## Abstract

An operational search and rescue (SAR) modeling system was developed to forecast the tracks of victims or debris from marine accidents in the marginal seas of the northwestern Pacific Ocean. The system is directly linked to a real-time operational forecasting system that provides wind and surface current forecasts for the Yellow Sea and the East and South China Seas and is thus capable of immediately predicting the tracks and area to be searched for up to 72 h in the future. A stochastic trajectory model using a Monte Carlo ensemble technique is employed within the system to estimate the trajectories of drifting objects. It is able to consider leeway drift and to deal with uncertainties in the forcing fields obtained from the operational forecasting system. A circle assessment method was applied to evaluate the performance of the SAR model using comparisons in buoy and ship trajectories obtained from field drifter experiments. The method effectively analyzed the effects of the forcing fields and diagnosed the model’s performance. Results showed that accurate wind and current forcing fields play a significant role in improving the behavior of the SAR model. Operationally, the SAR modeling system is used to support the Korea Coast Guard during marine emergencies. Additionally, some sensitivity tests for model parameters and wave effect on the SAR model prediction are discussed.

## 1. Introduction

Operational oceanographic systems have been developed to accurately predict both present and continuous future conditions for the marginal seas of the northwestern Pacific Ocean, including the Yellow Sea, the East and South China Seas, and the East/Japan Sea (Kagimoto et al. 2008; Miyazawa et al. 2008; You 2010; Dombrowsky 2011; Lim et al. 2011; Zhu 2011). Ocean forecast information obtained from operational forecasting systems is provided to marine industries, government agencies, scientific research communities, and to the public, to support safe and efficient marine navigation and environmental applications in coastal seas (Lee et al. 2009; Park et al. 2009). As an environmental application, the Korea Operational Oceanographic System (KOOS) is designed to respond rapidly to marine emergencies such as search and rescue (SAR) activities, oil spills, radioactive contaminants, and other marine ecological issues (Cho et al. 2012).

The Korea Coast Guard (KCG; http://www.kcg.go.kr/global/index.jsp) reports that more than 7300 maritime incidents occurred in the past six years, and about 520 victims were involved in search and rescue activities. To effectively support the KCG in the accurate prediction of the tracks of missing people and objects (such as the wreckage from aircrafts or ships, or the spread of oil spills, nuclear radiation, and red tides), an operational forecasting system incorporated within a reliable trajectory model is required.

In the past two decades, regional studies of the movement of drifting ships in relation to search and rescue activity around the Korean Peninsula have been conducted using field experiments and track computation (Kang 1993; Kang and Lee 1995; Kang 1999; Lee et al. 1999; Kang 2000a,b; Yun et al. 2001; Lee et al. 2005; Kim et al. 2007). Kang (2000a) developed and verified a prediction model for distressed craft drift, using fluid dynamics analysis based on Newton’s law of fluid dynamics. Most of the studies have focused on tracking ship drift via field experiments, and defining the effect of leeway drift. However, although such methods can simulate the trajectories of drifting objects in near–real time, the system is not a fully operational SAR forecast system because forcing fields (wind and current predictions) are extracted from the observed winds and harmonically analyzed tidal currents.

In other scientific areas, studies on trajectory modeling for drifting objects have been intensively performed over the past decade (Allen and Plourde 1999; Allen 2005; Ullman et al. 2006; Breivik and Allen 2008; Ni et al. 2010; Breivik et al. 2011, 2012; Mínguez et al. 2012). Allen and Plourde (1999) and Allen (2005) empirically derived the coefficients for 63 categories of search objects, which indicated the relation between the wind and the leeway of the drifting object. Based on their studies, the leeway drift model has been developed and used operationally by the U.S. Coast Guard and the Norwegian Meteorological Institute for search and rescue operations (Hackett et al. 2006; Breivik and Allen 2008). The leeway drift model is designed to utilize the wind and surface current fields taken from the operational atmospheric model and the operational three-dimensional baroclinic ocean model, respectively. In addition, Ni et al. (2010) dealt with the uncertainty of leeway and surface drift by using a theoretical model and a stochastic particle model combined with high-frequency (HF) radar-derived surface currents (Ullman et al. 2006; Abascal et al. 2012).

It is significant that the performance of a SAR model requires assessment with observed drifter trajectories. Trajectory assessment has been studied in various ways: using a spaghetti diagram (Toner et al. 2001; Nairn and Kawase 2001), statistical separation (Thompson et al. 2003), and circle assessment (Furnans et al. 2005). The use of a circle assessment is designed to evaluate how well a particle-tracking model reproduces the path(s) of one or multiple drifters. It applies a tertiary “perfect/acceptable/flawed” evaluation of model skill (Furnans et al. 2005). This method not only quantifies a particle model’s ability to reproduce the field drifter path over various temporal and spatial scales but also provides diagnostic information with regard to the model’s performance.

There has been a lack of research that contains a fully operational SAR modeling system and its assessment method in relation to the Yellow Sea and the East and South China Seas. The objective of the present study is, therefore, to develop a fully operational SAR modeling system with an adequate trajectory assessment method for drifting ships or objects; to determine quantitatively the acceptability of SAR predictions produced from the system; and to validate the applicability of the system to search and rescue operations in the Yellow Sea and the East and South China Seas.

## 2. Operational SAR modeling system

The operational search and rescue modeling system (Fig. 1) is mainly composed of the leeway model as a particle-tracking model, external forcing input from an operational forecasting system (which produces the predicted fields of winds and surface currents), and the system evaluation (using observed track data obtained from drifter field experiments). Each of these components is described below.

### a. Leeway model for search and rescue

The leeway model, developed by the Norwegian Meteorological Institute (Hackett et al. 2006), is adopted for search and rescue modeling. Assuming a linear relationship between wind speed and the leeway of a floating object and ignoring wave effects, the trajectory model calculates the arc traced by the superposition of the leeway vector and the surface current vector as follows (Breivik and Allen 2008):

where *x*_{0} is the initial position of the object, **x**(*T*) is the position at time *T*, **V** is the object velocity vector, **L** is the leeway vector, and **u**_{c} is the local surface current vector. The leeway vector (decomposed into downwind and crosswind components) is estimated by a linear regression with the empirical coefficients (leeway coefficients) listed in Allen and Plourde (1999).

In searching for drifting objects on the sea’s surface, a Monte Carlo integration (ensemble) technique is used. This deals with errors and uncertainties of winds, sea state, and sea surface currents from the last known position of the object type. By assigning probabilities to the relevant parameters perturbed in a stochastic fashion, this technique generates an ensemble of numerical integrations of the trajectories simulated in multiple times (Hackett et al. 2006). Under the assumption that the perturbations behave as a first-order autoregressive process, the trajectory is estimated in a stochastic approach as follows:

where *dε* is the random perturbations in the object’s displacement. The random perturbations have a known covariance and zero mean to represent the uncertainties in drift properties and external forcing (wind and current). The ensemble is composed of *N* samples drawn from the stochastic differential Eq. (2). As suggested in Allen and Plourde (1999) and Breivik and Allen (2008), the perturbations in leeway coefficients remain fixed throughout the simulation and some empirical perturbations at *W*_{10} = 10 m s^{−1} are added to both the slope and offset of the regression line of ensemble members *n* = 1, …, *N* as follows:

where is the wind speed adjusted to a height of 10 m above mean sea level, and *a* and *b* are the slope and offset of a linear regression line, respectively, which represents a relationship between the measured leeway component and the measured wind speed (see section 3b). The perturbations in external forcing (wind and surface current) are dealt with using a random walk method and a random flight method, assuming that the perturbations follow a circular normal distribution (see Breivik and Allen 2008 for details).

### b. Operational atmospheric and oceanic forecast models

Embracing the leeway model as an engine, the operational SAR modeling system is directly linked with KOOS, which uses an atmospheric model, the Weather Research and Forecasting Model (WRF; www.wrf-model.org), and a three-dimensional (3D) ocean circulation model, the Modelo Hidrodinâmico (MOHID; Cancino and Neves 1999). KOOS provides scientific guidance in relation to the regional seas of the Korean Peninsula, including a 72-h forecast system for use by marine industries, the general public, government agencies, and scientific research communities (Cho et al. 2013).

The WRF solves fully compressible, nonhydrostatic Euler equations formulated in an Arakawa C grid, staggering a horizontal grid and a terrain-following hydrostatic pressure vertical grid. It uses a third-order Runge–Kutta scheme for time-split integration, a second-order scheme for horizontal/vertical advection, and a second-order Smagorinsky approach for turbulence closure. The parameterization for the model physics used in the WRF is described in Heo et al. (2013). The WRF used in the present study is a one-way nesting system with two model grids: domain 1 (D1) and domain 2 (D2). D1 is a domain that ranges approximately from 14.9°N, 104.6°E to 52.5°N, 150.4°E with a horizontal grid resolution of approximately 20 km (163 × 217 grids) and covers the Yellow Sea, the East/South China Seas, the East Sea, and some regions of the northeast Pacific Ocean. D2 has a 4-km-resolution grid (270 × 270) and covers the regional seas around the Korean Peninsula (Fig. 2). The WRF uses the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) outputs as the initial and boundary conditions. The vertical grid used in the domain has 28 layers in stretched coordinates, and the model time step is set at 100 s. The WRF simulations start at 0000 and 1200 UTC without data assimilation and their results are saved every hour for 72 h.

The MOHID model is a 3D baroclinic ocean model operated by the Korea Institute of Ocean Science and Technology (KIOST). It solves 3D hydrodynamic problems using Navier–Stokes equations with hydrostatic and Boussinesq approximations. It uses a finite-volume method for the baroclinic pressure gradient and horizontal viscosity terms, which are treated explicitly, and for the barotropic pressure gradient and the vertical viscosity terms, which are treated implicitly. The MOHID treats advection in the transport equations with the total variation diminishing (TVD) scheme. The model adapts the generic length-scale turbulence closure through the General Ocean Turbulence Model (GOTM) with the *k*–*ε* scheme option, and uses an alternate direction implicit (ADI) time discretization scheme that minimizes stability restrictions.

The MOHID in the present study uses a one-way nesting system with four model grids: level 1 (L1), level 2 (L2), level 3 (L2), and level 4 (L4) (Fig. 2). We conducted 2D simulations with L1, and fully 3D simulations with L2–L4. L1 is an 18-km-resolution grid (180 × 192) and only forced by the National Astronomical Observatory of Japan tides (NAO.99jb; Matsumoto et al. 2000) for open boundary conditions. L2 is the second-level model domain ranging from 22.0°N, 117.0°E to 44.0°N, 135.0°E with approximately 9-km resolution (216 × 264) and forced by the WRF output for sea surface boundary conditions (winds, atmospheric pressure, and heat flux), the Hybrid Coordinate Ocean Model (HYCOM; www.hycom.org) output for initial and open boundary conditions (sea surface height, currents, water temperature, and salinity), and the tidal elevation computed in L1. A linear or bilinear interpolation method is used to generate the boundary conditions for MOHID, which are temporally and spatially interpolated from 1-h WRF and 1-day HYCOM outputs. L3 is a 2-km-resolution grid (90 × 155) and forced by the WRF output for sea surface boundary conditions and the L2 output for open boundary conditions (total water elevation, currents, water temperature, and salinity). L4 is a 300-m-resolution grid (252 × 258) and forced by the WRF output and the L3 output in the same manner as the L2 and L3 nesting. MOHID uses hybrid-vertical coordinates, which include both terrain-following sigma (σ) coordinates and Cartesian *Z* coordinates. The vertical grid used in the domain has 8 layers in σ coordinates and 32 layers in *Z* coordinates. The model time step was set at 120 s. MOHID has already been coupled with the Simulating Waves Nearshore (SWAN) model, which can be turned on to represent intense wind effect on the sea surface, but it is typically turned off for daily forecasts in order to reduce the cost of run time (Cho et al. 2013).

### c. Field drifter experiments

Surface drifter experiments were carried out in the Yellow Sea to evaluate the performance of ensemble techniques and models. Individual experiments were conducted for less than 12 h near Shin Island on 14 October 2010, Shin-Jin Island on 12 May 2011, and Ma-Ryang on 25 May 2011 (Table 1). Three drifters, with and without drogues, were designed to consider the differing effects of winds and surface currents (Fig. 3). Drifter A was exposed 20 cm from the sea surface without a drogue, to be mainly influenced by winds. Drifters B and C were employed with a drogue, to consider the effect of surface currents, but they were designed to be exposed in different positions, that is, at 20 cm and 10 cm above the sea surface, respectively. The trajectory data from the drifters were transferred through an ORBCOMM modem once every 5 min, and the drifters’ positions were monitored in near–real time. Surface currents were measured from an ADCP in the first experiment. Measured trajectories of the drifters on individual experiments are plotted in Fig. 4.

Three experiments were also performed using a drifting shipwreck by the National Marine Environmental Forecasting Center (NMEFC) near the Pearl River estuary (South China Sea), in February and April 2011 (Table 1). Experiment 1 (EXP1) took place on 17–19 February 2011 at Yuedong (lasting 2 days), and experiment 2 (EXP2) took place simultaneously in the Pearl River estuary (lasting 75 h). Experiment 3 (EXP3) was then conducted on 24 April in the Pearl River estuary (lasting 17 h). The initial location and schematic of the shipwreck used for the experiments is shown in Fig. 5. To estimate the leeway drift of the shipwreck, near-surface currents and winds were measured during the experiments.

We then tested the model’s applicability to a real aircraft crash scenario that occurred on 28 July 2011 off the western coast of Jeju Island, South Korea. Using the coefficients and parameters determined from the drifting buoy experiments, the SAR prediction was immediately implemented using the initial information from the incident.

### d. Trajectory assessment method: Circle assessment

The circle assessment method (Furnans et al. 2005) was applied to evaluate the performance of the SAR model. In this method, as depicted in Fig. 6, the predicted drifter path is classified as perfect when a model drifter is located within a target circle (with target radius δ) of the field drifter position. Likewise, it is considered acceptable when the model drifter remains in an error circle, with the error radius ξ larger than δ, of the field drifter position. When the model drifter is outside the error circle, it is considered flawed. We consider that δ is equal to the mean standard deviation of the model drifters’ positions and ξ = 2δ. The separation time of the modeled trajectory is defined as the time when the model drifter is first separated from the field drifter by a predetermined distance (Furnans et al. 2005). Within this study, the acceptable duration (*T*_{a}) is defined as the time when the model drifter first leaves the error circle of the field drifter. We believe that owing to errors in the modeled external forcing fields and the SAR model, the model drifters would eventually be separated from the field drifter and be found outside the target and error circles.

## 3. Results

### a. Performance of the operational forecasts

The SAR predictions are highly dependent on the performance of the model forecasts. It is necessary to incorporate the evaluation of a forecast system into the development and operational phases of the system, in order to assess its performance and accuracy (Hess et al. 2003), and the procedure used for skill assessment of the variables predicted by KOOS is described by Cho et al. (2013) in detail.

For the atmospheric variables (pressure and wind components), the predicted variables were compared with observed data obtained in May 2011. To compute skill metrics, that is, root-mean-square error (RMSE) and correlation coefficient (*R*), the outputs from WRF were interpolated to ensure that they had the same time intervals as the observation data. The skill scores for pressure and wind components were computed at five stations (Fig. 2), Deokjeok (DJ), Oiyeon (OY), Anheung (AH), Gunsan (GS), and Janghang (JH). The averaged values of RMSE and *R* are listed in Table 2. The RMSE and *R* of winds simulated in D1 range from 1.75 to 2.84 m s^{−1} and from 0.41 to 0.76, respectively.

An astronomical tide in MOHID was calibrated with respect to a bottom friction coefficient and spatial grid resolution, by simulating mean tide characteristics with the harmonic constants of 16 constituents. For the mean tidal ranges and phases of four major tidal constituents (*M*_{2}, *S*_{2}, *N*_{2}, and *K*_{1}) and associated skill scores, all RMSE values were below 0.05 m in amplitude and 5° in phase. The predicted total water elevations of MOHID were calibrated with the observed water elevations at the tide stations along the west coast of South Korea (not shown). The range of RMSE was 0.2–0.4 m (error percentages relative to total tidal ranges were below 5%) and *R* values were larger than 90%. Unfortunately, no measurement of currents was conducted in May 2011. Instead, the modeled currents were compared with a 15-day record available from 26 June to 10 July 2011, obtained from the Eocheong (EC) observation buoy. The RMSE was 0.14–0.17 m s^{−1} at three depths (i.e., 2, 22, and 42 m), and the skill scores computed at the different depths appeared to be close (Table 2).

### b. Calculation of leeway coefficients from field drifter experiment data

From the first field drifter experiment, we obtained ADCP current data measured in the Jangbong Strait, and wind data observed on Jangbong Island and Incheon International Airport. The drifters were tested three times in the first experiment (Table 1). Sea surface currents and winds were measured during the shipwreck experiments in the South China Sea.

The leeway vector was estimated by subtracting a sea current vector from the total displacement vector (Nash and Willcox 1991; Allen and Plourde 1999). The leeway coefficients for the drifters were calculated from the field drifter trajectories, surface current data, and wind data, using a linear regression with least squares best-fit coefficients as follows:

where *W*_{10} is the 10-m wind speed; *a*_{d}, *a*_{c}, *b*_{d}, and *b*_{c} are regression coefficients; and *L*_{d} and *L*_{c} are the estimated best-fit components of downwind leeway (DWL) and crosswind leeway (CWL), respectively. The coefficients estimated from the field data are tabulated in Table 3. A linear relationship between the downwind components of leeway speed and wind speed is depicted in Fig. 7.

According to Allen and Plourde (1999), the maximum wind speed used to compute leeway coefficients ranges from 20 to 25 m s^{−1}. It then allowed the linear regression of leeway coefficients to be meaningful. However, the wind speed measured from our shipwreck experiments was restricted to within 10 m s^{−1}. Moreover, our statistics from the linear regression of leeway coefficients presents that the value of *R* is nearly 0.3, and that the 95% confidence bound is approximately ±0.29 (%). It is therefore obvious that more field experiments are required to obtain adequate coefficients, by improving the value of *R* and the confidence level via a linear regression relationship in a large range of leeway components and wind speeds.

### c. Drifting buoy trajectory comparison

The model drifter trajectories were compared with the field drifter trajectories. During the first field experiment on 14 October 2010, the trajectory comparison between the model drifter and the field drifter was not carried out at the same time because the forecast system was not operated in near–real time. Thus, all data achieved from the first field experiment were used to calculate the leeway coefficients as described in section 3b. During the second field experiment, 12 May 2011, we predicted the model drifters’ trajectories using KOOS forecast outputs (winds in D1 and surface currents in L2) prior to releasing the drifters. We then released 30 model drifters and compared the trajectories with the field drifter tracks. As shown in Fig. 8a, the ensemble-mean trajectory compares reasonably well with the observed tracks. The difference in distance is plotted in Fig. 9a. Field drifter A was recovered earlier owing to a communication malfunction. Results show that the ensemble-mean trajectory of the model drifters remained within the target circle radius (δ = 0.5 km) and the error circle radius (ξ = 1 km) for the experiment period. The mean track was evaluated as being perfect from the beginning until noon, acceptable from 1200 to 1400 Korea standard time (KST), and then perfect after 1400 KST. Thus, an acceptable duration appears to continue for longer than 7 h. Wind forcing was eliminated to examine the effect of leeway drift. The drifters started to move northwestward during the flood, and then turned back to the southeast during the ebb. Without wind forcing, the predicted trajectory was not sufficiently in reach of the observed tracks (not shown). The difference between the final positions of the ensemble-mean tracks, with and without wind forcing, was approximately 1.5 km, and *T*_{a} was shortened to 5.5 h without wind forcing.

In the third field experiment, 25 May 2011, all field drifters were set up as type drifter C. The prediction was not well matched for the first forecast (Fig. 8b). After the flood tide, the drifters moved southward and southeastward, but the predicted particles had a tendency to move westward and southwestward. The first trajectory prediction was assessed as being flawed 4.5 h after seeding (Fig. 9b), and the forecast wind field was assumed to be the key issue. WRF winds were compared with the winds observed at Gunsan (Fig. 10). On the morning of 25 May, a northeasterly wind was forecast, whereas a northwesterly wind was observed around Gunsan (dashed circle). Even during the afternoon (dashed rectangle), WRF winds displayed an opposite direction to those of actual observed winds, which blew dominantly from the north. It appears, therefore, that WRF winds have an influence, not only on the leeway drift of the field drifters, but also on the wind-driven currents in the hydrodynamic forecast. As a diagnostic experiment, we applied the wind data observed at Gunsan instead of those of the WRF winds, to compute a leeway drift. As a result, we obtained an improved trajectory prediction (Fig. 11a), and a longer acceptable duration (Fig. 11b). With a combination of observed winds and tidal forcing, the perfect period was elongated to approximately 5 h, and the flawed period was shortened to 1.5 h. The *T*_{a} was nearly 10 h. It is therefore evident that the northeasterly winds predicted from WRF misled the model drifters to the west during the morning. Furthermore, it ensured that the observed clockwise wind change, from westerly to northerly, drove the model drifters close to the field drifters during the afternoon.

### d. Shipwreck trajectory comparison

We carried out a number of simulations using two types of leeway coefficients (in Table 3), for a shipwreck and a general fishing-vessel-type 43 (FV-T43). Leeway coefficients for a FV-T43 are provided from the leeway model manual (http://www.ifremer.fr/sar-drift/exchange-repository/leeway_documentation_v2.5.pdf). Observed winds and near-surface currents were utilized for the external forcing.

During EXP1, the mean trajectory of 100 model drifters was compared with the observed shipwreck track in Fig. 12a. Up until 24 h from launching, the difference in distance between predicted trajectories in two of the cases, and the observed track, remained within 4 km. However, after 24 h the trajectory for the FV-T43 bore a greater similarity to the observed track than to that of the shipwreck. When ξ = 5 km, the *T*_{a} for FV-T43 was nearly 10 h shorter than the *T*_{a} for the shipwreck (Table 4). However, in EXP2 at the Pearl River estuary, the shipwreck case scenario gave better results (Fig. 12b). Using the same circumstances, that ξ = 5 km, the *T*_{a} for the shipwreck was approximately twice as short as the *T*_{a} for the FV-T43. In EXP3 on 24 April 2011, the trajectory comparison for both cases appeared reasonable (Fig. 12c). When ξ = 5 km, the *T*_{a} for both cases remained for longer than 17 h. The distance difference for FV-T43 was nearly 1 km at 10 h, while that for the shipwreck was 2 km. Thus, the FV-T43 case reproduced the observed trajectory better than the shipwreck. The estimated *T*_{a} for individual ship types is summarized in Table 4. In general, it is assumed that damping and excitation is negligible for small objects (less than 30-m length) in a well-developed sea (Breivik and Allen 2008). However, wave effects should be considered under severe sea surface conditions such as tropical cyclones. Further discussion regarding this will be done in section 4.

### e. Application of SAR modeling to aircraft accident

On 28 July 2011, a cargo plane crashed off the western coast of Jeju Island, South Korea. The time of occurrence and the location were approximated from information gained when communication was lost with the aircraft. The KCG conducted search and rescue operations and recovered parts of the aircraft (the wreckage information provided by KCG is listed in Table 5). Using the coefficients and parameters determined from the drifting buoy experiments, the SAR prediction was immediately implemented using the initial information from the incident. WRF and MOHID outputs were used for the external forcing in the simulation. The radius of uncertainty in the initial position was set to 0.25 km (*r*_{0}), and 100 ensemble particles were released as a circular normal distribution with standard deviation δ = *r*_{0}/2. The predicted particles were compared with the wreckage location at 0700, 1100, 1200, and 1400 KST in Fig. 13. By setting the error circle radius ξ = 2δ, approximately 86% of the particles were predicted to be within the circle. Here we assumed that δ is temporally variable, which is the standard deviation of 100 ensemble particles. Results show that even though the equivalent leeway coefficients were applied for each wreckage item, the positions of the wreckage were reasonably well located within either error circles or polygons (representing convex hull), which encompass individual ensemble particles at the individual time steps.

## 4. Discussion

### a. SAR model sensitivity to model parameters

It is noteworthy that we should understand how sensitive the SAR model’s performance is to model parameters such as horizontal grid resolution, the error radius, number of released particles, and leeway coefficients. Because most of the SAR operations take place within 40 km from the coast, surface fields that accurately resolve the nearshore currents would greatly improve the performance of the operational SAR model. Realistically, detailed current fields are required for the SAR model to resolve the complicated bathymetry and the complex west coast of South Korea. In this section, we first computed skill scores of winds simulated in D2 (4 km). Their RMSE was decreased by 2.7% and *R* was increased by 4.6%. Skill scores of currents simulated in L3 (2 km) and L4 (300 m) became slightly (<2%) better than those simulated in L2 (9 km). It appears that a circulation model skill is not sensitive to a horizontal grid resolution because each model domain was calibrated with the same parameterizations (e.g., bathymetry, bottom friction, and etc.). It is certain that increasing the horizontal resolution of weather prediction models produces more skillful forecasts. However, the optimal calibration in each resolution grid model with its own parameterization is necessary for future research. Second, we diagnosed the SAR prediction results with regard to horizontal grid resolutions of the forecast models. We compared the acceptable duration (*T*_{a}) in four cases with combinations of two atmospheric model domains (D1 and D2) and two oceanic model domains (L2 and L4). The values of *T*_{a} estimated on 25 May 2011 are listed in Table 6. It shows that *T*_{a} using forcing in high-resolution grid domains was slightly increased.

It is significant to examine how sensitive *T*_{a} is to numerical parameters such as leeway coefficient (DWL, *a*_{d}), number of model drifters released (*N*), and the error circle radius (ξ) because *T*_{a} can be an important factor to determine the system’s accuracy when it is applied to SAR operations. To examine relationships between *T*_{a} and *a*_{d} and between *T*_{a} and *N*, data obtained from the field drifter experiment on 12 May 2011 was used. It is found that there was no significant difference in model prediction as *N* increases. However, the model results were clearly sensitive to *a*_{d} (Fig. 14). Trajectory comparison reveals that northwesterly winds restricted northwestward surface drift during the flood tide but enhanced surface drift during the ebb tide. It also showed that the difference in final positions tends to linearly decrease as *a*_{d} increases. The minimum difference was represented at 3%.

An extra field drifter experiment (type C) was carried out for 2 weeks from 17 November to 1 December 2011 to examine how sensitive *T*_{a} is to ξ. We released 100 model drifters at the positions (the filled circle ● denoted in Fig. 15a) where the field drifter was located at every 12 h from the initiation and computed *T*_{a} at a 12-h interval plotted in Fig. 15b. It shows that when each error circle is set to 1, 2, and 3 km, the averaged *T*_{a} values were approximately 4.5, 14.2, and 22.5 h respectively. The ratio of *T*_{a} to ξ is a concept of inverted speed. This speed implies how rapidly a drifting object avoids a certain search area. The estimated speeds (namely, avoidance speed) are 0.22, 0.14, and 0.13 km h^{−1}, respectively. A SAR model having higher avoidance speed seems to predict a larger uncertain search area. It would be a useful factor to evaluate an operational SAR model or to represent the model’s performance but further discussion is necessary.

### b. Wave effects: Stokes drift

As described in section 2b, the SWAN model is usually turned off for daily forecast except when winds and waves become intense. Especially when a tropical cyclone (i.e., typhoon) approaches the wave-induced velocity (i.e., Stokes drift velocity), it can significantly affect the upper-layer velocity through interaction with a sheared near-surface current. Stokes drift is the average velocity assumed when following a specific fluid parcel as it travels with the fluid flow. Under the assumption of a monochromatic wave condition, the Stokes drift velocity is estimated by using deep-water formulation proposed by Phillips (1977) and bulk wave parameters (Tamura et al. 2012) such as the significant wave height , surface wave peak period , and depth *z* as follows:

where and are peak wavenumber and peak angular frequency, respectively. In Eq. (5), and are model products from the SWAN model. We added this estimation of the Stokes drift velocity to the velocity term in Eq. (1) and examined its impact on a drifting object’s trajectory.

Moored in the middle of the Korean Strait, the sphere-type marine observation buoy (0.9 m in diameter and 1.25 m in height) was cut off by Typhoon Sanba on 16 September 2012. Information related to the buoy’s location was transmitted through a satellite iridium sensor until communication was lost. A maximum wind speed of 15 m s^{−1} and a maximum significant wave height of 8 m were recorded during the period 16–17 September 2012. The model buoy’s trajectories were simulated with the outputs of WRF, MOHID, and SWAN, and due to no existing information regarding leeway coefficients for the particular type of buoy, the DWL slope (*a*_{d}) and CWL slope (*a*_{c}) were set to 3% and 1%, respectively. The predicted trajectories against the observed trajectory are plotted in Fig. 16. The result of separation was improved by approximately 26% when Stokes drift was considered, but it was still underestimated. The WRF overestimated southwesterly winds on 17 September 2012. It appears that these winds pushed the buoy to move northeastward excessively. Tamura et al. (2012) noted that the bulk formulation tends to underestimate the surface Stokes drift in the North Pacific and possible refraction of strong wave in the currents along the Korean Strait. It suggests that extensive error analysis of the Stokes drift simulations should be implemented in future research.

### c. Suggestions for improving performance of forecast models

It is clear that an increase in the accuracy of atmospheric and oceanic forecast models would improve the performance of the SAR model. However, it is beyond the purpose of this study to examine how to highly increase the accuracy of atmosphere and ocean forecasts. Thus, we give several suggestions to increase the accuracy of forecast models. One is to carry out data assimilation (DA), which has not been implemented in KOOS. The four-dimensional variational (4DVAR) technique is the DA method that we are planning to attempt in future atmospheric forecast. The detailed formation and potential of WRF 4DVAR in operational applications are demonstrated in Huang et al. (2009). They clearly showed that the 4DVAR algorithm produces better typhoon track and intensity forecasts during Typhoon Haitang (2005) than 3DVAR and other schemes.

In addition to DA, there are several ensemble techniques to improve wind forecasts. Deppe et al. (2013) explored improving wind speed forecasts at a typical wind turbine height (80 m) using several WRF ensemble methods with different planetary boundary layer (PBL) schemes. They introduced three “prerun” approaches: different perturbations of the initial and lateral boundary conditions for the GFS model, an ensemble of different grid spacing, and an ensemble of different initialization times. They also proposed three “postprocessing” techniques: training of the model, the neighborhood approach, and bias correction of the wind forecasts. They found that the bias-correction approach reduced significantly the mean absolute error of wind forecasts.

Several studies have been intensively carried out to improve surface current prediction using HF radar surface current data (Ullman et al. 2006; Barth et al. 2010, 2011; Kuang et al. 2012; Barrick et al. 2012). HF radar–derived current fields and drifter studies can be used to qualitatively assess ocean circulation prediction. HF radar surface currents are directly used to improve trajectory prediction (Ullman et al. 2006) or assimilated to enhance surface current prediction (Barth et al. 2010) and surface wind prediction (Barth et al. 2011). Kuang et al. (2012) carried out a validation exercise to increase confidence of ocean circulation prediction in the New York Harbor Observing and Prediction System (NYHOPS) using HF radar– and Lagrangian drifter–derived surface currents. HF short-term prediction of surface current vectors using HF radar currents was revealed to be a technique with great potential for nearshore SAR operations (Barrick et al. 2012; Frolov et al. 2012). You et al. (2012) introduced HF radar systems to measure surface currents around the Korean Peninsula, and Fujii et al. (2013) discussed coastal applications using the South Korean ocean radar networks for search and rescue, ship tracking, and operational circulation models with data assimilation. Therefore, the usage of HF radar data to improve the performance of operational forecast models and the SAR model should be focused on in future research.

Last, hyperensemble (HE) or superensemble (SE) techniques on atmospheric, ocean, and wave models are recommended to improve an operational surface drift prediction. HE methods aim at combining models of different kinds, whereas SE methods aim at combining models of the same kind to minimize departure (Rixen and Ferreira-Coelho 2007; Rixen et al. 2008; Vandenbulcke et al. 2009). The operational SAR modeling system proposed in the present paper incorporates another atmospheric forecast Unified Model (UM) provided by the Korea Meteorological Administration (KMA) and two other ocean models, the Finite-Volume Coastal Ocean Model (FVCOM; Chen et al. 2003) and the Regional Ocean Modeling System (ROMS; Haidvogel et al. 2000). It is suggested to examine how HE or SE can improve the forecast of surface drift in the operational SAR modeling system for the Yellow Sea and the East and South China Seas.

## 5. Concluding remarks

The current study presents the development and validation of an operational SAR modeling system for the Yellow Sea and the East and South China Seas. The SAR modeling system is capable of linking directly with the near-real-time forecast system, and is forced by the wind, surface current, and wave forecasts. In the SAR system, the leeway model is employed to effectively treat the uncertainties from the initial conditions and forcing fields. The advantage of the leeway model is to provide empirical leeway coefficients for typical search objects and to recreate the expected surface drift of an object based on available wind and current forecasts (or measured data) by estimating the downwind and crosswind leeway linear regression coefficients.

A set of field drifter experiments was carried out to validate the SAR modeling system, and SAR model validation was conducted with the circle assessment method, which has the tertiary perfect/acceptable/flawed evaluation that is useful in representing errors in trajectory prediction and qualifying error sources. The circle assessment method employing acceptable duration (or separation time) and error circle is valuable to determine quantitatively the acceptability of SAR predictions. Several sensitivity tests revealed that accurate wind forecasts and proper downwind leeway coefficients play a significant role in improving surface drift prediction. It is verified that the Stokes drift induced by striking waves has a remarkable influence on the accuracy of the SAR model under severe weather conditions such as a typhoon. In the application of a real SAR operation, the simulated trajectories are reasonably well compared with the locations of the wreckage recovered from the cargo aircraft that crashed into the ocean. It is validated, therefore, that the present SAR modeling system is clearly acceptable and applicable to search and rescue operations in the Yellow Sea and the East and South China Seas.

## Acknowledgments

This research is a part of the project (PM57700) titled “Development of Korea Operational Oceanographic System (KOOS) Phase 2” funded by the Ministry of Oceans and Fisheries, South Korea, and a part of the project (under Contact 200905015) titled “China offshore maritime search and rescue emergency auxiliary decision-making system development and demonstration” supported by marine public welfare industry special scientific research funds. This research is also a part of the project titled “Cooperation on the development of basic technologies for the Yellow Sea and East China Sea Operational Oceanographic System (YOOS)” funded by the China–Korea Joint Ocean Research Center. Thanks to all the individuals who have contributed to the field drifter experiments for this study, and we especially thank Mr. In-Ki Min and Mr. Sang-Hun Jeong for their help with the observation data processing and the model skill assessment.

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