**1. Introduction**

Mangroves, saltmarshes, and seagrasses are important coastal ecosystems that are widely distributed in world's coasts [1–3]. The wave-damping capacity of these coastal wetlands has been increasingly recognized [1,4–8]. These coastal wetlands can significantly reduce wave energy even under storm or tsunami conditions [9,10], which provides valuable protection to the coastal communities and properties [11,12]. Over the past decades, the wave heights have a clear increase trend in extreme conditions, together with accelerated sea level rise [13–17]. Therefore, there is a demand for

better understanding and predictive ability of vegetation–wave interaction process to reduce coastal flooding risks [4,18–20].

The main impact of vegetation on incident waves is exerting an additional force on water motion [21,22]. This force can be described by the Morison equation, which is composed by drag force (*FD*) and inertia force (*FM*) [23]. For normal field conditions, the drag force is the dominant force, and most relevant for wave energy dissipation. In the Morison equation, *FD* is proportional to the square of impact velocity on vegetation stems. When the velocity scale is determined, the magnitude of *FD* varies linearly with vegetation drag coefficients (*CD*). In oscillatory (wavy) flows, the *CD* values have a large range of variations (i.e., 0.1 to 100) [24]. The *CD* values depend on canopy density, hydrodynamic conditions, as well as the morphology of the individual canopy elements. Thus, choosing appropriate *CD* values are important for accurate simulation of *FD*, and the resultant wave dampening in many modelling studies [18,25–30].

Currently, there are two methods available in determining *CD*: the calibration method and the direct measurement method. The calibration method is a convectional method developed in the 1990s [31,32], and has been widely used since [33–35]. It derives *CD* by calibrating its values to obtain the best fit between modelled and measured wave height evolution over vegetation fields. The direct measurement method is a new method, which has been developed since the 2010s [36–38]. This method directly applies the Morrison equation and measured in-phase force and velocity data to determine *CD*. The main differences between the calibration and the direct measurement method are: (1) the calibration method can only provide period-averaged *CD*, but the direct measurement method can derive both period-averaged and time-varying *CD*; (2) the direct measurement method can eliminate the potential errors often associated with the calibration method, and lead to *CD*–Re (Reynolds number) relations with better fits, which are desirable for model applications [37].

Since the direct measurement method relies on in-phase force and velocity data, there are two difficulties when applying this method. The first difficulty is the availability of suitable force sensors to assemble synchronized force–velocity measuring systems. The force sensors should be waterproofed and durable in wave flumes, where frequent water logging and splashing occur. Additionally, the sensors should be small enough to fit into wave flumes. The second difficulty associated with this method is the data processing technique required to obtain perfectly aligned force–velocity data for *CD* derivation [37]. The data alignment is critical for the direct measurement method, as there are time lags between original force data and velocity data signals (ca. 0.2 s), which may lead to large errors in the derived *CD*. These time lags may originate from small misalignments between force sensors and velocity measurement [37]. They may also be induced by intrinsic time shifts in instrument recordings. The maximum wave energy dissipation occurs at the peak wave orbital velocity in phase with the peak drag force when *CD* values matter the most. Thus, in order to obtain accurate *CD* values, it is important to minimize the time lags. Previous studies firstly set an intrinsic time lag between the force and velocity data, and then started iterations to reduce the time lag. Note that this intrinsic time lag varies with different instrument set-ups. This intrinsic time lag needs to be carefully tuned to obtain in-phase data. It is, however, preferable to have an automatic algorithm that can provide generic solutions to the alignment problem.

In this technical note, we have developed (1) a synchronized force–velocity measuring system by using standardized force sensors that can easily fit in wave flumes; (2) and an automatic alignment algorithm to obtain in-phase force–velocity data for *CD* derivation. The new force–velocity measuring systems are applied in a flume at four locations in a mimicked mangrove canopy, which were tested with various simulated wave conditions. The automatic alignment algorithm was then applied to reduce the time lags between force–velocity signals. The processed data were subsequently used to derive both time-varying and period-averaged *CD*. To evaluate the accuracy of the derived *CD* (and also the alignment algorithm), we used the derived *CD* to reproduce the total acting force on mimicked vegetation, and compared it with the measurements.

The rest of the technical note is organized as follows: Section 2 introduces the automatic alignment algorithm and the set-up of the synchronized force–velocity measuring system in the wave flume at the Fluid Mechanics Laboratory at Sun Yat-sen University, Zhuhai Campus. Section 3 demonstrates the original and processed force–velocity data, as well as the reproduced force data results. Section 4 discusses the current limitations and provides an outlook for future applications of this method. Finally, Section 5 provides conclusions of the current note.

#### **2. Materials and Methods**
