Hugo Deléglise

Yves Gérard Bazié

Agnès Bégué

Roberto Interdonato

Mathieu Roche
email: mathieu.roche@cirad.fr

Maguelonne Teisseire

Elodie Maître D'hôtel
email: elodie.maitredhotel@cirad.fr

Agriculture & Food Security

Keywords: Indicators, Food consumption score, Household Dietary Diversity Score, Coping strategies index, Household surveys, Spatiotemporal analysis

Background: The timely and accurate identification of food insecurity situations represents a challenging issue. Household surveys are routinely used in low-income countries and are an essential tool for obtaining key food security indicators that are used by decision makers to determine the targets of food security interventions.

Methodology: This paper investigates the spatial and temporal quality of the food security indicators obtained through household surveys. The empirical case of Burkina Faso is used in this paper, where a large-scale rural household survey has been conducted yearly since 2009. From this data set, three food security indicators (the Food Consumption Score, the Household Dietary Diversity Score and the Coping Strategies Index) are calculated at the regional level for each year during the 2009-2017 period.

Results: Results highlight that observed spatiotemporal variations in these indicators are consistent with the major regional food shocks reported in food warning system reports and are significantly correlated with variations computed from other sources of data, such as satellite images, rainfall and food prices.

Conclusion:

These results raise new research questions on food security monitoring systems and on the use of heterogeneous data and multiple food security indicators.

Introduction

The food situation in Africa is worsening again after an improvement of several years. Progress in reducing hunger in West Africa stabilized between 2000 and 2014. During these years, the prevalence of undernourishment progressively decreased from 12.3 to 10.7% before increasing again to almost 15% in 2019 and reaching a worrying projection of 23% for 2030 [START_REF] Fao | The State of Food Security and Nutrition in the World-Transforming Food Systems for affordable healthy diets[END_REF]. Burkina Faso ranks among the most affected countries by food insecurity in West Africa, recording a prevalence of undernourishment of 21.3% between 2015 and 2017 [START_REF] Fao | Addressing the threat from climate variability and extremes for food security and nutrition[END_REF]. The situation in the region is strongly impacted by the "triple burden of malnutrition", namely, undernutrition, micronutrient deficiency and obesity. By 2017, three key indicators of food security-the prevalences of childhood wasting, childhood stunting, and adult obesity-were 7.6%, 27.3% and 4.5%, respectively, which are some of the most critical rates in West Africa [START_REF] Fao | L'état de la sécurité alimentaire et de la nutrition dans le monde en 2018: renforcer la Résilience face aux changements climatiques pour La sécurité alimentaire et la nutrition[END_REF]. Several interrelated (climatic, socioeconomic and political) reasons have led to the deterioration of the food situation in Burkina Faso over the past few years.

Dissatisfaction regarding food security measurement persists, especially in the wake of food and financial crises [START_REF] Headey | Rethinking the measurement of food security: from first principles to best practice[END_REF]. To prevent food crises and design appropriate interventions, food security agricultural monitoring systems have been set up by non-governmental organizations and state organizations, such as GIEWS created by the FAO (Global Information and Early Warning System of the Food and Agriculture Organization) or FEWS-NET funded by USAID (Famine Early Warning Systems Network of the United States Agency for International Development). These systems rely on collaborations with stakeholders at local and national levels, on the use of data collected from households and markets, and on the use of agrometeorological data extracted from Earth observation data that are jointly analyzed by food security experts [START_REF] Fritz | A comparison of global agricultural monitoring systems and current gaps[END_REF]. Within countries, governments may have set their own food security monitoring systems that utilize individual nutritional data.

It has now been clearly established that food security is a complex concept and results from the interactions among several agro-environmental, socioeconomic and biological factors. There is no consensus on how food security should be measured or on what data should be preferentially collected. Food security monitoring systems integrate multiple sources of data, among which household surveys represent a fundamental source of information [START_REF] Carletto | Towards better measurement of household food security: harmonizing indicators and the role of household surveys[END_REF][START_REF] Jones | What are we assessing when we measure food security? A compendium and review of current metrics[END_REF][START_REF] Pérez-Escamilla | Food insecurity measurement and indicators[END_REF]. At the national level, governments tend to rely heavily on their own surveys both to compute proxies of domestic cereal production and to characterize food security at local levels. At the global level, the World Food Program [START_REF] Wfp | Comprehensive food security and vulnerability analysis guidelines[END_REF], the FAO and the World Bank produce food security indicators from food consumption data collected in household surveys [START_REF] Moltedo | Analyzing Food security using household survey data: streamlined analysis with ADePT Software[END_REF].

According to [START_REF] Headey | Rethinking the measurement of food security: from first principles to best practice[END_REF], four criteria are needed to gauge the usefulness of a food security indicator: its cost effectiveness, its capacity to deliver timely information, its nutritional relevance, and its temporal and spatial validity. Compared to indicators derived from individual consumption surveys, indicators derived from household surveys provide information on a similar time frame, but they are more cost effective as they do not enter into the very detailed quantification of consumed food items. On the other hand, in terms of nutritional relevance, household surveys provide indicators that are thus considered as less detailed but are still valid proxies for food security situations [START_REF] Leroy | Measuring the food access dimension of food security: a critical review and mapping of indicators[END_REF][START_REF] Wichern | Using household survey data to identify large-scale food security patterns across Uganda[END_REF]. On the temporal and spatial validity of food security indicators, most studies led have either focused on the spatial or on the temporal dimension. On the spatial dimension, household data indicators are commonly aggregated to generate food security maps that are used to determine the targets of food interventions (see https:// hunge rmap. wfp. org/), and the spatial validity has been investigated by studies conducted at the country [START_REF] Rautela | Prevalence and correlates of household food insecurity in Delhi and Chennai, India[END_REF], city [START_REF] Tuholske | Comparing measures of urban food security in Accra, Ghana[END_REF], and household [START_REF] Wichern | Using household survey data to identify large-scale food security patterns across Uganda[END_REF] scales. However, these studies are generally conducted for one specific time period. On the temporal dimension, longitudinal studies have been led to gauge the capacity of household indicators to adequately measure food security trends over time [START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF].

Studies on the spatio-temporal validity of food security indicators derived from household surveys are missing. This paper argues that, despite the biases inherent in household surveys [START_REF] Biemer | Total survey error: design, implementation, and evaluation[END_REF][START_REF] Dussaix | La qualite dans les enquêtes[END_REF][START_REF] Winter | Response bias in survey based measures of household consumption[END_REF], food security indicators derived from household surveys can be used to detect food crises on a sub-national scale and for different years. The approach is based on official household survey data collected in Burkina Faso over the last decade ("Materials and methods" section). The analysis is built on three household indicators that are commonly used as proxies of food access at the household level: HDDS (Household Dietary Diversity Score), FCS (Food Consumption Score) and rCSI (reduced Coping Strategy Index) [START_REF] Leroy | Measuring the food access dimension of food security: a critical review and mapping of indicators[END_REF]. In "Results and discussion" section, the spatiotemporal concordances of the three indicators in terms of the food security situation at the regional scale is analyzed ("Analysis of the spatiotemporal variability in food security" subsection), along with their consistency with indicators from other data sources ("Consistency between household surveys and other data sources" subsection). "Conclusion" section draws conclusions about the strengths and limitations of household surveys in delivering food security information and about future research directions regarding food security monitoring systems and the use of heterogeneous data.

Materials and methods

The study area: Burkina Faso Burkina Faso is a developing country located in West Africa, where food security is closely linked to agricultural production. It is a Soudano-Sahelian country with a semiarid climate in the north and a subhumid climate in the south, characterized by two seasons: a long dry season (approximately 8 months) and a short rainy season. Rainfall is generally low, irregular and unevenly distributed [START_REF] Tapsoba | Remittances, food security and climate variability: the case of Burkina Faso[END_REF]. The rainy season is shorter and less intense in the north, which allows for the production of traditional rainfed cereals (millet, sorghum) and cattle breeding only. In the south, the rains last longer and are sufficient to enable crop diversification (sorghum, millet, maize, rice, cotton and groundnuts) (see Fig. 1). Food security largely depends on the production of rainfed agriculture, which is undermined by the effects of climate change (an intensification of severe climatic events, including droughts and floods, affecting food availability [START_REF] Tapsoba | Remittances, food security and climate variability: the case of Burkina Faso[END_REF]) and by the consequences of conflicts in the northern and eastern parts of the country (a decrease in food production and distribution networks due to population displacement [START_REF] Lacher | Organized crime and conflict in the sahel-sahara region[END_REF]). These two phenomena are responsible for an economic slowdown, which has been worsened by the still fragile world economic context.

The analytical framework

Measuring food security at the household level

The concept of food security is complex and multifaceted, arising from many interrelated and interdependent factors. Food security is guaranteed "when all people have, at all times, physical and economic access to sufficient, safe and nutritious food" [START_REF] Shaw | World food security: a history since 1945[END_REF]. This definition involves four dimensions: the availability of appropriate quantities of food of adequate quality; access among all people to the resources needed to procure food; the stability of access to food over time despite natural or economic crises; and the adequate utilization of food (e.g., hygiene, storage, cooking). As a result, there are many food security indicators (Hoddinott [18] evaluated approximately 450 food security indicators), and it is important to use several indicators to fully estimate food security given its complexity [START_REF] Coates | Build it back better: deconstructing food security for improved measurement and action[END_REF][START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF]. The plurality of existing indicators and the lack of consensus on how to compare food security situations has led to the development of composite indicators [START_REF] Santeramo | Food security composite indices: implications for policy and practice[END_REF] whose construction is not neutral for a policy point of view [START_REF] Santeramo | On the composite indicators for food security: decisions matter![END_REF]. It is nowadays recognized than the use of one single indicator gives an incomplete picture of food security [START_REF] Matavel | Understanding the drivers of food security among agriculture-based households in Gurué district, Central Mozambique[END_REF] and that multiple indicators should be used to capture the complexity of food insecurity [START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF][START_REF] Moroda | Food insecurity of rural households in Boset district of Ethiopia: a suite of indicators analysis[END_REF]. In this paper, three food security indicators are used, who had been obtained at the household level, through surveys. The diversity in the types of food security indicators implies diversity in data collection scales, ranging from national and regional scales (country population, country cereal balance sheets, vegetation indexes, rainfall estimations, food prices) to household and individual scales (consumption proxies, caloric intakes and anthropometric measures) (Table 1). Indicators derived from individual observations are considered the most relevant for characterizing food security, but they are very costly, as they imply either measuring consumption directly or measuring health status. Indicators derived from remote sensing imagery may be delivered in a more timely manner and be cheaper than individual-level data, but they do not always match consumption measures well. Falling in between these extremes, indicators generated at the household scale through surveys are good compromises. They are considered a cost-effective means to proxy food consumption, and they have become central to the analysis of food security, as they adequately capture the food access dimension of food security [START_REF] Leroy | Measuring the food access dimension of food security: a critical review and mapping of indicators[END_REF]. Most food security indicators are constructed from data collected at the household level, and several indicators used at the regional or national level are derived from household data (through aggregation).

The Permanent Agricultural Survey data in Burkina Faso

In Burkina Faso, the Permanent Agricultural Survey of rural households has been conducted annually by the Ministry of Agriculture since 1982. This survey is a policy tool used in the field of agriculture and food security that provides decision-makers and food organizations with provincial crop forecasts during the growing period (around August) and with agricultural production estimates during the harvest period (around October). Since 2009, information on household food consumption has also been collected to calculate food security indicators after harvest (around December). Collected data are nationally representative and agricultural production estimates and food security indicators derived from Household Dietary Diversity Score [START_REF] Kennedy | Guide pour mesurer la diversité alimentaire au niveau du ménage et de l'individu[END_REF] Household

Coping Strategies Index [START_REF] Maxwell | The Coping Strategies Index; A tool for measurement of household food security and the impact of aid programs in humanitarian emergency[END_REF] Household

Food expenditures [START_REF] Smith | Measuring food security using household expenditure surveys[END_REF] Household Household Hunger Scale [START_REF] Ballard | Household hunger scale: indicator definition and measurement guide[END_REF] Household

Anthropometric measures [START_REF] Leyna | Food insecurity is associated with food consumption patterns and anthropometric measures but not serum micronutrient levels in adults in rural Tanzania[END_REF] Individual

Caloric intake [START_REF] Araujo | Association between food insecurity and food intake[END_REF] Individual this official survey are key elements used in national and regional food security warning systems [START_REF]Résultats Défnitifs de la Campagne Agricole 2014/2015 et Perspectives de la Situation Alimentaire et Nutritionnelle[END_REF]. The Permanent Agricultural Survey provides indeed the only available and nationally representative data set that explores the spatial and temporal dimensions of food security. 1 The data set used in this paper covers the 2009 to 2017 period and contains information from 41,751 farm households, i.e., an average of 4,640 farm households per year. The number of households varies from year to year. A farm household is defined as a household practicing at least one of the following activities: temporary crop cultivation (either rainfed or irrigated crops), fruit growing, or animal husbandry. Such households are distributed throughout 887 municipalities over 45 provinces and 13 regions. The paper is built upon three indicators that are validated as proxies of the food access dimension of food security [START_REF] Leroy | Measuring the food access dimension of food security: a critical review and mapping of indicators[END_REF] and that were obtained through the Permanent Agricultural Survey. The FCS and HDDS food security indicators have been calculated from 2009 to 2017 and the rCSI indicator has been calculated from 2014 to 2017 (information about coping strategies is available as of 2014).

As in any survey, biases can affect the reliability of the data obtained from household surveys. Some authors have shown that since the early 2000s, the quality of survey data has declined, as people are increasingly solicited to participate in surveys and are increasingly concerned about protecting their privacy [START_REF] Meyer | Household surveys in crisis[END_REF]. The non-observance biases related to the failure to collect information (coverage and sampling bias, non-consent bias, non-response bias) [START_REF] Lepkowski | Non-observation error in household surveys in developing countries[END_REF] and the measurement bias due to measurement error during collection (related to the investigator, the respondent or the questionnaire) [START_REF] Kasprzyk | Measurement error in household surveys: sources and measurement[END_REF] are the two main types of biases. In "Results and discussion" section, some biases and data limitations are discussed based on an analysis of the Permanent Agricultural Survey guidelines produced by the Burkinabe Ministry of Agriculture [START_REF]Résultats Défnitifs de la Campagne Agricole 2014/2015 et Perspectives de la Situation Alimentaire et Nutritionnelle[END_REF].

The household food security indicators

This paper focuses on three indicators: the Food Consumption Score (FCS), the Household Dietary Diversity Score (HDDS) and the reduced Coping Strategies Index (rCSI). These indicators furnish useful information on food frequency, quantity and quality and on households' economic access to food, and are some of the indicators that are most widely used in the research community by international organizations and governments [START_REF] Jones | What are we assessing when we measure food security? A compendium and review of current metrics[END_REF][START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF][START_REF] Vhurumuku | Food security indicators-WFP[END_REF].

Food Consumption Score (FCS): FCS is a measure of nutrient and energy intake. It represents an estimation of the cumulative frequency with which the various food groups are consumed over 7 days in each household surveyed. The frequency of consumption for each food group is weighted by its nutrient value (Eq. 1; Table 2). Thresholds set by the World Food Program are used to differentiate food consumption between households, as follows: acceptable (> 42), limit [START_REF] Leyna | Food insecurity is associated with food consumption patterns and anthropometric measures but not serum micronutrient levels in adults in rural Tanzania[END_REF][START_REF] Martini | Machine learning can guide food security efforts when primary data are not available[END_REF][START_REF] Matavel | Understanding the drivers of food security among agriculture-based households in Gurué district, Central Mozambique[END_REF][START_REF] Maxwell | The Coping Strategies Index; A tool for measurement of household food security and the impact of aid programs in humanitarian emergency[END_REF][START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF][START_REF] Meyer | Household surveys in crisis[END_REF][START_REF] Moltedo | Analyzing Food security using household survey data: streamlined analysis with ADePT Software[END_REF][START_REF] Moroda | Food insecurity of rural households in Boset district of Ethiopia: a suite of indicators analysis[END_REF][START_REF] Nasa | Description and data of MODerate resolution Imaging Spectroradiometer (MODIS) satellite images of composite Normalized Difference Vegetation Index (NDVI) (MOD13Q1) product[END_REF][START_REF] Ocha | Inondations; période du 1er au 30 septembre 2010[END_REF][START_REF]Plan de réponse stratégique -Burkina Faso[END_REF][START_REF]Résultats Défnitifs de la Campagne Agricole 2014/2015 et Perspectives de la Situation Alimentaire et Nutritionnelle[END_REF][START_REF] Pérez-Escamilla | Food insecurity measurement and indicators[END_REF][START_REF] Rautela | Prevalence and correlates of household food insecurity in Delhi and Chennai, India[END_REF][START_REF] Santeramo | Food security composite indices: implications for policy and practice[END_REF], and low (< 28) [START_REF] Wiesmann | Validation of the world food programme's food consumption score and alternative indicators of household food security[END_REF] x i ∈{Frequency of consumption for each food group i}, p i ∈{Weight of food group i} Household Dietary Diversity Score (HDDS): The HDDS captures the number of food groups consumed in the last 24 h and is considered an acceptable proxy for food consumption [START_REF] Kennedy | Proxy measures of household food consumption for food security assessment and surveillance: comparison of the household dietary diversity and food consumption scores[END_REF]. There is no consensus on the number of groups to use and their boundaries [START_REF] Kennedy | Guide pour mesurer la diversité alimentaire au niveau du ménage et de l'individu[END_REF]. In this paper, the HDDS (Eq. 2) is computed according to FAO guidelines, based on 12 food groups (cereals; roots and tubers; vegetables; fruits; meat products; eggs; fish and seafood; legumes, nuts and seeds; milk and dairy products; oils and fat; sweets; and condiments, spices and beverages; [START_REF] Swindale | Household Dietary Diversity Score (HDDS) for measurement of household food access: indicator guide[END_REF]).

x i ∈{0: food i is not consumed, 1: food i is consumed} Reduced Coping Strategies Index (rCSI): The rCSI takes into account the severity of the strategies that households (1) use to cope with deficits in their food consumption. It is an estimate of the cumulative frequency of five potential food reduction strategies used over 7 days within each household surveyed. The frequency of each behavior is weighted by its severity (Eq. 3; Table 3):

FCS = 9 i=1 x i • p i (2) HDDS = 12 i=1 x i
x i ∈{Frequency of behavior i}, p i ∈{Behavior weight} These three food security indicators are calculated for Burkina Faso using the food consumption data that have been collected through the Permanent Agricultural Survey since 2009. These indicators, defined at the households level, are then averaged at the province and region scales. The distribution of the indicators averaged by province is given Fig. 2. In "Consistency between household surveys and other data sources" subsection, they are also centered reduced (i.e., by subtracting the average and dividing by the standard deviation) in relation to provinces and years for comparison with food security proxies.

Other food security proxies

Other food security proxies that are routinely used in food security alert and monitoring systems have been identified [START_REF] Fritz | A comparison of global agricultural monitoring systems and current gaps[END_REF], namely, a vegetation index, rainfall estimation, and market food prices:

1. Vegetation index: Moderate resolution imaging spectroradiometer (MODIS) satellite images of the composite Normalized Difference Vegetation Index (NDVI), taken over 16 days at 250 m resolution (MOD13Q1 V6 product) [START_REF] Nasa | Description and data of MODerate resolution Imaging Spectroradiometer (MODIS) satellite images of composite Normalized Difference Vegetation Index (NDVI) (MOD13Q1) product[END_REF]. The S2 prototype land cover map at 20 m for Africa from 2016 [START_REF] Esa | Description and data of S2 prototype Land Cover map at 20m of Africa[END_REF] is used to mask the pixels that are located outside the cropland. 2. Rainfall: Climate hazards group infrared precipitation with station (CHIRPS) data, with a frequency of 10 days and a resolution of 6 km [START_REF] Chirps | Description and data of Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) product[END_REF].

( These three proxies are first aggregated monthly (maximum NDVI and the sum of the rainfall and the prices) and by province for the months from May to October (the agricultural period) and are then transformed into deviations (normalized) by being centered reduced in relation to all the provinces and months presented. Table 3 Food groups and corresponding weights used to calculated the reduced Coping Strategies Index (rCSI). Source: Maxwell [START_REF] Maxwell | The Coping Strategies Index; A tool for measurement of household food security and the impact of aid programs in humanitarian emergency[END_REF] Behavior Weight

) rCSI = 5 i=1 x i • p i 3
Use less popular and less expensive foods 1

Borrow food or seek help from a friend or relative 2

Limit the size of portions during meals 1

Reduce adult consumption to feed children 3

Reduce the number of meals per day 1

Results and discussion

Analysis of the spatiotemporal variability in food security

This section analyzes and compares the spatiotemporal variations in the FCS, HDDS and rCSI indicators, and discuss these variations in light of the information contained in independent data sources such as food security bulletins and reports.

To illustrate the inter-annual variability in food security in Burkina Faso, the annual values of the FCS and HDDS indicators have been used, calculated from the Permanent Agricultural Survey data over the 2009-2017 period (Fig. 3). The rCSI indicator is not depicted here, as a 4-year period (2014-2017) is too short for temporal analysis. At the national scale, the results of the Permanent Agricultural Survey show an increase in the average FCS and HDDS values between 2009 and 2013, followed by a sharp drop between 2013 and 2017 (resulting in the lowest value of the period in 2017). The two indicators provide different estimates of the prevalence of food insecurity, but depict generally similar food security trends over time. This confirms previous results where the FCS and HDDS were highly correlated [START_REF] Tiwari | Shorter, cheaper, quicker, better: linking measures of household food security to nutritional outcomes in Bangladesh, Nepal, Pakistan, Uganda, and Tanzania[END_REF].

Since 2009, many shocks have affected food security in Burkina Faso. Three events stand out because of their seriousness and have been widely reported in newspapers and NGOs' reports: the repeated floods in 2009 and 2010 [START_REF]Inondations du 1er Septembre 2009 au Burkina Faso. Evaluation des dommages, pertes et besoins de construction, de reconstruction et de relèvement[END_REF][START_REF] Ocha | Inondations; période du 1er au 30 septembre 2010[END_REF], the severe drought in 2011 that led to a famine [START_REF] Faso | Rapport d'évaluation approfondie sur la sécurité alimentaire des ménages en situation d'urgence (EFSA) dans 170 communes déclarées à risque d'insécurité alimentaire[END_REF]60], and the general deterioration of the security situation that has affected the whole country since 2014 [START_REF] Fao | Vue d'ensemble régionale de la sécurité alimentaire et la nutrition[END_REF], worsening globally each year and degenerating into a food and humanitarian crisis [START_REF] Fao | Burkina Faso: Aperçu de la réponse -juillet 2019[END_REF]. With regard to the floods of 2009 and 2010, two regions were particularly affected, the Est and Boucle du Mouhoun regions, which had among the highest number of victims in 2009 [START_REF]Inondations du 1er Septembre 2009 au Burkina Faso. Evaluation des dommages, pertes et besoins de construction, de reconstruction et de relèvement[END_REF]. Indeed, the data reveal that while Burkina Faso experienced an overall increase in its FCS and HDDS over the period 2009 to 2011, these two regions experienced a decrease in their FCS and HDDS values over at least 1 year between 2010 and 2011 (Fig. 3). The effect of the drought in 2011 is not clearly visible in the Permanent Agricultural Survey data. The HDDS decreased slightly in 2012, while the FCS increased in the same year. This could be explained by the fact that the FCS indicator collected during this household survey does not capture a decrease in caloric intake, which is a key indicator of a food crisis. The rCSI might have captured this effect, but it is only available from 2014 onward. The years 2012 and 2013 were two favorable years in terms of climate, which is reflected in a rise in the HDDS and FCS at the national level. In contrast, 2014 and 2015 were rain deficit years, which is reflected in the decrease in both the HDDS and FCS. Overall, it seems that both the HDDS and FCS indicators are able to capture the inter-annual variability in food security and notably to gauge the severe decrease of food security that is related to the occurrence of armed conflicts since 2015. In structurally food insecure areas as the eastern and the northern parts of Burkina Faso, the occurrence of violent conflicts had been severely impacting the ability of rural households to feed themselves.

To analyze the spatial variability in food security, three maps have been provided to represent the spatial distribution of the FCS, HDDS and rCSI indicators in Burkina Faso over the 2014-2017 period (Fig. 4). Figure 4a shows the distribution by region of the proportion of households with a low FCS (i.e., below 28). Figure 4b andc shows the rCSI and HDDS distributions by region. There is no cut-off point for determining critical HDDS [START_REF]INDDEX Project. Data4Diets: building blocks for diet-related food security analysis[END_REF] and rCSI [START_REF] Maxwell | The Coping Strategies Index; A tool for measurement of household food security and the impact of aid programs in humanitarian emergency[END_REF] values, and the class thresholds in Fig. 4b andc have been set empirically to illustrate the regional variability. The results show that between 2014 and 2017, the FCS and HDDS were lowest in the center of the country (Centre Nord, Plateau Central and Centre regions) and highest in the southwest (Cascades and Hauts-Bassins regions) and Sahel regions, while the rCSI was most critical in the north and the east of the country (Centre Nord, Sahel and Est regions) and better in the southwest (Cascades and Hauts-Bassins regions).

Several bulletins indicate that the Centre Nord, the Est and the Sahel are the most food insecure regions. Conversely, the regions in which food security is higher are the Hauts-Bassins, Cascades and Centre regions [START_REF]Plan de réponse stratégique -Burkina Faso[END_REF][START_REF] Wfp | Burkina Faso: Analyse Globale de la Vulnérabilité[END_REF][START_REF] Zida | Cartographie de la pauvreté et des inegalités au Burkina Faso[END_REF]. This directly reflects the agro-climatic conditions that are favorable in southern regions and unfavorable in eastern and northern regions. For most regions, the data obtained from the Permanent Agricultural Survey are consistent with NGOs' reports: the Cascades and Hauts-Bassins regions present the best HDDS (6.3 and 5.8, respectively) and rCSI (0.72 and 0.73, respectively) values, while the Est and Centre Nord regions have the worst HDDS (4.98 and 4.6, respectively) and rCSI (2.54 and 2.47, respectively) values. In the Sahel region, the results are more contrasting: The region has the worst rCSI score (2.76), which is consistent with NGOs' reports and the structural classification of this region as being in a food crisis, but has both an HDDS and a FCS higher than the average. An interpretation of this discrepancy could be that the HDDS and FCS take into account food groups such as meat and dairy products that may not be consistent in terms of caloric intake but that are nutritionally important food items. The relatively high levels of HDDS and FCS in the northern regions can be related to cultural food consumption habits. It appears that rCSI indicator is a good proxy for caloric consumption and reflects agro-climatic conditions, northern and eastern regions being "deficit regions", where grain production is regularly affected by drought while southern and western regions are "surplus regions", where production exceeds self consumption. This example shows how crucial it is to use several indicators to explain a phenomenon, and it appears that the HDDS and FCS are less useful for detecting food crises in the Sahel than the rCSI. Finally, the Centre region has critical HDDS and rCSI values (4.83 and 2.57, respectively), which contradicts what appears in the NGO reports [START_REF]Plan de réponse stratégique -Burkina Faso[END_REF][START_REF] Zida | Cartographie de la pauvreté et des inegalités au Burkina Faso[END_REF]. An interpretation of these discrepancies could be that in the Centre region, the population of surveyed farmers is not representative of the total population. Indeed, unlike the other regions where approximately 80% of workers have jobs related to agriculture, the Centre region contains the city capital Ouagadougou and its agglomeration [START_REF] Herrera | Les défis de l'agriculture paysanne: Le cas du burkina faso[END_REF]. If the results of the Permanent Agricultural Survey indicate that farmers in the Centre region are food insecure, this finding cannot be generalized to the rest of the population because of undercoverage bias.

Overall, it seems that HDDS, FCS and rCSI relate to different dimensions of food security: rCSI is a valid indicator for detecting food insecurity situations that can arise in specific regions because of a lack of access, while HDDS and FCS are valid indicators to detect food insecurity situations that are characterized by a low quality of the diets, either related to low access or cultural food consumption habits. In such a situation, using more than one indicator is advisable, as each indicator portrays different aspects of food insecurity. While the FCS and HDDS tend to indicate situations of low nutrient density diets, the rCSI tends to indicate situations of low caloric intake.

Consistency between household surveys and other data sources

In this section, the correlations between the three food security indicators' annual deviations (FCS, HDDS and rCSI) and indirect food security proxy variables are analyzed. The proxy variables used are the annual mean deviations of NDVI, rainfall and maize prices calculated for the year in which the food security indicators were collected and for the previous year (Table 4). The food security indicators obtained from the household surveys are globally poorly correlated with the proxies that represent only one aspect of food insecurity, with a maximum correlation of 0.3.

The NDVI correlates positively with the HDDS and negatively with the rCSI, which confirms the expected effect that good crop conditions generally lead to high crop production and thus to potential agricultural incomes (stored grains or marketed surplus), resulting in higher caloric intakes (no need to implement food reduction strategies, so rCSI decreases) and increased food consumption (possibility of eating more diverse foods, so HDDS increases). However, a high level of food consumption is not equivalent to having a diet with high nutritional value because the correlation between NDVI and the FCS is not significant. This could be interpreted as farm households having more diverse diets but that this diversity may be related to the consumption of food items that are not beneficial from a nutritional point of view, such as oils, sugar and drinks.

Rainfall correlates positively with the HDDS and the correlation with the FCS and the rCSI are not significant. The interpretation is the same as that provided for the NDVI (higher crop production, fewer food reduction strategies, increased food consumption, but not necessarily more nutritious consumption).

Maize prices correlate negatively with the HDDS and positively with the rCSI. Considering that most farm households are net buyers (they produce less maize than what they consume, and thus they have to buy part of their maize consumption from the market), this confirms the intuition that an increase in maize prices is detrimental to food security because households have lower economic access to maize and are obliged to reduce their consumption of grains and of other food items (increase in rCSI and decrease in HDDS).

Overall, it appears that the FCS has very little correlation with the indirect proxy variables of food security and that the HDDS and rCSI are more strongly correlated with the indirect proxy variables. The correlations of the HDDS and rCSI with the indirect proxy variables for the same year are significant (5 out of 6 significant correlations) but are also comparable to the indirect proxy variables of the previous year (5 out of 6 significant correlations). This indicates that food security is linked not only to the current climatic and economic context but also to elements of the past climatic and economic context that have an impact on food security. The comparison results are similar with normalized or non-normalized food security indicators for comparison to proxies deviations. One result is thus that there are concordances between the indicators and proxies of food security but that these concordances are limited, probably because food security consists of a complex combination of these proxies that cannot be fully captured through correlation calculations. One alternative

Conclusion

This paper analyzes the contribution of household surveys to our understanding of food security situations. Previous studies have established that indicators derived from household surveys are reliable in qualifying food consumption and are cheaper to obtain than individual consumption indicators [START_REF] Leroy | Measuring the food access dimension of food security: a critical review and mapping of indicators[END_REF][START_REF] Maxwell | How do indicators of household food insecurity measure up? an empirical comparison from Ethiopia[END_REF]. Our study shows that indicators derived from household surveys contain consistent spatial (structural) and inter-annual (conjunctural) information and that they can be used to monitor food crises at the sub-national scale despite their inherent biases. In particular, we show that household surveys provide information on food security that permits the identification of key trends that are consistent with food security warning systems, as well as with climatic and economic variables related to food security. However, our study also highlights three drawbacks related to the use of indicators derived from household surveys: the first one is that it takes time to calculate indicators from household surveys; the second one is that in the context of armed conflicts, it can be risky to conduct household surveys; and the third one is that indicators from household surveys provide only a partial view of food security situations. The fact that the process is time consuming is related to the definition of the sampling strategy, to the design of the questionnaire and its administration across a considerable number of households, and finally to the data entry, cleaning and analysis by experts. On the opposite, data on crop conditions and rainfall obtained from remote sensing imagery can be obtained more quickly, which is a major advantage. The fact than collecting data within households in conflict affected areas can be hazardous is clearly an argument in favor of mobilizing other data sources to predict food security situations. The fact that indicators derived from household surveys provide only a partial view is a drawback common to the use of any indicator. Variations in food security indicators correlate only partially with the climatic and economic factors that are considered to be indirect proxies of food security. Each indicator or proxy tends to focus on a specific component of food security, and the choice to consider several complementary indicators and proxies provides a more complete picture of food security situations.

In summary, if household surveys are a reliable tool for the characterization of food security situations and their spatial and temporal diversity, such surveys provide only a partial understanding of food security and have to be combined with other data sources that may not directly measure food consumption but rather its determinants. A major task is to understand how climatic, agronomic, economic, policy-related, and security-related events are interlinked and cause food insecurity at a given time and in a given place. This is a huge challenge given the complexity of food security. One way to address such challenging tasks would be to resort to data science techniques, and notably machine learning algorithms which are being increasingly used to extract relevant information from complex and heterogeneous data in the field of food security [START_REF] Martini | Machine learning can guide food security efforts when primary data are not available[END_REF][START_REF] Westerveld | Forecasting transitions in the state of food security with machine learning using transferable features[END_REF]. This type of research could contribute to food security warning and monitoring systems by detecting famines more quickly and accurately. The use of multiple data sources to generate knowledge on local food security situations is of special importance in the contexts where information in the ground may be lacking because of armed conflicts, which are nowadays considered as the primary driver of ongoing food crises in the world (72% of the people facing acute food insecurity in 2021 are living in conflict-affected countries2 ). Indeed, the conduction of household surveys could be a risky activity in armed conflict contexts, so that food security monitoring systems should encourage analysis combining heterogeneous data, obtained from different sources and processed through machine learning.

Fig. 1

 1 Fig. 1 Climate zones in Burkina Faso, based on May to October cumulative rainfall calculated over the 2014-2017 period for the 13 regions of Burkina Faso. Source: Daily CHIRPS precipitation data set

3 .

 3 Food price: Monthly maize prices by market, provided by the Société Nationale de Gestion du Stock de Sécurité Alimentaire (SONAGESS) in Burkina Faso (personal communication, 2019).

Fig. 2

 2 Fig. 2 Histograms of annual FCS, HDDS and rCSI distributions from 2014 to 2017, averaged by province

Fig. 3

 3 Fig. 3 Evolution of the mean annual (a) Food Consumption Score (FCS) and (b) Household Dietary Diversity Score (HDDS) in Burkina Faso (solid line) and in the Est and Boucle du Mouhoun regions (dashed lines) for the 2009-2017 period. Source: Permanent Agricultural Survey data

Fig. 4

 4 Fig. 4 Three-class maps of the (a) percentage of households with a low Food Consumption Score (FCS) (i.e., < 28 ), (b) average Household Dietary Diversity Score (HDDS), and (c) average reduced Coping Strategies Index (rCSI), calculated at the regional scale for the 2014-2017 period. Source: Permanent Agricultural Survey data

Table 1

 1 Overview of food security indicators at different scales

	Indicator	Scale
	FAO Undernourishment [52]	National
	Global Hunger Index [20]	National
	Global Food Security Index [48]	National
	Food Consumption Score [58]	Household

Table 2

 2 Food groups and corresponding weights used to compute the Food Consumption Score (FCS). Source: Wiesmann et al.[START_REF] Wiesmann | Validation of the world food programme's food consumption score and alternative indicators of household food security[END_REF]

	Food group	Weight
		(nutritional
		value)
	Cereals and tubers	2
	Pulses	3
	Vegetables and leaves	1
	Fruits	1
	Animal proteins	4
	Dairy products	4
	Sugars	0.5
	Oils	0.5
	Condiments	0

1 Data from the Permanent Agricultural Survey are not publicly available but can be obtained upon request at the Ministry of Agriculture of Burkina Faso. A Living Standard Measurement Survey was led in 2014 in Burkina Faso by the Institut National de Statistique et de Démographie: data are publicly available. Statistical Pearson tests have been led between indicators obtained from the Permanent Agricultural Survey and from the Living Standard Measurement Survey in 2014: Pearson correlations are significantly positive, indicating that results are consistent.

Table 4

 4 Correlations between the three annual food security indicators' deviations (FCS, HDDS and rCSI) and the annual mean deviations of NDVI, rainfall and maize prices for the year (Yt) in which the food security indicators were collected and for the previous year (Yt -1) between 2014 and 2017 (*p-value < 0.05; **p-value < 0.01; ***p-value < 0.001) explanation could be that our data set does not enable any seasonal analysis of what is going on within a year. Food consumption can differ widely between the harvest season and the lean season, but data are lacking to appraise the intra-annual evolution of food security situations. This could be further investigated in the future.

		NDVI Yt	Rainfall Yt	Maize price Yt	NDVI Yt -1	Rainfall Yt -1	Maize price Yt -1
	FCS HDDS rCSI	-0.02 0.16* -0.21**	0.13 0.30*** -0.01	-0.16* -0.28*** 0.19*	-0.02 0.17* -0.20**	-0.02 0.16* -0.29***	-0.13 -0.25*** -0.01

TETIS, AgroParisTech, CIRAD, CNRS, INRAE, Univ Montpellier, Montpellier, France

MOISA, CIHEAM-IAMM, CIRAD, INRAE, Institut Agro, Univ Montpellier, Montpellier, France Full list of author information is available at the end of the article

https:// www. fsinp latfo rm. org/ sites/ defau lt/ files/ resou rces/ files/ GRFC% 202022% 20KM% 20ENG% 20ART WORK. pdf.

Acknowledgements

This study was conducted with the help of the Ministry of Agriculture, Water Resources, Sanitation and Food Security of Burkina Faso and the Société Nationale de Gestion du Stock de Sécurité Alimentaire (SONAGESS), which provided data.

Funding

This work was supported by the French National Research Agency under the Investments for the Future Program #DigitAg, referred to as ANR-16-CONV-0004.

Availability of data and materials

Not applicable (no open access data).

Author contributions

Conceptualization: HD, AB, EMH, data curation: HD, formal analysis: HD, AB, EMH, funding acquisition: AB, MR, methodology: all authors, validation: HD, AB, EMH, writing-original draft: HD, writing-review and editing: all authors reviewed the manuscript. All authors read and approved the final manuscript.

Declarations Ethics approval and consent to participate

The authors confirm compliance with the ethical policies of the journal.

Consent for publication

We confirm that the manuscript has been read and approved by all named authors.

Competing interests

The authors declare no conflicts of interest.

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domain: shs math

text:
Eléda Robo

Rodica Ailincai

Antoine Delcroix

Quelle influence des contextes sur les pratiques effectives en classe de géométrie en Polynésie française et en Guyane française eu égard aux curriculaires ?

La Polynésie française et à la Guyane française sont deux territoires de l'Outre-mer français qui présentent de nombreuses similitudes et dissemblances que l'étude des contextes géographiques, démographiques, historiques, socioculturels, linguistiques, institutionnels et éducatifs mettent en évidence. En particulier, sur le plan éducatif, des difficultés communes en termes de réussite scolaire amènent les territoires à définir des orientations similaires, notamment une certaine adaptation aux réalités socioculturelles et linguistiques. La Guyane française, collectivité territoriale d'Outre-mer, possède un système éducatif calqué sur celui de la France hexagonale. La Polynésie française, en raison de son statut de territoire autonome, a la possibilité de définir des curriculums spécifiques indépendamment de ceux ayant cours sur le territoire national français. Cependant, l'analyse des " programmes ajustés et adaptés à la Polynésie française 2020 " pour l'enseignement primaire, ne fait apparaitre que très peu d'adaptions en mathématiques. Ces constats nous mènent à poser les questions suivantes : comment les enseignants répondentils aux injonctions territoriales à adapter leurs enseignements aux réalités contextuelles des territoires ? Quelle mise en oeuvre effective en situation de classe ? Peut-on identifier des pratiques de contextualisation qui soient spécifiques aux territoires ? Nous nous intéressons en particulier au domaine de la géométrie parce que ces territoires possèdent un héritage socioculturel et linguistique où les références aux formes géométriques, sont très présentes par exemple, les motifs des tatouages polynésiens et de l'art Tembé en Guyane française.

A partir du cadre théorique de la contextualisation didactique [START_REF] Delcroix | Vers un cadre d'analyse opérationnel des phénomènes de contextualisation didactique[END_REF][START_REF] Sauvage Luntadi | La compétence de contextualisation au coeur de la situation d'enseignement-apprentissage. (I. d. éducatives[END_REF] et celui du Pedagogical Content Knowledge [START_REF] Shulman | Those Who Understand: Knowledge Growth in Teaching[END_REF][START_REF] Mangane | Connaissances professionnelles des enseignants dans l'enseignement de la chimie : une étude de cas en stéréochimie[END_REF][START_REF] Mounsamy | Les opérations sur la grandeur temps à l'école et au collège : l'exemple du calcul de durée dans le contexte guadeloupéen[END_REF] Nous avons filmé plusieurs séances d'enseignement-apprentissages au cycle 3 de l'école primaire, avons sélectionnés trois séances en géométrie sur chacun des territoires sur la base des thèmes géométriques communs abordés et avons eu des entretiens semi-directifs avec les enseignants. Les six séances d'une durée totale de quatre heures et trente minutes ont été transcrites de manière multimodale et découpées en interactions tenant compte du verbal et du non verbal [START_REF] Ailincai | Un dispositif d'éducation parentale : sensibilisation des parents à leur röle d'accompagnateur de leur enfant dans le cadre d'un musée à caractère scientifique et technique[END_REF]Kerbrat-Orecchioni, 1998). Les entretiens en Polynésie française se sont déroulés dans le cadre d'un projet de recherche PrEEPP (Pratiques Éducatives Enseignantes et Parentale en Polynésie française) et ont été transcrits dans leur intégralité contrairement à la Guyane française où la transcription a porté sur des extraits portant sur des points particuliers en lien avec notre recherche.

Nous procédons à l'analyse de contenu des entretiens [START_REF] Bardin | L'analyse de contenu[END_REF], à l'analyse des situations d'enseignement-apprentissage par un découpage en phases (Brousseau, 2011) et à l'analyse des PCKC des enseignants.

L'étude comparative des pratiques enseignantes des professeurs des écoles de Polynésie française et de Guyane française montre que l'organisation et la mise en oeuvre des situations d'enseignement-apprentissage sont pratiquement les mêmes sur les deux territoires, sans adaptations spécifiques aux contextes des élèves. Il apparait qu'il est peu fait référence aux contextes socioculturel et linguistique des territoires. En particulier, le recours aux volets contextuels des curriculaires est peu convoqué. La contextualisation didactique s'opère surtout en référence à l'environnement immédiat de l'élève, au sein de la classe.

Comment peut-on expliquer cette frilosité par rapport aux contextualisations curriculaires, en particulier lorsque le statut institutionnel du territoire le permet ? Nous pensons que, bien que les enseignants pensent qu'il est indispensable de contextualiser [START_REF] Robo | Étude comparée des interactions à visée d'apprentissage lors de séances de géométrie au cycle 3 de l'école primaire : le cas de la Polynésie française et de la Guyane française[END_REF], restent absentes des pratiques ordinaires de classe mais s'exprime dans des manifestations scientifiques particulières (semaine des maths, fêtes de la science, Rallye mathématiques...). La place de la contextualisation didactique en mathématiques est celle existante dans les programmes d'enseignement primaire, faible en Polynésie française, et non demandée par les programmes nationaux La question étant alors de savoir comment répondre aux demandes d'adaptations définies au travers des politiques éducatives territoriales ? Quelle est la véritable portée des Chartes éducatives de Polynésie ou des Projets académiques de Guyane lorsqu'ils ne se traduisent pas dans les programmes d'enseignements ou de manière si faible pour la Polynésie. Comment demander aux enseignants d'adapter leurs enseignements aux réalités contextuelles des territoires sans données des outils concrets pour y parvenir ? Nous pensons que les questions de didactiques contextuelles mériteraient d'être abordées en formations initiale et continue en mathématiques. Cependant, nous nous interrogeons sur la possibilité de pratiquer une véritable didactique contextuelle au sein du système éducatif français, très centralisé.

  nous construisons un modèle " Pedagogical Content Knowledge Contexte " (PCKC) adapté à notre recherche et constituant un outil d'analyse des connaissances et croyances professionnelles des enseignants relative * Intervenant sciencesconf.org:arcd2023:429756 à la prise en compte des contextes.