Improving GOCI ocean color data under high solar-zenith angle over open oceans using neural networks

ABSTRACT

With hourly measurements available during daytime between local times of 09:00–16:00, ocean color data derived from the Geostationary Ocean Color Imager (GOCI) onboard the Korean Communication, Ocean, and Meteorological (COMS) satellite have been useful for research and surveillance of diurnal processes in the western Pacific Ocean region. However, in early morning and late afternoon measurements, there are significant errors in GOCI-derived ocean color products as the solar-zenith angle (θ₀) goes beyond 70°, especially in autumn and winter seasons. In this study, we employ a neural network (NN) model to make corrections on the GOCI-measured normalize water-leaving radiance spectra, nL_w(λ), with high θ₀ (>70°) in open oceans. Results show that NN-corrected nL_w(λ) are consistent with the previous-hour nL_w(λ) and make the diurnal variations in the region much more stable and reasonable. Specifically, the GOCI-measured nL_w(λ) with θ₀ ≤65° in earlier hours of the day (including some nL_w(λ) diurnal variation) are considered accurate and used as the ground truth to train NN models for nL_w(λ) correction with high θ₀. Further analysis of the relationship of ratios (between the NN-corrected and original nL_w(λ)) with θ₀ shows that the nL_w(λ) ratios increase as θ₀ increase, which indicates that there are more significant corrections with larger θ₀ (>70°). The performance evaluation of the NN models is based on the comparison of NN-corrected nL_w(λ) with the original previous hour nL_w(λ) data. The ratios of NN-corrected nL_w(λ) to the original previous hour nL_w(λ) are 0.968–1.045 for the short blue/blue and green bands, and the performance of nL_w(λ) correction at 14:00 and 15:00 is slightly better than that at 16:00, due to significantly large θ₀ at late afternoon hours. The NN-corrected nL_w(λ) data are also used to derive chlorophyll-a (Chl-a) concentration, showing significantly improved Chl-a in GOCI’s late afternoon measurements with θ₀ >70°.

KEYWORDS:

• Satellite remote sensing
• ocean color
• geostationary
• normalized water-leaving radiance

1. Introduction

The Geostationary Ocean Color Imager (GOCI) onboard the Korean Communication, Ocean, and Meteorological (COMS) satellite is the first ocean color sensor in Earth’s geostationary orbit, which was launched in June 2010 (J. K. Choi et al. 2012; Ryu et al. 2012). It has a fixed coverage region centered around the Korean Peninsula within 24.01–47.85°N and 112.81–148.28°E, and the total area is ~ 2500 × 2500 km² (Figure 1a). There are 5567 × 5685 pixels in a GOCI image with a spatial resolution of ~500 m. GOCI acquires data in eight spectral bands where six of them are in the visible spectrum with the nominal center wavelengths of 412, 443, 490, 555, 660, and 680 nm, and the remaining two bands are in the near-infrared (NIR) at 745 and 865 nm. Each day, GOCI takes eight hourly measurements during the daytime from Korean time of about 09:00 (00:00 UTC) to 16:00 (07:00 UTC). With this special advantage of high frequency measurements, GOCI-derived ocean color data have been useful for research and surveillance of diurnal ocean processes, especially in coastal waters (Doxaran et al. 2014; X. Liu and Wang 2016; Park et al. 2022; Wang, Shi, and Jiang 2023; Wang et al. 2013; Wu et al. 2022; Yang et al. 2014). GOCI data have also been used to study various biological and biogeochemical processes in oceans and inland lakes, including harmful algal blooms, sediment transport, tidal variations, river plumes, and so on (Cheng et al. 2016; J.-K. Choi et al. 2014; He et al. 2013; Huang et al. 2015; J. Liu et al. 2018; Lou and Hu 2014).

Figure 1. Areas of the studies and examples of the effect of high solar-zenith angle on nL_w(443) for (a) climatology Chl-a image, showing the GOCI field of view: bluish color indicates clear open oceans (climatology Chl-a ≤ 0.3 mg/m³), (b) nL_w(443) image in Box A on February 15, 2020, and (c) the corresponding solar-zenith angle θ₀ image on the same day.

GOCI mission-long ocean color products produced by the NOAA Ocean Color Science Team include normalized water-leaving radiance spectra nL_w(λ) at the six visible and two NIR bands, that is, nL_w(412), nL_w(443), nL_w(490), nL_w(555), nL_w(660), nL_w(680), nL_w(745), and nL_w(865), chlorophyll-a (Chl-a) concentration, and diffuse attenuation coefficient at 490 nm K_d(490) (Jiang and Wang 2014; Wang et al. 2013; Wang, Shi, and Jiang 2012). It is noted that Chl-a and K_d(490) are derived using the ocean chlorophyll-type (OC3)-based (i.e. blue-green nL_w(λ)-ratio-based) algorithm (O’Reilly and Werdell 2019; O’Reilly et al. 1998) and the combined empirical and semi-analytical algorithms (Wang et al. 2009), respectively. However, it has been a challenge to retrieve ocean color data under high solar-zenith angle (θ₀) conditions for satellite ocean color sensors (Mikelsons, Wang, and Jiang 2020), including the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) (McClain, Feldman, and Hooker 2004), the Moderate Resolution Imaging Spectroradiometer (MODIS) (Esaias et al. 1998; Salomonson et al. 1989), the Visible Infrared Imaging Radiometer Suite (VIIRS) (Goldberg et al. 2013), and the Ocean and Land Colour Instrument (OLCI) (Donlon et al. 2012). In the standard ocean color data processing, significant errors in atmospheric correction often occur in cases of high θ₀ (>70°) (Gordon and Wang 1994; IOCCG 2010; Wang 2007). Thus, the large θ₀ effect is more serious for GOCI in early morning and late afternoon measurements when θ₀ often goes beyond 70°, especially in autumn and winter seasons. In a recent study, Wang et al. (2023) evaluated the coverage for valid pixels for each GOCI shot from 09:00–16:00 in 2019 and found that at 15:00 and 16:00 local time there were sparse or even no GOCI ocean color data between late autumn and early spring due to cases associated with θ₀ >70°. Figure 1b,c shows an example of a GOCI-derived nL_w(443) image and the corresponding θ₀ in Box A marked in Figure 1a on 15 February 2020. As illustrated, when θ₀ became > 70°, nL_w(443) reduced significantly on the right side of the image (Figure 1b), while it was expected to be consistent in this region of oligotrophic waters.

In the meantime, diurnal variations in nL_w(λ) are also observed in GOCI-derived nL_w(λ) and other biological and biogeochemical parameters (Wang, Shi, and Jiang 2023). In this study, we employ a neural network (NN) model to make corrections on GOCI-derived nL_w(λ) with high solar-zenith angle θ₀, which takes account of both the θ₀ effect and diurnal variations in nL_w(λ). Since GOCI-measured nL_w(λ) with θ₀ ≤70° in earlier hours of the day are generally valid (Mikelsons, Wang, and Jiang 2020; Wang, Shi, and Jiang 2023) with the assumption that nL_w(λ) at the visible bands do not change significantly within a few hours over open oceans, we can use nL_w(λ) measured in previous hours to train the NN models for predicting and improving nL_w(λ) spectra with high θ₀ in the late afternoon. The NN method has been used in previous studies as atmospheric correction algorithms (Doerffer and Schiller 2007; Fan et al. 2017; Li et al. 2020; Tanaka et al. 2004), which are mostly trained with in situ data to predict nL_w(λ) from either top-of-atmosphere (TOA) or Rayleigh-corrected radiance. In this study, we take a different approach to make corrections and improvements on nL_w(λ) with high θ₀: we predict the correct nL_w(λ) from the original biased nL_w(λ) for θ₀ >70° using the NN model. Since the correction depends on many variables like previous hour nL_w(λ), θ₀, λ, sensor-zenith angle θ, relative-azimuth angle Δϕ, wind speed, sun glint, hours (local time), diurnal trend, and so on, the NN model serves as multi-variable regression algorithm for the correlation of these variables with the correction on nL_w(λ).

2. Data and methods

2.1. GOCI ocean color data

The NOAA Ocean Color Science Team obtained hourly GOCI Level-1B data and processed to Level-2 ocean color products using the Multi-Sensor Level-1 to Level-2 (MSL12) satellite data processing system (Wang et al. 2002), which has been used to process ocean color data from the SeaWiFS, MODIS, VIIRS, OLCI, GOCI, and other satellite sensors. GOCI contains two NIR bands but has no shortwave infrared (SWIR) bands for atmospheric correction (Wang 2007). To accurately estimate significant reflectance contributions in turbid waters at the NIR bands for the GOCI ocean color data processing, an improved atmospheric correction algorithm that iteratively adjusts nL_w(λ) at the two NIR bands has been used for atmospheric correction and the NIR nL_w(λ) have also been routinely derived (Jiang and Wang 2014; Wang, Shi, and Jiang 2012). For clear open ocean regions, the standard NIR atmospheric correction algorithm (Gordon and Wang 1994; IOCCG 2010) has been used. GOCI-derived nL_w(λ) have been evaluated and validated with the in situ measurements and VIIRS-derived ocean color data products (Wang et al. 2013; Wang, Shi, and Jiang 2023). Chl-a are calculated using the standard OC3 empirical blue-green reflectance ratio-based algorithm (O’Reilly and Werdell 2019; O’Reilly et al. 1998).

We use 10 years (2011–2020) of MSL12-derived GOCI ocean color data, which include nL_w(λ) at six visible and two NIR bands with wavelengths of 412, 443, 490, 555, 660, 680, 745, and 865 nm, as well as Chl-a concentration. Since high solar-zenith angle θ₀ occurs only in fall and winter seasons, we use only five months of GOCI data in January, February, October, November, and December for years 2011–2020. In addition, since geolocation and other ancillary data, such as solar-sensor geometry (θ₀, θ, and Δϕ), wind speed, sun glint coefficient L_GN (Wang and Bailey 2001), and so on, are also related to satellite-derived nL_w(λ) spectra (Gordon and Wang 1994; Mikelsons, Wang, and Jiang 2020; Wang 2007), these parameters are also obtained from the GOCI Level-2 data file and used for training and applications of the NN models.

The GOCI field of view covers highly turbid coastal oceans, such as the Bohai Sea and East China Sea (Shi and Wang 2014). Since nL_w(λ) data in highly turbid coastal waters have large uncertainty, our focus in this study is on the open ocean region. Specifically, the limit of clear open oceans is defined by the climatology Chl-a ≤0.3 mg/m³, which includes only bluish color pixels in Figure 1a. All green to red colored pixels are considered to be non-clear oceans (or turbid coastal waters) and are excluded in this study. It should be noted that the definition of clear open oceans in this work is more restrictive (an approximation) and likely covers slightly less pixels, comparing to the approach based on criterion from bio-optical model (Lee and Hu 2006) or through more extended water classifications (Wei et al. 2022). However, this simple approximation should be satisfactory for the purpose of our study in the region.

2.2. Neural network approach

In this study, we employ a NN approach to build prediction models for correction on the GOCI-derived nL_w(λ) with high θ₀ in late afternoon measurements. Preparing training data set is critical for the performance of the NN models. Although 70° is typically considered as the limitation of high θ₀ for ocean color products (Mikelsons, Wang, and Jiang 2020), to be more conservative and particularly for producing smooth data with θ₀, we assume that nL_w(λ) with θ₀ ≤65° are valid, while those with θ₀ >65° require the NN correction. In fact, this set of the θ₀ limitation is quite important to keep data consistency and continuation of corrected nL_w(λ) as a function of θ₀, i.e. there is a range connection from 65°–70° to those with θ₀ >70°. It is expected that the NN correction will be small for nL_w(λ) with θ₀ between 65°–70°. In a late afternoon GOCI image in fall or winter season, θ₀ increases from southwest to northeast directions as shown in Figure 1c. On the other hand, for a specific pixel (geolocation), θ₀ also increases with time (hours of the GOCI shot) in the afternoon. For example, at a given pixel location, θ₀ could be 54° in the GOCI-measured 14:00 image, 63° in the 15:00 image, and 72° in the 16:00 image on the same day. We use nL_w(λ) within three hours before the high θ₀ to train the NN models, that is, nL_w(λ) of the immediate previous hour is used as the ground truth, nL_w(λ) of two earlier hours are used to provide the diurnal trend, and the dataset is used to train the NN models. Specifically, the training dataset is established with the following criteria:

1. All data matchups collected are only from clear open oceans (Figure 1a).

2. Statistics of nL_w(λ) in 3 × 3 box is evaluated with the criteria: if more than 50% of pixels are valid and nL_w(λ) value is within the range of mean ± 1.5 × standard deviation (STD) of the box.

3. All matchup data are selected within ±3 hours.

4. Only pixels with 65° < θ₀ ≤80° are selected for training and corrections, and pixels with θ₀ >80° are discarded.

GOCI data with five odd years, that is, 2011, 2013, 2015, 2017, and 2019, are used for training and data with five even years, that is, 2012, 2014, 2016, 2018, and 2020, are employed for evaluation and testing. Since nL_w(λ) with θ₀ >65° mainly occur in the late afternoon in fall and winter seasons, GOCI data in the five months of January, February, October, November, and December are selected for training and corrections. There are various combinations of different solar-sensor geometry (θ₀, θ, and Δϕ), meteorological and other conditions (cloudiness, aerosols, sun glint, wind speed, etc.), and water optical and biological properties. After analyzing the testing results with various input parameters, it was found that the outputs are also affected by month and hour of the GOCI measurements, and that using a separate NN model for different month and hour combination improves the NN model performance. Therefore, we train NN models separately for each GOCI afternoon hour at 14:00, 15:00, and 16:00, and for each month of January, February, October, November, and December as listed in Table 1. The approach turns out to be quite effective. Since most data at the time of 16:00 in January, November, and December have θ₀ >80°, and most of data at 14:00 in February and October have θ₀ ≤65°, there are not enough data to train a NN model in these five month-hour combinations (Table 1).

Table 1. Number of training data extracted (number) from years 2011, 2013, 2015, 2017, and 2019 for the NN models for each month and hour combination (month, hour, and NN model name).

Month	Hour	NN model name	Number
January	14:00	Jan1400	4.44×10^5
	15:00	Jan1500	7.33×10^5
	16:00	—	Not enough data
February	14:00	—	Not enough data
	15:00	Feb1500	5.28×10^5
	16:00	Feb1600	5.40×10^5
October	14:00	—	Not enough data
	15:00	Oct1500	7.32×10^5
	16:00	Oct1600	5.12×10^5
November	14:00	Nov1400	5.27×10^5
	15:00	Nov1500	6.88×10^5
	16:00	—	Not enough data
December	14:00	Dec1400	4.64×10^5
	15:00	Dec1500	4.84×10^5
	16:00	—	Not enough data

We adopt a three-layer feedforward NN (FFNN) to build a model for nL_w(λ) corrections under the high θ₀ condition, which includes a single hidden layer with 64 units, an input layer, and an output layer (Figure 2). FFNN is suitable for solving complex regression problems, and it is implemented using the Keras API (https://keras.io/). The input layer has 34 elements, including θ₀, θ, and Δϕ, wind speed W, sun glint coefficient L_GN (Wang and Bailey 2001), time (hour, day, and month), location (latitude and longitude), and nL_w(λ) (with θ₀ >65°) and those measured with GOCI for the three previous hours (Table 2). Since the area of study is in the open ocean, nL_w(λ) at the short blue/blue and green bands (i.e. 412, 443, 490, and 555 nm) are predicted. Therefore, the output layer has four elements, that is, corrected nL_w(λ) at 412, 443, 490, and 555 nm. All input and output elements are normalized before being used in the training. The five odd-year data are randomly split into training and test dataset with an 80 to 20 ratio before the training process. Training, validation loss, and accuracy are closely monitored in the training process to prevent overfitting. The above NN models are implemented in Python (Version 3.7.4) with Keras (Version 2.3.1) libraries and trained on CentOS 7, which has one 16-core Intel(R) Xeon(R) Gold 6226 R CPU 2.90 GHz, NVIDIA Tesla T4 GPU, and 128 GB memory.

Figure 2. Diagram of the three-layer fully connected feedforward neural network.

Table 2. List of 34 input variables for the neural network.

Number	Symbol	Description
1	θ	Sensor-zenith angle of the pixel
2–5	θ0	Solar-zenith angles at the correction hour and three previous hours
6–9	Δϕ	Relative-azimuth angles at the correction hour and three previous hours
10–13	W	Wind speeds at the correction hour and three previous hours
14–17	LGN	Glint coefficients at the correction hour and three previous hours
18	hour	hour of measurement for the correction (9–16)
19	day	day of year (1–365)
20	month	month of year (1–12)
21	latitude	latitude of the pixel
22	longitude	longitude of the pixel
23–25	nLw(412)	nLw(412) at the correction hour, two and three hours earlier
26–28	nLw(443)	nLw(443) at the correction hour, two and three hours earlier
29–31	nLw(490)	nLw(490) at the correction hour, two and three hours earlier
32–34	nLw(555)	nLw(555) at the correction hour, two and three hours earlier

3. Results

The NN models listed in Table 1 are applied to GOCI late afternoon data for January, February, October, November, and December in the even years of 2012, 2014, 2016, 2018, and 2020. A case study of corrected nL_w(λ) in the western Pacific Ocean is presented in Section 3.1, and a second case study of corrected nL_w(λ) in the Japan/East Sea is provided in Section 3.2. Results in nL_w(λ) evaluations in all five months of the five even years are discussed in Section 3.3. An application of GOCI-derived Chl-a using the improved nL_w(λ) is presented in Section 3.4.

3.1. A case study in the western Pacific Ocean

For convenience in discussion, we define nL_w(λ) ratio, r(λ, θ_0, θ₀′, t, t′), for various evaluation and comparison situations, i.e.

r(λ, θ₀, θ₀′, t, t′) = nL_w(λ, θ₀′, t′)/nL_w(λ, θ₀, t),(1)

where nL_w(λ, θ₀′, t′) and nL_w(λ, θ_0, t) are GOCI-derived nL_w(λ) with conditions of solar-zenith angle and local time of (θ₀′, t′) and (θ₀, t), respectively. We also define corrected/new nL_w(λ) after applying the NN models, $\mathit{n}{L}_w^{\left(C\right)}\left(\mathit{\lambda }\right),$ with the corresponding corrected nL_w(λ) ratio of

r^(C)(λ, θ₀, θ₀′, t, t′) = $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀′, t′)/nL_w(λ, θ₀, t),(2)

where r^(C)(λ, θ₀, θ₀′, t, t′) is the ratio between the corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) and original (without correction) nL_w(λ) for given conditions of (θ₀′, t′) and (θ₀, t). In addition, we simplify the GOCI eight hourly measurements of 09:00–16:00 as numbers of 9–16 at local times for nL_w(λ, θ₀, t) (or $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀, t)) and r(λ, θ₀, θ₀′, t, t′) (or r^(C)(λ, θ₀, θ₀′, t, t′)). Therefore, r(443, ≤65°, >65°, 15, 16) represents a case with ratio of GOCI-derived nL_w(443, θ₀ >65°) at 16:00 over nL_w(443, θ₀ ≤65°) at 15:00, that is, nL_w(443, θ₀ >65°, 16)/nL_w(443, θ₀ ≤65°, 15), and r^(C)(443, ≤65°, >65°, 15, 16) is for a case with ratio of $\mathit{n}{L}_w^{\left(C\right)}$(443, θ₀ >65°, 16)/nL_w(443, θ₀ ≤65°, 15).

It is noted that nL_w(λ, θ₀ ≤ 65°, t) are considered valid data. In fact, GOCI-derived ocean color data with θ₀ ≤ 65° have been compared and validated with in situ and satellite measurements in previous studies (Wang et al. 2013; Wang, Shi, and Jiang 2023). With the assumption that nL_w(λ) do not change significantly within a few hours over open oceans, nL_w(λ, θ₀ ≤ 65°, t) can be used as the ground truth to validate the corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀′, t′). For open oceans, the assumption is reasonable, e.g. our validation approaches usually assume valid matchups between satellite and in situ within ±3 hours. For hour t’ and the previous hour t, there are many pixels with θ₀ ≤ 65° at both hours, and ratio r(λ, θ₀≤65°, θ₀′ ≤65°, t, t′) can be used as references to evaluate the ratio r^(C)(λ, θ₀ ≤65°, θ₀′ >65°, t, t′) from extensive statistical analyses and results, showing improved $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀′, t′) compared with the original ones.

Figure 3 shows the GOCI-measured original nL_w(λ) at bands of 412, 443, 490, and 555 nm from 12:00–16:00 in Box B noted in Figure 1a on 3 February 2020 (Figure 3a–e,h–l,o–s,v–z). Since the region is in oligotrophic waters (climatology Chl-a ≤0.1 mg/m³), there were limited biological activities due to lack of nutrients, and nL_w(λ) at all bands were expected to be stable within a day. However, although nL_w(λ) were consistent from 12:00 to 14:00 (Figure 3a–c,h,j,o–q,v,x), they decreased significantly for nL_w(412), nL_w(443), and nL_w(490) at 15:00 and 16:00 (Figure 3d,e,k,l,r,s) because of errors caused by increased θ₀ (Mikelsons, Wang, and Jiang 2020). The two right columns of images (Figure 3f,g,m,n,t,u) show the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) at 15:00 and 16:00, which exhibited consistent $\mathit{n}{L}_w^{\left(C\right)}$(λ) values with original nL_w(λ) from 12:00 to 14:00. It is noted that in the image of original nL_w(490) at 16:00 (Figure 3s) there was a patch of missing pixels near the right edge, which were negative due to large θ₀. As we can see in Figure 3u, these negative pixels were recovered smoothly in the new $\mathit{n}{L}_w^{\left(C\right)}$(490). Also, with the new $\mathit{n}{L}_w^{\left(C\right)}$(555) at 15:00 and 16:00, nL_w(555) did not show noticeable variation from 12:00 to 16:00 (as expected for open oceans).

Figure 3. The GOCI-measured original nL_w(412), nL_w(443), nL_w(490), and nL_w(555) images of Box B (noted in Figure 1a) at 12:00 to 16:00 on February 3, 2020 (first five columns). The last two columns are the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) images at 15:00 and 16:00.

To quantitatively compare the original nL_w(λ) and NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ), Figure 4 shows the hourly time series (09:00–16:00) of nL_w(λ) at the four GOCI spectral bands at the point P marked in Figure 3f. It is noted that, at the point P, θ₀ were 57.26°, 48.97°, 44.06°, 43.69°, 47.97°, 55.73°, 65.92°, and 77.50° from 09:00 to 16:00 on 3 February 2020. At 14:00, nL_w(412), nL_w(443), and nL(490) were 1.319, 1.125, and 0.788 mW cm⁻² μm⁻¹ sr⁻¹, respectively. At 15:00, nL_w(λ) values at these three bands decreased by ~ 7–12% to 1.214, 1.016, and 0.692 mW cm⁻² μm⁻¹ sr⁻¹, and further reduced by ~ 30–70% to 0.831, 0.619, and 0.214 mW cm⁻² μm⁻¹ sr⁻¹ at 16:00. Figure 4 also shows the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) of point P at 15:00 and 16:00. The new $\mathit{n}{L}_w^{\left(C\right)}$(λ) at these bands were 1.264, 1.058, and 0.751 mW cm⁻² μm⁻¹ sr⁻¹ at 15:00, and 1.219, 1.011, and 0.735 mW cm⁻² μm⁻¹ sr⁻¹ at 16:00, which are now consistent with the original nL_w(λ) at 14:00. It is noted that the new $\mathit{n}{L}_w^{\left(C\right)}$(λ) at 15:00 and 16:00 were not the same as those from the previous hour nL_w(λ) and showed diurnal changes with a slight decreasing trend between at 13:00 and 14:00.

Figure 4. Hourly time series (09:00–16:00) of original nL_w(412), nL_w(443), nL_w(490), and nL_w(555) (solid lines), and the corresponding NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) (dashed lines) at the location P in Figure 3f on February 3, 2020.

The evaluation of the performance for the NN models are based on the comparison of NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) with original nL_w(λ) from the previous hour. This essentially assumes that, for open oceans, the regional ocean diurnal variation should generally be small/negligible within a couple of hours. In clear open ocean waters, phytoplankton (or Chl-a) is the major factor that determines the spectral characteristics of nL_w(λ) (Gordon et al. 1988; Wei et al. 2022). Chl-a usually have small variations during a day in open ocean waters, particularly for within a few hours. Therefore, GOCI-measured nL_w(λ) at the previous hours with θ₀ ≤65° can be considered valid and accurate. We can effectively use these data for the NN model training, evaluations, and applications.

Figure 5 shows the comparison of nL_w(λ) at time of 16:00, nL_w(λ, θ₀, 16), with those at time of 15:00, nL_w(λ, θ₀, 15), for the same pixel for the month of February 2020. The top row in Figure 5 is the scatter/density plots of original nL_w(λ, θ₀ >65°, 16) versus nL_w(λ, θ₀ ≤65°, 15). It shows that nL_w(λ, θ₀ >65°, 16) at the three short blue/blue bands are significantly underestimated, while those at the green band are overestimated. Indeed, mean ratios, r(λ, ≤65°, >65°, 15, 16), are 0.859, 0.821, 0.700, and 1.174 for wavelengths of 412, 443, 490, and 555 nm, respectively. The middle row in Figure 5 shows the scatter/density plots of original nL_w(λ, θ₀ ≤65°, 16) versus nL_w(λ, θ₀ ≤65°, 15), and the mean ratios, r(λ, ≤65°, ≤65°, 15, 16), are from 0.935 to 0.970. The bottom row in Figure 5 shows the scatter plot of NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀ >65°, 16) versus original nL_w(λ, θ₀ ≤65°, 15), and the mean ratios of r^(C)(λ, ≤65°, >65°, 15, 16) are from 1.019 to 1.028. It is noted that comparison results of r(λ, ≤65°, ≤65°, 15, 16) serve as references for the NN-correction assessment as θ₀ ≤65° for both cases (at different times of 15:00 and 16:00). Indeed, results in Figure 5 show that, compared to r(λ, ≤65°, >65°, 15, 16), r^(C)(λ, ≤65°, >65°, 15, 16) are now generally consistent with r(λ, ≤65°, ≤65°, 15, 16). STD values in ratio of all four bands are also improved for new $\mathit{n}{L}_w^{\left(C\right)}$(λ). A summary of the statistics in r(λ, ≤65°, >65°, 15, 16), r(λ, ≤65°, ≤65°, 15, 16), and r^(C)(λ, ≤65°, >65°, 15, 16) for February 2020 is listed in Table 3.

Figure 5. Scatter/density plots of GOCI-derived original nL_w(λ, θ₀>65°, 16) (top row), original nL_w(λ, θ₀≤65°, 16) (middle row), and new $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀>65°, 16) (bottom row) versus original nL_w(λ, θ₀≤65°, 15) at spectral bands of 412, 443, 490, and 555 nm in the month of February 2020. The statistics show that nL_w(λ, θ₀>65°, 16) are underestimated by 15–30% for blue bands, and overestimated by 17% for green band. After correction, the ratio r^(C)(λ, ≤65°, >65°, 15, 16) is close to the reference r(λ, ≤65°, ≤65°, 15, 16).

Table 3. Evaluation results of r(λ, θ_0, θ₀′, t, t′) and r^(C)(λ, θ₀, θ₀′, t, t′) (mean, median, and STD) for the month of February 2020.

Ratio r(λ, θ0, θ0′, t, t′) or r^(C)(λ, θ0, θ0′, t, t′)	412 nm			443 nm			490 nm			555 nm
	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD
r(λ, ≤65°, >65°, 15, 16)	0.859	0.835	0.354	0.821	0.798	0.340	0.700	0.692	0.356	1.174	1.083	0.565
r(λ, ≤65°, ≤65°, 15, 16)	0.938	0.932	0.329	0.970	0.939	0.314	0.935	0.903	0.347	0.964	0.936	0.410
r^(C)(λ, ≤65°, >65°, 15, 16)	1.028	0.966	0.340	1.026	0.969	0.334	1.020	0.960	0.361	1.019	0.975	0.404
r(λ, ≤65°, >65°, 14, 15)	0.942	0.912	0.344	0.922	0.897	0.336	0.821	0.817	0.384	1.063	0.948	0.554
r(λ, ≤65°, ≤65°, 14, 15)	0.984	0.973	0.224	0.992	0.975	0.229	0.969	0.948	0.273	1.041	1.057	0.333
r^(C)(λ, ≤65°, >65°, 14, 15)	1.024	0.969	0.336	1.021	0.967	0.328	1.016	0.971	0.354	1.020	0.996	0.451

Similarly, we use the same pixel comparison of nL_w(λ) at 15:00, nL_w(λ, θ₀, 15), with those at 14:00, nL_w(λ, θ₀, 14), in February 2020 for evaluation, and a summary of the statistics is also listed in Table 3. Since θ₀ are smaller at 15:00 than those at 16:00, the original nL_w(λ, θ₀ >65°, 15) are closer to the previous hour values, nL_w(λ, θ₀ ≤65°, 14). Indeed, r(λ, ≤65°, >65°, 14, 15) and r(λ, ≤65°, ≤65°, 14, 15) are 0.821–1.063 and 0.969–1.041, respectively. The performance of correction of $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀ >65°, 15) are also acceptable with r^(C)(λ, ≤65°, >65°, 14, 15) from 0.971 to 1.024.

Since θ₀ increased from southwest to northeast in a late afternoon nL_w(λ) image (Figure 1c), the changes of nL_w(λ) with θ₀ can be further visualized and analyzed. The top row in Figure 6 shows the scatter/density plot of original nL_w(λ) as a function of θ₀ for 16:00 images on 3 February 2020. It can be seen that the original nL_w(412), nL_w(443), and nL_w(490) significantly decreased as θ₀ increased from 74° to 80°. For high-density pixels (purple color), the original nL_w(412) decreased from ~1.5 to ~0.7 mW cm⁻² μm⁻¹ sr⁻¹, nL_w(443) from ~1.2 to ~0.5 mW cm⁻² μm⁻¹ sr⁻¹, and nL_w(490) from ~0.75 to ~0.01 mW cm⁻² μm⁻¹ sr⁻¹. The middle row in Figure 6 shows the scatter/density plots of new $\mathit{n}{L}_w^{\left(C\right)}$(λ) of the four bands versus θ₀. After NN-corrections, the new $\mathit{n}{L}_w^{\left(C\right)}$(λ) at the three short blue/blue bands are all flat as a function of θ₀. The bottom row in Figure 6 shows the scatter/density plots of ratio r^(C)(λ, θ₀, θ₀′, t, t′) (new $\mathit{n}{L}_w^{\left(C\right)}$(λ)/original nL_w(λ)) versus θ₀, to further emphasize the effect of the NN correction. As the ratio increases with increasing θ₀, it means large corrections on cases with large θ₀. Furthermore, as the wavelength increases from 412 to 490 nm, the relative correction also increases, with nL_w(490) having the most corrections. On the other hand, for the green band nL_w(555), there are no significant corrections, compared to nL_w(λ) at the three short blue/blue bands.

Figure 6. Scatter/density plots of GOCI-derived original nL_w(λ) (top row), new $\mathit{n}{L}_w^{\left(C\right)}$(λ) (middle row), and ratio of new $\mathit{n}{L}_w^{\left(C\right)}$(λ)/original nL_w(λ) (bottom row) on February 3, 2020, as a function of solar-zenith angle (θ₀).

3.2. A case study in Japan/East sea

The Japan/East Sea is a more productive region than the western Pacific Ocean, and it has different optical and bio-optical properties. Figure 7 shows the GOCI-derived original nL_w(412) (Figure 7a–d), nL_w(443) (Figure 7g–h), nL_w(490) (Figure 7m–p), and nL_w(555) (Figure 7s–v) from 12:00–15:00 in Box C noted in Figure 1 on 5 November 2014. As shown in Figure 7, although the original nL_w(λ) at all four bands were consistent from 12:00 to 13:00, they decreased significantly at 14:00 and 15:00 (purple color) as θ₀ increased. The NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) at 14:00 (Figure 7e,k,q,w) and 15:00 (Figure 7f,l,r,x) made them consistent with the original nL_w(λ) from 12:00 to 15:00. Figure 8 shows the hourly time series of original nL_w(λ) from 09:00 to 15:00 on 5 November 2014, at the point Q marked in Figure 7f. For the region, among nL_w(λ) at the three short blue/blue bands, nL_w(490) and nL_w(412) had the highest (~0.7 mW cm⁻² μm⁻¹ sr⁻¹) and lowest (~0.3 mW cm⁻² μm⁻¹ sr⁻¹) values (Figure 8). The original nL_w(λ) at the four GOCI bands slightly increased from 09:00 to 12:00, but significantly decreased from 13:00 to 15:00. For example, nL_w(490) began with ~0.6 mW cm⁻² μm⁻¹ sr⁻¹ at 09:00, reached the maximum of ~0.7 mW cm⁻² μm⁻¹ sr⁻¹ at 12:00 and 13:00, but decreased to ~0.3 mW cm⁻² μm⁻¹ sr⁻¹ at 15:00. The corresponding θ₀ from 09:00–16:00 at the point Q were 61.86°, 56.09°, 53.49°, 54.54°, 58.75°, 66.25°, 75.39°, and 86.68°. Indeed, large θ₀ began after 13:00, and they were > 70° at 15:00 and 16:00 with 75.39° and 86.68° (no retrievals at 16:00), respectively. The NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) values (dashed lines) significantly improved the hourly time series, and they are now consistent with the original nL_w(λ) at times of 12:00 and 13:00.

Figure 7. GOCI-measured original nL_w(412), nL_w(443), nL_w(490), and nL_w(555) images of Box C noted in Figure 1a from 12:00–15:00 on November 5, 2014 (first four columns). The last two columns are for the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) images at 14:00 and 15:00, respectively.

Figure 8. Hourly time series (09:00–15:00) of original nL_w(412), nL_w(443), nL_w(490), and nL_w(555) (solid lines), and the corresponding NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) (dashed lines) at the location Q noted in Figure 7f on November 5, 2014.

As done in Section 3.1, the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) at 15:00, $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀, 15), are compared with those at 14:00, nL_w(λ, θ₀, 14), for the same pixel evaluation for the month of November 2014 (Figure 9). The top row of Figure 9 shows the scatter/density plot of original nL_w(λ, θ₀ >65°, 15) versus nL_w(λ, θ₀ ≤65°, 14). Similar to the first case study in the western Pacific Ocean, the original nL_w(λ, θ₀ >65°, 15) at the three short blue/blue bands are underestimated, while the green band nL_w(555, θ₀ >65°, 15) are overestimated. As expected, the mean ratio of r(λ, ≤65°, >65°, 14, 15) are 0.869, 0.867, 0.787, and 1.162 for wavelengths of 412, 443, 490, and 555 nm, respectively. The middle row shows the scatter/density plots of original nL_w(λ, θ₀ ≤65°, 15) versus nL_w(λ, θ₀ ≤65°, 14). The mean ratios of r(λ, ≤65°, ≤65°, 14, 15) are from 0.942 to 0.993 for the three short blue/blue bands and 1.056 for the green band. Again, results of r(λ, ≤65°, ≤65°, 14, 15) serve as references when θ₀ ≤65° for all cases in comparisons. The bottom row shows new $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀ >65°, 15) versus nL_w(λ, θ₀ ≤65°, 14). The mean ratios of r^(C)(λ, ≤65°, >65°, 14, 15) are 0.986, 0.997, 1.005, and 1.011 for spectral bands of 412, 443, 490, and 555 nm, respectively. These are more consistent with the reference ratios r(λ, ≤65°, ≤65°, 14, 15). A summary of statistics in r(λ, ≤65°, >65°, 14, 15), r(λ, ≤65°, ≤65°, 14, 15), and r^(C)(λ, ≤65°, >65°, 14, 15) for November 2014 is listed in Table 4.

Figure 9. Scatter/density plots of GOCI-derived original nL_w(λ, θ₀>65°, 15) (top row), original nL_w(λ, θ₀ ≤65°, 15) (middle row), and new $\mathit{n}{L}_w^{\left(C\right)}$(λ, θ₀>65°, 15) (bottom row) versus original nL_w(λ, θ₀≤65°, 14) from the region in Box C (noted in Figure 1a) at spectral bands of 412, 443, 490, and 555 nm for the month of November 2014. The statistics show that nL_w(λ, θ₀>65°, 15) are underestimated by 13–21% for blue bands, and overestimated by 16% for green band. After correction, the ratio r^(C)(λ, ≤65°, >65°, 14, 15) is close to the reference r(λ, ≤65°, ≤65°, 14, 15).

Table 4. Evaluation results r(λ, θ_0, θ₀′, t, t′) and r^(C)(λ, θ₀, θ₀′, t, t′) (mean, median, and STD) for the month of November 2014.

Ratio r(λ, θ0, θ0′, t, t′) or r^(C)(λ, θ0, θ0′, t, t′)	412 nm			443 nm			490 nm			555 nm
	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD
r (λ, ≤65°, >65°, 14, 15)	0.869	0.859	0.324	0.867	0.865	0.338	0.787	0.793	0.384	1.162	1.135	0.551
r (λ, ≤65°, ≤65°, 14, 15)	0.985	0.973	0.265	0.993	0.974	0.273	0.942	0.923	0.321	1.056	1.042	0.392
r^(C)(λ, ≤65°, >65°, 14, 15)	0.986	0.945	0.284	0.997	0.950	0.298	1.005	0.950	0.332	1.011	0.964	0.398
r (λ, ≤65°, >65°, 13, 14)	0.936	0.922	0.336	0.936	0.925	0.342	0.827	0.829	0.378	1.170	1.037	0.515
r (λ, ≤65°, ≤65°, 13, 14)	1.017	1.010	0.310	1.030	1.014	0.290	1.018	0.993	0.317	1.047	1.014	0.364
r^(C)(λ, ≤65°, >65°, 13, 14)	1.008	0.959	0.293	1.024	0.967	0.307	1.024	0.961	0.343	1.018	0.974	0.434

Similarly, nL_w(λ, θ₀, 14) are compared with nL_w(λ, θ₀, 13) for November 2014, and the statistics are also listed in Table 4. Due to smaller θ₀ at 14:00 than those at 15:00, the mean ratio of r(λ, ≤65°, >65°, 13, 14) are 0.827–1.170 with median ratios of 0.829–1.037, which are closer to 1.0 than r(λ, ≤65°, >65°, 14, 15) of 0.787–1.162. On the other hand, the mean ratios in r^(C)(λ, ≤65°, >65°, 13, 14) of 1.008, 1.024, 1.024, and 1.018 show that they are generally consistent with the reference r(λ, ≤65°, ≤65°, 13, 14) of 1.017, 1.030, 1.018, and 1.047 for the GOCI four spectral bands.

3.3. Evaluation results for all cases

Table 5 summarizes the statistical results of r(λ, ≤65°, >65°, t, t′), r(λ, ≤65°, ≤65°, t, t′), and r^(C)(λ, ≤65°, >65°, t, t′) associated with the GOCI measurement times at 13:00, 14:00, 15:00, and 16:00 for all five months (January, February, October, November, and December) and five even years (2012, 2014, 2016, 2018, and 2020). For the GOCI nL_w(λ) corrections at 16:00, the mean ratios of r^(C)(λ, ≤65°, >65°, 15, 16) are improved to 1.027, 1.025, 1.045, and 1.002 from the original r(λ, ≤65°, >65°, 15, 16) values of 0.899, 0.890, 0.817, and 1.145 for the GOCI bands at 412, 443, 490, and 555 nm. Similar results are shown for the GOCI nL_w(λ) corrections at 15:00 in Table 5. The mean ratios r^(C)(λ, ≤65°, >65°, 14, 15) for the GOCI four bands are 1.015, 1.005, 1.013, and 1.009, compared to r(λ, ≤65°, >65°, 14, 15) values of 0.947, 0.937, 0.926, and 1.089. Finally, for cases with the GOCI nL_w(λ) corrections at 14:00, r(λ, ≤65°, >65°, 13, 14), r(λ, ≤65°, ≤65°, 13, 14), and r^(C)(λ, ≤65°, >65°, 13, 14) have similar results with other two cases. For example, at the wavelength of 443 nm, r(443, ≤65°, >65°, 13, 14) values (mean, median, and STD) are (0.963, 0.947, and 0.391), compared to those from r(443, ≤65°, ≤65°, 13, 14) of (0.989, 0.980, and 0.316) and r^(C)(443, ≤65°, >65°, 13, 14) of (1.001, 1.011, and 0.356), showing improved $\mathit{n}{L}_w^{\left(C\right)}$(λ) results using the NN-models.

Table 5. Evaluation results r(λ, θ_0, θ₀′, t, t′) and r^(C)(λ, θ₀, θ₀′, t, t′) (mean, median, and STD) for all five months (January, February, October, November, and December) and in all five even years (2012, 2014, 2016, 2018, and 2020).

Ratio r (λ, θ0, θ0′, t, t′) or r^(C)(λ, θ0, θ0′, t, t′)	412 nm			443 nm			490 nm			555 nm
	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD	Mean	Median	STD
r (λ, ≤65°, >65°, 15, 16)	0.899	0.871	0.399	0.890	0.875	0.394	0.817	0.806	0.412	1.145	1.094	0.604
r (λ, ≤65°, ≤65°, 15, 16)	0.988	0.974	0.314	0.977	0.976	0.312	0.932	0.917	0.345	1.047	1.030	0.406
r^(C)(λ, ≤65°, >65°, 15, 16)	1.027	0.986	0.351	1.025	0.984	0.347	1.045	1.002	0.376	0.968	0.952	0.441
r (λ, ≤65°, >65°, 14, 15)	0.947	0.924	0.388	0.937	0.928	0.378	0.926	0.909	0.404	1.089	1.045	0.569
r (λ, ≤65°, ≤65°, 14, 15)	0.981	0.966	0.324	0.984	0.965	0.321	0.964	0.945	0.341	1.028	1.012	0.436
r^(C)(λ, ≤65°, >65°, 14, 15)	1.015	0.999	0.342	1.005	0.993	0.345	1.013	0.996	0.360	1.009	1.001	0.453
r (λ, ≤65°, >65°, 13, 14)	0.953	0.964	0.392	0.963	0.947	0.391	0.950	0.937	0.416	1.063	1.031	0.493
r (λ, ≤65°, ≤65°, 13, 14)	0.984	0.974	0.333	0.989	0.980	0.316	0.978	0.968	0.346	1.030	1.020	0.422
r^(C)(λ, ≤65°, >65°, 13, 14)	1.018	0.997	0.358	1.001	1.011	0.356	1.004	0.979	0.360	1.005	0.995	0.450

3.4. Improved Chl-a from the New $\mathit{n}{L}_w^{\left(C\right)}$(λ)

NN corrected nL_w(λ) are also used to derive Chl-a concentrations. Figure 10a shows the original GOCI-derived Chl-a image at 16:00 on 15 February 2020, in Box A of Figure 1. Since Box A covers an area of oligotrophic oceans, Chl-a were expected to be relatively uniform in the region. However, as shown in Figure 10a, Chl-a gradually increased from left to right in the image (following the increased θ₀ pattern in Figure 1c), which was attributed to the decreased nL_w(λ) at the blue bands as θ₀ increased (>70°). The original nL_w(λ) at the first four GOCI bands were corrected using the NN models, and Chl-a were then recalculated for each pixel based on the new $\mathit{n}{L}_w^{\left(C\right)}$(λ) spectra. Figure 10b shows the new Chl-a image based on corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ), which now displays relatively uniform Chl-a distribution across the region.

Figure 10. Comparison of GOCI-derived (a) original Chl-a and (b) new Chl-a in the region of Box A in Figure 1a on February 15, 2020.

Figure 11 shows quantitatively the hourly Chl-a time series on 15 February 2020, at the three locations as indicated in Figure 10a. Since location 1 is closer to the coast than locations 2 and 3 (Figure 10a), Chl-a were higher (~0.2 mg/m³) than other two locations (2 and 3). Specifically, from 09:00 to 15:00, θ₀ at the location 1 were less than 65°, and Chl-a were generally consistent during the first seven hours (blue solid line). At 16:00, θ₀ at the location 1 increased to 66.905°, and Chl-a slightly increased. The new Chl-a (blue dotted line) made a minor correction at 16:00 (~4% overestimation for θ₀ of ~67°), so that it looked more consistent from 09:00 to 16:00. It is noted again that, for θ₀ ≤70°, errors in GOCI-derived nL_w(λ) and Chl-a are generally small (Mikelsons, Wang, and Jiang 2020). The locations 2 and 3 are away from the coast and Chl-a were much lower (~0.1 mg/m³) on 15 February 2020 (Figure 11). For location 2, θ₀ were also less than 65° for the first seven hours and increased to 74.695° at 16:00. Consequently, Chl-a increased from 0.105 mg/m³ at 15:00 to 0.148 mg/m³ at 16:00 (green solid line), and the new Chl-a had a correction down to 0.117 mg/m³ (green dotted line). This was a relatively large correction for Chl-a (~26% overestimation) due to high θ₀ of ~75°. For location 3, θ₀ were less than 65° from 09:00 to 14:00, and increased to 66.69° and 78.93° at 15:00 and 16:00, respectively. Chl-a were constantly low (~0.1 mg/m³) for the first six hours and significantly increased to 0.198 mg/m³ at 16:00 (red solid line) (Figure 11). The new Chl-a at location 3 got a small correction at 15:00 to 0.088 mg/m³ (~10% overestimation for θ₀ of ~ 67°) and a significant correction down to 0.108 mg/m³ at 16:00 (~83% overestimation for θ₀ of ~79°) (red dotted line), now more consistent with the previous hourly Chl-a results (Figure 11). It should be noted again that, as shown in results of Figure 11, the NN-corrections for cases with θ₀ from 65° to 70° are critical for making data change smoothly and consistently (e.g. Chl-a in the location 3).

Figure 11. Comparison of hourly time series (09:00–16:00) for the GOCI-derived original Chl-a (solid lines) and new Chl-a (dashed lines) at the locations 1, 2, and 3 defined in Figure 10a on February 15, 2020.

4. Discussions and conclusion

With daytime hourly measurements, GOCI-derived ocean color data have been useful for research and surveillance of the diurnal ocean processes in the region. However, there are significant errors in GOCI’s late afternoon measurements when the solar-zenith angle (θ₀) goes beyond 70°, especially in autumn and winter seasons. It is found that nL_w(λ) at the three short blue/blue bands are underestimated by ~ 10–20% in the 16:00 images, and ~ 5–10% in the 15:00 and 14:00 images, while at the green band, nL_w(555) are often overestimated by ~ 3–10%. In this study, we developed a NN model to make correction on nL_w(λ) with high θ₀ (65°–80°). Since GOCI-derived nL_w(λ) with θ₀ ≤65° in earlier hours of the day are considered valid and accurate, nL_w(λ) measured at the previous hour are used to train the NN models. We use NN models to predict the correct $\mathit{n}{L}_w^{\left(C\right)}$(λ) from the original biased nL_w(λ) for θ₀ >65°. Because the correction depends on several variables such as previous hour nL_w(λ), solar-sensor geometry, spectral band, wind speed, sun glint, measurement hours (local time), diurnal trend, and so on, the NN model serves as multi-variable regression algorithm for the relationship of correction with other variables.

GOCI data from 2011 to 2020 are used in this study. The NN models are trained with five odd years from 2011 to 2020, that is, 2011, 2013, 2015, 2017, and 2019, and are applied to the even years, that is, 2012, 2014, 2016, 2018, and 2020 for evaluations. The model training and applications are both processed in clear open oceans (Chl-a < ~0.3 mg/m³). From the two case studies in the western Pacific Ocean and Japan/East Sea, it is found that as the time goes to the late afternoon at 15:00 or 16:00 with θ₀ >70°, the GOCI-measured original nL_w(λ) at the three short blue/blue bands are underestimated, with nL_w(490) the most significant, and the green band nL_w(555) are often overestimated. The NN-corrected $\mathit{n}{L}_w^{\left(C\right)}\left(\mathit{\lambda }\right)$ are consistent with the previous-hour GOCI-measured nL_w(λ), and as expected, making diurnal variations much more stable and reasonable.

Further analysis of the relationship between ratio in original nL_w(λ)/new $\mathit{n}{L}_w^{\left(C\right)}$(λ) and θ₀ shows that the ratio decreases as θ₀ increases, indicating that there are more significant corrections with larger θ₀. It is also found that, for the same θ₀, the NN-corrections on nL_w(490) are usually more significant than those from nL_w(412) and nL_w(443). The evaluation of the performance in NN models are based on the comparison of NN-corrected new $\mathit{n}{L}_w^{\left(C\right)}($λ, θ₀ >65°, t′) with the previous hourly nL_w(λ, θ₀ ≤65°, t), in particular, we use the information of the diurnal variations in nL_w(λ, θ₀ ≤65°, t), which are employed as the reference for comparison. Analysis of five years of data indicates that for the GOCI spectral band set of (412, 443, 490, and 555 nm) the mean ratios of r^(C)(λ, ≤65°, >65°, 15, 16), r^(C)(λ, ≤65°, >65°, 14, 15), and r^(C)(λ, ≤65°, >65°, 13, 14) are (1.027, 1.025, 1.045, and 0.968), (1.015, 1.005, 1.013, and 1.009), and (1.018, 1.001, 1.004, and 1.005), respectively, with the corresponding median ratios of (0.986, 0.984, 1.002, and 0.952), (0.999, 0.993, 0.996, and 1.001), and (0.997, 1.011, 0.979, and 0.995), respectively. The corresponding STD values are (0.351, 0.347, 0.376, and 0.441), (0.342, 0.345, 0.360, and 0.453), and (0.358, 0.356, 0.360, and 0.450), respectively. In fact, STD values are all reduced with the NN-corrected r^(C)(λ, ≤65°, >65°, t, t′). However, it should be noted that the lowest STD values are always from r(λ, ≤65°, ≤65°, t, t′), which serves as references for the NN-model evaluation. Therefore, in general, the performance of the NN models is reasonable and encouraging, and the GOCI-derived new $\mathit{n}{L}_w^{\left(C\right)}($λ, θ₀ >65°, 14) and $\mathit{n}{L}_w^{\left(C\right)}($λ, θ₀ >65°, 15) are typically a little better than those of $\mathit{n}{L}_w^{\left(C\right)}($λ, θ₀ >65°, 16). In addition, the statistics of r^(C)(λ, ≤65°, >65°, t, t′) are consistent with the reference ratio r(λ, ≤65°, ≤65°, t, t′), which also indicates that the model performance is acceptable.

Although nL_w(λ) of the previous hours are used for training and evaluations, the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) are not exactly equal to the previous hour nL_w(λ). Since nL_w(λ) measured at the two previous hours are used to make the correction of nL_w(λ) with θ₀ >65°, the NN model is able to do a multivariate regression to predict $\mathit{n}{L}_w^{\left(C\right)}$(λ) based on previous hour data, along with θ₀ and other ancillary data. Therefore, the new $\mathit{n}{L}_w^{\left(C\right)}$(λ) can fit into a stable diurnal variation with the assumption that over open oceans nL_w(λ) do not change significantly within couple hours. The assumption of stable diurnal variations within a few hours over the open ocean region is certainly not always true and there are associated errors in the new $\mathit{n}{L}_w^{\left(C\right)}$(λ). In fact, these errors, including also other uncertainties from various sources, for example, atmospheric correction, are built in the NN-models during the model training processes and reflected in the corrected new $\mathit{n}{L}_w^{\left(C\right)}$(λ). Despite its multiple-factor complexity in nature, the uncertainty in the corrected new $\mathit{n}{L}_w^{\left(C\right)}$(λ) is reduced in comparison with the original and reference dataset in the open ocean. Furthermore, in coastal and inland waters, GOCI data may have larger uncertainties, and particularly there are more frequent nL_w(λ) variations due to ocean biological and biogeochemical processes under the effects of tidal currents, river discharges, sediment variations, and so on. Thus, the required relatively stable water property at least within a few hours for the NN method is often not meet over coastal/inland waters. However, with careful selections of applicable regions and the training data, it may be possible to improve nL_w(λ) under high solar-zenith angles (accounting for the high θ₀ effect) using the NN method. In addition, there are an increasing number of floating algae (e.g. Sargassum) reported in recent years in the western Pacific Ocean. Since these surface/submerged algae tend to be under strong influence of wind and ocean current forcing, and they are also subject to vertical movement, frequent nL_w(λ) variations are expected on these pixels. Therefore, the NN model performance in correction of those floating algae pixels with high θ₀ is limited.

Inaccurate nL_w(λ) also introduces errors in Chl-a calculations. Since the Chl-a algorithm uses a blue-green nL_w(λ) ratio, underestimated nL_w(λ) at the blue band leads to overestimated Chl-a. A case study in the western Pacific Ocean shows significant increased Chl-a as θ₀ goes from 70° to 80° in the original GOCI-derived Chl-a data. With the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ), the newly derived Chl-a are improved, showing generally uniform Chl-a distribution in clear open oceans. It is noted that further evaluation of Chl-a is still needed for the complete GOCI dataset. In addition, we plan to use the NN-corrected $\mathit{n}{L}_w^{\left(C\right)}$(λ) to derive K_d(490). Satellite-measured Chl-a and K_d(490) data have been widely used in the ocean operational user community, and improved GOCI Chl-a and K_d(490) data will have a great potential for research and applications on understanding of the diurnal ocean processes in the western Pacific Ocean region. It is also noted that ocean optical and bio-optical property measured from active satellite sensors, e.g. the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) (Behrenfeld et al. 2022; Zhang et al. 2023), may have a great potential for studying the ocean diurnal variations and to further evaluate the GOCI ocean color data derived at high solar-zenith angles.

Acknowledgments

This research was supported by the Geostationary Extended Observations (GeoXO) and Joint Polar Satellite System (JPSS) fundings. The GOCI Level-1B data were provided by the Korea Institute of Ocean Science and Technology (KIOST). We thank four anonymous reviewers for their useful comments. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the author(s) and do not necessarily reflect those of NOAA or the Department of Commerce.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.