others would not.

NSBAS

NSBAS is a processing chain that handle InSAR computation from raw data to time series analysis [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: the Etna deformation monitoring from 2003 to 2010 using ENVISAT data[END_REF]. A large part of the chain is based on ROI PAC programs, with original routines rearranged and combined with new routines to process in series and common radar geometry (figure 1 shows NSBAS output compared to ROI PAC). NSBAS ground deformation measurment is based on the phase information by interferometry. As said previously, we operated with a set of constrains in this context. Moreover, modifications to the ROI PAC files cannot not be accepted by the upstream team.

We observed that many tasks processed independently the input data set. Basic parallelism was already implemented to split the execution in multiple process. This system can scale up to the resources on one host. To bring this code to the next scale, we implemented a small task dispatcher that tries to mimic the previous one. This new dispatcher uses the MPI standard, so it can create and execute process over a pool of hosts. This allows us to scale the parallelism up to the size of the input size: for example, if we have 63 images to process, a single host would not have enough cores available to process all of them in a single pass, but 4 hosts with each 8 cores do. In regard of the task set scale (at most, a few thousands) a simple single master with multiple workers process model worked quite well.

EFIDIR

The EFIDIR tools package is a set of programs to process images (SAR and optic), and provides tools for many basic and complex operations such as large displacements [START_REF] Vernier | Fast correlation technique for glacier flow monitoring by digital camera and spaceborne SAR images[END_REF], displacement fusion [START_REF] Yan | Fuzzy uncertainty representations of coseismic displacement measurements issued from SAR imagery[END_REF], look up tables and so on (figure 2 shows results produced by EFIDIR).

Taking into account the observations from 2.1, we noticed that a file input/output based process was very similar to the software building process. We decided to implement a system based on the make build automation system, which would allow us to delegate tasks such as task dependency resolution, error handling and resumption.

This system was capable of scaling up to the resources of a single machine, but we wanted to be able to use more power if possible. Then, we paired it with a dispatcher to allow remote execution on a cluster of computers. Once again, we designed it taking into account the observations from NS-BAS in 2.1: we also used a MPI-based system which relied on a single master processus due to the scale of the envisioned experiments. But, contrary to what was implemented in NS-BAS, this dispatcher is a clean subsystem separated from the chain itself dedicated to the execution of subcommands.

Linking both systems was simple. Since we generate make input, we could generate commands that were called through a wrapper program that send the command execution towards the dispatcher. Since this system to work under make, the wrapper is synchronous and blocks until the dispatcher returns the task completion. In this context, make is started specifying a number of maximum concurrent jobs equals to the process pool size minus one (to account for the master).

The critical aspect of those systems is that they are meant to do a lot of their work in a invisible way to the user. We proposed a simple API which requires the user to specify, for each elementary task:

• which commands are to be run • which files are needed (inputs)

• which files are produced (outputs) Since the system is based on make, the dependency tree is created automatically from those. To ease this workflow description, we allowed the processing to be written as Python scripts. For example, to convert a serie of images to jpeg:

t a r g e t s = [ ] f o r f i n f i l e l i

a p p e n d ( t ) c h a i n = c h a i n c r e a t e ( " c o n v e r s i o n " , t a r g e t s ) c h a i n r u n ( c h a i n )

This framework allows both complex and large scale automation and makes a lot of operations easier.

EXPERIMENTAL RESULTS

Our quantitative evaluation focused mainly on processing speeds. To that end, we have access to two platforms:

• A 12 Xeon cores host with 64GB of memory, hosted at the ISTerre laboratory. Dedicated to InSAR processing, this is our reference for state-of-the-art laboratory server.

• The other is the Froggy platform of the CIMENT infrastructure 4 .

NSBAS

In order to evaluate the performance boost of our work in NS-BAS, we processed a zone of roughly 50x50 km centered on Mount Etna, Sicily, which was used as illustration of figure 1.

The input set is constitued of 63 images from the ERS satellite. Details about NSBAS processing are described in Doin & al 2011 [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: the Etna deformation monitoring from 2003 to 2010 using ENVISAT data[END_REF], but can be summarized as:

• Convert data from raw to Single Look Complex images

• Coregister a Digital Elevation Model to a "master" image 4 https://ciment.ujf-grenoble.fr

• Coregister all the images to this master

• Create an inteferogram list and compute them Those steps are usually followed by more refinements, unwrapping and inversion, but as our work is not complete in those parts, they were left out from the benchmarking process.

Those steps were run on both our test platforms. The results of this experiment are presented on figure 3.

Fig. 3. NSBAS benchmark

In theory, when using a single host, the MPI version should be slower than the old fork() version, due to the usage of a process to coordinate tasks. In practice, we are seeing the MPI version begin a little faster, mainly due to better coding practices used during the rewrite. Moving to the cluster, which only the MPI implementation can do, results in a execution twice faster.

But, to achieve this, we used four time more computing power, which means our efficiency factor is only 0.5 on this scale. There is mainly two reasons for this result. The first is that while we scaled up pure computing power, we did not scale storage performance at the same rate, which lessen the speedup.

The second is the fact that task based distribution is bound to hit a limit when the ideal ressource size is attained. At this point, the execution of specific tasks is, once again, the most time consuming part of the processing.

With that point in mind, and our target being to improve execution speed, we find those results satisfying.

EFIDIR

The first EFIDIR chain developed is dedicated to the computation of 2D displacements from SAR Images by pixel offset tracking based on amplitude (whereas NSBAS use phase interfometry). The workflow of this chain is described by the following main steps:

• an initial co-registration is performed • 2D displacements are computed for pairs of images • a range/azimuth offset correction is performed

• the corrected 2D displacements are ortho-rectified This chain is executed on a set of 3 TerraSAR-X stripmap images of the Chamonix -Mont Blanc valley. The objective is to monitor the glacier flows of this valley. Figure 2 illustrates one of the results.

Using our test platforms, we measured the duration of the processing, starting with a scripted execution up to using the fully distributed workflow system. The results are presented on figure 4.

Fig. 4. EFIDIR benchmark

Compared to a scripted, single-core, execution, the benefits of the system are overwhelming. Despite the input set being only 3 images, execution speed profit greatly from much more resources as the most time-consuming task (correlation) was adapted to use the framework system to split and process images in regions.

FUTURE WORK

There are still perspectives to the present work. The first is the usage of chains as elements of others chains. Our first approach showed that make would not communicate properly the pool size in those cases and revert to linear execution. We are working to fix this and allow ressources to be splitted as needed between sub-workflows.

The other area is file storage systems. Experience with CIMENT showed us we could not expect data to be available in a single, shared, filesystem, but could be presented through various interfaces. We need to include this aspect in our framework to also automate data retrieval and submission.

We would also intend to deploy those tools on ESA's GPOD platform, and are currently collecting information about how to do so.

CONCLUSION

In this paper, we presented two scenario : one where we improve only the speed of execution with as little changes as possible, and the other where we implements a complete framework. Both aims to improve the workflow of nonrealtime large optical and SAR image series processing using the power of distributed computing.

Our analysis showed that despite the common usage of those resources and existing tools, the best place to implement this framework if you operate under certain constrains is the software packages themselves.

We also provided a first speedup increment and, in the case of the EFIDIR tools, a more robust way of executing theses tasks.

Fig. 1 .

 1 Fig. 1. Comparison of wrapped interferogram produced by NSBAS (left) and ROI PAC (right) bewteen the 2010-06-09 and the 2010-09-22, using ERS images on Mount Etna. One colour cycle represent 2.8cm of phase signal.

Fig. 2 .

 2 Fig. 2. 2D displacement field in cm (top is east displacement, bottom is north) of Bossons, Argentière & Taconnaz glaciers between the 2009-11-03 and 2011-09-25 using TerraSAR-X images.

http://research.cs.wisc.edu/htcondor/dagman/ dagman.html

http://ipython.org/ipython-doc/rel-0.12.1/ parallel/parallel_task.html

http://brainvisa.info/soma/soma-workflow/

ACKNOWLEDGEMENTS

This work was sponsored by the CNES (France) through the TOSCA/CESTENG project, and we received additional support through the Tera-SAR project (défi Mastodons) sponsored by the CNRS (France).

Part the computations presented in this paper were performed using the Froggy platform of the CIMENT infrastructure, which is supported by the Rhne-Alpes region (GRANT CPER07 13 CIRA), the OSUG@2020 labex (reference ANR10 LABX56) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d'Avenir supervised by the Agence Nationale pour la Recherche.