Geometric characterization of cylinders overgrown by marine biofouling

Abstract

Marine growth on cylindrical structures alters their hydraulic roughness and thus affects load predictions, such that parameters beyond the traditional ratio must also be taken into account when analyzing the loads and hydrodynamics around these structures. However, for cylinders overgrown by marine biofouling, usually composed of hard and soft biofouling communities, little information exists on the relevant additional geometric roughness parameters. Thus, a method is proposed to retrieve flat-surface geometric roughness parameters from an overgrown cylinder using structure-from-motion (SfM) photogrammetry. Eleven cylinders, exposed to the marine environment at two locations in the Jade Bight, Germany, for up to 29 months are characterized by root-mean-square height, skewness, kurtosis, mean of maximum peak-to-valley height, surface coverage ratio, probability density, autocorrelation, and power spectral density; these data exhibit a comprehensive and novel characterization of the geometric surface roughness of cylinders overgrown by marine biofouling to date. Cylinders located further offshore were overgrown by a higher percentage of hard biofouling and a larger roughness height than the cylinders closer to the shoreline. The cylinders are classified to be overgrown by medium to very large roughness, with ranging from 0.085 to 0.613. The probability density function and the power spectral density of the measurements can be combined for artificial surface generation to conclude upon hydraulic roughness in future research.

1 Introduction

To mitigate greenhouse gas emissions for climate protection, an expanded exploitation of renewable and sustainable energy sources is needed (Sims, 2004). Offshore wind turbines, with its abundant wind resources and the possibility of installing high capacity systems, play a particularly important role in shifting to carbon-neutral energy supplies (Hau, 2013). Support structures of offshore wind turbines commonly consist of slender cylindrical piles submerged in the water, such as monopiles or jacket foundations for shallower water depths, but also floating offshore wind turbines often consist of piles partially submerged in the water, such as spar-buoy type floating systems (Guo et al., 2022).

Offshore structures founded on cylindrical piles are subject to marine biofouling (Apolinario and Coutinho, 2009). This increases the cylinder surface roughness and affects the hydrodynamic load regime on the cylinders (Maduka et al., 2023). Increased loads on support structures of an offshore wind turbine decrease their lifespan, through more severe fatigue and (bio-)corrosion (Ziegler and Muskulus, 2016; Martinez-Luengo et al., 2017).

The calculation of forces on (slender) cylindrical pile structures has been studied for decades (Morison et al., 1953; Jusoh and Wolfram, 1996a; Marty et al., 2022) and these insights have been widely applied during guided design processes (DNV, 2021), using the Morison equation (Morison et al., 1950), either in linearized or non–linear form (Terro and Abdel-Rohman, 2007). Two forces act on a pile according to the Morison equation: first, the drag force which is influenced by the pressure on the pile and the surrounding friction force dependent on the projected area of the pile, and second, the inertia force which is dependent on the displaced water volume by the pile along with its rough surface. The drag and inertia forces are calculated using the associated load coefficients, namely, the drag and inertia coefficients, which are dependent on the Reynolds number, the Keulegan-Carpenter number, and the relative roughness of the pile (Morison et al., 1950; Chakrabarti, 2005; McCormick, 2009).

Apart from hydrodynamic parameters, these force coefficients also depend upon various geometric roughness parameters such as: skewness (Fuss, 2011; Zeinoddini et al., 2016; Zou et al., 2023a), number of species layers (Schoefs et al., 2022), roughness arrangement (Zou et al., 2023a), coverage ratio (Jadidi et al., 2018; Zou et al., 2023b), and probability density function (i.e., the Abbott-Firestone-Curve Landmann et al. (2019)). These studies proved the influence of geometric roughness parameters other than upon the load coefficients using mainly surrogate models. Some surrogate models consisted of very simple structures such as sandpaper (Henry et al., 2016), pyramids (Zeinoddini et al., 2016; Zou et al., 2023a; b) or artificial fur and carpet (Nedrebø, 2014; Rashki et al., 2022; Aalami Harandi et al., 2024; Krautwald et al., 2026). Other studies developed surrogate structures of higher complexity, such as cones for barnacle representation (Jadidi et al., 2018), 3D-printed mussel surrogates (Landmann et al., 2021; Marty et al., 2021b), and generic surfaces based on the probability density function of realistic biofouling (Landmann et al., 2019). Although an influence of the different geometric roughness parameters (other than ) has been proven by the use of these various surrogate models, a general understanding of the geometric roughness parameters of cylinders overgrown by realistic biofouling with a clear focus on load effects remains largely missing in the pertinent literature.

The process of determining the influence of geometric roughness parameters on the load coefficients should consist of two steps: First, the measurement of the geometric roughness parameters by methods of surface metrology (Hitzegrad et al., 2022); second, the measurement of loads upon the cylinders with varying geometric roughness parameters (determined in step one) using hydrodynamic methods, such as performing tests in a wave flume or computational fluid dynamics simulations (Zou et al., 2023a). On the path toward determining the influence of geometric roughness parameters on the load coefficients, the present research work adresses the first of these two steps: providing a novel methodology and experimental results of cylinders overgrown by marine biofouling using multiple describing geometric roughness parameters.

Section 2 provides an in-depth overview on definitions, and elaborates upon the need for determining the various geometric roughness parameters. Based on the findings in the literature, the specific research objectives of this paper are then presented. In Section 3, the specimen and the equipment are described. The methods Section 4 follows separately, defining the roughness parameters used and describing the data acquisition procedure. Section 5 displays the measurement results: first, the cylinder surfaces in general, then the individual roughness parameters, and lastly, measurement deviations due to the unfolding of the cylinder surface are considered. In Section 6, the results are discussed, and future research questions are identified. The conclusion in Section 7 summarizes the findings of this research, specifically the answers to the research objectives defined in Section 2.

2 Theoretical background

2.1 Biofouling community description

When considering biofouling, a distinction is usually made between hard and soft biofouling (Callow and Callow, 2002; Marty et al., 2022), each of which affects the hydrodynamic loading differently. Typical community species in hard biofouling structures are mussels. Understanding the roughness parameters of hard biofouling is of significant relevance, since, e.g., Mytilus edulis and Magallana gigas have been identified as dominant species on natural hard substrates in the North and Wadden sea (Krone et al., 2013; Markert, 2020; Hitzegrad et al., 2025). Nevertheless, the biofouling community composition is highly dependent upon its geographical location (Macleod et al., 2016), as well as the water depth in which the community grows (Jusoh and Wolfram, 1996a; Aalami Harandi et al., 2024).

Soft biofouling can be further classified into two categories: algae, such as green algae (Krone et al., 2013), and “soft” invertebrate animals, such as soft corals, sponges, anemones, tunicates, and hydroids (Callow and Callow, 2002; Halder et al., 2021). Soft biofouling tends to deflect to a greater extent than hard biofouling when subjected to hydrodynamic loads (e.g., tidal currents, oscillatory flows from surface gravity waves) (Baarholm and Skaugset, 2008; Krautwald et al., 2026). Typically, emphasis in literature is placed on hard marine fouling while the amount of knowledge, specific data and metrics pertaining to soft biofouling is particularly scarce.

Little can be stated about other soft biofouling of higher stiffness, such as soft corals or anemones, as the influence of hard and soft biofouling on hydrodynamic parameters still remains largely unexplored (Busch et al., 2024). Furthermore, the question remains to which extent each type of soft biofouling can be described by the use of geometric roughness parameters. In order to reduce measurement complexity, and because of the presumed higher stiffness, a geometric roughness characterization by the standard methods of surface metrology, as presented in Section 4, shall be deemed sufficient for this purpose.

2.2 Surrogate modelling and biofouling surface metrology

Marty et al. (2021b) and Landmann et al. (2021) used uniform arrangements of 3D-printed mussels for their tests on cables and ropes of relatively small diameter compared with the cylinder structures of monopiles or jacket foundations. Ropes and cables overgrown by blue mussels M. edulis were observed to grow in such a way that several clusters of mussels comprised multiple growth layers along the rope, alternating with other areas with single layers of mussels growth. This growing pattern was modeled by Marty et al. (2021b) using 3D-printed mussels attached to cylinder segments of varying diameter. In a follow-up study, Marty et al. (2022) compared this growing pattern with further types of structures, where measurements were taken on golf balls attached to a cylinder, representing coral reef structures. For both, the clustered mussel and the coral reef surrogates, it was found that is the main geometric roughness parameter to influence the force coefficients at high numbers, if defining as the original cylinder diameter before subject to biofouling. To further improve their surrogate modeling, Marty et al. (2021b) calls for millimeter accuracy of measurements in future research and good statistical approaches for a representative description of biofouling surface geometry.

Some data with millimeter accuracy of the surface geometry was already collected by Landmann et al. (2019), using laser scanning of a rope overgrown by M. edulis to extract the Abbott-Firestone-Curve of the material distribution. Based on this measurement, three surrogates were derived. The first surrogate consisted of 3D-printed mussels, where each printed mussel had the mean volume, length, and width values of the initially measured mussels. This, however, resulted in an Abbott-Firestone-Curve dissimilar to the original measurement. The other two surrogates attempted to create generic geometries with similar Abbott-Firestone-Curves. Tests on force coefficients (Landmann et al., 2021) of the surrogates were conducted and compared with tests of real mussels. The 3D-printed mussel surrogate showed the best fit with regard to the real mussel force coefficients, showing that characterizing the surface roughness solely by using the Abbott-Firestone-Curve is not sufficient to draw conclusions on the force coefficients of a cylinder overgrown by biofouling.

Warby et al. (2024) calls for more data on roughness parameters of cylinders overgrown with biofouling, while Marty et al. (2022) identifies the need for an extensive database on roughness parameters of different kinds with large values. This data can be gathered from digital surface models (DSM) derived from 3D terrestrial laser scans (Landmann et al., 2019) or structure-from-motion (SfM) photogrammetry. Jester and Klik (2005), Schoefs et al. (2021), and Hitzegrad et al. (2022) showed that SfM photogrammetry is a fast and easy-to-implement method to determine high-resolution DSMs of complex topographies. While SfM photogrammetry has already been applied in other fields of study, Schoefs et al. (2021) specifically proposed a scanning setup for cylindrical structures overgrown by mussels. Attaching two cameras on a pole and using the appropriate lighting, this scanning setup enabled rough objects to be scanned below and above the water surface. The authors stated that creating DSMs of roughness on cylinders would be a promising research direction. As to the author’s knowledge, extensive characterization of biofouling on cylinders has yet to be performed. Furthermore, a step-by-step methodology for retrieving flat surface roughness parameters such as the skewness from photogrammetry of piles overgrown by biofouling is not yet described.

Hitzegrad et al. (2022) and Hitzegrad et al. (2024) provide a comprehensive geometric roughness characterization of oyster reef and mussel bed surfaces using DSMs based on SfM photogrammetry. The authors classified several reef structures with distinct statistical roughness parameters derived from the surface level elevations of the DSMs, such as total roughness and root-mean-square (RMS) roughness height, skewness, kurtosis, individual oyster mean properties, probability density function, and a second-order structure function. Hereby, the authors applied a morphological filter to separate the species-related roughness from the underlying morphology. The question remains, to which extent these measurements can be applied to cylinders overgrown by biofouling, instead of flat reefs.

2.3 Research objectives

3 Materials

3.1 Specimen of biofouled cylinders

This study focuses on roughness characterization of test cylinders placed in the tidal channels of the Jade Bight, Germany (53°37′N 8°08′E, see Figure 1). Test cylinders with a length of 65 cm were suspended into the water column, using two pontoons, A and B, with a distance of about 1km–2 km to the shoreline. The locations differed in water depth and the amount of suspended substrate concentration, while salinity and water temperature were constant (see Table 1). Furthermore, location B is near the navigation channel and a report by the Lower Saxony Water Management, Coastal and Nature Protection Agency investigated the maximum flood and ebb velocities using a calibrated Telemac-3D model in the study area for average conditions between 28th of August 2018 to 13th of September 2018 (IMDC, 2023). Their results indicate significantly (66%) larger flood and ebb flow velocities of 1.2–1.3 ms⁻¹ for location B than for location A with 0.7–0.8 ms⁻¹. Each pontoon was equipped with three cylinders of 0.273 m and 0.102 m diameter, respectively. The cylinders were mounted to an open frame structure for fastening and shock reduction; the mounting structure was approximated from those specimen fasteners described in Isbert et al. (2023). A PVC-covered steel chain of approximately 1.5m length was used to hang the mounting structure into the water column. Thus, the cylinder was able to freely rotate around its vertical axis. The cylinders were permanently submerged at least 1.0m below the free surface, independent of the tidal range. All components except for the chain were manufactured from stainless steel (1.4571). To allow biofouling to populate the cylinders, these were submerged in the sea over a period from 28 to 29 months, from June 2022 to October and November 2024. Upon retrieval of the cylinders from the sea, they were mostly overgrown by Mytilus edulis, Asteroidea, Amphipod tubes, and Actiniaria. The cylinders were then transported in barrels filled with saltwater to the laboratory facilities at Leichtweiß-Institute for Hydraulic Engineering and Water Resources, Technische Universität Braunschweig, Germany. At the laboratory, the cylinders were stored for 2–4 days in a saltwater tank (Goseberg et al., 2025), which was continuously fed with conditioned saltwater (2.5% salinity, 12 °C water temperature, oxygen saturation between 90! to 110%, and a pH-range between 7.4 and 8.0) as well as nutrients (Nannochloropsis sp.). Storage was necessary, as the current research work had been part of an experimental campaign, and therefore the organisms have to be conditioned to the new ambient conditions (Goseberg et al., 2025). After that, photos of the cylinders were taken for photogrammetry at fresh air. At fresh air, the Actiniaria contracted but did not fall off, similar to the reports of Wolfram and Theophanatos (1985).

FIGURE 1

Four cylinder classes are defined, representing the pontoon location and the cylinder diameter, as it was expected that the diameter of the cylinder and the distance to the shore have a significant influence on the type of biofouling growth. Cylinders 1–3 (A27) and cylinders 7–9 (A10) visually appeared to be overgrown by similar ratios of hard and soft biofouling and show less coverage by mussels than the other cylinders. Cylinders 4–5 (B27) show a reduced amount of mussels and a higher amount of soft biofouling than cylinders 10–12 (B10). In the following, the individual cylinders are referenced by combining the cylinder class and the individual cylinder number. For instance, cylinder four is arranged into class B27, which indicates that the cylinder had a diameter of about 0.27 m and was located at location B, therefore, the cylinder will be called B27-4. Each class comprises three individual cylinders, except for class B27. For this class, cylinder B27-6 got lost due to heavy corrosion of one of the subcomponents and was not available for further analysis. See also Figure 2 and Table 2.

FIGURE 2

3.2 Photography and processing applications

A Sony Alpha 7C II camera was used for photography. The ISO was kept low and a constant focal length of 35 mm was used. All photos had a resolution of 24 Megapixels, saved to the JPEG format. Shadows that lay outside the color range were avoided. Sufficient overlap of more than 90% between the photographs was achieved for good alignment in photogrammetry. The high complexity of the biofouling requires the recording of numerous photographs at different angles. Photographs were taken from distances between 0.3 and 2 m. About 191–350 photos were taken per cylinder within less than 30 min to minimize the effect of air exposure on the biofouling. For calibration, identical L- and I-shaped reference bars were taken, as described by Hitzegrad et al. (2022).

Photogrammetry models were created using Agisoft Metashape Professional, Version 2.0.1 (Agisoft LLC, 2024). Further point cloud processing was performed using CloudCompare Version 2.6.3. Further processing was facilitated by Python 3.11 during the data analysis steps.

4 Methods

Three distinct topics are discussed in the methods section: First, the photogrammetry process and the point cloud processing used in this research is explained in Section 4.1. Then, a large portion is dedicated to helping the reader understand the roughness parameters used in Section 4.2. Lastly, a method for determining deviations due to the unfolding of the cylinder surface is proposed.

4.1 Photogrammetry and point cloud processing

This section describes the method used for retrieving surface roughness parameters of marine biofouling from photos using SfM photogrammetry (Szeliski, 2011), and an overview of the steps leading from the photos to the roughness parameters is shown in the process diagram 3. First, during the overall process, the cylinder is photographed, as described in Section 3.2. In the following, the photos are processed in Agisoft Metashape for point cloud generation and to clean up outliers, which is described in detail in Section 4.1.1). Then, the point cloud model is exported and transferred to CloudCompare where a deviation height map (Section 4.1.2) is created. The deviation height map refers to the height data .

4.1.1 Photogrammetric model generation

In this step, a dense point cloud is generated in Agisoft Metashape for further processing. First, the photographs were imported into Metashape. Only high-quality (Metashape quality value ) images were used. The camera was calibrated automatically in Metashape, and the pictures had sufficient overlap for calibration. In the next step, the photographs were aligned to each other to form a 3D point cloud. Multiple settings have been tested within this work. Alignment of photos in the case of cylinders overgrown by biofouling was achieved with at least 191 photos per cylinder. Upon alignment, a dense point cloud could be generated.

The next step was to delete undesired sections and outliers of the point cloud. These had to be selected manually due to the complexity of the model. The manual filtering, however, was performed according to a defined set of rules, and with consistency in manual data curators, as to reduce the bias from employing different persons. In the case of cylinders overgrown by biofouling, reasonable identification of outliers was achieved in orthographic view, positioning the cylinder as seen in Figure 3B. After removal of outliers in that position, the cylinder model was rotated in its axial direction by less than 15°, and outlier removal was repeated. The rotation and outlier removal steps were repeated until the cylinder had been rotated by a total of 180°. Points with a distance of more than 3 mm to their next neighbors were removed.

FIGURE 3

Second to last, the model was calibrated with the markers that were placed next to the cylinders during the recording of the photographs. The markers were automatically detected. In Metashape, three scale bars in three different directions are created, choosing two targets per direction. The scale bars were then filed with the physical distances of the points from each other. The calibration error averaged 0.0017 m 0.0049 mm (Agi, 2024). All models were individually quality checked by measuring point to point distances of the cylinder height and the diameter of the force transducer (Figure 3A) to confirm the right scaling of the specimen. It would have been beneficial to do multiple rounds of photogrammetry either by different persons, using different cameras or even perform underwater photogrammetry to avoid systematic errors. However, this was not possible due to the relevance of keeping the biofouling alive for the subsequent research phase on hydrodynamic loads. Finally, after finishing calibration, the model was exported for further use in CloudCompare. An example of the point cloud resulting from the previous steps is seen in Figure 3B.

4.1.2 Model processing and height map generation

A height map derived from previous processing steps depicts a flat two-dimensional map containing surface elevation values of the biofouled surface. The roughness parameters presented in Section 4.2 are usually defined for measurements of surface height deviations of a flat 2D plane. Since the considered specimen is a cylinder, a mathematical projection of the surface is generated by unfolding the surface of the cylinder. This may distort some height parameters, therefore potential distortion effects are considered in Section 4.3. The difference between the height points caused by biofouling and the original surface height of the cylinder creates the deviation height map and is described by . CloudCompare was used to develop deviation height maps.

In CloudCompare, the point cloud resulting from the photogrammetric model generation was imported. In order to create a deviation height map in CloudCompare, a generic cylinder was created, and the distances between the point cloud and the generic cylinder calculated. The generic cylinder represents the original cylinder before subjected to biofouling. The distance between point cloud and original cylinder then represents the additional height applied to the cylinder by biofouling.

In the following, the generic cylinder and the point cloud were aligned in such a way that the generic cylinder was positioned exactly where the original metal cylinder was positioned. Then, the shortest distance between each point of the point cloud and the generic cylinder surface was calculated. For this, CloudCompare offers the “Compute radial distances” tool. The radial distances, as well as the resulting two-dimensional deviation height map, are displayed in Figures 3C,D.

The grid resolution of the resulting deviation height maps of all cylinders is 0.5 mm in and direction, and a height resolution below 0.01 mm. The spatial resolution in and direction corresponds with the size of coarse sand. The investigated biofouling exceeds the resolution in dimension and should therefore be appropriate for geometric roughness characterization of the biofouling.

4.2 Roughness and its parametrization

“Roughness” can be used a collective term for the texture of a surface. This becomes evident with the fact that more than 40 different roughness parameters are defined throughout the literature (Gadelmawla et al., 2002; Czichos et al., 2011; Fuss, 2011; Thakkar et al., 2017; Zou et al., 2023a). Besides its importance in hydrodynamics, roughness is a large field of research in mechanical engineering - especially in the sub-fields of material characterization and tribology (Czichos et al., 2011), as well as aerodynamics (Chakroun et al., 2004; Fuss, 2011).

Due to the variety of research fields and roughness parameters, as well as the pivotal role of roughness in the present research, this section is dedicated to explaining the individual roughness parameters used. In Section 4.2.1, the commonly used relative roughness is examined, and ambiguities in the literature are outlined. Then, core parameters for providing new research insights are chosen in the following sections.

4.2.1 Relative roughness

The influence of geometric roughness on Morison force coefficients is typically only defined by the relative roughness . The roughness appears to be rather consistently defined throughout literature; however, not all definitions are documented without ambiguity. One of the most prominent definitions defines as the mean roughness height (Barltrop et al., 1990). However, the definition of remains vague in this source, with being called “mean roughness height” and defined only qualitatively, effectively representing the difference between peaks and troughs of a sinusoidal surface. This “mean roughness height” likely corresponds best to the mean of maximum peak to trough height as defined by Gadelmawla et al. (2002).

In comparison, the definition of a diameter varies throughout literature. Fuss (2011) used the diameter of a cylinder before being subject to biofouling, denoting it as . The more commonly used definition is the use of the total volume diameter , also called effective diameter (Barltrop et al., 1990; Jusoh and Wolfram, 1996b; Zeinoddini et al., 2016). This diameter definition increases the initial cylinder diameter by the thickness of the cylinder. Marty et al. (2022) investigated the difference between these diameter types. The authors found that the choice of can greatly affect the determination of force coefficients when measuring the force on cylinders for large values. At , the force coefficients did more than double when calculating them with the diameter of the cylinder before subject to biofouling instead of calculating them with the total volume diameter (Marty et al., 2022). In order to decouple the force coefficients from the diameter, Marty et al. (2022) proposes the use of the projected total volume diameter , as described below.

In order to separate the influence of the cylinder thickness due to biofouling from individual surface roughness parameters, most parameters in the following subsections require calibration by centering over the mean line. Centering over the mean line means that the elevation data of a surface measurement is offset in such a way that the average height of the profile equals zero (see Figure 5A). This results in Equations 1,2:andwhere the centered data is denoted with in the continuous form and for discrete measurements. The number of points of the measurement in - and -direction is denoted by and , respectively. The height data equals in the continuous form.

The centering of the data is necessary to ensure the comparability of multiple surfaces. For instance, two surfaces can have the same root-mean-square (RMS) height (see Section 4.2.3) when calculated by use of , while the RMS may differ when calculated based on .

The calculation of is representative of the added volume by biofouling. Thus, the offset value can be used for deriving the mass increase (when the biofouling mass density is known) and calculating the total volume diameter. The latter parameter shall be defined and calculated as given in Equation 3:

Figure 4 provides a visualization of the coordinate system and the roughness parameters. In Figure 4A, the cylinder coordinate system is defined. Furthermore, the cylinder diameter before subject to biofouling is depicted. In Figure 4B, the roughness height along an intersection of the pile is displayed. Here, , as well as further roughness parameters as discussed in Section 4.2.3 are visualized. Furthermore, Figure 4B shows the segmentation relevant for the calculation of (see also Section 4.2.3). In Figure 4C, typical skewness surface shapes and their accompanying value ranges are displayed.

FIGURE 4

Given the influence of the diameter definition, both definitions and shall be used in the following.

4.2.2 Relationship between cylinders and flat surface geometric roughness

Geometric roughness is a central characterization element of this research. The most suitable roughness parameters for characterization of piles overgrown by marine biofouling within this context are identified and described in Section 4.2.3 through Section 4.2.6.

Geometrical surface roughness parameters describe the surface roughness solely by its geometry. They can be classified into two types: flat surface parameters, and surface parameters in cylindrical coordinates. Geometrical surface roughness parameters on flat surfaces have been studied for decades and are widely applied, with many being standardized (Leach, 2010), especially in materials science. Surface parameters originating from materials sciences typically assume the surface to be of flat shape, yet these parameters have also been used for the characterization of the rough surface of cylinders (Fuss, 2011; Jadidi et al., 2018; Zou et al., 2023b). Geometric surface parameters in cylinder coordinates are commonly less elaborate and established. However, the use of cylinder coordinates can prove to be useful for cylindrical surfaces of very small diameters, such as mussel dropper lines, where the length of one individual mussel can be larger than the diameter of the dropper line (Landmann et al., 2019). As the present research aims to generate relevant data on cylinders overgrown by biofouling leading to the characterization of even bigger cylindrical offshore wind piles, and since there is more data and deterministic equations’ availability on flat surfaces, the flat-surface parameters will be applied for the measurements in the following sections. One limitation of this characterization method is overcome by unfolding the surface as proposed in Section 4.1.2. Deviations and deviations due to unfolding are discussed in Section 5.5. Measurements are of discrete form, thus most of the following equations are presented in their discontinuous form. The surface is characterized as a height over a surface that spans in - and -direction.

4.2.3 Single value parameters

Especially the parameters regarding surface amplitude (Gadelmawla et al., 2002) are often used for roughness characterization, and some parameters have been proven to influence the hydrodynamic roughness, as outlined in Section 1. The parameters relevant for this research are the root-mean-square roughness , the mean of the maximum peak-to-valley height , the skewness , the kurtosis , and the surface coverage ratio . , and have a similarly high effect upon the force coefficient (Zou et al., 2023a). and have been chosen for their presumed influence upon the force coefficients, as the probability density function influences the force coefficients Landmann et al. (2021). Most parameters are dependent upon the distribution of the roughness elevation data , as shown below. Thus, the change of one parameter through a different surface may, but does not always have to, affect the other parameters as well.

The root-mean-square roughness (Equation 4) effectively describes the standard deviation of the height profile from its mean line (Gadelmawla et al., 2002):where is the total number of measurement points. As surfaces are measured in 2D, instead of a line measurement, is defined as and the sum counts from one to and , respectively. Then, and are the number of measurement points in - and -direction, and is denoted as , instead.

The metric is simple to use, as it is a rather universal, single-value parameter. Nonetheless, it can be strongly influenced by height measurement outliers (Gadelmawla et al., 2002).

The maximum height of the profile, (Equation 5), is defined as the difference between the highest and lowest point of the measurement (Thakkar et al., 2017):

The mean of the maximum peak-to-valley height, , is typically used to describe . It decreases the effect of outliers on . For calculation, the surface is cut into sections. Then, (Equation 6) simply describes the mean of calculated for each section:

The choice of section size, determined by and the cylinder dimensions, can greatly affect the resulting value of . If is too high, the low wavelength components of the surface are filtered out. Thus, the section size should always be as large or larger than the largest dimension of any roughness element on the cylinder. For periodic surfaces with section sizes equal to or larger than the periodic length of the surface, becomes equivalent to .

The skewness, Sk (Equation 7), describes the symmetry of a profile over the mean line (Gadelmawla et al., 2002) (see Figure 4C):

The kurtosis, Ku (Equation 8), describes the surfaces’ sharpness, measuring the relative number of high peaks and troughs (Gadelmawla et al., 2002).

For further information on and visualization of both skewness and kurtosis, the reader shall be referred to Kadivar et al. (2021).

The variable depicts the percentage of measurement points for which . As measurements are typically not precise enough to yield exactly 0 for the surface without biofouling, a certain threshold is defined. Then, is the percentage of measurement points .

4.2.4 Probability density

The probability density function (PDF), or amplitude density function, displays amplitudes over their probability of occurrence. To that end, a number of bins of certain amplitude ranges is defined when analyzing surface measurement data. The amplitude is here defined as . It is then counted how many measurement points can be allotted to a certain bin. This count is normalized to a percentage so that the area under the resulting PDF curve equals 1. For comparison, the number of bins for the definition of the PDF is an important parameter. From the PDF, the skewness, and the kurtosis can be determined by means of the third and fourth central moment, respectively (Gadelmawla et al., 2002).

4.2.5 Autocorrelation function

The autocovariance (autocorrelation) function (ACF) indicates how fast a signal can change in time (Broersen, 2006) or space. In this case, ACF (Equation 9) describes the dependence between data at two spatial positions (Thakkar et al., 2017):with and denoting the distance between the points in - and -direction. The ACF can also be used to better describe surface roughness arrangement patterns, which do also influence the drag coefficient (Zou et al., 2023a).

The correlation length is the distance to the origin after which the ACF drops to a certain predefined fraction. Typical correlation lengths are calculated for the directions parallel and perpendicular to the flow (Thakkar et al., 2017), or the maximum and minimum correlation lengths are determined (Hitzegrad et al., 2022). In this study, the correlation lengths in - and -direction shall be determined, since these directions are parallel and orthogonal to the flow, respectively. Following Thakkar et al. (2017), the correlation lengths are for x- and y-direction given in Equations 10,11, respectively:In Equations 10, 11 denotes the physical length between two measurement points. shall be defined as the value by which the autocorrelation function drops to a certain fraction. Points not within the correlation length may be considered as uncorrelated (Gadelmawla et al., 2002). The values for chosen throughout the literature vary; however, typical values for are 0.1, 0.2 or 0.3 (Gadelmawla et al., 2002; Thakkar et al., 2017; Hitzegrad et al., 2022; Hitzegrad et al., 2025).

The correlation lengths are used to describe the isotropy of a surface. The surface anisotropy ratio, SAR (Equation 12), is the ratio of the correlation lengths in - and -direction (Thakkar et al., 2017):

A surface is considered isotropic when (Yang et al., 2023b). If highly anisotropic, the application of surface generation and characterization methods proposed by Yang et al. (2023b) becomes non-representative. However, the surface generation method independent of the flow direction and the surface can also be similarly geometrically anisotropic when . Thus, should also be less than 1.7 for isotropy. Then, a surface shall be defined in the present research as isotropic if .

4.2.6 Power spectral density

In surface engineering and tribology, surfaces may also be described by means of a power spectrum or power spectral density (PSD). A PSD is a plot in which energy quantities or their derivations are plotted against a wave vector.

In the case of an ideal isotropic surface, and contain the same information, but the line graph in makes it easier to read and compare different PSDs. Furthermore, is chosen, as it is suitable for generation of an artificial surface as described by Yang et al. (2023b). Yang et al. (2023b) propose a method where artificial surfaces are generated using the PDF and PSD of the surfaces of samples of sandpaper and accreted ice on metal. For sufficiently isotropic original surfaces, unidirectional flow and a friction Reynolds number of 500–2000 (with dependent upon the mean wall shear stress, the friction velocity, the flow channel and the kinematic viscosity, as of Yang et al. (2023b)), the proposed method was suitable to properly reproduce hydrodynamic and thermal properties. This implies that, for the aforementioned conditions, measurement of surface topography in the form of PDF and PSD may be sufficient to conclude upon the hydrodynamic roughness of the surface.

The PSD contains information unbiased from pixel size and resolution (Jacobs et al., 2017) and parameters like can be derived from the PSD (Jacobs et al., 2017). The generation of a PSD from measurement can prove especially useful, as it enables the calculation of measurement bounds, identify instrumental artifacts, and may offer the opportunity to extrapolate into surface dimensions beyond the limits of the measurement technique (Jacobs et al., 2017).

In a 2D PSD, the height PSD is plotted against the wave numbers in - and - direction of the surface. The squared absolute of the surface’s Fourier transform , scaled by the area of the topographic profile yields (Jacobs et al., 2017) the 2D PSD, (Equation 13):where and are the wave numbers in - and -direction. Together, they form the 2D wave vector . The area of the topographic profile is , where and are the length of a periodic profile in the - and -direction, respectively. Under the assumption that the profile in and -direction is periodic, it is the length after which the pattern will repeat itself. In this study, however, the length of a periodic profile is unknown and random processes will dominate the surface. Thus, and shall be equal to the whole area of the deviation height map that results from photogrammetry and unfolding (see Section 4).

For the calculation of an isotropic 1D PSD , the radial average of the 2D PSD is computed over the radial average of the wave vector. For ideally isotropic surfaces, is radially symmetric, letting contain the same information as the 2D PSD (Jacobs et al., 2017). is determined by Equation 14:

As is designed to represent radially symmetric 2D PSDs, inherently, great asymmetry in the 2D PSD will make less representative of . Thus, will only be calculated for isotropic surfaces.

4.3 Unfolding deviation

The deviation height map process yields measurement points that are equidistant. The distance of two grid points relative to each other in the -direction of the deviation height map is measured in meters, whereas the distance of two grid points in the -direction is measured in degree. This distance is converted into meters by the use of the inner diameter.

One measurement point represents a certain surface area. The calculations in the above sections assume each measurement point to have the same surface area size, as the surface area of one pixel is given in Equation 15:with and the lengths represented by the pixel in and direction. The length of the pixel in the -direction can be calculated as given in Equation 16:with denoting the length of the pixel in degree. The radius is constant. Thus, each pixel has the same surface area and each pixel value has equal weight to each other.

The above calculation can be compared to a measuring device rotating at constant angular speed around the center of the cylinder, recording height measurements at equidistant time intervals and uniform angular increments.

Typically, only small values are measured in literature, where unfolding deviations become negligible. Surface roughness parameters for large values are characterized by Landmann et al. (2019) and Marty et al. (2021a), with measurements in circumferential direction in degrees, similar to the results shown in Section 5.

In order to take roughness parameter deviations due to unfolding of cylinders with large into account, a weight is proposed that can be attributed to each pixel, depending on the surface height. The radius as a function of the distance for large roughness shall be (Equation 17):with the reference area of one pixel at . A weighted height is then defined as given in Equation 18:

This calculation approach can be compared to a measuring device moving over the rough surface at constant speed and determining the height at equidistant time intervals. In this way, areas of the surface that protrude outward (i.e., have larger roughness) receive appropriately more weight, reflecting their surface area.

When considering Equation 18, with increasing diameter , the influence of unfolding becomes negligible, as for .

5 Results

This section consists of five parts. Section 5.1 provides an overview of the cylinders and their surfaces. From the cylinder surfaces, the main roughness parameters are then derived and analyzed in Section 5.2. After a short description of the biofouling communities in Section 5.3, the parameters necessary for artificial surface generation are derived and analyzed in Section 5.4. The influence of cylinder unfolding upon the various roughness parameters is then investigated in Section 5.5.

5.1 Cylinder surfaces

Figure 5 presents the averaged data for each cylinder type as defined in Table 2 to provide an overview on the general trends when comparing the individual cylinder types. The top row shows cross-sectional views and the bottom row shows the roughness height along the cylinder length, for each cylinder type. Because the data have been averaged for each cylinder type, the height values in Figure 5 will be referred to as the average roughness height. The average roughness height of the A27 cylinders is the lowest among all cylinder types and fluctuates around 0.01 m. The highest average roughness heights along the cylinder length can be found in location B, especially for cylinder type B10, where the average is around 45 mm. Roughness heights at location A vary less along the cylinder length and for each cross-section compared to the roughness heights at location B. The same applies for the standard deviation of the roughness height along the cylinders: the variability and standard deviation are significantly higher for the cylinders at location B (around 0.01–0.02 m) than for those at location A (around 5–10 mm). Especially for the cross-sections of type B10, large roughness height peaks up to 52 mm 12 mm are found. Furthermore, a slight decline in average roughness height is observed with increasing cylinder height .

FIGURE 5

The deviation height maps for each individual cylinder are displayed in Figure 6. The difference in the mean roughness height between the cylinders at locations A and B observed in Figure 5 is also clearly observed in Figure 6. Furthermore, the cylinders at location B are covered by a higher amount of mussels than cylinders at location A, which explains the elevated mean roughness height. As was observed in Section 3.1, the environmental parameters varied only minimally between location A and B, except for the water depth, resulting in much higher current velocities at location B. It is therefore likely that the differences in the growth and biofouling community composition between the two locations can be attributed to the differences in current velocity.

FIGURE 6

The distinct oval shapes observed in Figure 6 for, e.g., cylinder A27-1 represent individual mussels (Hitzegrad et al., 2022), as observed in Figure 2. Although the average roughness height for type A27 does not vary much in Figure 5, the growth patterns for each individual cylinder vary significantly in Figure 6: cylinder A27-1 shows vertical line-shaped growth patterns of mussels, cylinder A27-2 shows only one large cluster of mussel coverage, while cylinder A27-3 shows a random distribution of mussels along the cylinder. Cylinders B27-4 and B27-5 appear similar in shape, with the latter cylinder displaying a higher coverage by mussels and higher average roughness height than the former. On cylinders of type A10 no distinct clusters of mussel growth are identified. The biofouling structures of type A10 have a tendency to be distributed vertically. Vertical orientation can also be found for the cylinders of type B10. Cylinders of type B10 show almost complete coverage by mussels. In areas of mussel clusters, the roughness height is high, and the clusters exhibit a vertical (perpendicular to the water surface) orientation. These mussel cluster areas with high roughness height consist of multiple layers of mussels growing on top of each other. The diameter of the cylinder appears to have an effect on the capacity of mussel growth and cohesion of mussel clusters, since B10 is more densely populated than B27. At Site B, the presence of hard marine fouling (M. edulis) indicates a site-specific advantage: the mussels benefit from their structural resilience, which allows them to withstand the by about 66% increased ebb and flood currents for location B accompanied by larger water depths and exposure to more severe wave conditions.

5.2 Roughness characterization

The probability density functions (PDFs), defined in Section 4.2.6 for each cylinder type, are displayed in Figure 7. The bold line represents the average PDF per cylinder type. All cylinder types show one pronounced peak in their average PDF, except for type B27, where multiple maximum probability bins form a plateau of values. The PDFs at location A show a narrower distribution around the peak, which indicates that there is a high percentage of similar roughness heights. For location B, the PDFs are more widely distributed and have a flatter distribution around its peak. This behavior is correllated to the biofouling community compositon because of the higher amount of mussels on the surface and the higher percentage of mussels whithin the biofouling community, as M. Edulis exhibits relatively flat PDF curves (Landmann et al., 2019). B27 is observed to have a plateau around 2% for roughness lengths between −20 and 10 mm. A similar plateau shape is also observed for cylinder A27-3. While the cylinders A27-1 and A27-2 have a distinct peak in their respective PDFs, the PDF of cylinder A27-3 has a much flatter distribution and, as was observed in Figure 2, is overgrown by a larger amount of mussels that are not clustered. The plateau shape indicates a rather even growth pattern along the surface, with a high percentage of mussels present in the biofouling community, but no mussels growing on top of each other (no multiple mussel layers). For increasingly large , the probability density of the cylinders associated with a cylinder type converges. However, for cylinders of type A10 the probability densities vary also for larger roughness lengths above 20 mm. The structure of the A10 cylinder biofouling consists different amounts biofouling compounds with high elevation data values, which leads to the differing convergence behavior.

FIGURE 7

Based on the deviation height map and the PDF analysis, single number parameters are determined and provided in Table 3. These parameters are displayed for all cylinders, as well as the arithmetic mean and standard deviation of all parameters for each cylinder type. of the cylinders vary between 0.085 and 0.613. In comparison, shows reduced values from 0.080 to 0.321. The increase of to the initial diameter is between 13 and 92 mm, thus reducing each value compared to . The differentiation between the two diameter sizes and for high values is therefore justified and necessary. The environmental conditions enabled significant biofouling growth, as the surface coverage is high for all cylinders: with 10 out of 11 cylinders covered by more than 90%. All cylinders’ PDFs are positively skewed (as also indicated in Figure 7), as the biofouling grows on top of the cylinder and damages to the originl cylinder surface remain minimal in comparison. The majority of cylinders exhibit a positive kurtosis, while the rest of the cylinders show slightly negative kurtosis. The average kurtosis of both types of cylinders at location B ( 0.43 and 1.06 at 27 and 10 cm diameter, respectively) is lower than for cylinders at location A ( 1.57 and 1.07 at 27 and 10 cm diameter, respectively). The differences in skewness can mainly be explained by the amount of mussels present, as well as the amount of other biofouling species that sharply protrude from the surface: At location B, the cylinders are overgrown mainly and almost completely by M. edulis. This uniformity (see Figure 4C), as well as the comparatively large size of the mussels lead to both lower and at location B.

The skewness and kurtosis standard deviation values are significantly higher for the cylinders at location A than those of location B. Apparently, a high amount of mussels at location B reduces the standard deviation for and . Although is larger at location B, values are significantly higher for both 10.2 cm diameter than for both 27.3 cm cylinder types.

5.3 Biofouling community description

The biofouling communities vary for each class (Figure 2). Especially the cylinders located farther from the shoreline (location B) are overgrown by no or only a thin layer of soft biofouling and dominated by hard marine growth (M. edulis), resulting in a representative geometric roughness characterization for hard marine biofouling. The cylinders closer to the shoreline (site A) are overgrown by equal amounts of hard (mostly M. edulis) and soft biofouling (mostly structures from tube-dwelling Amphipoda). These observations are supported by the weights of the cylinder. Cylinder weights (Table 3) showed clear differences in biomass accumulation between the two sites starting with 5.32 kg (A10, B10) and 17.0 kg (A27, B27) for the bare cylinders without biofouling. At Site A, cylinder masses increased on average to 8.33 kg (A10) and to 25.0 kg (A27), while at Site B they reached substantially higher values of 17.37 kg (B10) and 33.05 kg (B27), respectively. This represents an additional biofouling mass of about 8–9 kg at Site B compared to Site A.

5.4 Characterization towards artificial surface generation

An autocorrelation analysis is shown in Figure 8 for - and -offset values of mm. All autocorrelation plots are point symmetric and show the highest correlation around their origin. A faster drop-off of correlation in and offset direction is present for the cylinders of 10 cm diameter than for the cylinders of 27 cm diameter. Cylinders A27-1, A10-8, A10-9, B10-10, and B10-11 are strongly dependent upon the direction of the shift. The vertical orientation of mussels in A27-1 and the vertical cluster orientation on cylinders A10-8, A10-9, B10-10, and B10-11 contribute to this anisotropic behavior. Cylinders A10-7, B10-10, and B10-12 show an orientation not in line with the - or -offset axis. Table 4 contains correlation lengths in -direction and surface anisotropy ratio values of all cylinders. Additionally to the already observed anisotropies, cylinder B27-5 is also labeled as anisotropic. For each cylinder type, at least one isotropic cylinder and at least one anisotropic cylinder exists. No clear trend in anisotropy over the different cylinder classes is observed.

FIGURE 8

The 1D isotropic PSDs of the isotropic cylinders are displayed in Figure 9. The power ranges from around to around . All PSDs show a generally similar trajectory: starting at high spectral power values, an inverted S-curve follows. All 1D PSD curves are not smooth, but noisy. The cylinders with higher values have higher power values at low frequencies than those with lower values.

FIGURE 9

Based on the PDFs, the 2D PSDs (see Supplementary Appendix Figure 10), and the 1D isotropic PSDs, artificial surfaces were generated (see also Supplementary Appendix, Figure 11,12) with the artificial surface generation method from Pérez-Ràfols and Almqvist (2019). Most original surfaces appear well represented using the artificial surface generation method, especially in the large-wavelength range and even for some anisotropic surfaces.

5.5 Unfolding deviation

The values of this research reach from 0.085 up to 0.613, and therefore the biofouling height is larger than the radius of the cylinder for some surfaces. Thus, considering potential deviations due to unfolding is necessary, especially as comparable literature lacks a detailed investigation of unfolding deviations on surface roughness (such as Landmann et al. (2019); Marty et al. (2022)).

Roughness parameters are calculated by inserting the weighted measurement points in place of (see Section 4.2.3). The deviation of these parameters compared to the single number parameters calculated without weight is displayed in Table 5. This analysis highlights, which cylinder types and parameters may be more or less affected by unfolding.

As assumed, the parameters tend to deviate more with higher or lower . For instance, regarding the RMS height of cylinders of type B27 (average ), the unfolding deviation lies between 10.7% and 12.2%, whereas the deviation lies between 62.9% and 65.6% for type B10 (average ). Especially cylinder type B10 shows strong deviation for all parameters except . All parameters increase in value when weighted except . This increase is attributed to nearly all . shows extreme deviation for all cylinder types (ranging from −286.7% to 108.5%), due to its sensitivity to weighing, with height values calculated to the power of four. and appear relatively insensitive to weight changes.

Measurements in Section 5 stay valid within their defined calculation methods. However, it becomes apparent that surface roughness parameters for large are connected with the cylinder thickness and the biofouling thickness.

6 Discussion

Section 5, for the first time, introduces a broad set of roughness parameters of biofouled cylinders with two distinct locations of hydrodynamic exposure (Lojek et al., 2024), helping to close a research gap that arises from the fact that the geometric roughness of biofouled cylinders has so far been quantified almost exclusively by . In this study, the relative roughness is reported to range between 0.085 and 0.613; and it can be classified to be from large to very large roughness, according to Marty et al. (2022). Particularly very large roughness, as observed in this work, has received little attention in previous research (Henry et al., 2016). The positive skewness (0.30–2.13) of all cylinders can be attributed to the growth pattern of hard and soft biofouling, covering almost the whole surface and protruding from the cylinder along its surface. Similarly, positive skewness of biogenic surfaces is observed for oyster reefs by Hitzegrad et al. (2022) and a positive skewness is reported to be typical for biofouling (Thakkar et al., 2017). The investigations of Hitzegrad et al. (2022) include reefs of Magellana gigas. These oysters measured around 100 mm, about twice as large than M. edulis, the hard biofouling species of this research with the longest dimension. Nonetheless, for both studies, , , and lie within similar orders of magnitude, adding to the validity of the present study. High SCR values correspond with the visual observations: the cylinders are almost completely overgrown by at least a small layer of biofouling.

The question remains to what extent geometric roughness parameters can characterize soft biofouling. Nonetheless, the structures of soft biofouling on cylinders at location A may have a higher stiffness than algae and therefore may be better suited for surface characterization by the methods presented in this work, compared to surfaces covered by algae. Further investigation on and comparison of the stiffness of different species of soft biofouling is necessary. Such investigations could, for instance, be conducted in a similar manner to the bending tests as described by Krautwald et al. (2026). Such bending tests could generally significantly contribute to an understanding of soft biofouling mechanical properties.

Potential ways of better characterizing hard and soft biofouling on overgrown structures may be the use of artificial intelligence, which identifies the different biofouling species and their location on the pile, as, e.g., proposed by Signor et al. (2023). In their work, they successfully use a convolutional neural network to identify three different types of hard biofouling. Their method could be expanded to soft biofouling species identification. After segmentation of the soft and hard biofouling areas, the areas of hard biofouling could be classified as described in Section 4.2, and soft biofouling species could be characterized by different methods yet to be developed, taking into account the flexible shapes of soft biofouling. This differentiated methodology would then enable a more detailed characterization of the cylinder’s hydraulic roughness in systematic experimental and numerical analyses.

Measurements have been performed with the cylinder suspended in air, taken out of its salt water storage container for the sake of measurements. This resulted in some heavier and less stiff components of the soft biofouling hanging down. Furthermore, the Actiniaria did contract at fresh air. This work has resorted to this measurement arrangement, since it allowed for better lighting conditions and improved clarity of the SfM pictures. More recently, the measurements presented by Schoefs et al. (2021) were however performed in water, using an underwater photogrammetry test setup, and this might be an alternative to in-air measurements; however a more specific comparison of methods remains for future research. In doing so, potential errors due to the gravitational pull and contraction of the Actiniaria on the biofouling can be determined.

A very small number of height values of the deviation height map were below zero. No corrosion holes were visible, thus these values are identified as measurement errors from photogrammetry. There are potential explanations for the negative height values. The cylinders could have been deformed when hanging underwater. A height measurement of the cylinder after photographing and then removing the biofouling from the cylinder has not been performed. Another explanation for the negative height value may be slight deviations in photogrammetry modeling accuracy. In order to quantify potential errors due to photogrammetry, a comparison with other measurement methods, like laser scanning (Landmann et al., 2019), structured light 3D scanning (Liu et al., 2025), or potentially even stylus measurements (Czichos et al., 2011), is necessary. However, the negative values are one to three orders of magnitude smaller than the mean of the maximum peak-to-trough height . Thus, the influence of the negative roughness values on the general roughness characterization remains marginal. Notwithstanding potential errors, the provided method of retrieving a deviation height map and roughness parameters from photogrammetry proved to be quick, non-destructive, and easy to set up and thus ideal for this situation.

Although new insight on the geometric roughness of mussels has been generated, the results only present a momentary frame within time. Biofouling growth, however, underlies seasonal variations (Garen et al., 2004; Brenner et al., 2012), and depends on the location within the sea. A future investigation of both spatial and temporal variation of geometric roughness parameters within the north sea would therefore be beneficial for engineering applications in this area, such as load prediction and construction site selection. Furthermore, a sample size of two to three cylinders per location and cylinder diameter may not suffice for a high statistical confidence level and should therefore be increased in future investigations, if possible.

7 Conclusion

Apart from values, the current literature provides little data on roughness parameters of cylinders overgrown by biofouling. The main goal of the present work was to address this knowledge gap. A deviation height map was created by use of photogrammetry for eleven cylinders of 10.2 cm and 27.3 cm diameter, overgrown by biofouling, which were retrieved from two locations in the Jade Bight, Germany.

This work provides a database for future investigations on the relation of geometric roughness parameters and force coefficients of cylinders overgrown by marine biofouling. Generated data has relevance for numerical modeling, characterization of artificial surrogates, as well as potential tests in the newly built saltwater-wave-current flume of the Leichtweiß-Institute for Hydraulic Engineering and Water Resources at the Technische Universität Braunschweig, Germany. Especially the probability density function and power spectral density proved to be useful parameters for surface characterization. They can be used for realistic artificial surface generation of 3D-printed surrogates for wave flume testing, or for numerical simulations on the correlation between geometric roughness and the loads on cylinders overgrown by marine biofouling.

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