Simulation and Analysis of Sea Surface Skin Temperature Diurnal Variation Using a One-Dimensional Mixed Layer Model and Himawari-8 Data

Highlights

• The improved PWP model reproduced the SSTskin diurnal cycle consistently with observations of Himawari-8, matching significant warming regions and achieving a mean bias of −0.37 °C. Identified abnormal SSTskin overestimation in low-wind-speed areas when using the improved PWP model, which is attributed to rapid mixed-layer thinning and the lack of horizontal diffusion in this 1D model.
• The improved PWP model provides a computationally efficient tool for studying upper-ocean vertical processes, thanks to its stable SSTskin parameterization scheme. The finding of PWP’s limitation under low wind speeds points out a direction for future model optimization—evaluating vertical mixing schemes in low-wind conditions to enhance the capability of numerical models to simulate SSTskin.

Abstract

Sea Surface Skin Temperature (SSTskin) derived from satellites and its diurnal variation are crucial for climate research, yet conventional ocean models, which primarily solve for the foundation or bulk SST, are not designed to simulate the very thin skin layer temperature (SSTskin). Consequently, specialized parameterizations or coupled model components are often required to obtain SSTskin. This study aimed to capture SSTskin diurnal warming events and evaluate the performance of the improved one-dimensional mixed-layer model (PWP: Price-Weller-Pinkel) in simulating SSTskin. Using high-frequency Himawari-8 satellite observations, a typical diurnal warming event was detected in the coastal waters off northwestern Australia, with the maximum SSTskin diurnal variation reaching 3 °C. The reliability of Himawari-8 data was validated using iQuam in situ observations, showing a mean bias of −0.28 °C. The improved PWP model (incorporating an SSTskin parameterization scheme), forced by ERA5 datasets, was used to simulate SSTskin and its diurnal variation at 90 (0.25° × 0.25°) grid points. Results indicated that the PWP model reproduced the diurnal variation cycle consistently with observations, accurately matched regions with significant warming, and achieved a mean bias of −0.37 °C. However, in low-wind-speed areas (<1 m/s), abnormal SSTskin overestimation (>3 °C) occurred due to rapid thinning of the mixed layer and the absence of horizontal diffusion in this one-dimensional model. The improved PWP model, with its relatively stable SSTskin parameterization scheme, provides a computationally efficient tool for studying vertical processes in the upper ocean. Future work should evaluate vertical mixing schemes under low wind speed conditions to enhance the capability of numerical models to simulate SSTskin.

1. Introduction

The sea surface temperature (SST) used in many studies is essentially a generalized concept, and it represents different seawater temperatures for different research objects. Although SST is not a simple, single variable, many researchers previously regarded it as the temperature of the ocean’s upper mixed layer (10 m depth). However, with the advancement of observational techniques, it has become necessary to consider the vertical structural changes in the upper mixed layer caused by factors such as heat, momentum, air–sea fluxes, and turbulence, changes that lead to highly complex temperature variations within the “mixed layer” [1]. Therefore, when fusing SST data obtained through different methods, this complexity and variability must be taken into account.

To standardize the definition of upper mixed layer temperature, the Group for High-Resolution Sea-Surface Temperature (GHRSST) developed a set of SST definitions [2]. This framework specifies five distinct SST categories: (1) Interface Temperature (SSTint), representing the air–sea interface temperature at the molecular scale; (2) Sea Surface Skin Temperature (SSTskin), the temperature typically measured by infrared radiometers at wavelengths of 3.7–12 μm, corresponding to the thermal emission from the very top 10–20 μm of the ocean (the skin layer); (3) Subskin Sea Surface Temperature (SSTsubskin), the temperature at the base of the conductive sublayer near the ocean surface, approximately equivalent to the temperature measured by microwave radiometers within the 6–11 GHz frequency range; (4) Depth Sea Surface Temperature (SSTz or SSTdepth), encompassing all water temperatures measured below the SSTsubskin layer; and (5) Foundation Sea Surface Temperature (SSTfnd), the temperature free of diurnal variations. Currently, the infrared satellite-retrieved SST widely used by most researchers corresponds to SSTskin.

A key characteristic of SSTskin is its diurnal variation. Influenced by solar radiation and wind-driven mixing, SSTskin exhibits periodic fluctuations on a daily scale [3]. Studies have confirmed that the diurnal variations in SST can exert a regulatory effect on the climate in specific regions [4]. Observations of SSTskin diurnal variation date back to early shipborne measurements [5]. With the development of satellite observation technology, the widely used MODIS (Moderate Resolution Imaging Spectroradiometer) achieves four daily observations (two in the morning and two in the evening) through a dual-satellite configuration [6]. However, for SSTskin observations with higher temporal resolution, geostationary satellites remain one of the most important tools today—and will continue to be in the future.

As early as the initial stages of satellite development, the potential contribution of geostationary orbit imagery to improving nowcasting and weather forecasting had already received attention. The three-axis-stabilized satellite ATS-6, launched in 1974, carried the Geostationary Very High Resolution Radiometer (GVHRR) [7], which was equipped with an infrared channel (with a bandwidth of 10.5–12.5 μm) for the first time, making it possible to retrieve SSTskin from geostationary satellites. In the same year, the Visible and Infrared Spin-Scan Radiometer (VISSR) was launched aboard the Spin-Stabilized Meteorological Satellite-1 (SMS-1) [7]. VISSR featured one infrared channel (10.5–12.6 μm) with a 7 km nadir spatial resolution, generating full-disk images of the Earth every 30 min [8]. Although a single infrared channel prevented the use of split-window atmospheric correction algorithms to retrieve SSTskin, VISSR brightness temperature images still clarified many upper-ocean processes, including westward-propagating tropical instability waves [9,10]. With advances in satellite remote sensing technology, the latest infrared imaging payloads on geostationary satellites are the Advanced Himawari Imager (AHI) [11] and the Advanced Baseline Imager (ABI) [12], which are onboard Japan’s Himawari-8/9 and NOAA’s GOES-R series geostationary satellites, respectively. Both payloads are equipped with five infrared channels for SST retrieval and can observe key regions at temporal resolutions of 10 min or higher. The advent of AHI and ABI represents a significant advancement in SST research driven by geostationary satellites. High-frequency intraday SST observations also provide an extremely valuable data source for studies on SST diurnal variation [12,13].

Numerical simulation of SSTskin has long been a challenge. Due to limitations in vertical resolution, ordinary ocean numerical models cannot simulate SSTskin—their simulated SST often disagrees with satellite-observed SSTskin. Due to the pervasive cool-skin effect, these models, which typically solve for bulk or foundation temperature, often overestimate the temperature when compared to satellite-observed SSTskin. Although numerical assimilation techniques have enabled SST correction in three-dimensional ocean numerical models, the process remains highly complex and computationally intensive. Thus, there is an urgent need to investigate the capability of numerical models to simulate SSTskin. Initially, Price et al. developed a mixed-layer model and used observational evidence obtained during measurement campaigns to evaluate the basic conditions for SSTskin simulation [14]. A simplified cool-skin correction version of this model was later developed by Fairall et al. [15]; subsequently, Fairall et al., Zeng and Beljaars, Schiller and Godfrey, and Gentemann et al. adopted similar approaches to simulate SSTskin [16,17,18]. Through parameterization based on observations of wind and surface warming, Webster et al. [19], Clayson and Curry [20], Kawai and Kawamura [21], Gentemann et al. [22], Stuart-Menteth et al. [23], and Filipiak et al. [24] proposed alternative methods and conducted comparative analyses of different diurnal warm layer models [25,26]. Existing parameterizations show wind-regime dependence: weak winds favor strong stratification and diurnal warming, while stronger winds and wave-related mixing can suppress the diurnal signal and alter the skin–bulk contrast. Accordingly, several studies refined schemes by adding wind dependence and additional processes [27,28], and satellite-derived (sub)skin SST has also been used for validation [29]. Refining SSTskin matters because it directly affects air–sea heat-flux estimates, especially sensible heat flux and net longwave radiation. While many of these studies have undertaken systematic validation with in situ data—the optimal approach for evaluating the physical fidelity of 1D models—a direct, spatially extensive comparison with satellite-observed SSTskin diurnal cycles remains less common. Therefore, it is necessary to leverage the high-frequency observation advantages of geostationary satellites to identify the strengths and limitations of SSTskin and its diurnal variation simulations, while evaluating the consistency between satellite-observed SSTskin and numerical simulation results. This helps evaluate the model’s ability and limitations in simulating SSTskin.

In this study, Himawari-8 was used to observe the diurnal variations in SSTskin, and an improved one-dimensional mixed-layer model (Price-Weller-Pinkel model) was employed to simulate SSTskin. The SSTskin results and their diurnal variations from both methods were analyzed, and the ability and limitations of the improved one-dimensional model to simulate SSTskin were evaluated. The remainder of this paper is organized as follows: Section 2 provides a detailed description of the data and model used; Section 3 presents the satellite-observed diurnal warming events and model simulation results; Section 4 focuses on discussing the limitations of the model simulations and their causes; and Section 5 contains the conclusions.

2. Materials and Methods

2.1. Materials

2.1.1. Himawari-8 Data

Himawari-8, the first new-generation geostationary meteorological satellite operated under the leadership of the Japan Meteorological Agency (JMA), was successfully launched on 7 October 2014, and put into operational service on 7 July 2015. The satellite is positioned at 36,500 km above the equator at 140.7°E. Its primary payload, the Advanced Himawari Imager (AHI), is a 16-channel multispectral imager capable of acquiring images in visible and infrared bands. This sensor covers a range from 80°E to 160°W in longitude and between 60°N and 60°S in latitude, enabling all-weather continuous monitoring of the western Pacific Ocean and eastern Indian Ocean regions. The AHI onboard Himawari-8 is equipped with five near-infrared channels (3.9, 8.6, 10.4, 11.2, and 12.4 μm) specifically for SSTskin retrieval, with a spatial resolution of 2 km at nadir and a full-disk scanning interval of 10 min [30].

In response to the SST retrieval characteristics of the AHI’s multispectral channels, a novel multi-band SSTskin retrieval algorithm (4-channel algorithm) has been proposed and applied operationally. This algorithm is improved based on the traditional 2–3 channel empirical regression method [31]. Compared with the SSTskin retrieval methods used in traditional polar-orbiting satellites and geostationary satellites, the core difference in the new algorithm lies in its use of four characteristic channels: thermal infrared bands with central wavelengths of 10.5 μm (Channel 13), 11.2 μm (Channel 14), and 12.3 μm (Channel 15), as well as a mid-infrared band of 8.6 μm (Channel 11). By combining these four channels, a unified retrieval formula for both daytime and nighttime data has been established. Since the traditional day-night separate algorithms tend to cause data discontinuities in the terminator transition zone [31], the multi-band algorithm, through the optimized integration of radiative transfer models, possesses the technical potential to effectively address the boundary effect in SSTskin retrieval during twilight periods [32]. Therefore, this study uses the SSTskin products derived from this multi-band retrieval algorithm, and the data can be obtained from the JMA website (ftp.ptree.jaxa.jp (accessed on 12 November 2025)).

2.1.2. In Situ Data

In this study, in situ SST data from the in situ SST Quality Monitor (iQuam) project were used as validation data. The iQuam dataset is developed by the National Oceanic and Atmospheric Administration (NOAA) and supports the calibration and validation (Cal/Val) of satellite-derived SST [30,33]. The iQuam project collects in situ SST data from various platforms, including Argo floats, drifters, and IMOS (Integrated Marine Observing System) ships. To minimize in situ measurement errors, it has designed a consistent quality control (QC) algorithm to process in situ SST data from these different sources. Quality flags (ranging from 1 to 5) are used to specify the QC status of SST data, with the following definitions: 1 = invalid, 2 = unused, 3 = bad, 4 = low quality, and 5 = acceptable. In this study, drifter buoy SST data were used to validate the satellite SST products. This choice was based on two key advantages of drifter buoys: their large quantity, and their shallow measurement depth (only tens of centimeters), which makes them closer to the sea surface than moored buoys or ships [34]. Additionally, to minimize errors, only drifter buoy SST data with the highest quality (quality flag = 5) were selected for use. All iQuam data can be accessed from the NOAA website at https://www.star.nesdis.noaa.gov/socd/sst/iquam/data.html (accessed on 12 November 2025).

2.1.3. Meteorological Data

ERA5 is the fifth-generation reanalysis dataset developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). It is used to analyze global climate and weather over the past 80 years, with data available since 1940. ERA5 provides hourly estimates of a wide range of atmospheric, wave, and land parameters [35]. ERA5 regrids the data: the latitudinal-longitudinal grid for reanalysis data is 0.25°, while that for uncertainty estimation data is 0.5°. The dataset consists of four main subsets: hourly and monthly products, available in both pressure levels (upper atmospheric fields) and single levels (atmospheric, wave, and land surface variables). The parameters used in this study include net longwave radiation flux, net shortwave radiation flux, upward latent heat flux, upward sensible heat flux, and precipitation, all with a resolution of 0.25°. For wind field data, the 0.125° global wind field reanalysis dataset provided by ECMWF was adopted.

2.2. Methods

2.2.1. The Improved PWP Model

The Price-Weller-Pinkel (PWP) vertical mixing model is a one-dimensional (vertical) mixing model, initially proposed by Price et al. in 1986 [14], to describe the dynamic processes of the upper ocean in response to diurnal heat fluxes, cooling, and wind-driven mixing. Based on physical observations, the model simulates vertical mixing processes using the dynamic instability of the mixed layer. Its core idea is to update the temperature, salinity, and momentum fields in the upper ocean through a series of mixing processes, according to stability criteria for local density and velocity distributions. Currently, PWP has also been adapted for vertical mixing calculations in the Hybrid Coordinate Ocean Model (HYCOM).

The PWP model used in this study is the improved PWP2.0 version (https://www.soest.hawaii.edu/pwp/ (accessed on 12 November 2025)) based on the classic PWP model, which incorporates additional parameterization processes. To better simulate SSTskin and its diurnal variation, a specific SSTskin parameterization scheme was added to the classic PWP model. The initial fields of the model were derived from the Global Ocean Physics Reanalysis Dataset (GLORYS12V1), including parameters such as temperature, salinity, and sea surface current fields. The forcing data were obtained from ECMWF’s ERA5 dataset, including net longwave radiation, upward latent heat flux, upward sensible heat flux, and precipitation. For wind field data, the 0.125° global wind field reanalysis dataset provided by ECMWF was used. Considering that radiation penetration parameterization involves seawater chlorophyll concentration, satellite (MODIS-AQUA) observation data near the study area were used as input for the model’s chlorophyll concentration.

In the SSTskin simulation experiments using the PWP one-dimensional model, the basic configuration remains consistent except for the initial and forcing parameters, which vary with different regions and simulation periods. The key model configurations are as follows (See

Table 1. The key model configurations.

Parameter	Configuration
time step	300 s
upper water layer thickness	0.1 m
simulated mixed layer depth	150 m
threshold for bulk Richardson number	0.65
threshold for gradient Richardson number	0.25
background diffusion coefficient	1 × 10−5 m2/s
maximum bottom temperature rise threshold	0.012 °C
bottom absorption rate threshold	0.001
mixed-layer calculation scheme	the density gradient method
the density gradient threshold	1 × 10−4 (kg·m−3)/m
calculation scheme	Runge–Kutta

): time step of 300 s; upper water layer thickness of 0.1 m; simulated mixed layer depth of 150 m; threshold for bulk Richardson number calculation of 0.65; threshold for gradient Richardson number calculation of 0.25; background diffusion coefficient of 1 × 10⁻⁵ m²/s; maximum bottom temperature rise threshold of 0.012 °C; bottom absorption rate threshold of 0.001; surface albedo parameterization scheme adopting the albedo model by Jin et al. [36]; mixed layer calculation scheme using the density gradient method with a threshold of 1 × 10⁻⁴ (kg·m⁻³)/m; and iterative calculation scheme using the Runge–Kutta procedure.

2.2.2. Parameterization of SST_skin

The PWP model, improved by Fernando Santiago-Mandujano and Roger Lukas, specifically accounts for the dynamic processes of the sea surface skin layer. Since this study focuses on the capability to simulate SSTskin, we adopted the validated parameterization scheme for ocean surface microstructures proposed by Zhang et al. [37]. In ocean numerical models, “SST” usually denotes the temperature of the uppermost model layer, whose representative depth depends on vertical discretization, e.g., in a coarse global NEMO ORCA1 configuration, the first layer can be ~10 m thick, whereas in eddy-permitting ORCA025.L75 the near-surface spacing can be ~1 m [38]. However, satellite-observed SST, retrieved from brightness temperatures in the near-infrared bands, represents the temperature of the ocean skin layer (10 μm). Therefore, it is necessary to design a targeted parameterization scheme for SSTskin in ocean numerical models, i.e., the cool skin layer parameterization scheme by Zhang et al. adopted in this study [37].

In this parameterization scheme, $∆T$ is first defined as the difference between the temperature of the model’s first layer and SSTskin. Based on the flux boundary conditions, the following equation is derived:

$$∆T={\displaystyle \frac{Q_0}{\rho c_p{\kappa }_T}}·{\delta }_T$$

(1)

where $\rho$ is the density of seawater, $c_p$ is the specific heat capacity, ${\kappa }_T$ is the molecular diffusivity for temperature, $Q_0$ is the total skin cooling flux, and ${\delta }_T$ is the depth of the thermal sublayer. The key parameter ${\delta }_T$ is given by:

$${\delta }_T={\displaystyle \frac{{\lambda }_T\upsilon }{u_{\ast }}}$$

(2)

where $\upsilon$ is the viscosity of seawater, $u_{\ast }$ is the sea surface friction velocity, and ${\lambda }_T$ is the modified Saunders coefficient. The equations for ${\lambda }_T$ under two conditions—free convection-dominated (low wind speeds) and shear-forced convection-dominated (high wind speeds)—are as follows:

$$Ri>1: {\lambda }_T=\lambda {Ri}^{-{\displaystyle \frac{1}{4}}}{C}_2^{-{\displaystyle \frac{1}{4}}}{\left(1+{\left({\displaystyle \frac{C_1}{C_2{C}_3^3}}\right)}^{{\displaystyle \frac{3}{2}}}{Ri}^3\right)}^{-{\displaystyle \frac{1}{6}}}$$

(3)

$$Ri<1: {\lambda }_T=\lambda C_2^{-{\displaystyle \frac{1}{4}}}{\left(1+{\left({\displaystyle \frac{C_1}{C_2{C}_3^3}}\right)}^{{\displaystyle \frac{1}{2}}}{Ri}^3\right)}^{-{\displaystyle \frac{1}{6}}}$$

(4)

where $Ri$ is the Richardson number (free convection: $Ri$ > 1; shear-forced convection: $Ri$ < 1), $\lambda$ is Saunders’ coefficient, which is fairly constant as indicated by different observations, and $C_1$, $C_2$, and $C_3$ are empirical coefficients. Ultimately, the above equations establish the parameterization scheme for SSTskin. This method has been validated to further correct the underestimation issue compared to the classic Fairall model [37]; thus, it was selected as the parameterization scheme for SSTskin simulation in this study.

3. Results

3.1. A Diurnal Warming Event Observed by Himawari-8

3.1.1. Validation

Before analyzing the diurnal variations in SSTskin using Himawari-8 SST data, it is necessary to validate the satellite data to ensure the stability and reliability of the results. And it is worth mentioning that the persistent negative bias is now explicitly and prominently framed as the expected signature of the cool-skin effect, which improves the perception of the satellite’s physical consistency and accuracy. Currently, for statistical analysis of the consistency between satellite-derived and in situ SST, numerous studies have widely used metrics such as mean bias (MB), absolute bias (AB), robust standard deviation (RSD), root mean square error (RMSE), and correlation coefficient (R) for evaluation [30,39,40,41,42,43]. Among these, the RSD value is obtained by fitting a Gaussian probability density function to the bias data, a method that can effectively characterize the characteristics of most datasets [39,44]. However, due to the large volume of Himawari-8 data, only the cross-validation results of Himawari-8 SST for the key study period (12 September 2020) are presented in detail below.

Results for 12 September 2020 show that the full disk SST retrieval results from Himawari-8 are generally stable and exhibit good consistency with in situ measured SST. The specific statistical indicators are as follows: a bias of −0.28 °C, a mean absolute bias of 0.48 °C, an RMSE of 0.69 °C, an RSD of 0.20 °C, and a correlation coefficient (R) of 1.00 (Figure 1a). Validation of Himawari-8 data with reference to different intervals of in situ SST (Figure 1b) reveals that the overall biases are dominated by negative values, approximately −0.70 °C, with relatively larger negative biases in the high-temperature range. Figure 1c shows that the bias distribution of all validation data exhibits an approximately normal distribution pattern, with notable negative biases—consistent with the results of the scatter density plot.

Statistics on validation matching points across different time periods indicate that the distribution of statistical points throughout the day is relatively uniform (Figure 1d). The number of matching points between 14:00 and 18:00 is relatively small, but the difference from other time periods is not significant. Figure 1e also presents statistics on biases and matching points for different in situ SST intervals. The results show that the bias between Himawari-8 SSTskin and in situ SST remains relatively stable across most SST ranges, while the number of matching points increases significantly in the high-temperature range. Similarly, the results confirm that the negative bias of Himawari-8 SST relative to in situ SST is somewhat stable, but the bias gradually decreases with increasing temperature in the high-temperature range.

Overall, the cross-validation of Himawari-8 retrieved SST with in situ SST indicates good data stability. The bias relative to in situ data maintains good consistency both across different temperature ranges and different time periods. Notably, Himawari-8 SST corresponds to SSTskin and thus consistently exhibits a certain degree of negative bias compared to in situ SST in most cases; it still meets the requirements for studying SSTskin diurnal variation and conducting consistency comparisons with model-simulated SSTskin. Moreover, the use of shipborne infrared radiometer data for verifying satellite-observed SST can further enhance the accuracy of the verification.

3.1.2. The Spatiotemporal Distribution of Diurnal Warming Events

As a geostationary satellite, Himawari-8 conducts observations hourly over its full-disk coverage, enabling the monitoring of diurnal variations in SSTskin. Using Himawari-8 SSTskin data, a typical diurnal warming event was observed on 12 September 2020, along the northwestern coast of Australia—a region previously identified as prone to such events by Zhang et al. [34]. Figure 2 presents the SSTskin variations at a selected observation point (122.25°E, 13.75°S) within the diurnal warming event area, spanning from 9 September 2020 to 13 September 2020. Strong diurnal warming events occurred consecutively over three days at this location. From the perspective of event progression, the daily maximum SSTskin continued to reach new highs over the three days, with the intradaily variation amplitude gradually increasing; this trend peaked on 12 September 2020, when the maximum SSTskin reached 29.7 °C and the intradaily variation exceeded 1.5 °C.

For the single-day diurnal variations in SSTskin on 12 September 2020, the process exhibited a highly typical diurnal warming pattern. Starting from 06:00 LT (Local Time) on 12 September 2020, driven by solar shortwave radiation, the upper ocean warmed significantly. After 6 h, the SSTskin reached its maximum value. As solar shortwave radiation weakened, wind-driven upper-ocean mixing intensified, causing the SSTskin to begin decreasing. Eventually, the SSTskin returned to a baseline level comparable to that of the previous day.

Figure 3 presents the spatial distribution of the diurnal warming event observed by Himawari-8 on 12 September 2020, in the northwestern Australian seas. The main diurnal warming events can be divided into two distinct regions: a Northern Region (120–125°E, 13–14°S) and a Southern Region (118–120°E, 16–18°S). Compared with the Southern Region, the Northern Region exhibits a larger spatial extent and greater intensity of diurnal warming. The overall evolution of the diurnal warming events is consistent with the results from the single observation point in Figure 2. Starting from 06:00 LT on September 12, as solar shortwave radiation intensified, seawater in both the Northern and Southern Regions began to warm, reaching peak temperatures at 14:00 LT. Subsequently, the surface seawater temperature in both regions started to decrease. Notably, in local areas of the Northern Region, the diurnal variations in SSTskin reached 3 °C during this diurnal warming event, which can be classified as an extreme diurnal warming event [43]. Beyond the Northern and Southern Regions, the diurnal warming effect in other sea areas was insignificant, with the average diurnal variations in SSTskin not exceeding 1 °C.

3.2. Simulation of SST_skin Diurnal Variation by PWP

3.2.1. Simulation Results

In Section 3.1, we have captured a highly stable and significant diurnal warming event using Himawari-8 SSTskin data. Subsequently, we simulated this diurnal warming event using the PWP model in a subset of the event-affected area. Figure 4 shows the simulation area. Since the PWP model is a one-dimensional mixed-layer model, which is constrained by the resolution of input data, the simulation area was divided into 90 simulation points with a 0.25° × 0.25° spatial resolution—a resolution consistent with that of the input forcing data. SSTskin variation simulations were then conducted for each of these 90 points individually.

Figure 5 presents the simulation results for a specific location (122.25°E, 13.75°S) and the corresponding forcing conditions. Figure 5a shows the simulated temperature of the 0.1 m seawater layer and SSTskin results. It can be observed that the overall process of the 12 September 2020 diurnal warming event is simulated correctly. However, the maximum intradaily SSTskin reached 30.3 °C, which is 0.5 °C higher than the observation result from Himawari-8; consequently, the intradaily SSTskin difference exceeded 2 °C. Considering the simulated mixed-layer depth results (Figure 5b), as well as the input energy fluxes (Figure 5c), wind speed (Figure 5d), and precipitation forcing (Figure 5e), the simulation of the entire diurnal warming event is reliable. Under the condition of low wind speeds (<2 m/s), the increase in shortwave radiation flux led to a rapid increase in stratification and a significant warming of the surface seawater. One hour after the shortwave radiation flux reached its maximum, the SSTskin attained the daily maximum. Subsequently, the shortwave radiation flux decreased, wind-driven water mixing intensified, the mixed layer depth increased continuously, and the SSTskin gradually decreased, eventually returning to the foundation sea surface temperature. This process is also consistent with the classical dynamic theory of SST diurnal variation. On the other hand, a comparison between the 0.1 m seawater layer temperature and SSTskin results reveals that the difference between the two during the warming phase is smaller than that during the cooling phase. This confirms that the cool skin effect is relatively weak during the warming phase of the diurnal warming event. It is important to note that no precipitation occurred within the spatiotemporal framework of this study; therefore, rainfall effects are not considered here. When present, however, precipitation can rapidly modify SSTskin by cooling the skin layer (via rain heat flux and surface disturbance) and by generating rain-induced cool and fresh lenses that alter near-surface stratification, with impacts on minute-to-hour time scales; these processes are increasingly documented and parameterized, although they are not yet consistently represented in many modelling applications [45,46].

Figure 6 presents the spatial distribution of simulated SSTskin in the study area, generated by arranging the results of 90 simulation points by latitude and longitude, with a 2 h time interval for presentation. From the spatial distribution, it can be observed that on 12 September 2020, the maximum simulated SSTskin in this area was concentrated in the southeastern part of the simulation area; the maximum SSTskin at 3 of these simulation points exceeded 32 °C, and this region also exhibited the most significant intradaily variation in SSTskin. Although the magnitude of SSTskin diurnal variation varied across different sub-regions, the overall pattern still conformed to the general evolutionary law of SSTskin diurnal variation: rapid warming in the morning, followed by a gradual cooling after reaching the maximum SSTskin, and an eventual return to the foundation sea surface temperature.

3.2.2. SST_skin Diurnal Variation Between Himawari-8 and PWP

To better evaluate the SSTskin simulation results of the PWP model, the Himawari-8 observed SSTskin in the same area and at the same time was resampled to match the simulation resolution, and its spatial distribution is presented in Figure 7. By comparing the spatial characteristics of the diurnal warming event from the PWP simulation results and Himawari-8 observations, it is evident that their spatial distributions of significant diurnal warming events are basically consistent, both concentrated in the southeastern part of the study area. However, the Himawari-8 observations exhibit a relatively larger spatial extent of the diurnal warming event and a generally lower overall intensity. The PWP simulation results show significant overestimation at some key locations; one of the key reasons is that the one-dimensional mixed-layer model used in this study does not account for horizontal mixing. Nevertheless, in most regions where diurnal warming is not very significant, the difference between the PWP simulation results and Himawari-8 observations is not substantial.

Furthermore, a one-to-one statistical analysis was conducted between all simulation points and Himawari-8 observations, with the results presented in Figure 8. Figure 8a uses a box plot to show the diurnal variations in SSTskin from the PWP model and Himawari-8 for all simulation points. It is evident that the PWP results exhibit significant overestimation in the high-temperature range and slight underestimation in other ranges. The distribution of differences between Himawari-8 and PWP simulation results is presented in Figure 8b. Overall, negative biases dominate (median within −0.5 °C), indicating that the PWP simulation tends to underestimate SSTskin relative to Himawari-8. This underestimation is primarily linked to the wind regime: stronger winds promote turbulent mixing and damp the diurnal warm-layer development in the model, leading to lower simulated SSTskin; the wind–bias relationship is examined further below. Notably, large biases are mainly concentrated in the time window of 14:00 to 18:00 LT, and these biases are positive, reflecting significant overestimation by the PWP model. Figure 8c depicts the hourly differences in SSTskin warming rate between Himawari-8 observations and PWP simulations. For most simulation points, the median of the warming rate differences is around 0 °C/h. However, a small number of simulation points show abnormal warming rate differences, with the maximum reaching 1.7 °C/h. These abnormal warming rate differences mainly occur during the daytime periods when the mixed layer is changing—specifically, the rapid warming and cooling phases of SSTskin. Figure 8d presents the statistical results of the differences between Himawari-8 SSTskin and PWP simulation results. The maximum positive difference occurs at 16:00 LT, reaching 6.11 °C, while the minimum negative difference occurs at 12:00 LT, being −1.87 °C. The mean difference is relatively small, at −0.37 °C.

To better evaluate the difference in SSTskin diurnal variation between the PWP simulation results and Himawari-8 observations, a spatial comparison was conducted between the two datasets, and a scatter density plot was generated. Figure 9a,b present the spatial distributions of SSTskin diurnal variation from Himawari-8 observations and PWP simulations in the study area, respectively. For Himawari-8, the regions with significant SSTskin diurnal variation are concentrated in the southeastern part of the study area, with a maximum value of 2.89 °C; in contrast, the diurnal variation values in areas with general SSTskin diurnal variation are relatively scattered.

Compared with the Himawari-8 results, the PWP simulations show extreme diurnal variation values exceeding 3 °C at 4 simulation points. Additionally, the regions with significant diurnal variation in the PWP results are more concentrated, and the diurnal variation values in areas with general diurnal variation are relatively uniform. Figure 9c shows the scatter density distribution of SSTskin diurnal variation between the two datasets. It is clearly observed that for some points with large diurnal variation values in Himawari-8 observations, the PWP simulations exhibit significant overestimation, with the maximum overestimation nearly 3-fold. However, most simulation points are distributed around the 1:1 line—this indicates that the PWP model can provide relatively stable simulation results for most SSTskin diurnal variation processes.

3.3. Impact Factors of SST_skin Simulation

Section 3.1 and Section 3.2 presented the SSTskin diurnal variation results of the PWP model in the study area and compared them with Himawari-8 observations. Although the PWP simulation results are relatively consistent with satellite observations at most simulation points, it cannot be denied that there are significant discrepancies at individual points. For the PWP simulation experiment of SSTskin diurnal variation, all simulation points share the same model configuration, with differences only in the initial and forcing field settings. Since numerical calculation biases caused by model initialization were avoided during the model run, only the impact of forcing field differences on simulation discrepancies needs to be considered. Numerous studies have confirmed that solar shortwave radiation and wind speed are key factors influencing SST diurnal variation [40,47,48,49]. Thus, Figure 10 and Figure 11, respectively, present the spatial distributions of net solar shortwave radiation flux and wind speed in the simulation area during the upper ocean heating period (10:00–15:00 LT) on 12 September 2020.

The overall spatial distribution of net solar shortwave radiation is uniform, peaking between 12:00 and 13:00 LT with an average net solar shortwave radiation flux exceeding 900 W/m², followed by a gradual decrease. While the spatial distribution of net shortwave radiation was relatively uniform during the heating period (Figure 10), and thus is unlikely to be the primary driver of the spatially patchy simulation anomalies, we acknowledge that absolute inaccuracies in the ERA5 shortwave product could contribute to the overall model bias, particularly in low-wind areas. In contrast, the spatial distribution of wind speed exhibits distinct regional characteristics, though its temporal variation is negligible. Low-wind-speed areas are mainly concentrated in the southeastern part of the study area, while high-wind-speed areas are concentrated in the northeastern and southwestern parts. The average wind speed in low-wind-speed areas is less than 1 m/s, whereas that in high-wind-speed areas exceeds 5 m/s. In terms of spatial distribution, there is a high spatial overlap between low-wind-speed areas and regions with significant SSTskin diurnal variation, and these areas are also prone to simulation anomalies. This confirms that wind speed is the main influencing factor for anomalies in SSTskin diurnal variation simulations.

4. Discussion

Through high-frequency observations from Himawari-8, we captured a typical SSTskin diurnal warming event. Concurrently, the improved PWP model was used to simulate the SST diurnal variation in this region. The simulation results show that, in most cases, the model can alleviate the underestimation of SST diurnal variation that is common in ordinary ocean numerical models [24,25], with the mean bias reduced to −0.37 °C. However, there remain several simulation points with significantly anomalous results.

As shown in Section 3.2, compared with the SST diurnal variation observed by Himawari-8, the SST diurnal variation results at 4 simulation points exceeded 3 °C, and even 2 of these points showed values exceeding 7 °C—values that are highly atypical. Further analysis of the forcing conditions influencing SSTskin simulation preliminarily identified wind speed as the key factor contributing to these anomalies. Figure 12 presents a scatter density plot comparing the average wind speed during the warming period at 90 simulation points with the corresponding biases of SST diurnal variation between Himawari-8 observations and PWP simulations. It is clearly observed that simulation points with large biases are concentrated in the range of average wind speed < 1 m/s, corresponding to nearly calm conditions. In contrast, points with stable biases fall within the average wind speed range of approximately 3–4 m/s. This further indicates the PWP model’s simulation of SSTskin is highly sensitive to the different physics that dominate under very low wind speeds.

The limitations of the PWP model in SSTskin simulation may be associated with its vertical mixing mechanism—the core of the model lies in the vertical mixing parameterization process established based on the dynamic instability of the mixed layer. Under ultra-low wind speed conditions, the mixed layer becomes highly stable and thins rapidly under the heating effect of net solar shortwave radiation flux, leading to rapid warming of the seawater temperature in the near-surface layer. Under the same net heat flux, the seawater temperature in this extremely thin surface mixed layer also rises abnormally. On the other hand, as a one-dimensional vertical mixed-layer model, the PWP model does not account for horizontal diffusion effects. However, in regional simulations, horizontal diffusion is also a key factor in the uniform distribution of heat. Influenced by horizontal diffusion, the heat accumulated in the extremely thin mixed layer would be reasonably transferred to the upper ocean. Since the PWP model currently lacks a horizontal diffusion term and focuses solely on vertical mixing processes, special attention should be paid to the phenomenon of abnormal warming in the upper ocean caused by ultra-low wind speeds when using the PWP model to simulate SSTskin or the diurnal variations in upper ocean temperature. But if a diurnal warming event is continuous across 100 km², then the core of the diurnal warming layer will likely warm more similarly to how it is simulated by PWP, because of the spatial continuity.

Furthermore, although the improved PWP model has incorporated parameterization schemes such as those for SSTskin, albedo, and radiation penetration, it still exhibits certain limitations in simulating the complete air–sea process, such as the lack of two-way air–sea coupling (where SST changes feed back on atmospheric boundary layer properties) and the parameterization of wave effects. The most effective approach to accurately reproducing the diurnal variations in SSTskin likely involves the use of a fully coupled air–sea model, with particular attention paid to the parameterization of heat exchange processes at the air–sea interface. Different parameterization schemes for air–sea processes may exhibit varying sensitivities in their outcomes, necessitating further systematic evaluation.

In summary, the PWP model can fully simulate the diurnal variation process of upper ocean temperature. Particularly after the integration of the SSTskin parameterization scheme, it maintains high simulation accuracy with small biases under non-low wind speed conditions.

5. Conclusions

In this study, leveraging the high-frequency observation capability of the geostationary satellite Himawari-8, a diurnal warming event was captured along the northwestern coast of Australia. This event lasted for more than 3 days, with the maximum intradaily variations in SSTskin reaching 3 °C. Furthermore, the improved PWP model was used to simulate the SSTskin diurnal variation at 90 simulation points in this region. The results indicate that the PWP model can fully simulate the entire process of SSTskin diurnal variation, with its evolutionary cycle consistent with that of the actual SSTskin diurnal variation. Compared with satellite observations, the model exhibits a consistent spatial distribution of significant diurnal warming regions, with a mean bias of −0.37 °C. However, abnormal overestimation occurs in some low-wind-speed areas, where biases exceed 3 °C.

The failure of the improved PWP model under certain low-wind-speed conditions also highlights its limitations, consistent with findings from coupled-model assessments of the SST diurnal cycle: Voldoire et al. showed that sub-daily coupling is needed to represent diurnal SST variability and that 3 h coupling can delay the phase, while adequate coupling frequency together with fine near-surface resolution improves realism; they also point to the importance of near-surface mixing under weak-wind/stable conditions [50]. Our analysis suggests that the primary factors contributing to these anomalous results are likely the increased stratification of the mixed layer under low wind speeds and the lack of horizontal diffusion processes in the one-dimensional vertical model. Meanwhile, employing a fully coupled air–sea model for simulating and analyzing the diurnal cycle of SSTskin may further enhance simulation accuracy.

Validation against geostationary satellite observations allows for an effective evaluation of the improved PWP model’s capability in simulating SSTskin, providing a basis for considering additional parameterization schemes to further improve SSTskin simulation accuracy. Future research could focus on assessing the contributions of different vertical mixing parameterization schemes to SSTskin simulation under low-wind-speed conditions. Such work is expected to improve the consistency between numerically simulated SSTskin and satellite-observed SSTskin, thereby enhancing the capability of numerical models in simulating SSTskin.