## 2 Materials and Methods
### Method  
Our innovative methodology seamlessly integrates emerged and underwater photogrammetry into a unified workflow, starting from the definition of a common reference system. Terrestrial and aerial photogrammetric surveys can be easily georeferenced by GNSS measurements performed by the UAV itself or via GCPs (Ground Control Points). Notably, underwater environments present unique challenges for georeferencing, due to technical limitations or high costs of underwater positioning systems. To overcome these challenges, our proposed methodology was developed with multiple objectives. Its primary goal is to merge the underwater and land models into a unified representation with a cost-effective solution. Additionally, this allows us to evaluate the feasibility of dynamic control points localization from images instead of GNSS, offering a viable alternative where GNSS has limitations for instance due to electromagnetic interference. The methodology relies on defining a fixed reference frame for both environments, where sea level serves as the zero level for altitude and for estimating the underwater camera position during the UAV survey within the external reference frame. As introduced before, the external reference frame may be realized by the UAV GNSS positioning and/or by the GCPs positions. In this approach, a snorkeler equipped with a fixed underwater camera, mounted on the chest and oriented in radial direction, conducts the underwater photogrammetric survey. An easily identifiable target, aligned to the underwater camera, is placed on the snorkeler's back so to be clearly visible from the UAV. Thus, the snorkeler's position during the underwater photogrammetry survey, represented by the target center, can be determined with respect to the external reference frame. This requires consistent intersection between the snorkeler and the UAV paths, ensuring that the snorkeler is detected in multiple images during the UAV flight. Consequently, the snorkeler serves as a dynamic control point with respect to the UAV, while the UAV acquires the photogrammetric data and detects the snorkeler in multiple locations, so to connect emerged and submerged data (Figure 1). The UAV captured aerial images in parallel with the snorkeler, who began acquiring underwater videos. Both instruments were synchronized with a known starting time. At a specific moment, the UAV captured the snorkeler, while the snorkeler simultaneously recorded underwater features. By matching the timestamps, accurate for a level of fractions of a second, it was possible to associate each UAV frame with its corresponding underwater frame based on timing. Let \(t_{\mathit{UAV}}\) represent the timestamp when the UAV captures the snorkeler's position and \(t_{\mathit{UINV}}\) denote the timestamp when the snorkeler's camera records an underwater frame. The underwater video is captured at a known frame rate, \(\mathit{FPS}_{\mathit{UINV}}\), measured in frames per second. The corresponding underwater frame at time \(t_{\mathit{UAV}}\) is calculated by Equation (1):  
\[\mathrm{Frame}_{\mathit{UINV}}+1\ =(t_{\mathit{UAV}}-t_{\mathit{start}})\cdot \mathit{FPS}_{\mathit{UINV}} \tag{1}\]  
where \(t_{\mathit{start}}\) is the start time of the underwater video. For example, if the UAV captures the snorkeler at 11:02:00 AM, and the underwater video begins at 11:00:00 AM with a frame extraction rate of 2 frames per second, the corresponding underwater frame can be determined considering that 240 frames would have been recorded by the underwater camera (2 min \(\times\) 2 frames/second = 240 frames) when the snorkeler is captured by the UAV (at 11:02:00 AM). Thus, the frame captured at 11:02:00 AM by the UAV corresponds to the239 th frame of the underwater video as the naming starts from zero. After identifying the UAV frame corresponding to the underwater frame, the corresponding frames positions can be determined.