Drone-Derived Nearshore Bathymetry: A Comparison of Spectral and Video-Based Inversions

Highlights

What are the main findings?

• Wave signal tracking using drone-captured video achieves suitable bathymetry estimation.
• Field comparisons show wave tracking performs better than spectral depth inversions under specific conditions.

What is the implication of the main finding?

• Wave signal tracking for depth inversions extends opportunities in nearshore regions where optical spectral methods may struggle such as in turbid waters.
• Results support drone use as a suitable method for collecting coastal monitoring data.

Abstract

Accurate nearshore bathymetry is an essential dataset for coastal modelling and coastal hazard management, but traditional surveys are expensive and dangerous to conduct in energetic surf zones. Remotely piloted aircraft (RPA) offer a flexible way to collect high spatial and temporal resolution bathymetric data. This study applies deliberately simple workflows with accessible instrumentation to compare video-based and spectral inversion techniques at two contrasting coastal settings: an exposed open beach with relative higher wave energy and turbidity, and a sheltered embayed beach with lower energy conditions. The video-based (UBathy) approach achieved lower errors (0.22–0.41 m RMSE) than the spectral approach (Stumpf) (0.30–0.71 m RMSE), confirming its strength in semi-turbid, low- to moderate-energy settings. Stumpf’s accuracy matched prior findings (~0.5 m errors in clear water) but declined with depth. Areas with sun glint areas and breaking waves are challenging but UBathy performed better in mixed wave conditions. While these errors are higher than traditional hydrographic surveys, they fall within expected RPA-derived ranges presenting opportunities for use in specific coastal management applications. Future improvements may come from reducing reliance on ground control and advancing deep learning-based hybrid methods to filter outliers and improve prediction accuracy on sub-optimal imagery caused by environmental conditions.

1. Introduction

1.1. Background and Motivation

Coastal areas are highly complex and dynamic regions that represent significant socio-economic services, such as tourism and fisheries, as well as socio-cultural values like heritage sites and recreational spaces, protection from coastal hazards, and ecological values including biodiversity and habitat preservation [1,2,3]. Effective coastal management relies on understanding the morphodynamic processes of coastal zones, namely the mutual interactions between coastal landforms and waves/currents through sediment transport [4], that continually reshape the coastline at appropriate temporal and spatial scales. High-quality topo-bathymetric datasets are essential for modelling solutions to better understand inherently dynamic systems under the impacts of increased human activity, such as coastal development and pollution, and a changing climate, including rising sea levels and changing patterns of extreme weather and tsunami events [5,6]. Collecting frequent and accurate data, particularly in high energy coastal zones, is challenging, expensive and often dangerous [7].

Recent advances in data-assimilation frameworks for shoreline prediction have shown promise by combining physical principles with empirical data to improve predictive capacity. Coastal process models remain essential for simulating sediment budgets and nearshore transport, with approaches ranging from nested compartments to recognition of leaky boundaries and storm-driven transfers into deeper sinks [8,9,10,11,12,13]. These models rely on bathymetric data of appropriate temporal and spatial resolution, which form the bottom boundary for simulating wave behaviour and sediment transport. When forcing and boundary conditions are well defined, predictive performance improves [14,15]. Recent literature highlights an expansion beyond traditional process-based methods: Warrick and Buscombe [15] emphasise the need for robust, reproducible shoreline change techniques, Mao and Coco [16] assess diverse prediction models over multi-decadal scales, and Simmons and Splinter [16] show that data-driven approaches can capture variability from daily to annual timescales. Collectively, these studies underscore that whether process-based or data-driven, the success of shoreline models ultimately depends on the quality of bathymetric and shoreline boundary conditions.

1.2. Remotely Piloted Aircraft in Coastal Monitoring

In recent years, remotely piloted aircraft (RPA), also known as Uncrewed Aerial Vehicles (UAVs) or drones, have emerged as highly flexible and accessible tools for collecting coastal datasets. RPAs are particularly useful in areas that are difficult to access or not suited for fixed infrastructure [17,18] or where satellite resolution does not provide sufficient detail. RPAs are widely recognised as low-cost, rapidly deployable tools for coastal monitoring [19,20]. Consumer-grade RPAs with survey-grade positioning and multispectral payloads are relatively affordable, with the widely used DJI Mavic 3 RTK priced at approximately AUD $3500 and the Mavic 3 Multispectral at around AUD $7000. At altitudes < 100 m, these systems can achieve a ground sampling distance of 1–5 cm. By contrast, freely available satellite products such as Sentinel-2 (10 m) or Landsat-8/9 (30 m) provide decametre-scale resolution and are constrained by revisit times of 5–16 days, with paid alternatives available that enable higher resolution and improved revisit timing. While satellites provide valuable long-term consistency and regional coverage [19], they are limited by cloud cover which can obscure observations. RPAs by comparison, offer the flexibility to capture centimetre-scale resolution on-demand, such as pre- and post-storm profiles. However, RPAs are not without limitations, as operations are constrained by local weather conditions and airspace regulations that can restrict flights [21].

These advances have expanded coastal studies, enabling the monitoring of shoreline erosion, morphological analysis, nearshore bathymetric mapping, and ecosystem research at appropriate spatial and temporal scales [18,22,23]. RPA imagery has been successfully employed in various coastal environments globally, demonstrating flexibility and effectiveness, particularly in dynamic surf zones and shallow waters that present significant logistical challenges for conventional surveying methods [19,20]. Furthermore, advanced computer vision and machine learning techniques, such as structure-from-motion (SfM) and deep learning, have significantly extended the applicability of RPA-derived data to broader coastal monitoring tasks, including habitat mapping, sediment budget analyses, and rapid post-event assessments [22,24,25,26]. More recent approaches build on traditional SfM and spectral data, applying machine learning to correct systematic biases and infer depth where other algorithms may struggle [27,28], representing a shift toward hybrid data-driven bathymetry techniques that reduces dependence on in-situ training data.

1.3. Aims

In many coastal settings, turbidity or turbulence in the surf zone obscures the bottom visuals, making it challenging to use remote capture techniques employed for bathymetric inversions. While numerous iterations have been made to improve spectral inversions, enhancing their performance particularly in areas characterised by varying bottom types and turbidity [18,25,29], their applicability remains constrained under more energetic or turbid conditions. Conversely, video-based methods relying on the linear wave dispersion relationship, using observed wave properties to estimate depth, and are therefore not limited by optical water clarity.

This study aims to evaluate the use of RPA-derived imagery for nearshore bathymetry estimation through two approaches: a video-based inversion (UBathy [2]) and an empirical spectral inversion (Stumpf ratio [30]). To further leverage the capabilities of RPA-derived bathymetry, we compare two locations with varying wave conditions. Our approach emphasises simple post-processing to ensure convenience and reuse, relying on accessible tools and practical workflows suitable for a wide range of coastal managers.

2. Review of Bathymetry Inversion Approaches

Approaches to creating bathymetric data are complex, as the distinction between collection platforms and post-processing methods is often unclear. A platform for collection may support several processing techniques, while an alternative platform may generate data required for different analytical pathways or meet the dataset’s specific requirements. This overlap can create confusion when comparing methods, particularly as direct survey measurements and indirect estimation approaches are frequently discussed together in the literature.

In-situ bathymetry collection methods have evolved from lead-line sounding [31,32] to acoustic methods, including single-beam, multi-beam, and side-scan sonar technologies [33]. While in-situ, vessel-based, and acoustic-based approaches are well accepted for seafloor surveys with data error in the order of 0.1 m or less, they suffer from temporal frequency and geographical sparsity [34]. Typically, surveys are conducted within limited time frames that are dictated by financial constraints or a response to an immediate need within the area. This results in limited information about seasonal variations or extreme weather events [1]. Additionally, traditional approaches are subject to limitations in the nearshore region, where wave energy poses challenges to safety and data quality.

Remotely operated watercraft and bottom crawlers minimise the risk to personnel by allowing the use of acoustic sonar technology without direct human exposure, particularly in nearshore regions. However, these watercrafts are limited in their ability to cover large spatial scales, especially when compared to personal watercraft or larger marine vessels [35]. Additionally, their use is restricted in breaking wave conditions, which can further limit their applicability in dynamic nearshore environments. In place of remotely operated watercraft, round-crawling vehicles are suitable, particularly in challenging conditions such as shallow water, high wave energy, and turbid environments [9]. However, these devices are resource-intensive over large spatial scales.

Given the diversity of approaches, classifying the broad families of bathymetry retrieval is a helpful way to situate both traditional and emerging methods. While accuracy is the focus of several research topics, the appropriate technique is closely dependent on site conditions, cost, and operational feasibility. Table 1 Summarises the prominent families of nearshore bathymetry retrieval methods and their underlying principles, providing context for the approaches compared in this study.

Table 1. Nearshore bathymetry retrieval families and core principles. (Source: adapted from [36,37], with additional nearshore-specific RPA/video-based approaches).

Family	Method/Sub-Type	Platform/Tool	Principle
Traditional physical/field based	Lead line	Vessel	Manual depth sounding with a weighted line
	Single-beam/multi-beam echo sounder	Vessel/RPA	Acoustic travel time, single or multiple beams
Active remote sensing	Airborne bathy LiDAR [38]	Aircraft/RPA	Laser penetration through the water column
	Radar altimetry	Satellite	Radar pulse travel time
	Microwave/SAR (spacebourne)	Coastal station/Vessel	Image backscatter, surface roughness, and wave fronts
Spectral-derived optical	Physics-based—Radiative Transfer Models [39,40]	Satellite/RPA	Light/water interactions using radiative transfer equations
	Empirical log-ratio [30]	Satellite/RPA	Log-linear ratio against in-situ depth
	Semi-empirical [41,42]	Satellite/RPA	Depth-invariant transform with regression
Wave-based/computer vision	Wave speed from video [8]	Fixed camera	Wave phase speed inversion via linear wave theory
	cBathy [43]	Fixed camera/RPA	Wave celerity tracking—PCA and filtering
	UBathy [44,45]	Fixed camera/RPA	Wave feature tracking—EOF/DMD wave decomposition
Machine learning/computer vision/hybrid	Neural network [46]	Satellite	Predicts depth from multispectral image features using machine learning
	SfM—spectral hybrid frameworks [27,28]	Satellite/RPA	Fuses SfM-MVS DSMs with multispectral imagery, correcting refraction and filling gaps
	Transformer deep learning architecture [47]	Satellite	Uses transformer architecture with high-resolution multispectral imagery for data-driven depth retrieval

Passive optical methods, such as satellite-derived bathymetry (SDB), are widely acknowledged as a cost-effective means of generating bathymetric data in shallow waters, typically to depths of 20–30 m [48]. Categorising the various optical approaches is challenging due to the numerous methods available; however, they can generally be split into two main domains. First: physics-based approaches, semi-empirical or analytical, such as the radiative transfer model [39,40,49,50]. Physics-based approaches have gained popularity because depth can be derived without actual field measurements [48,51]; however, these models require high-quality images and an intricate calibration procedure [37]. Consequently, this paper concentrates on the second domain: statistical approaches using empirical methods.

Empirical optical methods for bathymetric inversions were initially introduced by [41,42], who developed a basic linear model relating multispectral reflectance directly to water depth. This model was later developed by Stumpf, Holderied [30] using the classical linear ratio model (CLRM), which relies on a logarithmic relationship between multispectral reflectance ratios and measured depths. This method reduces sensitivity to variability in bottom type and illumination conditions. These methods are computationally efficient, require fewer input parameters, and are easier to implement operationally; however, they depend heavily on calibration against ground truth data [51,52]. Perhaps due to simplicity, empirical methods are susceptible to degradation under conditions of high turbidity, bottom reflectance variability, and dynamic surface conditions [29]. While airborne LiDAR is also an option for highly accurate bathymetry in shallow coastal waters, it involves higher operational costs and specialised processing requirements that limit its use by local coastal managers and are not explored in this paper [38,53]. More recently, the ICESat-2 ATL24 product has introduced the first global spaceborne bathymetric LiDAR dataset, demonstrating a promising capability for nearshore mapping, although accuracy remains variable across different environments [38].

Empirical methods, synonymous with SDB, are widely acknowledged as effective for generating depths in shallow, optically clear waters. The increase in popularity has led to several methods that improve empirical methods under different environmental conditions. Numerous researchers have sought to review and clarify the complexities across various SDB techniques [36,51,52,54,55]. Two prominent themes consistently emerge from empirical methods: first, empirical inversion methods exhibit substantial sensitivity to turbidity and other surface-related interferences such as breaking waves; second, maximising inversion accuracy typically involves highly technical workflows with advanced radiometric corrections and environmental parameterisation [25,56,57,58]. Consequently, empirical optical methods tend to degrade significantly under conditions of high turbidity, bottom reflectance variability, or dynamic surface disturbances, limiting their suitability in surf-zone environments or where wave-induced sediment resuspension is common [58].

In response to the challenges faced by remote sensing inversions, surface-based observations can leverage the dynamic nature of the nearshore environment to deliver depth estimates where spectral methods may demonstrate reduced performance [43]. The advancement of image-capturing systems has facilitated the rise of video-based coastal monitoring systems [23], recognised as powerful, cost-effective tools with diverse applications, including shoreline tracking and socio-cultural studies, such as beach visitation patterns [3]. Holman, Plant [43] introduced a foundational approach whereby the pixel intensity of an image on the sea surface is incorporated into a time series from video recordings to derive wave period and wavenumber using the cBathy toolbox [43]. This method captures the cross-shore wave gradient and leverages the dispersion relationship from linear wave theory to estimate water depth [43] using Cross Spectral Matrices (CSM) applied to an Empirical Orthogonal Function (EOF). Video-based inversions with cBathy, and the later released guiBathy [59], have gained popularity for depth inversion in several studies, where initial approaches proposed by Holman, Plant [43] have been evaluated and enhanced [23,49,60,61,62].

More recently, the UBathy and UBathy 2.0 algorithms [2,45] have emerged as flexible tools for estimating nearshore bathymetry from optical imagery. UBathy 2.0 is a Python toolbox designed to be deployed as an out-of-the-box solution, accommodating a range of input types, including fixed coastal cameras and RPA video, with workflows that support combined datasets at different time scales. UBathy extends the approach of cBathy through an alternative approach to image preparation and wave signal processing. For wave decomposition in UBathy, either EOF or Dynamic Mode Decomposition (DMD) can be used. The latter enables improved isolation of wave modes and temporal variations, which is further explained in Section 3.3.

3. Materials and Methods

3.1. Study Site

Two coastal sites on the Sunshine Coast, Queensland, Australia were selected to assess the effectiveness of bathymetric inversion methods (Figure 1). The sites are exposed to waves and wind, with the water generally classed as semi-turbid. Turbidity refers to the reduction in water clarity caused by suspended sediments, organic matter, and other particles that scatter and absorb light, often quantified using Secchi depth. Government issued water quality objectives for open waters at the study sites report Secchi depth percentiles of 5.0 m (20th), 6.0 m (50th), and 10.0 m (80th) [63], indicating generally good clarity under calm conditions but variability with weather and runoff. Between the two sites, Noosa Main Beach is comparatively more sheltered, whereas Burgess Creek typically exhibits higher turbidity due to the exposure to the open coast and neighbouring creek system (Table 2).

Figure 1. Study area context showing the two sites, Noosa Main Beach and Burgess Creek (a). Location of the Mooloolaba waverider buoy with study area context outlined in red (b). Wave rose from the Mooloolaba buoy for the period 2000–2024, derived from publicly available data from the Queensland Government wave monitoring network (c).

Table 2. Summary of key site characteristics for Noosa Main Beach and the open coast. (Source: adapted from [64]).

Parameter	Noosa Main Beach	Burgess Creek
Orientation	North-facing, headland-protected embayment	East-facing, open coast
Wave exposure	Low-energy, highly refracted east–northeast swell	Low–high energy, direct exposure to ENE–SE swell
Dominant wave direction	Oblique ENE swell wrapping around Noosa Headland	ENE–SE swell, occasional northerly swell in spring/summer
Morphodynamic state	Intermediate classification, generally exhibiting a longshore bar trough. Stable to erosional depending on nourishment regime; influenced by groynes and structures.	Intermediate classification generally fluctuates between a low tide terrace and rhythmic longshore bar trough. Dynamic and seasonally variable; rapid erosion is possible during high-energy events. The area features a highly variable dry beach profile and bar trough system, influenced by the creek and moderate wave conditions.

3.2. Data Acquisition

Two DJI platforms were employed to capture RPA imagery, with each selected to meet the requirements of its respective inversion method (Table 3). A Phantom 4 RTK (Real Time Kinematic) was used for video-based inversion because it features a high-resolution sensor and RTK module to capture video that supports accurate feature tracking, which is critical for drone image stabilisation [44]. For these methods, stable and well-referenced imagery was essential for extracting wave characteristics [23]. A Phantom 4 Multispectral RTK was used for the spectral inversion method, as its discrete, and narrow, spectral bands enable the application of band-ratio algorithms that exploit wavelength-dependent light attenuation to estimate depth. The multispectral sun sensor, however, was sensitive to factors such as cloud cover, surface waves, and sun glint [65], although we sought to mitigate these effects by conducting flights under (near-)optimal conditions as recommended by Joyce et al. [66].

Table 3. RPA platforms used for data collection.

Platform	Sensor	Mode	Flight Altitude
DJI Phantom 4 RTK (P4)	1″ CMOS, 20 MP RGB	4 K (3840 × 2160, 30 p) video	50 m
DJI Phantom 4 Multispectral RTK (P4MS)	6 sensors: Blue (B) 450 nm ± 16 nm; Green (G) 560 nm ± 16 nm; Red (R) 650 nm ± 16 nm; Red Edge (RE) 730 nm ± 16 nm; Near-Infrared (NIR) 840 nm ± 26 nm; integrated RGB sensor	Still imagery, 80/80% overlap front/side	90 m (GSD 5 cm)

For each location, both platforms were flown in sequence under the same external flight conditions, ensuring that differences in model output reflect the inversion method rather than environmental variability. The P4 hovered at a static location and the P4MS followed a single “lawn-mower” grid pattern as outlined in Figure 2. For the video-based inversion, a minimum of six ground control points (GCPs) were established and, following suitable practice for camera calibration, distributed across the model frame rather than concentrated to one side, as broad spatial coverage of GCPs has been shown more important than their number for minimising distortion [44]. The GCPs were surveyed using an Emlid Reach RS3 RTK-GNSS (Global Navigation Satellite System) rover setup, which utilised NTRIP corrections from HxGN SmartNet and have a nominal precision of 10 mm horizontal and 20 mm vertical. Horizontal datum was referenced to GDA94—MGA 56 and vertical datum to AUSGeoid09. This approach was complemented by horizon tracking, which is discussed further in Section 3.3. Flights were conducted in clear weather with low winds, and tidal levels were recorded at the nearest tide gauge Table 4. The locations of both survey sites and their corresponding GCP distributions, along with the indicative capture footprint, are outlined in Figure 2.

Figure 2. Flight plan overview for data collection. Burgess Creek (a) and Noosa Main Beach (b).

Table 4. Environmental conditions.

Site	Date	Tidal Level (mLAT)	Estimated Breaking Wave Height (m)/Period (s)	Wind Speed (kts)/Peak Direction
Burgess	22 April 2025	1.1	1.0/11	20 SSW
Noosa	28 April 2025	0.6	0.6/9	31 SE

3.3. Data-Analysis

3.3.1. Video-Based Bathymetry Inversion

The UBathy toolkit [44,45] was selected for this study because it offers an open-source Python workflow with tools to resolve intrinsic and extrinsic camera parameters from drone imagery, making the workflow straightforward and incorporating features that are expected to improve alternative approaches. UBathy is based on analysing pixel intensity variations from video keyframes to estimate water depth, using principles derived from linear wave theory. In general, the wave period (T) describes the temporal spacing of waves, while the wavenumber (k) characterises their spatial frequency; these are linked through the linear dispersion relation:

$${\omega }^2\mathrm{ }=\mathrm{ }gk\mathrm{ }\tanh \left(kh\right)$$

where $\omega = {\displaystyle \frac{2\pi }{T}}$ is the angular frequency, g is gravitational acceleration, and h is water depth.

UBathy builds upon this by extracting coherent wave frequency ($\omega$) and wavenumber (k) from each stabilised video keyframe and then directly rearranges the dispersion relation to solve for the local depth (h) as:

$$h\mathrm{ }=\mathrm{ }{\displaystyle \frac{1}{k}}\mathrm{atanh}\left(\gamma \right),\mathrm{ }where\mathrm{ }\gamma \mathrm{ }=\mathrm{ }{\displaystyle \frac{{\omega }^2}{gk}}$$

with $\gamma$ representing a normalised wave frequency term. Full details of the UBathy methodology, including calibration and mode decomposition, are provided by Simarro and Calvete [45].

The UBathy 2.0 Python toolbox [45] was used to estimate depth from georeferenced plan-views. The uBathy v2.0 software and supporting tools (UDrone, UClick) are open-source and available at https://github.com/Ulises-ICM-UPC/UBathy (accessed on 2 November 2025). All processing followed the published workflow [45].

Videos were split at a two frames per second sampling rate in the UDrone toolkit. Select frames were used to perform camera intrinsic and extrinsic calibration using a combination of GCPs and the horizon line. UDrone resolves both intrinsic (lens distortion, focal length) and extrinsic (orientation, position) camera parameters to construct a complete calibration model. This enables the transformation of oblique imagery to georeferenced plan views as an input for UBathy.

The UBathy v2.0 system comprises three stages for generating video-based bathymetric data. The initial phase involves configuring the analysis mesh parameters by specifying the spatial boundary and resolution. The second phase focuses on mode decomposition, which can be performed using either Empirical Orthogonal Functions (EOF) or Dynamic Mode Decomposition (DMD); in this case, DMD was utilised. DMD is generally acknowledged to enhance the accuracy of wave period extraction in environments with noise or mixed wave conditions, albeit at an increased computational cost. This stage required setting parameters such as the time step, temporal window lengths, wave period bounds, and the number of decomposition iterations. Wavenumber fields are computed by fitting planes to the spatial phase of wave modes within a defined search radius, incorporating iterative refinement to optimise performance. Finally, bathymetry was estimated by combining the extracted wavenumber and wave period fields using the linear wave dispersion relationship.

3.3.2. Spectral Inversion

The Stumpf method [30] was used for spectral inversion, as it provides a simple processing approach that is widely understood and frequently applied in the literature [25,29,36,52,67]. After collection, individual images were calibrated using the internal sun sensor. Image processing was completed in Agisoft Metashape 2.2, including alignment, cleaning, and optimisation of images, generation of dense point cloud, and construction of an orthomosaic. Due to the lack of consistent texture and movement of the water, an orthomosaic was created by aligning images based on the internal RTK-GNSS coordinates and projected onto the AUSgeoid09 surface using an average blending mode. The orthomosaic included all five spectral bands, but only the blue, green, and red bands were used individually for subsequent analysis.

The Stumpf ratio was applied in two stages. The algorithm estimates depth based on the log ratio of two spectral bands, where D is the relative depth, R1 and R2 are reflectance values from the spectral bands, and m0 and m1 are site-specific calibration coefficients.

The Stumpf ratio method [30] estimates relative water depth by leveraging the differential attenuation of light in different spectral bands. The algorithm uses the logarithm of the ratio of reflectance values from two bands, scaled by empirical calibration coefficients. This relationship is given by:

$$D\mathrm{ }\mathrm{ }=\mathrm{ }m0\mathrm{ }+\mathrm{ }m1\mathrm{ }\cdot \mathrm{ }{\log }_{10}\left({\displaystyle \frac{R1}{R2}}\right)$$

where D represents the relative depth, R1 and R2 are reflectance values from two spectral bands, and m0 and m1 are site-specific coefficients calibrated against echo sounder measurements. The site-specific coefficients were acquired for two different band combinations, the blue/green and blue/red, at the known depth points across the area. The calibration coefficients for each band combination were obtained separately using the ground reference data, after which both models were used to generate a constant depth surface over the extent. Site-specific calibration values for the Stumpf ratio were m0 = 11.403 and m1 = −10.008 at Burgess, and m0 = −37.697 and m1 = 44.772 at Noosa.

Extreme values caused by sun reflectance or whitewater were masked using a threshold filter. A processing and analysis flow chart of both methods is presented in Figure 3.

Figure 3. Processing and analysis workflow 3.4. Ground Reference and Validation.

The ground reference was collected at each site using a single-beam CEE ECHO echosounder that was attached to a bespoke watercraft (Figure 4). The craft enabled shallow water surveys even when waves were present and was paired with the Emlid RX RTK-GNSS positioning with setup as per Section 3.2. Reference data were captured across the shore-normal profile to sample a range of depths, as outlined in Table 5. Raw bathymetry was processed using Eye4Softeware Hydromagic Survey 11.0. Raw soundings were manually edited using the echogram and filtered with a median filter. Soundings were referenced to AHD using the AUSGeoid09 model.

Figure 4. Bespoke surf-zone single-beam echosounder vessel.

Table 5. Number of ground reference sample points per location by depth bin.

Depth Bin (m)	n (Burgess)	n (Noosa)
−1 to −2	465	151
−2 to −3	648	105
−3 to −4	365	26
−4 to −5	114	10
Total	1592	292

The accuracy of the depth estimations was assessed using two standard statistical metrics. For a set of n paired depth observations, where n is the number of coincident estimated and reference depth points.

The Root Mean Square Error (RMSE) quantifies the average magnitude of the error between the estimate and reference depths.

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(z_{\mathrm{est},i}-z_{\mathrm{ref},i}\right)}^2}$$

Bias represents the mean signed difference, with positive values indicating overestimation of depth and negative values indicating underestimation of depth.

$$Bias={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left(z_{\mathrm{est},i}-z_{\mathrm{ref},i}\right)$$

Metrics were calculated in two ways: (i) a global RMSE and Bias, using all points across the survey domain, and (ii) depth-bin-wise RMSE and Bias, where points were grouped into discrete depth ranges. The number of points in each bin (n) for Burgess Creek and Noosa Main Beach is provided in Table 5.

4. Results

4.1. Overview of Bathymetric Model Performance

The estimated bathymetries are presented in Figure 5. The cross section supplied compares the estimated outputs with the echosounder reference data.

Figure 5. Comparison of nearshore bathymetry results at Noosa Main Beach (top) and Burgess Creek (bottom). Panels show (a,d) Stumpf estimation, (b,e) UBathy estimation, and (c,f) corresponding cross-shore profiles. In the profile plots: blue = Stumpf; orange = UBathy; black = echosounder.

The statistical performance of the UBathy and Stumpf methods was evaluated at both sites. Table 6 summarises the overall RMSE, bias, and coefficient of determination (R²). UBathy achieved lower RMSE and less bias at both locations compared to the Stumpf ratio approach. The lowest RMSE was produced at Noosa using UBathy (RMSE = 0.26 m, R² = 0.90), while the maximum error was at Burgess using Stumpf (RMSE = 0.55 m, R² = 0.59). The bias was marginal across all method/site combinations (<0.04 m); however, Burgess Stumpf showed a tendency to overestimate depth. At Burgess Creek, UBathy produced lower overall error (RMSE = 0.40 m, R² = 0.79, bias = −0.12 m) compared with Stumpf (RMSE = 0.55 m, R² = 0.58, bias = +0.03 m).

Table 6. Overall statistical performance of UBathy and Stumpf methods.

Site	Method	RMSE (m)	Bias	R2
Burgess	UBathy	0.40	−0.18	0.79
	Stumpf	0.55	0.03	0.58
Noosa	UBathy	0.26	0.02	0.90
	Stumpf	0.45	0.00	0.70

4.2. Model Accuracy and Bias by Depth

To investigate model sensitivity across depth ranges, RMSE and bias were calculated at discrete 1 m depth intervals ranging across the depth of the location between −1 and −5 m (Figure 6, Figure 7 and Figure 8).

Figure 6. Modelled versus ground reference depths for UBathy (blue circles, solid line) and Stumpf (orange crosses, dashed line) at Burgess Creek (a) and Noosa Main Beach (b).

Figure 7. Depth-dependent RMSE for UBathy and Stumpf methods at Burgess Creek (a) and Noosa Main Beach (b).

Figure 8. Depth-dependent bias for UBathy and Stumpf methods at Burgess Creek (a) and Noosa Main Beach (b).

Across depth bins, UBathy RMSE was lowest in the deepest range (0.26 m at −4 to −5 m) and highest at mid-depths (0.43 m at −3 to −4 m). Bias values remained close to zero (−0.09 to +0.13 m). By contrast, Stumpf errors increased steadily with depth, from 0.40 m in the −1 to −2 m bin to 0.94 m in the −4 to −5 m bin, accompanied by progressive positive bias (from +0.27 m to +0.63 m).

At Noosa Main Beach, UBathy again showed the lowest overall RMSE (0.26 m, R² = 0.90, bias = +0.02 m), outperforming Stumpf (RMSE = 0.44 m, R² = 0.69, bias = +0.002 m). Depth-binned results revealed minimal UBathy error in the −3 to −4 m bin (RMSE = 0.13 m) and slightly higher values in shallower bins (0.22–0.31 m). Bias was negligible across bins (−0.07 to +0.06 m). Stumpf RMSE was higher and more variable, ranging from 0.31 m (−2 to −3 m) to 0.77 m (−4 to −5 m). The bias remained small overall (+0.01 to +0.32 m), although it was consistently positive.

Overall, UBathy provided lower RMSE and more stable bias across depth ranges compared to the Stumpf ratio method. While both approaches demonstrated potential for nearshore bathymetry estimation from RPA imagery, absolute errors remained greater than those generally achieved with conventional hydrographic survey techniques.

5. Discussion

5.1. Prediction Performance

This study highlights the contrasting performance of wave-based inversion (UBathy) and log-linear spectral ratio (Stumpf) empirical approaches to RPA-derived nearshore bathymetry. Our results indicate that for semi-turbid waters, UBathy performed best under both low- and moderate-energy wave conditions. Errors (~0.22–0.41 m RMSE) were consistent with, or in some cases lower than, those reported in previous applications of cBathy and RPA-derived UBathy [43,44,56]. These findings support wave-tracking inversions for robust results in low-moderate wave climates while also suggesting improvements in the decomposition techniques in UBathy, contributing to enhanced performance compared to cBathy.

By contrast, the Stumpf method showed higher errors (~0.30–0.71 m RMSE), with accuracy decreasing at greater depths, consistent with its sensitivity to light attenuation, water clarity, and substrate heterogeneity [47,68]. Our implementation was intentionally simplified, without advanced filtering, atmospheric correction or compositing, and ultimately relied upon the onboard sun sensor for spectral calibration, which may have limited performance under variable illuminations. Even so, the error patterns aligned with those reported in the literature, where spectral inversions perform well in clear, calm, and optically shallow waters such as reef lagoons and sandy bays [30,47,67,68]. In these settings, an accuracy of ~0.5 m is typical, underscoring that the method is best suited for clear water and low-energy environments.

Both approaches together indicate district strengths. These comparisons suggest that spectral approaches are more appropriate for clear, low-energy coasts [65], while video-based inversions suggest better reliability in turbid or energetic environments [23]. Both methods, however, face unique challenges in the shallow surf zone.

In shallow waters (<40 m), the International Hydrographic Organisation (IHO) specifies standards for surveys that can be simplified to a requirement of ±0.25 m for Special Order surveys. Although these errors are substantially larger than those typically reported for hydrographic survey methods (e.g., acoustic systems often achieve an accuracy of ~0.1 m), they fall within the range commonly observed in optical and video-derived bathymetry studies.

5.2. Morphological Influences

Both study sites exhibited a bar trough morphology, with the −2 to −3 m depth range corresponding to the trough zone. Within this range, UBathy returned notably different levels of accuracy, with Burgess recording an RMSE of 0.30 m compared to 0.13 m at Noosa. This contrast likely reflects geomorphic and hydrodynamic differences between the two sites. At Burgess, the presence of a double bar system caused wave breaking at the offshore bar, disrupting coherent wave tracking and limiting UBathy’s reliance on linear wave motion. Brodie, Palmsten [56] demonstrated that when the significant wave height exceeded 1.2 m, cBathy overestimated depths by up to 2 m, with RMSE values exceeding 3 m. Holman and Bergsma [61] further refined this threshold, noting the difficulty of applying dispersion-based approaches in highly energetic bar trough systems.

By comparison, Noosa’s gently sloping low tide terrace morphology supported more stable wave propagation, with the trough more likely shaped by the neighbouring groyne and associated rip channel rather than offshore breaking. These patterns suggest that bar trough morphology mediates inversion accuracy even within the same nominal depth range. Energetic bar systems amplify wave breaking and turbulence, reducing the reliability of wave-based inversions [56,61]. In calmer, dissipative settings, wave signals are more coherent and therefore more favourable for accurate inversion [8,44]. This finding demonstrates that inversion suitability cannot be assessed solely by depth and must account for the morphodynamic context in which waves propagate.

5.3. Limitations of Research in Energetic Zones

The limitations of spectral inversion methods are underexplained in the literature in energetic nearshore environments. Several studies have explored empirical bathymetric approaches, specifically satellite derived approaches, due to freely available imagery over large spatial and temporal extents. This includes our approach using log-linear inversion [30], which examines the challenges of bottom type heterogeneity, water column turbidity, and atmospheric corrections for satellite capture techniques [36,58]. However, few studies have explored the topic of directly examining performance in moderate-to-high-wave energy settings, with capture by RPA at high resolution, an area that is even less understood; this may reflect an underlying assumption that remote sensing approaches are best suited to optically stable, low-dynamic zones, including lagoons, estuaries, or reef systems. As such, the benchmark to apply to our findings is limited due to the challenges experienced in determining bathymetry in the surf zone [25,52,69].

Our results reinforce the challenges of the spectral approach. Spectral inversion produced acceptable results at Noosa, where the water was calmer and less turbid compared to Burgess, which exhibited degradation of accuracy likely due to wave breaking activity and a higher potential for suspended sediments, introducing error. The use of RPA may also have limited vertical accuracy due to the limited temporal resolutions available with satellite-derived datasets. Whitewater, glint, or foams nearshore are all factors that may interfere with the empirical model developments. The higher wave energy at Burgess stresses the Stumpf inversion under more realistic open-coast conditions, where nearshore bathymetry is particularly difficult to capture. The results demonstrate that empirical methods, such as the log-linear ratio, experience challenges without additional filtering or multi-temporal compositions to perform effectively.

The wave-based inversions with UBathy, similarly to cBathy, do not succumb to the same challenges of turbidity, as the estimations are achieved by extracting wave period and wave number values from pixel intensity changes and applying the linear dispersion relationships. However, the approach relies on coherent wave motion, which is impacted when wave energy leads to shoaling, steepening and breaking of waves. This process introduces turbulence, surface foam, and glint, which impact spectral methods, but also violate the assumptions of linear wave theory that UBathy relies upon. Indeed, synthetic evaluations using Boussinesq wave models have demonstrated that wave-tracking inversions can incorrectly estimate depth when nonlinear shoaling and breaking alter phase speeds [19]. Breaking waves exhibit reduced phase speeds and distorted wave estimates, leading to an overestimation of water depth [8,56].

5.4. Future Directions

The modular design of UBathy, combined with clear documentation, makes it particularly attractive for coastal researchers and practitioners seeking a repeatable and scalable workflow that requires minimal customisation. Crucially, UBathy is well-suited to the challenges of RPA-derived datasets, including dynamic camera motion, varied viewpoints, and shorter-duration time series. However, the most resource-intensive step remains the establishment of ground control, which is essential for stabilising and georeferencing the RPA video. Future developments should therefore aim to minimise these requirements, for example by incorporating SfM techniques to resolve camera position and orientation, or by further exploitation of stable environmental features.

For spectral inversions, their strength remains in clear, low-energy waters, but improvements may come from multi-temporal compositing, filtering, or coupling with deep learning approaches. Recent works by Lv, Gao [47] demonstrate alternatives to band-ratio methods in clear water settings, reducing reliance on empirical calibration and enabling scalable mapping. Hybrid SfM-spectral frameworks with refraction correction [27,28] and the continued development of green LiDAR also highlight the growing sophistication of optical approaches. By contrast, in energetic or turbid settings, video-based inversions may remain as more viable options.