## 1 Introduction  
In Europe, about 4.7 million tons carrots are produced, representing 103 thousand hectares [1]. Like many other vegetables, carrots represent an essential food component for humans, mostly for baby food. Minimizing plant protection product (PPP) residues is therefore a strong driver for limiting the use of PPPs [2]. In modern agriculture, PPPs are widely used to increase the yield and the quality of the harvest. For example, alternaria leaf blight (caused by Alternaria dauci) is one of the harmful diseases of carrot crop affecting yield. The sensitivity to the disease depends on fertilization, fungicide applications, and cultivars [3]. However, their use can cause environmental and sanitary problems through direct operator exposure during spray application [4] or indirect exposure of residents, bystanders, and off-target areas via spray drift [5; 6]. Ground losses may contaminate the soil, air, and water with adverse effects on plants and wildlife [7]. One way to mitigate the impact of PPP is to improve the efficiency of the spray application, i.e., to deposit the product on the target crop and to limit losses to the environment. That is one of the goals of the H2020-project OPTIMA (_OPTTinised Integrated pest MAnagement for precise detection and control of plant diseases in perennial crops and open-field vegetables_, www.optima-h2020.eu (accessed on 1 April 2022)) in which a concept of smart sprayer includes several functionalities among which variable nozzle spacing, specifically for bed-grown carrots  
Raised bed cropping is a traditional farming system for some open field vegetables such as carrots. Raised beds encourage the concept of controlled traffic [8], where all vehicle wheels travel along the furrows between the beds, thus limiting compaction of the soil on the majority of the field [9]. Taproot length and yield are generally negatively affected by soil compaction [10]. Carrots grow best on deep, loose, well-drained mineral and organic soils with good water holding [11]. They are therefore typically grown on sandy-loam soils that are deeply cultivated to reduce compaction. However, when those ideal soil types are not available, farmers are often advised to plant carrots on raised beds [12]. In addition, raised beds are a primary tool for field drainage [9; 13], and can thus improve water relations in the root zone, possibly resulting in longer carrots [12], whereas in more arid parts of the world, raised beds are successful in improving the efficiency, and thus sustainability, of irrigation of arable crops, such as maize and wheat [14; 15]. As for other row crops, these bed-raised vegetables are generally sprayed against diseases using a conventional horizontal boom sprayer applying a broadcast application. Such a broadcast application generally does not consider any modification of the nozzle spacing or boom height with regard to the raised bed configuration and developmental changes in canopy width and density related to the growth stage. Broadcast applications can thus result in substantial losses of product between beds, especially during the early stages of the crop growth. Indeed, adjusting the width of the spray pattern to match the width of the target plants has been shown to have economic benefits by saving products, as well as resulting in better deposition efficiency compared to a broadcast application. For example, a precision band spraying system using vision sensors and rotating nozzles was studied [16]. The nozzle rotation allowed the spray band to be adjusted to match the target width. The authors demonstrated a 66 to 80% reduction in spray application rates, a 2.5 to 3.7 times increase in target deposition efficiency, and a 72 to 90% reduction in non-target deposition on the soil surface compared to conventional spraying. In addition, the reduction in airborne displacement of spray liquid [16] suggests a considerable decrease in spray drift with such precision spraying techniques.