# Territorial solar baking potential: A socio-technical analysis for planning the sustainable energy transition of the bakery world

Guillaume Guimbretière, Benjamin Pillot, Christophe Révillion, Corrie Mathiak, Romain Authier

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## To cite this version:

Guillaume Guimbretière, Benjamin Pillot, Christophe Révillion, Corrie Mathiak, Romain Authier. Territorial solar baking potential: A socio-technical analysis for planning the sustainable energy transition of the bakery world. Cleaner and Responsible Consumption, 2025, 17, pp.100276. 10.1016/j.clrc.2025.100276. hal-05088441

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Submitted on 28 May 2025

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# Territorial solar baking potential: A socio-technical analysis for planning the sustainable energy transition of the bakery world

Guillaume Guimbretière<sup>a, ∗</sup>, Benjamin Pillot<sup>b</sup>, Christophe Révillion<sup>b</sup>, Corrie Mathiak<sup>c</sup>, Romain Authier<sup>b</sup>

## ARTICLE INFO

### Keywords:

- Artisan bakery

- Solar energy

- Spatio-temporal modeling

- Social-technical transition

- Multi-scale organization

- Small island

## ABSTRACT

Nowadays, for energy reasons bread consumption appears unsustainable in the long-term. Direct solar baking can be part of the solution, but tools allowing for the estimation of the social-technical potential of solar baking at the territorial scale are lacking. In this article a socio-technical solar bakery's workflow model and two socio-economic indicators were developed. Then, these numeric tools were used in the frame of a full solar production and soft mobility scenario in a small tropical island (Réunion, France). Results show that in the best sites solar baking can be performed at least once a week with a production up to 16 tons/year and ≈ 32,000 tCO₂ emissions per year could be saved.

## 1. Introduction

The science of this work follows the paradigm of Sustainability Science (Nagatsu et al., 2020): an oriented-solution transdisciplinary Science (Miller et al., 2014). Consistent with the bioregionalist movement, our approach is to “reimagine ourselves and the places where we live in ecological terms and [work] to harmonize human activities with the natural systems that sustain life”. (Glotfelty and QuesnelEllul, 2015). In this paper, by mean of a scenario analysis, we specifically address the socio-technical problem of population accessibility to baker's bread cooked in a sustainable way. Currently, like in France, in most of the countries, the bread consumption is not long-term sustainable: Not to mention the unsustainability of the cereal production system, the unsustainability discussed here comes from the energy system. Indeed, in lot of countries energy transition is in progress and it is traditionally regarded as mainly an energy-centered transition (Slameršak et al., 2022; Leach, 1992). With this focus, the energy system being multi-scalar, it is possible to make energy supply more sustainable according to different scales (Clarke et al., 2021) by replacing utility-scale power plants based on finite resources by renewable energy systems. Another way is to substitute the electricity supply locally, using a stand-alone renewable energy system such as solar photovoltaic panels coupled with storage (Meyer and Von Solms, 2018). In the short and mid-term, this is likely a good option for mitigating CO₂ emissions from the energy sector (Clarke et al., 2021) and thus for combating climate

change. However, in the long-term, the sustainability of such variable renewable energies systems should be questioned: They (1) are much more adapted to small-scale remote applications (Pillot et al., 2019), (2) strongly depend on mining and limited materials, such as rare earth elements (Dutta et al., 2016), (3) subject to electronic failures, and (4) complex to the extent that most of the technical maintenance cannot be performed by end users (Pillot et al., 2019). If a proof is needed, the unsustainable nature of the energetic system recently induced that the sharp rise of energy and electricity prices in France has jeopardized many small-scale commercial activities such as artisan bakeries (Monde, 2023).

Looking in details on the bakers cooking technical systems, one can note that more than 50% of the energy consumed by a bakery is dedicated to baking (Chambre de metiers et de l'artisanat, 2011) and nowadays this heat is mostly converted directly from combustion of wood (Manhiça et al., 2012) or fossil fuels, or from the electricity provided by the national grid using an electric oven (Therdthai and Zhou, 2003). Instead of these, a sustainable baking tech should (1) be based on a one-conversion chain, i.e. from primary to heat energy, (2) use the least possible material and rare earth elements, (3) be very reliable in the long-term, and (4) be easily usable and maintainable by the bakers. The direct solar-thermal oven does fit this definition: even with the lack of a complete life cycle analysis, with no electrical part, no emissions of CO₂, greenhouse gas or small particles during

<footnote><sup>a</sup> Laboratoire de l'Atmosphère et des Cyclones (LACy), UMR 8105, Univ Réunion - CNRS - Météo-France, Saint-Denis, 97400, France</footnote>

<footnote><sup>b</sup> ESPACE-DEV, Univ Montpellier, IRD, Univ Antilles, Univ Guyane, Univ Réunion, 500 rue Jean François Breton, 34090 Montpellier, France</footnote>

<footnote><sup>c</sup> Friedrich-Schiller-Universität Jena, Jena, Germany</footnote>

<footnote>* Corresponding author.
E-mail address: guillaume.guimbretiere@cnrs.fr (G. Guimbretière).</footnote>
## Acronyms

<table><tr><td>NREL</td><td>USA National Renewable Energy Laboratory</td></tr><tr><td>NSRDB</td><td>National Solar Radiation Database</td></tr><tr><td>DNI</td><td>Direct Normal Irradiance</td></tr><tr><td>CAMS</td><td>Copernicus Atmosphere Monitoring Service</td></tr><tr><td>SRTM</td><td>Shuttle Radar Topography Mission</td></tr><tr><td>CGIAR-CSI</td><td>Consortium for Spatial Information of the Consultative Group on International Agricultural Research</td></tr><tr><td>EWSB</td><td>Eaten Where Solar Baked index</td></tr><tr><td>SBEI</td><td>Solar Bread Economic Intensity index</td></tr></table>

operation, one can legitimately expect a high degree of sustainability for this kind of low-tech technology (Guimbretière et al., 2022; Tanguy et al., 2023). As an evidence, due to its abundance and worldwide distribution, solar energy has long been identified as the main energy source from which a sustainable society should be built (Georgescu-Roegen, 1979), and direct solar cooking technology has been known for a very long time (Kundapur, 2020): Since more than 250 years. Up to recently, the thermal solar ovens are mainly considered following their energetic response as heat power sources: Engineers mostly tend to pass over usability and the needs of the targeted users in their context of use, while focusing on technical attributes only (Moses et al., 2019). Therefore, scientific studies mostly dealt with the efficiency of specific solar cooking setups numerically modeled or empirically tested on one or some places and at several moments (days). This approach cannot allow to estimate the practical solar potential of a territory for cooking or in our case, for baking. Effectively, within the problem of sustainable accessibility to bread, the technical ability to heat the oven from the solar energy is only one, among others, of the critical points having to be considered. One has to consider also, in one hand the compatibility between the solar variability, the solar oven response and the baker's organization, and in other hand the proximity between the solar bread production site and the population's location.

## Solar cooking at the territory scale

To our best knowledge, some works deal with the territory scale through solar cooker's potential mapping: Yettou et al. (2018) modeled both a box and parabolic solar cookers to create a temperature map. For this, the clear sky model of the European Solar Radiation Atlas (ESRA) for the Heliosat method and a heat loss model was used to determine the temperature of the solar cooker. Floess et al. (Floess, 2019) developed a solar resource map for a stored solar cooker: From energy balance and environmental models calculations, they address the solar variability problem through the building calculation of monthly maps of the number of days in which at least one, two or three stored-solar vessel can be charged, plus maps of average energy stored in the phase-change salt of a vessel each day. Ramachandra et al. (2011) identified “hot spots” in India, defined as “the regions characterized by an exceptional solar power potential suitable for decentralized commercial exploitation of energy”. Unfortunately, even if these works give a global territorial view of the solar cookers efficiency, the solar cooking potential of a territory is always estimated from an energy perspective only: if the incident solar energy (in kWh/m²) or oven's heating is strong, then the cooking solar potential is considered as strong. Following this approach, for industrial (Kalogirou, 2003) or household applications, the key point for an efficient solar cooking solution is still the development of an efficient solar cooker conversion technology.

## The solar cooker context of use

The paper of Indora et al. (Indora and Kandpal, 2019) is more grounded to the context of the solar cooker use: For institutional

cooking in India, they estimate the maximum utilization potential of the solar energy technologies for specific end use. They take into account context factors such as the solar resource availability at the selected location, the minimum acceptable value of DNI during the period of cooking, the number of days when available DNI is above this minimum acceptable value. Next, from the number of beneficiaries and the useful cooking energy required per person per day, they estimate the annual useful energy savings with institutional solar cooking, and CO₂ emissions mitigation: 57% of the annual useful energy required for cooking in the institution-types considered in this study can be met with solar energy.

## The solar baking

Has for solar cooking, most of the papers about solar baking have an energy or temperature focused approach: Ayub et al. (2018b,a) developed a solar oven based on a 10 m² Scheffler reflector and performed energy- and exergy-based thermal analyses of the solar bakery unit plus computational fluid dynamic-based 3D simulation in order to analyze the design for uniform air distribution in the baking chamber. The temperature at the inlet of baking chamber was in the range 200–230 °C, and the average value of energy utilization ratio was found to be 45%. Forsythe et al. (Forsythe and Madyira, 2019) estimated the nice sizing with a power target in order to bake bread at Johannesburg, in an evacuated tube collector with compound parabolic concentrators. A bread sample was baked in 40 min. Mishra et al. (2019) performed computational fluid dynamics analysis of the temperature and air flow distribution inside a solar oven with a target temperature: They concluded on the nice theoretical sizing for the area collection.

## Solar baking oven in the real social-economic world

Different is the paper of Müller et al. (2009): the paper is a kind of debriefing of what the solar baking oven really do. In Argentina, in an area that receives one of the highest amounts of solar radiation in the world (around 6–7 kWh/m² per day in average), a solar bakery oven using a fix focus 8 m² Scheffler reflector reaches 350 °C after 1 to 2 h of preheating. The villagers traditionally bake their own bread once a week, and as the oven is available for more than 6 h each day, up to 60 kg of bread can be baked each day. That means that 4–5 families can do their weekly baking on one day. Over one week a village like Misa Rumi with 20–30 families can substitute its tola bush consumption. In Normandie (France), an artisan bakery has been using a solar oven for commercial purposes for the past few years (NeoLoco, 2023). The solar oven is a Lytefire with a mirrors collector area of 11 m² and that can reach 300 °C during winter. The bakery's products and the organization of its activity have been adapted to the use of the direct solar-thermal oven: The Neoloco baker bakes bread once a week on a fixed day. If the sun is not there, cooking is done in a wood oven. The bread is ordered in advance by consumers and delivered by bicycle to drop-off points. Neoloco produces around 150 kg per week on average and cooks with solar energy every other time.

With in mind the problem of bread baking's unsustainability, one can note that the solar oven scientific literature is lacking of studies that take account global criteria of solar cookers adoption: economic, social, cultural, environmental, political and technical (Otte, 2013), and that are less focus on the technical efficiency of the solar ovens, but more one the grounded practice of specific cooking (Iessa et al., 2017). By this way only, one will progress on the route to sustainably provide bread to the population. To adopt direct solar concentration baking as a sustainable solution for bread baking, it is necessary to conduct research that addresses the following questions, (i) at the individual artisanal level: What is the optimal location for solar baking? What is the best organizational structure to adapt solar baking to solar variability? (ii) at the territorial level: What network structure of artisans is required to meet the specific demand in bread of the territory?

Therefore, in order to provide some answers to the planning issues of the baker, this article presents in a first section a socio-technical
model designed for assessing the bread production potential (output) of a solar baker in relation to sunlight level (input). This generic model is implemented in the context of the Lytefire solar oven and following two working strategies. In a second section, two indicators are also developed in order to characterize consumer access to bread and the viability of a bakery. In a third section, to illustrate the information that can be obtained with this model and these indicators, the outcomes of two soft mobility scenarios following the two strategies are calculated and discussed in the context of Réunion, a French department located in the south-west of the Indian Ocean, where solar energy is abundant and, according to the 2015 *Energy Transition Act*, France's energy policy is to reach full energy self-sufficiency by 2030 (European Commission, 2019). We conclude with the implications of an energy transition vision and the case study of Réunion.

The manuscript is structured as follows: A first *Materials an methods* part explains how the solar bread production potential is calculated through a socio-technical solar bakery workflow model. In this first part are also developed solar bakery sector's indicators and described French references bakeries and Reunion Island. Next, in a *Results and discussion* part compared two production organizational strategies. Next, in an *Implications* part, energetic, CO₂ mitigation and societal implications are discussed. The last part is *Conclusion*.

## 2. Material and methods

The chosen method to study the solar bakery model as part of a solution to the problem of bread accessibility unsustainability is the construction of “If the world was like this: is it sustainable?” scenarios. This kind of scenario analysis (Swart et al., 2004) does not reproduce a past reality nor a trend projection: its objective is to provide benchmarks for transforming society towards sustainable functioning. For this reason, the model and indicators developed are kept as simple as possible to allow for maximum flexibility for further adjustments.

### 2.1. The solar bread production potential

#### 2.1.1. A socio-technical solar bakery workflow model

In order to find out how a network of artisan bakers equipped with concentrating solar ovens could fulfill population needs for baked bread using the solar resource, a socio-technical workflow model was built. It is depicted in Fig. 1 with bottom-up flow. On the left of the workflow is a downward arrow representing the evolution of need from the original need for baked bread as food: the need for baking bread leads to a need for energy which must be mobilized by a cooking technology.

The bakery's process workflow model is composed of a series of numeric filters and functions pictured in full red or green rectangles on the Fig. 1. Regarding the solar oven model (technology filter), we have calibrated the filter output (number of continuous hours, i.e. service continuity) with real data from the NeoLoco solar bakery depicted below (NeoLoco, 2023). Also, DNI (Direct Normal Irradiance) satellite-based data from NSRDB (National Solar Radiation Database), implemented in the resource filter, have already been compared and validated against in situ data for different regions in the world (Salazar et al., 2020; Kenny and Fiedler, 2022; Sengupta et al., 2018). The output data of each step is the input data of the next step and are pictured in rounded rectangles, lightly shaded red, green or blue. For instance, starting at the model's beginning: The first input in the numeric model is the solar energy time series data (yellow rounded rectangle at the bottom). After numeric filtering by the DNI threshold filter, only time steps with DNI value above the DNI threshold (>$ 700 W/m² in the present case study<fnref n="1" />) are kept in the Output Rated Energy time series

data. This later dataset is next numerically filtered though the Number of continuous hours filter, etc ...Now, regarding the meaning of the model in details: For solar concentration, aggregated and averaged DNI gives spatial information about what we might call the gross solar income of a given territory. But, for activities such as bread baking, the core of a successful implementation is also linked to heat supply stability. For this to happen, DNI must remain above a given threshold for a time period corresponding to the duration required for preheating the oven plus baking one batch of bread. This threshold will differ from oven to oven, depending on their specific energy focus capacity (based on mirror reflection rate and total surface, oven insulation, etc.). Therefore, the DNI is two times filtered because of the response of the solar oven to solar radiation: a first high-pass power numeric filter removes values of solar power that are under a critical threshold for heating the solar oven (the DNI threshold filter). A second numeric filter is related to the minimum continuous time period above the threshold of the first numeric filter so that the oven maintains the necessary temperature to bake a full batch of bread (the number of continuous hours numeric filter). At the output of these two filters, one obtains the number of periods in the year during which the solar oven can, if one needs it, bake a batch of bread: the number of working periods. Then, depending on the baker's time management, a number of periods used for baking can be set. The oven allows for a specific quantity of bread to be baked per batch (in kg) and from it, one can estimate the daily productivity (in kg/day). Productivity is mainly based on the daily craftsman's time management and from it, a production (in kg/year) can be calculated, depending on the mid (weekly) to long (yearly) time organization of the baker. This organization results from the integration of social constraints like rate consumption, food practices and the environmental constraint of solar energy availability. Different types of solar ovens can be analyzed based on this process workflow model, through parameterization of the filters: DNI threshold, number of continuous hours and quantity of bread to be baked per batch. Also, the model can be applied to other territories (real or model) by changing the DNI data input. In fact, the DNI and the type of solar oven define what can be called the solar baking physical potential of the bakery's site. Effectively, the available baking time consists of time when the baking chamber remains in a given operating temperature range. The targeted temperature range is fixed by physicochemical processes of bread baking (Therdthai and Zhou, 2003; Mondal and Datta, 2008), and the heat comes from a physical process of solar flux conversion in the oven. In the model, the physical potential of solar baking is expressed in number of available working periods. In the following, a day is called bakeable when multiple continuous hours of high DNI allow for baking at least one batch of bread. Next, in order to analyze the physical potential of a Lytefire 11 oven (see below), two new parameters were built from the number of working periods output: the Maximum number of bakeable days per year and the Average production shortage per year (see Fig. 1, at the right). These parameters are thresholds that correspond to the baker's time periods for baking bread throughout the year, and emphasize both the frequency and intensity issues of the activity. In other words, frequency is given by the number of effective bakeable days as well as the amount of time corresponding to bread shortage (unbakeable days). Intensity corresponds to the number of bread batches that can be baked on a given bakeable day. Shortage period is retrieved by collecting the different spans of consecutive unbakeable days along the year. Finally, the solar baking physical potential managed by the baker through a work strategy results in a bread daily productivity and yearly production.

with daily DNI dynamics over the same period, enabling the DNI threshold to be manually set. The continuous hours correspond to a pre-heating time followed by a baking time. Baking would be possible with short falls in DNI below the threshold (cloud), but the choice of 3 continuous hours is robust insofar as the solar potential estimates are then minimum values. No detailed Neoloco's baking logs were used.

<footnote n="1">¹ The DNI threshold (> 700 W/m²) and continuous hours (3 h) were validated against Neoloco operational data: average production and typical daily production over a winter (Neoloco private communication) were compared</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Direct solar bakery's process workflow. Numeric filters' values in the purple boxes are given based on the Lytefire 11 solar oven model.</figcaption></figure>

### 2.1.2. The craftsman's solar bakery oven

For the present work, the Neoloco (NeoLoco, 2023) solar baking setup is considered: it uses a Lytefire 11 (Lytefire, 2023), a solar oven model allowing up to 38 kg of bread to be baked per batch. The Lytefire 11 has a 11 m² surface of solar energy collection made up of 23 mirrors. Collected light is then concentrated in the oven consisting of two floors: a lower floor into which the light enters through a window, and which contains absorbent elements performing the conversion of light into heat and limiting losses by outgoing reflections. The second floor is the baking chamber to which the craftsman accesses through a door. The two floors are open to each other and the heat circulation is done by natural convection. The solar collector/concentrator and oven assembly form an integral system mounted on wheels to follow the course of the sun. All operations are carried out manually and no electricity is required to operate the oven. Following Neoloco's practice feedback (private communication), the DNI threshold high-pass numeric filter is set to DNI > 700 W/m², and the number of continuous hours numeric filter to 3 hours: 2 h of preheating and 1 h of baking. The maximum load of the Lytefire 11 is 38 kg of bread per batch (the quantity/batch filter).

### 2.1.3. The baker's work strategy

Once the solar baking physical potential is estimated through the identification of the periods allowing bread baking (the “working periods”), the baker must organize all the stages of his production so that the time of baking matches the solar oven “working period”. Thus, the baker has to develop a work strategy for the short (daily) and long (yearly) term. For the daily time management, regarding our hypotheses, it is assumed that the maximum number of batches over the year is estimated by maximizing the daily number of batches up to 3 for every bakeable day. For the yearly strategy, two strategies are considered: the “max production strategy” and the “weekly operating strategy”. In the “max production strategy” we consider that the baker produces the maximum bread quantity allowed by the solar baking physical potential and within the limit of the adopted daily time management (max of 3 batches per day). In the “weekly operating strategy”, the baker bakes only from one to two days a week. The chosen bakeable days are days where the maximum number of batches is in the 1 to 3 range.

### 2.2. Solar bakery sector's indicators

The bakery's process workflow in Fig. 1 allows for the estimation of a baker's production according to the solar oven model, the management of his working time and the solar resource of his baking site. Because of the long term work objective of gaining new insight into the sustainable development transition of the territory, one wants to have an territorial-wide vision of the potential of a solar-powered bakery sector. Classically, the matching between production and consumption is one of the key-points for the viability of an economic activity. For instance in Réunion: Regarding consumption, the population is heterogeneously distributed (Fig. 2). Concerning the production, one main difference between the solar bakery compared to the classical electrified one is that the energy source is the solar radiation that is also heterogeneously distributed across the island (Fig. 3). For these reasons, two indicators were built in order to analyze the solar baking production/consumption potential match. First, following a systemic view of the territory sustainability, we argue that sole identification of the most efficient areas for solar bread production is not enough: energy and CO₂ emissions savings that may result from the solar oven utilization cannot be transferred to transporting solar bread to the consumers or the consumers to the bakery. That is why a built indicator called *Eaten Where Solar Baked* (EWSB) gives insight into whether bread consumption matches solar bread production in the immediate vicinity. This indicator is useful for identifying the region where even if the solar bread potential is high, the population of bread consumers is too low and the solar bread production from these regions requires transport to other areas. Based on this indicator, locations that are unsuitable for installing bakeries can be excluded. In order to assess where bakeries should be established, a second indicator called *Solar Bread Economic Intensity* (SBEI) was built. This later indicator estimates whether production matches consumption and assesses the most relevant regions for a potential solar bakery economy.

#### Construction of the indicators

Here, dealing with the proximity between bakery sites for solar bread production and the consumers, a honeycomb mesh of the territory is defined and then, both indicators in every hexagonal cell are
<figure><img src="image_4.png" /><figcaption>Fig. 2. Population density of Réunion Island.</figcaption></figure>

computed. The mesh resolution is based on a specific distance threshold from bakery to bread consumer. This threshold may depend on the mobility scenarios to be implemented, including sustainable ones where mobility-based CO₂ emissions would not balance CO₂ emissions spared through the use of a solar bakery. Small enough cells might for instance ensure soft mobility scenarios, where customer travels are realized on foot or by bike.

Overall, bread consumption in cell i is defined by both frequency and intensity: does an individual consume bread and how much quantity if he does? Probability $p_c$ that consumed bread quantity will be higher than the bread produced by the solar bakery is given by:

$$p_c = P \left( q_c \geq \frac{X_p}{\eta_c} \right) \qquad (1)$$

where $q_c$ is the final quantity consumed, $\eta_c$ is the number of bread consumers and $X_p$ is the supplied bread quantity. The number of bread consumers in cell i is given by the number of inhabitants $\eta_h$ in that cell and the probability that they actually consume bread. One may retrieve the probability $P_{h,c}$ of a human h to be a bread consumer c in cell i from the distribution of the ratio between the number of bread consumers and the number of inhabitants among all cells. Using the expectation of that ratio $\mathbb{E}(\eta_c/\eta_h)$, the number of bread consumers $\eta_c^i$ in cell i is therefore given by:

$$\eta_c^i = \eta_h^i \cdot P_{h,c} = \eta_h^i \cdot \mathbb{E}(\eta_c/\eta_h) \qquad (2)$$

where $\eta_h^i$ is the number of individuals in cell i. Expectation of the ratio between number of consumers and number of inhabitants among geographic cells is given by:

$$\mathbb{E}(\eta_c/\eta_h) = \sum_{i}^{N} p_i \frac{\eta_c^i}{\eta_h^i} \qquad (3)$$

where $p_i$ is the probability of the outcome $\eta_c^i/\eta_h^i$ and $\sum_{i}^{N} p_i = 1$. By definition, considering the expected value as the weighted average of all cell ratios, $p_i$ can be expressed as the population weight of cell i, such as:

$$p_i = \frac{\eta_h^i}{N_h} \qquad (4)$$

with $N_h$ the total number of inhabitants. One therefore gets:

$$\mathbb{E}(\eta_c/\eta_h) = \frac{1}{N_h} \sum_{i}^{N} \eta_c^i = \frac{N_c}{N_h} \qquad (5)$$

with $N_c$ the density of bread consumers and $N_h$ the population density in the island. Therefore, from the probability defined in Eq. (1), we can define the “Eaten Where Solar Baked” index EWSB$^i$ in cell i:

$$EWSB^i = P \left( q_c^i \geq \frac{X_p^i N_h}{\eta_h^i N_c} \right) \qquad (6)$$

where $X_p^i$ is the produced bread quantity in cell i, and $q_c^i$ the final quantity consumed in cell i. The EWSB index stands for the probability that the local production of solar bread in cell i is actually consumed in cell i. Accordingly, from a sustainability perspective, the bread is eventually baked and consumed in a sustainable manner, i.e. solar bread is supplied to the consumers through sustainable trips. Next, the “Solar Bread Economic Intensity” index SBEI$^i$ in cell i is defined as the product between the expected rate of return of the bread production and the EWSB index:

$$SBEI^i = X_p^i \cdot \alpha \cdot EWSB^i \qquad (7)$$
<figure><img src="image_5.png" /><figcaption>Fig. 3. Daily mean shaded direct normal irradiation (in kWh/m²) for the 2017–2019 period in Réunion.</figcaption></figure>

<table><caption>**Table 1**
Reference bakeries data.</caption><thead><tr><th>Name</th><th>Location</th><th>Fuel</th><th>Sales model</th><th>Work strategy<br>(baking days/week)</th><th>Yearly production<sup>a</sup><br>(tons/year)</th><th>Price range<br>(€/kg)</th></tr></thead><tbody><tr><td>Neoloco</td><td>Normandie<br>(France)</td><td>Sun or Wood</td><td>Pre-sale<br>& bread deposit</td><td>1</td><td>7–8</td><td>6–10</td></tr><tr><td>Le pain nourricier</td><td>Entre-Deux</td><td>Wood</td><td>Market place</td><td>1</td><td>6</td><td>6–12</td></tr><tr><td>Au coin du levain</td><td>Sainte-Marie</td><td>Electricity</td><td>Shop</td><td>3</td><td>12–15</td><td>8–15</td></tr><tr><td>Cassava</td><td>Saint-Paul</td><td>Electricity</td><td>Shop</td><td>5</td><td>16–20</td><td>–</td></tr></tbody></table>

where $α$ is the rate of return (€) of 1 tonne of bread. The SBEI index expressed in €per cell underlines among the best EWSB sites which one are the best for a sustainable economic bakery’s activity; that is the sites where a significant solar bread production can actually be consumed in the surroundings.

## 2.3. French reference bakeries

A survey to 63 french bakeries (2008–2010) (Chambre de metiers et de l’artisanat, 2011) shows that on average, 53% of the energy consumed by the bakeries is for baking. The average energy consumption for baking depends of the fuel type of the oven: ≈ 26000 kWh/y for electric ovens, ≈ 63000 kWh/y for gas ovens, and ≈ 98000 kWh/y for fuel oil ovens. In 2022, we conducted a series of interviews with bakers. Elements are summarized in Table 1: Neoloco is a solar baker located in Europe (Normandie, France). Le pain nourricier, Au coin du levain and Cassava are bakeries located in Réunion. All of them bake sourdough breads.

## 2.4. The solar resource

### Direct normal solar radiation

Solar thermal bakery is mainly fueled by direct solar radiation, which is concentrated through parabolic or flat mirrors into the solar cooker’s focus (Ayub et al., 2018b; Wentzel and Pouris, 2007). In first

instance, knowledge of both (1) spatial and (2) temporal distribution of the solar direct irradiance is essential to assess how solar baking may match the current and future behavior of potential bread consumers. Satellite-based models stand for a good trade-off between accuracy and the need for apprehending the geographical distribution of solar radiation (Salazar et al., 2020). However, all models are not equal in terms of temporal and spatial resolution as well as final precision or data access (Salazar et al., 2020; Sengupta et al., 2018). The satellite-based physical model (PSM-3) developed for more than 20 years by the NREL (USA National Renewable Energy Laboratory) to produce the National Solar Radiation Database (NSRDB) provides good balance between all these requirements for Réunion. Data access is also kept as straightforward as possible in order to get a full dataset of hourly Direct Normal Irradiance (DNI) maps in W/m², and accuracy is close to the one from other satellite-based products such as CAMS (Copernicus Atmosphere Monitoring Service) and SARAH2 (Salazar et al., 2020; Kenny and Fiedler, 2022), but with a better spatial resolution than those two over Réunion because of the satellite’s location: NSRDB is based on the Meteosat IODC geostationary satellite against Meteosat 11 for CAMS and SARAH2 over Réunion (ECMWF, 2022; Gracia-Amillo et al., 2021; NREL, 2022).

### Topography shadow correction of the DNI

Another significant information for solar thermal bakery is the topography of the territory, that directly influences available direct solar radiation through terrain shadowing. In order to integrate the

<footnote>a Yearly production is calculated from daily or weekly with a year equal to 50 weeks.</footnote>
shading effect into the DNI maps, one can use the SRTM (Shuttle Radar Topography Mission) data released by the CGIAR-CSI (Consortium for Spatial Information of the Consultative Group on International Agricultural Research), the horizon model instantiated in Pillot et al. (2016) and the solar position algorithm developed at NREL (Reda and Andreas, 2004).

## 2.5. Réunion island

Réunion is an island located in the Indian Ocean, about 800 km east of Madagascar (Fig. 2). With an area of 2512 km², this territory has an ovoid shape with a diameter between 50 and 70 km.

### Geography

The island culminates at 3 069 m on the Piton des Neiges. The terrain of Réunion is characteristic of volcanic islands with steep slopes and alluvial plains of limited size (Cazes-Duvat and Paskoff, 2004). The climate is tropical, with a hot and humid season from December to March, and a cooler and drier season from June to September. In addition, the insularity, the circulation of trade winds and the high relief of Reunion Island generate significant climatic contrasts: The windward coast (east and north) can be distinguished from the leeward coast (west and south). The windward coast receives the trade winds from the front, bringing masses of humid air which are blocked on the relief of the center of the island by pouring a great part of their rains there. In fact, the leeward coast has a much drier climate.

### Population

With nearly 900,000 inhabitants, the island has a population density close to 350 inhabitants/km². The majority of these inhabitants are located along the coast (Fig. 2) (ARCEP, 2022).

### Solar resource

The geographical contrast affects the sunshine rate, the coasts and the west of the island being sunnier than the east and the center. It is therefore relevant to study in more detail the spatial distribution of solar radiation over this small area. Accordingly, original NSRDB-based hourly DNI maps have been downscaled to the resolution of the 90 m Digital Elevation Model of Réunion. Finally, the result is a set of hourly shaded DNI maps over a 3 years range from 2017 to 2019; to give an idea to the reader, the daily mean direct normal irradiation (in kWh/m²) for the 2017–2019 period is depicted in Fig. 3.

### Bread consumers

To calculate both solar bread indicators described in the next section, a specific population location data is used. This set is calculated from population data on administrative entities, the population being distributed over all buildings of more than 20 m² located in these entities, proportionally to the size of the buildings (ARCEP, 2022). Accurate information is retrieved from this data and allows for calculating the number of inhabitants $\eta_h$ and number of bread consumers $\eta_c$ among the cells in which a potential solar bakery could be implemented. Hypotheses about bread consumers profile have been simplified, with yearly individual consumption of bread taken as a normal distribution $N(\mu, \sigma)$ with $\mu = 50$ kg (Reunionnais du monde, 2006) and $\sigma = 20$ kg.

## 3. Results and discussion

In order to address the problem of unsustainable baking, this work targets an estimation of the solar baking potential of a territory depending on its solar energy and population context. Since solar baking is a solar technology, first a gross estimation (without modeling) can be made from the cumulative data of incoming solar energy (Fig. 3): in the first subsection, such gross estimation is discussed. To go further, in the second and third subsections, the modeling of the “maximum production strategy” and the comparison with the “weekly operating strategy” described in Section 2.1.3, are respectively discussed. For both strategies, first the solar baking physical production potential

from a purely energy and technology point of view without taking into account the current population distribution, is discussed. Then, the solar bread accessibility by mapping the *Eaten Where Solar Baked* and *Solar Bread Economic Intensity* indicators, that take population density into consideration, is discussed. In a last subsection, the modeled solar production potentials for both strategies are compared with the production of existing bakeries.

### 3.1. Solar baking potential from DNI data

Regarding solar variability, the “Daily mean shaded DNI map” (Fig. 3) shows a heterogeneous spatial distribution of the solar energy in the range 1.9–6.5 kWh/m². As a gross estimation of the solar bakery potential, the most irradiated areas are expected to have the highest potential: the highest DNI values are located in the northeast and west coasts, as well as in the southwest. The slopes of the summits receive little solar radiation due to shadowing effect, while the Piton de la Fournaise volcano in the south-east gets the lowest DNI potential because of micro climate effects. Ultimately, the high summits of the island and the cirque of Mafate are the regions with the highest solar potential. It is important to underline the large size of the satellite pixels projected on a territory with very sharped and rugged field. Future work will engage into enhancement of these satellite-based data, as well as comparison with data from ground stations.

### 3.2. The maximum production strategy

Remember that in the “maximum production strategy”, the baker produces the maximum bread quantity allowed by the solar baking physical potential and in the limit of the adopted daily time management: 3 batches per day maximum.

#### 3.2.1. Solar bread production potential

Once DNI was identified for the period, the related thresholds (Section 2.1.1) for solar bread production were derived. “Max number of bakeable days”, “production shortage” and “Max number of batches” are respectively depicted in Fig. 4(a), Fig. 4(b) and Fig. 4(c). “Maximum solar bread production” is then derived from the range of possible batches (1–3) per bakeable day combined with the maximum quantity baked per batch. In Lytefire 11 user guide, the batch quantity range is given between 30 and 38 kg, and the result when the batch is set to 38 kg is described in Fig. 4(d). It is interesting to note that while the DNI map of Fig. 3 gives information about spatial distribution of the solar resource, the set of figures in Fig. 4 actually gives more insight into the temporal variability of the solar radiation, and thus into the bread production we may derive from it. Color scales are bicolor gradients with tipping values chosen at significant thresholds: for the “max number of bakeable days” map, the tipping value is 175 days which is close to half a year. For the “average production shortage” map, the tipping value is 5 days which is the shelf life of a sourdough bread. For the “max number of batches” map, the tipping point is 280 batches which is close to half the maximum value on the island. 280 batches is also $1/4$ of the theoretical maximum number of batches (i.e. $1095 = 3 * 365$) and 75% of the theoretical maximum of bakeable days per year (i.e. 365).

It is important to note that the need for energy is not a need per se but a need directly connected to a social service through a technological tool using energy. In the case of the solar bakery, the bakery’s process workflow transforms energy and raw materials into baked bread using a direct concentration solar oven. Therefore, this process transfers the issue of solar variability to the issue of temporal and spatial variability of bread production. The maps in Fig. 4 represent several parameters that allows for the consequences of this variability on the production potential of solar bread and its regularity across Réunion to be taken into account. Regarding the various parameters of the solar bread production potential (Fig. 4): essentially, the thresholds maps rather fit
<figure><img src="image_6.png" /><figcaption>Fig. 4. Solar bread production thresholds in Réunion following the maximum production strategy. (a) Max number of bakeable days per year, (b) Average production shortage per year, (c) Max number of batches per year, and (d) Max yearly solar bread production (in tons).</figcaption></figure>

the DNI maps (Fig. 3); the sunniest areas are those where there is the largest “max number of bakeable days per year”, the lower “average production shortage per year”, the “maximum number of batches per year” and therefore ultimately the greater “bread production potential”. However, the quantitative outcome is significantly different with a solar bread production range being two times the DNI range. In more details:

* The max number of bakeable days per year map (Fig. 4(a)) shows that in the areas exhibiting the highest number of bakeable days (in green), baking can be performed more than half of the days a year.

* The average production shortage per year map (Fig. 4(b)) shows that except in the Piton de la Fournaise volcano area at the south-east (in pink), in the rest of the island there is less than 5 consecutive unbakeable days in average. In a nutshell, it means that baking can be performed at least once a week. It is compatible with some sourdough bakery's business model like the Neoloco one (NeoLoco, 2023).

* The max number of batches per year map (Fig. 4(c)) shows that in the area where the number of bakeable is greater than 175 (more than half of the days a year), the number of batches is well above 175: two or three batches per day should be a common situation.

* The solar bread production potential map (Fig. 4(d)) shows information close to the max number of batches per year map: in order to obtain the solar bread quantity, the number of batches are just multiplied by the oven capacity of: 38 kg per batch. Nevertheless, on one hand this map gives the bread quantity in tons that can be directly compared to a typical bread production or consumption.

On the other hand, the bread quantity scale's levels are chosen in order to identify sites in the sunniest areas where the solar bread production potential is the best: the summits and the Mafate mountain cirque at the island's center are the most relevant areas. On the coast, Sainte-Marie, Sainte-Suzanne (north-east) and Saint-Pierre (south) are the best populated areas for solar baking. Following this calculation, nice area for solar baking allow to produce 10–20 tons/year while worst area allow to produce 4–9 tons/year.

### 3.2.2. Solar bread accessibility

Here, the study is positioned in the context of a scenario of 2023 population density and soft mobility system (bicycles and pedestrians). Obviously, it is not the scenario of the whole mobility system shift to soft mobility because the current distribution of the population on the island is highly dependent on the dominant mode of transportation, which is the private car. It is likely that a whole transition to a soft mobility system would lead to a change in the distribution of the population on the island. Soft mobility is considered only for solar bread collection, because it would be counterproductive to reduce electrical energy consumption and polluting emissions with solar baking while transferring this energy consumption to polluting trips required for collecting the bread. Moreover, the soft mobility framework is deeply sustainable and robust, even when facing with a context of energy crises which affect not only energy required for baking bread, but also mobility.

The spatial distribution of both the EWSB and SBEI index over Réunion is depicted in Fig. 5, for hexagonal cells of 500 m radius and a fixed rate of return $\alpha = 8 \epsilon / \text{kg}$.
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Eaten where solar baked and (b) Solar bread economic intensity indicators in Réunion.</figcaption></figure>

The EWSB index (Eq. (6), Fig. 5(a)) gives information on the ability of the population to consume the entire solar bread production in an area very close to the solar bakery site. It is an accessibility index showing how accessible a batch of bread would be to the surrounding consumers when it is actually produced. The index range is from 0 (the bread is not consumed) to 1 (all bread is consumed). High accessibility does not mean that the solar bakery would eventually be viable, but only that the bread which is effectively produced is highly accessible to the local consumers. Globally, without surprise, the EWSB indicator map shows high index values in the area where the population density is the highest: in the cities of the north (Saint-Denis), the north-west (Le Port), the east (Saint-Andre and Saint-Benoît), and the south (Saint-Louis, Saint-Pierre and Le Tampon). The high potential solar bread production areas of the center of the island (see Fig. 4(d)) where population density is very low exhibit very low EWSB values.

The SBEI index (Eq. (7), Fig. 5(b)) shows the areas where the solar bread production is the highest AND can be consumed in the immediate vicinity of the solar bakery site. It gives combined information about solar bread production and accessibility, and hence shows how viable a solar bakery might be. Viability is defined locally, that is the density of potential consumers is computed from the number of inhabitants and surface area of each pre-defined cells. Finally, it is important to note that obviously the resulting map does not give a full realistic view of *how much* a solar bakery might be viable locally, because of the simplified hypotheses about individual consumption, the rate of return, etc. However, it gives a very interesting relative information about the most suitable locations for developing solar baking in the island. These most suitable locations are especially in cities of Saint-Pierre, Saint-Andre, Saint-Benoît and the eastern part of Saint-Denis. Finally, Le Tampon, Le Port and the western part of Saint-Denis where the EWSB index is high are not suitable places for solar baking because of the too low solar bread production potential.

A detailed discussion of the map is beyond the scope of this paper, but one can note here the sharp split-up between west Saint-Denis and east Saint-Denis. This pattern is probably due to the large size of the DNI pixels (see Fig. 3). No higher resolution DNI map is currently available, but as said previously (see Section 3.1), we will study the pixel size effect in future works.

### 3.3. Comparison with the weekly operating strategy

Remember that the “weekly operating strategy” consists in baking at most two days a week. The chosen bakeable days are days with the maximum number of batches in the range 1–3 (see Fig. 1 at right). According to this strategy, the baker manages his time with at least 5 days a week dedicated to activities besides baking. Following the

solar energy availability, the baker could possibly bake only one day a week or consider some weeks with no production. This solar baker organization comes from the consideration of breads' types that the artisan can bake: for instance, Neoloco bakes sourdough breads one day a week. The sourdough breads are long shelf life breads (3 to 5 days) compare to only yeast breads (1 to 2 days), and they suit the solar baking variability.

#### 3.3.1. Solar bread production potential

Fig. 7 shows the maps of the solar bread production potential for the weekly strategy. One can compare this map with the map corresponding to the maximum production strategy (Fig. 4(d)). The color scales are the same. The map of Fig. 7 shows that globally, the best area for solar baking remains the same with the weekly strategy as for max production strategy: the coast, especially the north-east, and in a lesser extent the south. With the weekly strategy, nice area for solar baking allow to produce 9–14 tons/year while worst area allow to produce less than 4.5 tons/year.

To go further, Fig. 6 plots the yearly solar bread production of the weekly strategy versus the production of the max production strategy (black dots). Lines are empirical references that correspond to a percentage of the max production strategy minus one ton: the blue, yellow, red and green lines respectively correspond to a percentage of 100, 70, 60 and 50%. The trend of the production switch between the maximum and the weekly strategies is linear with a 1 tonne systematic decrease (about 26 batches). First, one can see that all the locations are between the 100% (blue dashed) and the 50% (green dashed) lines. Next, one immediately distinguishes a first group of locations where the production is very high according to the max production strategy (between 16 and 23 tons/year), and falls down between 8 and 11 tons/year based on the weekly strategy. The production of these locations is very impacted by the implementation of the weekly strategy: points are close to the 60% line (dotted red), while the scatter plot of all other locations is centered on the 70% line (dotted yellow). However, the production of the locations following the weekly strategy are close to the maximum theoretical production of 11,856 kg (38 kg * 3batches * 2days * 52weeks). The maximum theoretical production with the maximum production strategy is 41,610 kg (38 kg * 3batches * 365days) and almost every site under study is below half this value. Finally, for a weekly strategy where more than 70% of the time (5 days out of 7) is dedicated to other activity than baking, in the majority of places considered for solar baking, the average decline of the maximum production is only of 30% minus 1 t.
<figure><img src="image_8.png" /><figcaption>Fig. 6. Mass production for the weekly strategy vs mass production for the max production strategy (black dots). Colored dotted lines are empirical references (see text) and the gray dotted line shows the maximum theoretical production level with the weekly strategy.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Yearly solar bread production (in tons) for a weekly operating strategy in Réunion.</figcaption></figure>

### 3.3.2. Solar bread accessibility

The soft mobility context is the same as for the “max production strategy” and the spatial distribution of both the EWSB and SBEI indexes over Réunion is depicted in Fig. 8. Fig. 8(a) shows the mapping of the EWSB index for the weekly strategy. With the weekly strategy, a lower amount of bread is produced (see the solar bread production potential, Fig. 7) and an increase of the EWSB is mechanically expected. This is the case: areas where the EWSB index was the highest for the max production strategy still stand for higher values according to the weekly strategy, and the low value areas of the coast in the “max production strategy” show higher values in the “weekly operating strategy”. Globally, with the “weekly strategy”, all solar bread baked along the inhabited coast of Réunion should eventually be consumed.

Fig. 8(b) shows the SBEI index’s map for the weekly strategy. Compared to the maximum production strategy map (Fig. 5(b)), the decline of the SBEI index between both strategies in areas where it was formerly the most significant is only 30% in average (from 100–115 $k\epsilon$ in Fig. 5(b), to 64–81 $k\epsilon$ in Fig. 8(b)). Globally, the most suitable area lies in the same color level and are the same as for the “max production strategy”: the eastern part of Saint-Denis, cities of Saint-Pierre, Saint-Andre and Saint-Benoit. But even more interesting,

north-east areas that had intermediate suitability in the “maximum production strategy” (in orange in Fig. 5(b)) are now the best areas (in red) in the weekly strategy, following a decline of only 20% in average (80–100 $k\epsilon$ range to 64–81 $k\epsilon$ range) or less on some points.

### 3.4. Comparison with the productions of existing bakeries

Fig. 9 plots the EWSB index versus the solar bread production for all the hexagonal cells and for both the max and weekly production strategies (respectively blue and red dots). In order to compare the calculated solar productions to those of existing bakeries, the yearly productions of reference bakeries (Section 2.3) are reported on the plot by mean of bakeries’ names located on the axis at their respective range production. For the max production strategy, the sites that produce more than 15 tons/year or less than 5 tons/year exhibit EWSB index values close to zero: they are irrelevant for solar baking. For the weekly strategy, irrelevant sites for solar baking are those corresponding to a production higher than 10 tons/year or lower than 2 tons/year. Hence we assume that the most robust organization for the bakery sector should consider a work strategy with site production between 5 and 10 tons/year (with the Lytefire 11 oven). This range of production includes the production of Neoloco and Le pain nourricier bakeries (their work strategy is based on one baking day per week). The production level of Au coin du levain bakery (3 baking days per week) can be reached with the max production strategy in some areas showing a high EWSB index. The production level of Cassava can be reached (5 baking days per week) in Réunion but the bread will not be consumed in close vicinity (EWSB index close to zero), for the sustainable mobility scenario.

## 4. Implications

### 4.1. Energetic and CO₂ mitigation implications

In 2016 (Observatoire du pain, 2016), 98% of french people eat bread regularly: 93.9 g per day in average. From this, with nearly 900,000 inhabitants, the Réunion yearly consumption can be estimated to be around 31,000 tons of bread. Based on the Cassava yearly average production of 18 tons/year (see Section 2.3), one can calculate that 31,000/18 = 1722 bakeries of Cassava model (electric with shop) are necessary in order to address the Réunion bread consumption.

A classic electrical bakery energy consumption is ≈ 26000 kWh/year for electric ovens (Chambre de metiers et de l'artisanat, 2011) and
<figure><img src="image_10.png" /><figcaption>Fig. 8. (a) *Eaten Where Solar Baked* and (b) *Solar Bread Economic Intensity* index for a weekly operating strategy in Réunion.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. EWSB index vs production for both strategies — LPN is for *Le pain nourricier* and ACDL is for *Au coin du levain*.</figcaption></figure>

the average ratio of direct emissions per electrical kWh consumed in 2019 in Réunion is ≈ 719 gCO₂/kWh (Gilboire et al., 2020): In this full electrical scenario, the CO₂ emissions for bread cooking is ≈ 32,190 tCO₂ per year. This emissions could be saved in a full solar scenario: This is a maximum value. A more realistic short-term projection should take into account an hybridization of the energy sources used for baking, as it is the case in Neoloco's practice. However, 100% solar conversion is possible, but will require profound changes in the eating habits of consumers on Reunion Island (frequency of consumption, types of bread and prices), as well as in the organization of the bakery, with a deconcentrating of production in particular. A scenario-based approach would enable progress to be made towards ambitious targets, while remaining aware of the real issues at stake. For example, a seasonal organization of solar bread production is an interesting breakthrough scenario (Pillot et al., 2024).

## 4.2. Societal implications

Knowing the current average bread consumption per French person, one can calculate, based on the organizational scenario and the equipment of the bakers, how many artisans would be necessary to sustainably meet the population's needs within a soft mobility scenario. In 2022, 353 bakeries are working at Réunion (Institut Supérieur des Métiers, 2022): It is very far from the 1722 Cassava-type bakeries.

We assume that the majority of bread production may be performed in industrial bread cooking structure, but unfortunately no data were found on it. Nevertheless, it is possible to calculate some social impacts of a full solar scenario: From Fig. 9, one can estimate that 10 tons/year of bread is a nice order of magnitude for a typical solar bakery whatever is its organization. In this case, 31000/10 = 3100 solar bakeries equipped with the Lytefire oven should be necessary in order to address the Réunion bread consumption. The positive consequences of such scenario are job creation, CO₂ mitigation and, an increase of the energetic and feed autonomy. Because land cover is a critical aspect of small island (Authier et al., 2024), it will be necessary to further discussed the land cover of solar oven in use. It is not a simple question due to the numerous parameters having to be considered: for instance, solar oven can be mobile, electric systems can have energy storage and other options. Nevertheless, a grossly comparison allows to see the difference of land cover magnitude between both systems: The Lytefire (Lytefire, 2023) land cover is a circle of 12 m diameter ≈ 28 m², while that only the electric production system of a 38 kW electrical oven (Chambre de metiers et de l'artisanat, 2011) powered by electric solar panel has a land cover of ≈ 190 m² (typically 5 m² per kW). Thus about the question of the land cover, in first approximation, the direct solar oven seems a more sustainable system than the electric one. The solar baking scenarios will be more precise with the future higher-resolution DNI data availability. In any case, it should be relevant to
perform one full year of hourly DNI ground measurements at the place under consideration for future solar bakery.

Beyond these numerical aspects, the approach of the paper is based on a shift from the traditional view of energy transition as an energy-centered concept, to a focus on the *energy - technology - society* system. Based on this socio-technical view of the energy transition, the corresponding solar bakery workflow model shows how it is not energy which is eventually produced, but *baking time* for bread production. In this way, even if the direct solar baking is a very sustainable option for baking and energy consumption management, it can hardly be taken into account in the energy mix calculation. Similarly, it is not rigorously possible to calculate energy savings as it was shown how an appropriate implementation of the direct solar bakery technology would impact both the baker's time management and the organization of the whole bakery sector: Even if above, we grossly calculate a CO₂ mitigation, the shift from a part of the electrical bakery sector to direct solar baking cannot be reduced to the sole replacement of the electrical oven by direct solar ovens. That is why the *EWSB* and *SBEI* indexes were calculated for a slow mobility scenario. However, even in this case, one is still looking at energy transition as a substitution of *fuel tap*, while the results strongly suggest that consuming *solar bread* would necessarily be different from the current consumption of *electrical bread*. If the heat energy fuel tap is only substituted, one implicitly considers that a solar bakery can deliver the exact same service as a current classical bakery. This is very unlikely, precisely because of the inherent volatile nature of direct solar radiation against the dispatchable nature of electrical supply. In order to look beyond sole substitution, one must understand how changes in bread consumer's behavior could meet the new paradigm of the solar baker's activity.

As an example, in Réunion, by considering one or two full bakeable days a week, i.e. with at least 6 continuous hours for bread production, a solar bakery could significantly enhance its viability. But it would require to bake a different type of bread on those specific days, a bread that could be stored and consumed during a greater period of time. In some way, this solar bread would serve as a bio-chemical storage of the solar radiation. It could address a current need for long-term bread storage, as well as a new manner of living that would have been co-constructed between the baker and its community of consumers. Different groups of consumers may be considered even within the same community, whose behavior would match the different bakery's ways and days of operating. Short-term or long-term bread consumption, and conservation, emphasize how solar radiation variability might be handled by the solar baker, without even considering another dispatchable backup resource. Apprehending this *social time* (see Fig. 1) is fundamental for ensuring a win-win between both production time and consumption time, and eventually promoting solar bakeries over electrical ones. This aspect sheds light on the *social-cultural dimension* of energy transition and on how it ultimately affects energy service sustainability.

## 5. Conclusion

In conclusion, this article reports a methodology based on a socio-technical approach to modeling sustainable baking scenarios in the frame of a direct solar economy and soft mobility: First, with an objective of decision-support help for land-use planning around the use of direct solar cooking, the simplest possible solar bakery workflow deeply anchor to reality was developed for assessing solar bread production based on (1) the historical solar data of a territory, (2) the empirical response of the solar oven and (3) the baker's time management embedded into a social and geographical context. Time and space are the trans-disciplinary dimensions allowing the homogeneity of the socio-technical model. Second, we defined two socio-economical indexes that identify the best and worst locations for solar bakeries based on the radical sustainability perspective of slow mobility. More precisely: the socio-technical model allows for calculating the time-resolved solar

production potential (in kg/day and tons/year) for a given site at a daily time resolution. The EWSB index indicates how local consumption matches production. The SBEI index demonstrates how local consumption matches production AND whether the production is substantial. As example of application, the methodology introduced above allows to estimate, if a high use intensity is realistic for a given solar oven model and a given territory: From this, it could supplement the work of Mendoza et al. (Mendoza et al., 2019) that studied the sustainability benefits of using solar cookers in developed countries in place of microwaves ovens. The finding suggest that a high use intensity (240 days) can reduce environmental impact by up to 65 per cent, including global warming potential.

In this article, as case study, the model and indexes were applied to Réunion island. Two solar bread production management strategies were studied and compared to active bakeries: the maximum possible production and solar baking only during the two best days per week. Calculations show that **two or three batches per day should be a common situation** and with a maximum production strategy, **baking can be performed at least once a week and more than half of the days a year.** Up to **16 tons/year** can be solar baked in the populated areas. With the two best days strategy, 5 days a week are released for other activities and the whole coastal area of the island (except the south-east volcano) becomes suitable for solar baking. The average decline of the maximum production is only of 30%. Solar production level is comparable to sourdough only active bakeries that perform one or three baking days a week with solar, wood or electrical oven, but under the production level of an electrical 5 days a week bakery.

To conclude, in Réunion a robust organization for the bakery sector considering a work strategy with site production between 5 and 10 tons/year could ensure sustainable solar bread's availability almost over the entire year. A bakery sector made of ≈ 3100 craft solar bakers could saved ≈ 32,000 tCO₂ per year with a smaller land cover than electric systems. The best place for a first sustainable solar bakery activity in Réunion is the city of Saint-Pierre.

## CRediT authorship contribution statement

**Guillaume Guimbretière:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Conceptualization. **Benjamin Pillot:** Writing – review & editing, Supervision, Software, Project administration, Methodology, Conceptualization. **Christophe Révillion:** Writing – review & editing, Visualization, Investigation. **Corrie Mathiak:** Writing – review & editing, Visualization, Methodology, Investigation. **Romain Authier:** Writing – review & editing, Visualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

The authors would like to thank the CNRS and the IRD for their financial support through the MITI interdisciplinary programs.

## Data availability

Data will be made available on request.
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