1. Introduction
A storm surge is an unusual change in sea level induced by tropical cyclones (typhoons, hurricanes) or temperate cyclones (cold tides). For a long time, the damage caused by storm surges has been a major threat to human life, financial status, and infrastructure in coastal areas [
1,
2,
3,
4,
5,
6,
7,
8]. Southeastern coastal areas in China are often affected by tropical cyclones from the Northwest Pacific Ocean. These disastrous typhoons could bring about serious economic losses and threaten people’s lives in low-lying coastal areas [
9,
10,
11,
12,
13,
14,
15]. The disasters and losses brought by storm surges are difficult to estimate. In 1953, a huge storm surge caused tremendous disaster in Britain, Germany, the Netherlands, and other European countries, and resulted in thousands of deaths in the Netherlands [
1]. In 2005, Hurricane Katrina produced a storm surge level of 4–7 m; at least 1833 individuals were injured or killed and the direct economic loss amounted to USD 108 billion [
5]. Therefore, some factors of the storm surge model need to be thoroughly investigated in order to effectively prevent and assess storm surge disasters.
Grid resolution and assimilation window size are two important factors that can affect a storm surge model. In recent years, many scholars have conducted a lot of research on these factors. Jing et al. [
16] utilized the Weather Research and Forecasting (WRF) model to explore the large eddy simulation (LES) of the high-wind area near the maximum wind radius of “Tiantu” (2021) using various grid resolutions. They found that altering the grid resolution could significantly affect the local turbulence structure of LES within a limited area, resulting in notable variations in eddy structure and intensity under different grid resolution conditions. Kerr et al. [
17] used the Simulating Waves Nearshore (SWAN) model and an Advanced Circulation model (ADCIRC) to simulate the tidal harmonic components and hurricane wave results for Hurricane “Ike” (2008). Their study found that lower resolutions compromised simulation accuracy in coastal areas due to incorrect transmission or lateral attenuation. Moon et al. [
18] highlighted that higher-resolution models for complex terrains and coastlines tend to produce higher average surges with a better simulation performance. Dukhovskoy et al. established a storm surge model with high resolution and used it in the Appalachian Gulf in the northeastern Gulf of Mexico during Hurricane Dennis (2005) [
19]. Through accurate-resolution simulations of coastal areas and waterways with intricate geometries, they unveiled the unexpected high storm surge processes in this region. Mentaschi et al. [
20] developed a wave and storm surge prediction model with high resolution, which exhibited a good predictive ability for both sea level and effective wave height compared with satellite altimeters, tide gauges, and buoys as well as notable improvements compared to previous studies with lower resolutions regarding the reproduction of nearshore dynamics. Garzon et al. [
21] found that the North American Mesoscale Forecast System (NAM) and European Center for Medium-Range Weather Forecasts (ECMWF) systems have the highest vertical and horizontal resolution, and indeed displayed the best root mean square deviation (RMSD) and correlation coefficient (CC), while the simulations of water levels based on the weather forecast systems with a higher horizontal resolution obtained better results. Makris et al. [
22] used phase-resolving models with a fine resolution for the prediction of average ocean currents at sea level and depth in coastal areas, which are affected by atmospheric forcing and astronomical tides. The results address the significant needs of port authorities, ship pilots, and navigators in battling the problems of vessels impacting the harbor bed during mooring, towage, and berth operations using high-resolution and short-term sea-state forecasting. Fernández-Montblanc et al. [
1] designed an unstructured hydrodynamic storm surge and tidal model for Europe. The tidal surge model accounts for the atmospheric pressure, wind, and astronomical tide. It was found that increasing the resolution of atmospheric forcing also improves the predictive ability, most extremely in shallow areas where wind is the main driver of surge production. Mohanty et al. [
23] made an attempt to improve the storm surge prediction with a longer lead time using high-resolution mesoscale model outputs. Their findings suggest that the early warnings of tropical cyclones (TCs) obtained by the India Meteorological Department (IMD) should include the surge predictions from these highly reliable mesoscale model products with a 96–72 h lead time in order to mitigate the catastrophic loss associated with storm surges. Based on the research conducted by relevant scholars on grid resolution, it is evident that the effect of grid resolution on simulations of storm surge cannot be disregarded and is an important factor in storm surge simulation.
When analyzing the diurnal variation and hot wave phenomenon of Mars, Zhao et al. introduced different assimilation window lengths into a 4D local ensemble transform Kalman filter (4D-LETKF) to eliminate the artificially caused resonance phenomenon [
24]. The study found that the short assimilation window length can effectively eliminate false resonance. Wang et al. [
25] used the ensemble Kalman filter (EnKF) method to compare the influence of assimilating T-TREC-retrieved winds (VTREC) versus radial velocity (Vr) on analyzing and forecasting Typhoon “Qaxi” (2008). The study found that the different assimilation windows had different effects in terms of data assimilation on the inversion wind field and radial wind speed. Zheng et al. [
26] used a data assimilation scheme based on the 4DVar method to improve the prediction ability of an existing storm surge model in the North Sea of Germany. By diminishing the assimilation window’s size, they found that the prediction accuracy was enhanced. Based on the ensemble Kalman filter, Kim et al. used a carbon tracker inverse simulation system to study the influence of assimilation window size on the estimation of surface carbon dioxide flux in Asia [
27]. The study found that when the assimilation window is shorter, the uncertainty of the optimized surface carbon dioxide flux is greater. DiNapoli et al. [
28] applied a preoperative 4-day storm surge ensemble prediction system, called Model for Storm Surge Simulations (M3S), to the southwestern Atlantic continental shelf (SWACS) region. The system assimilated tidal level and elevation data using the four-dimensional ensemble square root filter (4DEnSRF) method. Their study showed that the first 2 days of the 4-day prediction depended on initial conditions, while the last 2 days were influenced by external forcing. Optimal initial conditions were obtained with a 12 h assimilation window size. Khan et al. [
29] used numerically efficient hydrodynamics–waves coupled modeling and presented its practical real-time computational set-up; the results show that along this landfalling coastal section, the standard error in the maximum surge level amounts to 2.06, 1.73, and 0.66 m for the T—60 h, T—36 h, and T—12 h forecasts, respectively. Madsen et al. [
30] demonstrated the positive impact of coastal altimetry observations when used in a statistical blending method together with tide gauge observations. A positive impact was demonstrated when the blended product was assimilated into a hydrodynamic model of the North Sea and Baltic Sea, showing that the simplified, computational cost-effective assimilation method improves the modeled sea level field. The aforementioned studies suggest that further investigation is warranted to explore the impact of assimilation window size on simulating storm surge levels.
In order to assess the influences of grid resolution and assimilation window size on simulating the storm surge levels, seven experiments were designed in this paper. In order to produce a more realistic wind stress drag coefficient, we have corrected the adjoint assimilation model using a finer grid resolution and smaller assimilation window size. Firstly, we designed four experiments (E1–E4) to examine the influence of different grid resolutions on both the numerical storm surge model and the adjoint assimilation model. Subsequently, we also discussed the impact of assimilation window size on the adjoint assimilation model of storm surges in E4–E7.
This paper consists of four sections. The second section introduces the numerical storm surge model and adjoint assimilation model, as well as the experimental design. A detailed investigation into how the grid resolution and assimilation window size affect the simulated levels of storm surge is provided in the third section. Conclusions are presented in the last part.
4. Conclusions
In relation to Typhoon 7203, we have explored the effects of the grid resolution and assimilation window size on simulations of storm surge levels in the Bohai Sea, Yellow Sea, and East China Sea in this paper. In the adjoint assimilation model, we used the inverted spatial distribution of the wind stress drag coefficient to calculate the storm surge level via the data assimilation method based on the linear expression Cd = (a + b × U10) × 10−3.
In order to investigate the influences of different grid resolutions on simulations of storm surge levels, we conducted four experiments. In E1 and E2, two grid resolutions of 10′ × 10′ and 5′ × 5′ were set up in the numerical storm surge model. Similarly, two experiments were carried out on the adjoint assimilation method using grid resolutions of 10′ × 10′ and 5′ × 5′ in E3 and E4. The results of the evaluation indicators, comprising the values of RMS error, AMD error, PCC, WSS, and their average, reveal that in E1 and E2, the impact of the grid resolution was minimal and practically negligible in the numerical model of storm surges. However, in E3 and E4, when using the adjoint assimilation model, varying grid resolutions were found to significantly affect the simulation accuracy. It was found that finer grids can yield more precise simulation levels.
The influence of the assimilation window’s size on simulations of storm surge levels with a 5′ × 5′ grid resolution was investigated in the present study. Using the adjoint assimilation method in E4–E7, assimilation window sizes with intervals of 6 h, 3 h, 2 h, and 1 h were assessed, respectively. The results demonstrate that the performance in E6 and E7 was superior to that in E4 and E5, as suggested by the comparison of RMS error, AMD error, PCC, and WSS. In particular, the average PCC and WSS values reached 97% and 98% when the assimilation window sizes were 2 h and 1 h in E6–E7. Therefore, the effect of assimilation window size on storm surge levels is also very important. Smaller assimilation window size showed enhanced accuracy and higher PCC and WSS in simulating storm surge levels.
In addition to the grid resolution and assimilation window size, there are many other factors that can also affect the storm surge model, such as the bottom friction coefficient, the time interval of external forcing, the type of external forcing, and the wind stress drag coefficient. In future research, we will consider the effects of these factors on model performance.