Mechanistic Drifting Forecast Model for A Small Semi-Submersible Drifter Under Tide–Wind–Wave Conditions

Understanding the drifting motion of a small semi-submersible drifter is of vital importance regarding monitoring surface currents and the floating pollutants in coastal regions. This work addresses this issue by establishing a mechanistic drifting forecast model based on kinetic analysis. Taking tide–wind–wave into consideration, the forecast model is validated against in situ drifting experiment in the Radial Sand Ridges. Model results show good performance with respect to the measured drifting features, characterized by migrating back and forth twice a day with daily downwind displacements. Trajectory models are used to evaluate the influence of the individual hydrodynamic forcing. The tidal current is the fundamental dynamic condition in the Radial Sand Ridges and has the greatest impact on the drifting distance. However, it loses its leading position in the field of the daily displacement of the used drifter. The simulations reveal that different hydrodynamic forces dominate the daily displacement of the used drifter at different wind scales. The wave-induced mass transport has the greatest influence on the daily displacement at Beaufort wind scale 5–6; while wind drag contributes mostly at wind scale 2–4.


Introduction
Traditional satellite tracing buoys, such as Argo buoys, have been wildly used in monitoring ocean circulation systems. Moreover, with the popularization of mobile communication technology in nearshore areas, some small GPS-GPRS embedded drifters have been developed for research purposes, and the small-scale design of drifters is an effective prevention against stranding. Xu et al. (2013) gathered the drifting data of a small drifter during three tidal cycles, which witnessed flood-dominated tidal currents in the Xiyang trough of the Radial Sand Ridges (RSRs). Quan (2014) utilized the drifting data of small drifters to validate the simulated tidally induced Lagrangian residual currents, which is the result from the numerical model in the Xiangshan bay. Given the fact that the above drifting experiments were carried out under calm wind conditions, it is acceptable that tidal currents were the dominant hydrodynamic force.
In order to follow water currents closely, the major part of a small drifter is designed to be immersed in water. Ho-wever, there is at least a part of the small drifter exposed to the air to keep a floating state and avoid suspending. As a result, it is a common situation that a small drifter is subjected to both water currents and wind, known as a small semisubmerged drifter (SSD). Wind exerts intermittent influence over sea surface water, accompanied by the formation and development of wind-induced currents and waves. Thus, the drifting behavior of an SSD depends on how it responds to the dynamic environment influenced by tide, wind and waves.
Great efforts have been made to understand drifting motions of semi-submerged drifters, such as survivors or life rafts, because accurate locations of potential targets of these drifters are essential to search and rescue campaigns. A related drifting forecast model, usually referred as AP98 leeway model, was established by Allen and Plourde (1999) and this model has become the general forecasting technique so far (Breivik et al., 2011;Chen et al., 2014). In the AP98 leeway model, the influence of wind drag and waves on drifting motion can be addressed with the leeway speed, which is considered as a simple linear function of 10 m wind speed W 10 (Breivik and Allen, 2008;Breivik et al., 2013). The linear relationship between the leeway speed and W 10 relies on the results of preliminary drifting experiments of specific drifters, and can be represented by the leeway parameters including the leeway angle, the downwind leeway component, and the crosswind leeway component (Fig. 1).
AP98 leeway model enforces the linear rule between the leeway speed and W 10 , and it is an empirical and rough drifting forecast model. More research is clearly needed to clarify kinetic mechanism of the drifting motion, and its reaction to the external force such as tide, wind, and waves. In this paper, we focus on the drifting features of SSDs floating in coastal areas exposed to strong tide currents and normal wind conditions. These SSDs with small sizes and regular geometric shapes such as a sphere or cylinder are suitable for monitoring shallow surface water. Hence we do not discuss the big and irregular drifters due to their inapplicability.
A 2-day in situ drifting experiment of a cylinder SSD was conducted in the RSRs. In contrast to previous studies, which only followed empirical frameworks, we explore the kinetic mechanism of the drifting motion of SSDs. First, because the hydrodynamic environment of the drifting experiment is essential for the analysis of the drifting motion, we establish numerical models of waves and ocean currents respectively to offer the information of tide currents, winddriven currents and waves. Next, we propose a mechanistic drifting forecast model based on kinetic analysis. The forecasting results are validated by the 2-day measured drifting data. Finally, we introduce a set of trajectory models to quantify the contributions of each external force to the drifting motion and analyze their different performances reacting to a changing tide-wind-wave environment.

The drifting experiment of an SSD
The in situ drifting experiment took place in the RSRs, located in Jiangsu Coast, China. The large-scale fan-shaped RSRs are generally regarded as one of the most remarkable coastal landscapes in the world, with deep troughs and sand ridges crossly distributed (Wang et al., 2015) (Fig. 2a). Tidal regime in the RSRs is of semidiurnal tide, and the tidal current field in the RSRs is mainly dominated by the moving stationary tidal wave system, where the phase difference between the current velocity and tidal level is about 90° (Zhang et al., 1999). We released the GPS-GPRS embedded SSD at the junction of the Langshayang and Huangshayang troughs. One hundred and ninety location tracking data were compiled at 15-minute intervals (very rarely at 30-minute intervals) during two days. The measured trajectories from December 31, 2013 to January 1, 2014 (Beijing Time) are shown in Fig. 2b. The used SSD is a cylinder, with an immersion ratio of 60.8% (Fig. 2c).

Wind conditions
The measured wind speed was compiled at 1-hour intervals with an ultrasonic anemometer mounted at the reference height of 3 m in the Xiyang trough (S1), 130-160 km SW of the drifting areas (Fig. 3). In consideration of the spatial variation of the wind speed between S1 versus the drifting areas, we obtain the wind speed at the center of drifting areas (P1) by using the extrapolation method.
First, due to the lack of the measured wind data at P1, we downloaded the set of wind data at the reference height of 10 m with 6-hour intervals and 0.2-degree grid resolution from the second version of the NCEP Climate Forecast System (CFSv2) (Saha et al., 2014). We adopted the bilinear interpolation method to calculate the wind speed at P1 and S1. Next, we evaluated the reliability of CFSv2 by comparing the wind speed extracted from it with the measured wind speed at S1. The measured wind speed at S1 was converted to the reference height of 10 m using the logarithmic law . As is shown in Fig. 4, wind data at S1 extracted from CFSv2 agree well with the measurements  during the drifting experiment. Thus, CFSv2 is a dependable wind data source for the RSRs, and the wind data extracted from which are suitable for wind speed (wind direction) correlation analysis. Based on the 2-month CFSv2's wind data from December 2013 to January 2014, the wind speed correlation ana-lysis at S1 versus P1 was carried out. The results indicate that the wind speed (direction) at S1 has a good linear relationship with the wind speed (direction) at P1. The linear regression equations, the correlation coefficients, and the 99% confidence intervals are respectively shown in Fig. 5. As a result, the reliable wind speed at P1 can be acquired by means of extrapolation from the measured wind speed at S1 according to the linear relationships.

Hydrodynamic conditions 2.3.1 Numerical models in the RSRs
Numerical models are established to simulate ocean currents and waves. The models cover from 119.2°E to 123.2°E in the longitudinal direction and from 30.9°N to 36.1°N in the latitudinal direction. With high spatial resolution in coastal areas, the tidal numerical model would not only be able to simulate the tide system in the Southern Yellow Sea, but also capture the detailed current field in the RSRs.
(1) A 3-D tidal numerical model This model solves the Reynolds-averaged momentum equations by introducing the turbulent model, the hydrostatic assumption, and the terrain-following sigma-coordinate transformation. A numerical technique based on the finite volume method with unstructured grids is applied. The open boundary conditions are provided by a global ocean model (Matsumoto et al., 2000). The measured water Fig. 3. Model geometry and the locations of measuring stations. Yellow squares (T1-T10) denote locations where tidal currents were observed, red triangles (C1-C3) denote locations where water levels were observed, and fuchsine rhombus (W1) denotes locations where waves were observed. The measured data in the above stations are applied to the validation of numerical models. The purple circle (S1) shows the location of the wind station during the drifting experiment and black cross (P1) denotes the center of the drifting areas. Fig. 4. Comparison between the measured wind and the CFSv2's wind data at S1.

Fig. 5.
Wind speed at P1 (direction) versus wind speed at S1 (direction) from CFSv2. The linear regression parameters are given and the dashed lines indicate the 99% confidence intervals.
C d levels at Xuliujing are set as the upstream boundary conditions. Surface boundary conditions are also taken into consideration when wind-induced currents are considered. The wind stress τ s is given by the quadratic empirical relation and the wind stress coefficients utilized were reported by Wu (1982): where is the air density.
(2) Spectral wave model Wave propagation is described by the conservation equation of the wave action density N: where E is the wave energy; denotes the Cartesian co-ordinates; is the wave angular frequency; is the wave direction and t is time. The physical processes include the growth, transformation and decay of wind waves. This spectral wave model takes into account the water level and water current variation.

Model validation
The simulated tidal levels, tidal current velocities, and wave parameters including the spectral significant wave height ( ), mean wave direction and wave period ( ) were compared with the measured data, respectively. The locations of measuring stations are shown in Fig. 3. Here, consistent with the period when the field investigation of tide currents was conducted, the validation period of tidal model was set on January 3-4 2007 during that time the wind influence was negligible. Moreover, the tidal harmonic analysis was made to obtain tidal levels in this period, based on 1-month measured tidal levels in January 2014. The comparison between the simulated results and the measurements at representative stations are shown in Fig. 6. Controlled by the moving stationary tidal wave system, the moment of the slack tide when the direction of tide current reverses occurs around a high or low water level in the RSRs. Overall, verification results indicate that both the simulated tidal levels and simulated tidal current velocities are in reasonable agreement with the measurements. The validation period of wave model is set on December 29, 2011. Considering the inefficiency of the spectral wave model in simulating wave diffraction processing, the results of simulated tidal parameters at W1 surrounded by sand ridges should be considered satisfactory. However, the in situ drifting experiment was conducted in an open sea where the wave diffraction cannot take place and thus the spectral wave model would perform better. Above all, numerical models are calibrated and suitable for further analysis.

Kinetic analysis of an SSD
The schematic of the kinetic analysis of an SSD under flow conditions, referring to dynamic forcing including water currents and wind, is illustrated in Fig. 7. The drifting motion equation of an SSD with the mass m and drifting position x can be written as: where F a is the wind drag; F c is the water drag. Wind and water drag can be expressed by the relative velocity of drifting speed versus the velocity of ambient flow medium. The water drag force of an SSD is calculated as: Fig. 6. Comparison between simulated results and the measurements of tidal levels, tidal current velocities and wave parameters.
ρ c where is the water density; A c is the cross-section of the SSD exposed to the water; C c is the water drag coefficient; and U c is the surface water current velocity.
Similarly, the wind drag force of an SSD is given as: where A a is the cross-section of the SSD exposed to the wind; C a is the wind drag coefficient and U a is the wind velocity passing through the SSD, which can be calculated from the wind speed at the reference height of 10 m with the logarithmic law.

Measured drifting characteristics of an SSD
The locations of the used SSD at 15-min intervals were recorded in the course of the drifting experiment. The parabola interpolation method was used to calculate the drifting velocity and further applied to calculating the drifting acceleration. Fig. 8 shows the time series of the drifting acceleration, which reaches peak values in slack tide at around 00:00, 06:00, 12:00 and 18:00 everyday, and the magnitude of the drifting acceleration is between 10 -5 m/s and 2×10 -4 m/s 2 .

Foundation of the mechanistic drifting forecast model
SSDs are advected by the Lagrangian current which in-cludes the Eulerian current and wave-induced mass transport (Röhrs et al., 2012). SSDs are too small to generate diffraction waves or reflection waves when floating on a wave surface, and the wave field would not be affected by it. The drifting areas meet the requirement for deep water depth or finite water depth (Fig. 8), and the second-order Stokes mass transport is considered as the dominant wave-induced currents here. For the regular wave with the wave height H, the second order Stokes mass transport velocity at the water surface is calculated as follows (Zou, 2005): From the view of the wave energy spectrum, we use the wave parameters including the spectral significant wave height and the significant wave period to calculate Stokes mass transport velocity. The Stokes mass transport for random waves is calculated as follows: where, h is the water depth. The wave number k and the angular frequency are related to the wave length L and the wave period T by and , respectively. We can obtain the spectral significant wave height and wave period from the validated spectral wave model. Here, we use the relationship proposed by Li (2007) to obtain the significant wave period : In the drifting forecast model, the model time step for simulation of the drifting velocity depends on the temporal and spatial scale of the external forcing acting on the SSD, which changes appreciably in minutes or hours, not seconds. Constant velocities for the duration of a model time step are acceptable (Breivik and Allen, 2008). Considering the small drifting acceleration (Fig. 8) and the lightweigh SSD, we suppose that the acceleration force is negligible at every model time step i and specify the model time step size is equal to 1 min: F ai F ci According to Eq. (9), we can see that and must be equal in magnitude and opposite in direction. Combined  ZHANG Wei-na et al. China Ocean Eng., 2018, Vol. 32, No. 1, P. 99-109 103 Eq. (4) with Eq. (5), the simplified equation of the drifting velocity at the model time step i is proposed: here is the velocity of Lagrangian current at model time step i, which is equal to the velocity of Eulerian current (including tide current and the wind-induced current ), plus Stokes mass transport velocity , by U ci = U ti + U wi + U si ; is the wind speed passing through the SSD at the model time step i.
Furthermore, based on Eq. (10), we can predict the drifting trajectory of the SSD. Suppose that the initial position of the SSD is at the starting time , the final position is at the end time , and we have ∆t where is the time step size, and n is the total number of predicted time steps.
We would give attention to the choice of a proper value of for achieving better performance of the drifting forecast model. According to Eq. (11), is proportional to 1/2 power of , letting us focus on choosing a proper , instead of defining C a and C c directly. The wind drag coefficient C a and the water drag coefficient C c of a cylinder under turbulent flow conditions roughly change from 0.8 to 1.2, up to Reynolds number (Deng et al., 2009

Evaluation of the simulated drifting velocity
The validation period of the drifting forecast model was set in the course of the in situ drifting experiment, when the wind condition at P1 is from Beaufort wind scale 2 to 6, as shown in Fig. 9a. The simulated drifting velocity simultaneous with the measured drifting velocity both at 15minute intervals is obtained based on Eq. (10). The agreement between the measurements and the simulations can be evaluated by the vector correlation equation as follows: C a /C c The correlation coefficient r becomes equal to one for identical velocities and minus one for opposite velocities. The corresponding time series of correlation coefficients r resulted from the three alternative values of are shown in Fig. 9b, which indicates that most of the correla- C a /C c tion coefficients are above 0.5, no matter which is applied. However, the correlation decreases rapidly in slack tide at around 00:00, 06:00, 12:00 and 18:00 everyday, leading to the occurrence of trough value. This is due to the relative small measured drifting velocity in slack tide which appears in the denominator of Eq. (13), and thus poorer correlation happens even though with a small forecast error.
The value of has slight influence on the results of the simulated drifting velocity, revealed by indistinctive changes in correlation coefficients. A larger equal to 1.2/0.8 is better at a certain time, while a smaller equal to 0.8/1.2 performs better at other times, but with the medial performance of . The selection of parameter cannot be determined directly depending on how strong the magnitude of the tidal current or the wind, and it is not straightforward to confirm an accurate value of at the air-sea boundary layer with wave disturbance. But, there is a possibility to compromise by setting equal to 1, due to the result of the simulated drifting velocity is not sensitive to the value of .

Evaluation of drifting forecast trajectories
The performance of drifting forecast model not only depends on the ability of simulating the drifting velocity at a predetermined time and place, but also depends on the capacity of predicating the final position of the SSD when only the initial position is specified, which demands every computational time step's forecast accuracy from the starting time to the ending time. We specify the initial position at the measured location of the SSD at 0:00 each day and predict 24-hour trajectories based on Eq. (12). According to the three alternative values of , we predict three branches of 24-hour trajectory both on December 31, 2013 and January 1, 2014, as is shown in Fig. 10. Moreover, the performance of the predicted trajectories after experiencing n time steps are described by the skill score proposed by Liu and Weisberg (2011), with implying a perfect fit between the predictions and the measurements. And this evaluation method simultaneously introduces a separation degree S between the predicted trajectory and the measured one: where d i is the separation distance between the predicated location and the measured location at time step i; is the measured trajectory length from the initial position at the starting time to the measured location at time step i.
On December 31, 2013, the predicted trajectories resulted from the three alternative values of generally have northwestward deflections compared with the measured trajectories (Fig. 10a) and these three trajectories are incapable of enveloping the measured trajectory. The higher value reaches, the farther downwind displacement the SSD takes place. The main reason why the predicted trajectories deviate from the measurements is that some wind data at P1 derived from the wind extrapolation are less accurate at a certain time. It is likely that predominant wind direction at P1 is W in reality, but what we obtain from extrapolation is WSW. But most of the wind data are gener- Fig. 10. Comparison between the measured and predicted trajectories resulted from the three alternative values of (a, b) and the time series of the skill score (c, d). The comparison between measured trajectories and tidal current trails is also given. Black triangles denote start-point; black circles (red circles) denote the turning point of the measured trajectories (the tidal current trails) and their occurrence time is shown next to them with the same color.

S S (n)
ally reliable, which we will clarify when we analyze the time-varying performance of the predicted trajectories by the skill score .
On January 1, 2014, the predicted trajectories are roughly consistent with the measurements and different values of can have but a faint influence on forecast results below the level of wind scale 4 (Fig. 10b), because when weaker wind prevails, the predicted results would be less sensitive in reaction to different values of . At the end of the day, it is likely that the east wind had potentially prevailed over the west wind in the open sea, whereas the wind at P1 derived from the extrapolation was still blowing from the west towards the east. That is why the end-point of the predicted trajectories has eastward deflection in contrast to the measurements. l oi We evaluate the performance of the generated predicted trajectories after every computational time step, because we are concerned of the forecast accuracy of every time step. The time series of the skill score in each day is shown in Figs. 10c and 10d, respectively, where the fluctuation trend can reflect the performance of the forecast model on the corresponding time step. Here, our drifting forecast model performs well with most of the skill scores over 0.9, though relative low skill scores exist at the beginning of the day. This is because the accumulation of a series of small would appear in the denominator of Eq. (14) within a short period after 00:00 (in slack tide), and low skill scores occur even though with a small forecast error. The skill scores show a slight downward trend at about 06:30 on December 31, 2013 and 07:30 January 1, 2014, but have risen steadily later on. This indicates that the short-term imprecise wind data at P1 are responsible for the temporary fall in the skill scores, but the reliability of wind data at other times improve the skill scores firmly. The result of prediction supports the view that the wind extrapolation method is allowed to be adopted in the drifting forecast model, provided that the in situ wind data are inaccessible.
Overall, the forecast results are less sensitive to the value of , especially under weak wind conditions, and we still recommend that the optimum value of is equal to 1. Our predicted results agree well with the feature of measured drifting trajectories: migrating back and forth twice a day with intersections as well as daily downwind displacements. Given that the coarse temporal resolution of measured wind data at 1-hour intervals, the agreement between the predications and the measurements should be considered satisfactory though lacking complete consistency. Our drifting forecast model is reasonable for simulating the drifting velocity and predicting the drifting trajectory for SSDs.

Discussion and analysis
The 2-day in situ drifting experiment experienced a normal and changeable dynamic environment, subjected to fluctuated wind (from Beaufort wind scale 2 to wind scale 6), waves, and periodic tidal currents. Figuring out the roles played by different dynamics including atmospheric effects and hydrodynamic effects is essential to understanding the drifting behavior of SSDs. A set of trajectory models are established to quantify the contributions of each external force to drifting motion and analyze their different performances reacting to a changing tide-wind-wave environment.

Hydrodynamic effects on the drifting motion
Eq. (10) indicates that the hydrodynamic effects are proportional to the velocity of Lagrangian current and the reduction parameter , which is approximately equal to 1. Next, when we analyze the contribution rate of each hydrodynamic forcing on the drifting motion, we would neglect the influence of the reduction parameter on hydrodynamic force. Firstly, "the trajectory model for surface tidal currents" is defined to describe the 24-hour tidal current trail as follows: Secondly, "the trajectory model for wind-driven currents" is defined to describe the 24-hour wind-driven current trail as follows: Thirdly, "the trajectory model for wave-induced mass transport" is defined to describe the 24-hour wave-induced mass transport trail: The above three trajectory models are all applied to describe the specified transport state under a certain hydrodynamic condition. Thus, Lagrangian water particle transport trail is defined to describe the surface water-mass transport under the tide-wind-wave condition: x In Eqs. (16)-(19), , , , and are the corresponding final positions of each trajectory model, and these trajectory models share the same initial position which is specified at the measured position at 00:00.
Both of the 24-hour tidal current trails are shown in Fig.  10, with daily ebb (eastward)-flood (westward)-ebb-flood motion features due to the control of semidiurnal tide, and accompanied by daily westward displacements. The ellipse-shaped tidal trails indicate rotational tidal flow, and the tidal trail generated in shallower water areas on December 31, 2013 is characterized by two flatter ellipses compared with that on January 1, 2014. Due to the influence of the shallow water depth and the bottom friction in the coastal zone, the tidally induced Lagrangian residual currents are worth to be mentioned here, characterized by the net displacement in one tidal cycle. On December 31, 2013, the tidal trail shows that the duration of flood tide is roughly equivalent to the duration of ebb tide , with daily westward displacements of 4.0 km. This phenomenon is clearly different from the measured trajectory, which shows a shorter period of the westward drifting from 6:00 to 10:47, a longer period of the eastward drifting from 10:47 to 18:21, and daily eastward displacements of 20.4 km. On January 1, 2014, the tidal trail indicates that the duration of flood tide (6:17 − 12:31) is close to the duration of ebb tide (12:31 − 18:39), with daily westward displacements of 2.0 km. While the measurements indicate the SSD moved westwards from 6:12 to 12:15, and then moved eastwards from 12:15 to 18:33, with daily northward displacement of 4.4 km. These tidal trails deviate remarkably from the measured trajectories under normal wind conditions (wind scale 2-6) and thus we cannot directly treat the measured drifting data of SSDs as research materials of surface tidal currents. To clarify this further, we obtained the vector correlation between the surface tidal current velocity and measured drifting velocity based on Eq. (13), as is shown in Fig. 9b. The existence of wind causes the gap between surface tidal currents and the SSD's drifting velocities, when the maximum deviation occurs at wind scale 5-6. The predicted drifting trajectories apparently provide a better representation of the measured drifting trajectories than the tidal trails do. Fig. 11 summarizes the results of the above trajectory models for better analysis of the performance of each hydrodynamic forcing in a changing tide-wind-wave environment. When the dominant wind scale 5-6 prevailed the drifting areas on December 31, 2013, the length scale of the wind-driven current trail is the same size as the displacement of the 24-hour tidal current trail, but the direction of them are nearly the opposite. When the dominant wind scale 3-4 prevailed on January 1, 2014, the length scale of the wind-driven current trail becomes shorter, and is still close to the displacement of the 24-hour tidal current trail. The wind-driven currents show comparable influence on the daily displacement of the SSD with surface tidal currents. However, the wind-driven currents have the least contribution to the drifting distance of the SSD.
Wave-induced mass transport has great influences on the daily displacement of the SSD. On December 31, 2013, wave-induced mass transport is two or three times as large as the wind-driven currents; on January 1, 2014, wave-induced mass transport is one or two times as large as the wind-driven currents. This indicates that wave-induced mass transport depends more sensitively on the fluctuation of wind speed than wind-driven currents. The predictability of drifting forecast model can be highly improved by adding wave information. It is important to have reliable estimation of wave-induced mass transport.
The Lagrangian water particle transport trails travel back and forth twice a day with intersections but less daily downwind displacements. This feature is qualitatively similar but quantitatively different from the characteristic of the measured drifting trajectories. Thus, the atmospheric effects should be taken into account when studying the drifting motion of SSDs.

Atmospheric effects on the drifting motion
When the wind passes over an SSD, it would apply drag force on the emerged part of the SSD due to the friction and pressure effects, similar to the case of water drag. Eq. (10) shows that the atmospheric effects are proportional to the wind speed at the SSD's height and the reduction parameter , which is equal to 0.028 when is set to 1. The last trajectory model is designed for wind drag trails (Fig.  11) and its corresponding final position is : As for the SSD with the immersion ratio of 60.8% in our study, atmospheric effects have the most significant influence on the daily displacement of the drifting motion at wind scale 2-4; whereas it loses its leading role at wind scale 5-6, when the wave-induced mass transport contributes mostly to the daily displacement. Our conclusions about the atmospheric effects on the drifting motion based on the mechanism analysis are more detailed than those resulted from semi-empirical methods. Röhrs et al. (2012) concluded that the wave-induced mass transport is twice as large as the atmospheric effects for semi-submerged spherical drifters without giving certain wind conditions. Moreover, the empirical drifting forecast model, such as AP98 leeway model, considers the effect of the wind drag and waves on SSDs as a linear function of the wind speed at the reference height of 10 m, which is apparently unreasonable, because the wave-induced mass transport reacts sensitively to the growth of wind speed, beyond linear responses.

Summary
We have shown in situ drifting experiment results of a cylinder SSD during December 31, 2013 to January 1, 2014 in the RSRs. The measured drifting trajectories indicate migration back and forth twice a day with intersections as well as daily downwind displacements and these drifting features are successfully modeled by the mechanistic drifting forecast model proposed by this study, which differs from the traditional empirical drifting models.
The RSRs are characterized as tidal inlet systems, in terms of hydrodynamic forcing, by a dominance of tidal currents over wind-driven currents or oceanic waves. However, our study shows that tidal currents are not significant to the daily displacement of the surface water-mass transport. The wind-driven currents are on the same order of the magnitude as tidally induced Lagrangian residual currents under normal wind conditions. Wave-induced mass transport is one or two times as large as the wind-driven currents at wind scale 2-4, and two or three times at the wind scale 5-6. Thus, we cannot directly treat the measured drifting data of SSDs as the research materials of surface tidal currents, even though exposed to the strong tidal dynamic such as in the RSRs. Moreover, it is necessary to emphasize the effect of wind-driven currents and wave-induced mass transport when studying the surface water-mass transport or even the mass transport under normal wind conditions. Examples may, for instance, be the simulations of the surface drifting algae, suspend sediment transport and nutrients.
For our used SSD, the wind drag has the greatest impact on the daily displacement of the drifting motion at wind scale 2-4, whereas its effect is inferior to the influence of wave-induced mass transport at wind scale 5-6. The wind drag effect is usually on par with water drag effect on the drifting motion of a semi-submersible drifter and need to be honored.