Assessing Radiance Contributions Above Near-Space over the Ocean Using Radiative Transfer Simulation

Highlights

What are the main findings?

• Radiative transfer simulations revealed that in most non-glint contaminated observation areas, the contribution of atmospheric upwelling radiance above scientific balloon platforms to the total radiance (L_t) at the TOA exceeded 2%, demonstrating that this path radiance cannot be neglected in near-space radiometric calibration.
• The study established a transformability from near-space radiance to L_t using a multilayer perceptron model, achieving a mean absolute percentage deviation not exceeding 0.5%, which verifies the feasibility and high accuracy of near-space radiometric calibration.

What are the implications of the main findings?

• This research confirms that near-space radiometric calibration platforms offer greater flexibility and lower sensitivity to variations in inherent optical properties compared to traditional vicarious calibration, making them a significant complementary approach for calibrating satellite ocean color sensors, especially in waters with low chlorophyll or dominated by non-algal particles.
• The near-space radiometric calibration highlights its sensitivity to aerosol vertical distribution and demonstrates the potential to reduce error propagation from the platform to the satellite under high aerosol conditions, providing a theoretical basis for developing more robust calibration schemes that are less affected by the lower atmosphere.

Abstract

Using the near-space platform to conduct radiometric calibrations of ocean color sensors is a promising method for refining calibration precision, but there is knowledge gap about the radiance contributions above near-space over the open ocean. We used the radiative transfer (RT) model (PCOART) to assess the contributions (L_R) of the upwelling radiance received at the near-space balloons to the total radiance (L_t) measured at the top of the atmosphere (TOA). The results indicated that the L_R displayed distinct geometric dependencies with exceeding 2% across most observation geometries. Moreover, the L_R increased with wavelengths under the various solar zenith angles, and the L_R values fell below 1% only for the two near-infrared bands. Additionally, the influences of variations in oceanic constituents on L_R were negligible across various azimuth angles and spectral bands, except in nonalgal particle (NAP)-dominated waters. Furthermore, the influences of aerosol optical thicknesses (AOTs) and atmospheric vertical distributions on L_R were examined. Outside glint-contaminated areas, the atmosphere-associated L_R variations could exceed 2% but declined substantially as AOTs increased under most observation geometries. The mean height of the vertically inhomogeneous layer (h_m) significantly influenced L_R, and the differences in L_t could exceed 5% when comparing atmospheric vertical distributions following homogeneous versus Gaussian-like distributions. Finally, the transformability from near-space radiance to L_t was examined based on a multiple layer perceptron (MLP) model, which exhibited high agreement with the RT simulations. The MAPD averaged 0.420% across the eight bands, ranging from 0.218% to 0.497%. Overall, the radiometric calibration utilizing near-space represents a significant innovation method for satellite-borne ocean color sensors.

1. Introduction

Ocean color remote sensing has significantly advanced our knowledge in understanding the global ocean ecosystems and has contributed to knowledge of the global climate changing trends by providing detailed spatial and temporal distributions of biogeochemical constituents and inherent optical properties (IOPs) in both upper and coastal oceans [1]. Compared with the total radiance (L_t) measured by radiometry at the top of the atmosphere (TOA), the water-leaving radiance (L_w) is extremely low, and generally does not exceed 10% within the visible spectrum [2]. This is to say, 1% radiance calibration uncertainty could lead to 10% atmospheric correction uncertainties, so the accuracy requirements for radiometric calibration are particularly stringent [3]. To achieve the 5% accuracy goal in atmospheric correction (AC) over the global oceans advocated by National Aeronautics and Space Administration (NASA), when considering some compensation between vicarious calibration and AC, the radiance calibration uncertainty should not exceed 3% at blue ranges [4]. Consequently, achieving high radiometric calibration accuracy is crucial for meeting the precision requirements of quantitative oceanographic applications of ocean color products [5,6].

Prelaunch radiometric calibrations, which include spectral and radiometric calibrations, are generally performed [7,8]. The in-orbit calibration process is further conducted to address sensor changes and degradation after launch [9]. Onboard calibration combines multiple methods for high-precision radiometry. The primary method uses a solar diffuser for absolute calibration, while internal lamps provide relative monitoring of performance changes. Lunar calibration complements these by tracking scan-angle-dependent degradation. The onboard calibration, successfully applied to sensors like SeaWiFS, MODIS, VIIRS, and HY-1C, achieves an overall calibration uncertainty of better than 2%. On-orbit and prelaunch calibrations usually have some inherent discrepancies due to the differences between laboratory and space environments. And then, vicarious calibration can be adopted to monitor instrument stability during its lifetime using homogeneous and spatially stable target observations in the open oceans [5,10]. For example, the hyperspectral L_w data provided by the in situ measurements at various oceans over the world, such as Marine Optical Buoy (MOBY) and Aerosol Robotic Network (AERONET), has been widely used for the radiometric calibration of ocean color sensors [11,12,13,14]. The L_w is typically measured using the “above-water method”, which involves isolating the upwelling water-leaving radiance by subtracting the sky-glint contribution at the air–sea interface. Commonly, vicarious calibration, employed to address instrument calibration deficiencies and systematic biases, integrates instrument calibration with AC to align retrieved L_w values with field observations [5].

However, the quality of L_w retrievals is often limited by deficiencies in current AC algorithms [15,16,17,18]. Moreover, the in situ L_w data, which often contain unpredictable errors, can be used as inputs to generate the L_t via the operational AC algorithm and radiative transfer (RT) model. When the field measurements are carried out following the strictest measurement standards [19], the field-measured L_w data still contain 3–5% uncertainties [20]. Although accurately isolating surface-reflected skylight radiance is extremely difficult in above-water methods, it is an essential parameter for the calculation of L_w [21]. When the imperfect field measurements are used in vicarious calibrations, these measured uncertainties will transfer to L_t at the TOA [22,23]. And thus, aligning various calibration methods with a unified radiance standard to ensure the stability and consistency of ocean color products across different sensors remains a significant challenge. With the anticipated exponential growth in ocean color sensors in the future, the demand for such alignment has become even more pressing. Currently, satellite remote sensing payloads require a highly stable, reliable, and traceable radiance calibration source for on-orbit radiometric calibration [24].

To avoid uncertainties originating from AC and field measurements, Europe, the United States, and China have implemented many plans providing stable radiance sources for radiance calibration such as the Traceable Radiometry Underpinning Terrestrial- and Helio-Studies (TRUTHS), the Climate Absolute Radiance and Refractivity Observatory (CLARREO), and the Chinese Space-Based Radiometric Benchmark Research Plan, respectively [25,26,27]. In the 1980s, the Laboratory for Atmospheric and Space Physics (LASP) in the United States pioneered high-altitude balloon-based calibration by conducting spectroradiometer calibrations in the stratosphere above 35 km, demonstrating the advantages of balloon platforms with low cost, recoverability, and near-AM0 (Air Mass Zero) conditions [28]. However, due to limitations in tracking accuracy (solar tracking errors > 1° at the time), the data repeatability was insufficient. Concurrently, Europe established a balloon calibration network under the Atmospheric Radiation Measurement (ARM) program, developing AM0 calibration standards for multi-junction solar cells and hyperspectral imagers. The National Institute of Standards and Technology (NIST) in the U.S. developed the Cryogenic Solar Absolute Radiometer (CSAR) as a primary standard, achieving a radiometric accuracy of 0.01% (k = 2) through balloon flights, thereby providing a ground-to-high-altitude comparison benchmark for subsequent satellite calibrations [29]. The TRUTHS mission, proposed in 2020, integrated near-space calibration with satellite platforms for the first time. It employed a spaceborne CSAR to trace measurements directly to SI units while utilizing high-altitude balloons for regular “ground-high-altitude-satellite” three-level comparisons [29]. The approach addressed on-orbit degradation of satellite payloads, reduced radiometric calibration uncertainty to 0.16–0.26%, and established a new paradigm of near-space calibration supporting long-term satellite stability monitoring. Since 2015, China has implemented comparison studies through Dunhuang Gobi ground simulations and 35 km balloon flights, developing atmospheric correction models to further reduce data uncertainty to 1.5–2% [27]. This progress provides critical support for the energy system design of future near-space aircraft, such as high-altitude long-endurance drones.

These initiatives seek to establish near-space radiometric benchmark platforms by transferring radiometric standards to satellite systems. By performing synchronized ground observations in conjunction with satellite overpasses, these platforms collect radiometric reference data that serves to calibrate on-orbit radiation measurements acquired by on-orbit satellites. Theoretically, this approach could provide the radiance with high accuracy and traceability for radiance calibration for the satellites with absence of lower atmospheric interference and a relatively simplified radiative transfer path [30]. Particularly, deploying the radiance standard on a high-altitude, near-space platform and transferring the radiometric standard to satellite ocean color sensors through synchronized Earth observations has emerged as a viable approach to increase the accuracy of on-orbit radiometric calibration [31], advantageous for minimizing the calculation uncertainty bellowing near-space platform using radiation transfer model. This is to say, near-space scientific balloons, as a representative class of near-space, offer distinct advantages for radiance calibration, where the atmospheric radiance path was much shorter than field measurements for vicarious calibration [25]. These characteristics render them as a viable option for on-orbit radiometric calibration [32].

The upper atmosphere is usually relatively rarefied, and near-space platform balloons typically fly at an altitude of approximately 30 km [31]. While it is well established that atmospheric density is markedly reduced at such altitudes, there are knowledge gaps about the necessity for removing the atmospheric contributions originating from atmospheric paths between balloon and satellite, which is considered as the primary issue we will address in this study. Moreover, the contributions, which vary with the vertical distribution of atmospheric molecules and aerosols as well as water optical properties, should be clearly understood, which is essential for near-space radiometric calibration. To account for these, we utilized RT simulations to examine the contributions of upwelling radiance derived from scientific balloons to the TOA, and then the influences of aerosol optical thicknesses (AOTs) and atmospheric vertical distributions on the contributions were studied. The specific goals of our study are as follows: (1) to address the L_R with the variations in the observation geometries and ocean constituents; (2) to show the sensitivity of L_R on the AOTs and aerosol vertical distributions (3) to clarify the transformability from near-space radiance to the L_t at the TOA radiance in the calibration processes, and (4) to assess the performance of near-space platform radiometric calibration. We anticipate these quantitative findings to be a starting point for a novel radiometric calibration for ocean color satellites with near-space platform.

2. Materials and Methods

2.1. RT Simulation and Data

The coupled ocean–atmosphere system vector RT model, named the PCOART model, developed by He et al. [33] was employed to simulate the angular distributions of intensity within the atmosphere–ocean system (AOS). The model’s key strength resided in its capability to dynamically configure the stratified structures of the atmosphere and ocean. By adaptively adjusting layered parameters, it enabled simultaneous and precise inversion of both upward and downward radiative fluxes at arbitrary vertical levels. By comparison with CDISORT/AccuRT, the accuracy of PCOART is validated, with relative differences generally less than 0.5% and even below 0.2% within the main observational angles [34]. Moreover, the comparison of component I of Stokes vectors between PCOART and the look-up tables (LUTs) in SeaDAS for different observation zenith angles and relative azimuth angles with sea surface windspeed of 5 m/s were lower than 0.5% [33]. Additionally, the polarizing remote sensing data from POLDER was used to test the capacity of PCOART to simulate the polarization radiance at the top-of-atmosphere, which showed that PCOART can perfectly reproduce the linear polarization reflectance measured by POLDER [33]. Hence, the PCOART can serve as a good tool for ocean optics and ocean color remote sensing communities with high accuracy.

When IOPs for hydrosol and the atmosphere were predefined in the RT model, the upward and downward radiation fields spanning the near-ultraviolet, visible, and infrared spectra are simulated within any stratified AOS. The AOS exhibits an aerosol–molecular mixed atmosphere and an oceanic plane-parallel homogeneous layer. In accordance with the US Standard Atmosphere Model, which was provided by Song et al., [35], the atmosphere comprises ideal molecules and aerosols and is divided into 32 vertically inhomogeneous layers. Notably, atmospheric molecules are defined by Rayleigh scattering, and the single-scattering albedo and depolarization factors of the molecule are 1 and 0.0279, respectively [36]. Following the aerosol models of Shettle and Fenn [37], atmospheric molecules were mixed with maritime aerosols at 90% relative humidity (M90) and urban aerosols at 50% relative humidity (U50). The optical thickness of each vertically inhomogeneous layer was the sum of those of the gaseous molecules and aerosols. Additionally, to address the influence of the aerosol vertical distributions on the contribution of the upwelling radiance above the near-space platform to L_t at the TOA, a Gaussian-like vertical distribution was used to describe the AOT, formulated as follows [38,39]:

$$\tau ={\tau }_m{e}^{-{\displaystyle \frac{{(z_i-h_m)}^2}{2{\sigma }^2}}}$$

(1)

where τ is the AOT of each vertically inhomogeneous layer, z_i is the height of this layer, σ is the standard deviation, and τ_m and h_m are the optical depth and altitude at the mean height of the vertically inhomogeneous layer, respectively. The AOTs at 865 nm ranged from 0.02 to 0.7 based on the AERONET and Dunhuang site (Dunhuang, China) measurements. The RT simulations were performed for homogeneous distributions and vertically inhomogeneous distributions, with mean heights ranging from 1 to 5 km per 0.2 km. The vertical distribution of the AOTs in the RT simulations used the US Standard Atmosphere Model.

Four key components contributed to the IOPs of the oceanic layers: pure water, phytoplankton (represented by Chla concentration), nonalgal particles (NAP), and colored detrital matter (CDOM). For pure water, we used the spectral absorption coefficients from Pope and Fry [40]. The absorption coefficients of phytoplankton can be computed as follows [41]:

$$a_{Chla}(\lambda )=A_{\Phi }(\lambda )\times {[\mathrm{Chla}]}^{E_{\Phi }(\lambda )}$$

(2)

where A_Φ(λ) and E_Φ(λ) are wavelength-dependent parameters, given by Bricaud et al. (1998) [41]. The attenuation coefficient for phytoplankton can be expressed as follows [42]:

$$c_{Chla}(\lambda )=c_{Chla}(660)\times {({\displaystyle \frac{\lambda }{660}})}^{\upsilon }$$

(3)

The attenuation coefficient for phytoplankton at 660 nm can be obtained as follows [43]:

$$c_{Chla}(660)={\gamma }_0\times {[\mathrm{Chla}]}^{\eta }$$

(4)

where γ₀ is 0.407, and η is 0.765. The spectral variation in the scattering coefficient for phytoplankton can be calculated as follows:

$$b_{Chla}(\lambda )=c_{Chla}(\lambda )-a_{Chla}(\lambda )$$

(5)

The absorption coefficient for NAPs can be given as follows [44]:

$$a_{NAP}(\lambda )=a_{NAP}(443)\times [\exp (-0.0123(\lambda -443))]$$

(6)

where the absorption coefficient for NAPs at 443 nm can be expressed as follows:

$$a_{NAP}(443)=0.031\times 0.75\times NAP$$

(7)

where NAP denotes the nonalgal particle concentration. The attenuation coefficient can be calculated as follows:

$$c_{NAP}(\lambda )=c_{NAP}(555)\times {({\displaystyle \frac{\lambda }{555}})}^{-c}$$

(8)

where c = 0.3749, which can be obtained as follows:

$$\begin{array}{cc}\hfill c_{NAP}(555)& =a_{NAP}(555)+b_{NAP}(555)\hfill \\ \hfill & =[0.041\times exp(-0.0123(555-443))+0.51]\times \mathrm{NAP}\hfill \end{array}$$

(9)

The spectral variation in the scattering coefficient for NAP can be obtained as follows:

$$b_{NAP}(\lambda )=c_{NAP}(\lambda )+a_{NAP}(\lambda )$$

(10)

Moreover, the absorption coefficient of CDOM (a_g) can be expressed as follows [45]:

$$a_g(\lambda )=a_g(443)\times \exp (-0.0176(\lambda -443))$$

(11)

Using Mie theory with specified complex refractive indices (1.05 for Chla and 1.165 for NAP) and a Junge size distribution [46], we computed the scattering phase matrices for each hydrosol type. Their total scattering phase matrices were subsequently obtained by combining these results according to the respective scattering coefficients, as follows:

$$F_{Bulk}={\displaystyle \frac{b_{nap}\times F_{nap}+b_{ph}\times F_{ph}}{b_{nap}+b_{ph}}}$$

(12)

where F_Bulk, F_nap and F_ph are the bulk scattering matrix, inorganic particle scattering matrix, and phytoplankton scattering matrix, respectively. The Chla concentrations ranged from 0.01 mg/m³ to 1 mg/m³, which were referenced as the Chla distributions in oceanic, marginal sea, and coastal waters based on annually average products. Moreover, the NAP concentrations were from 0.1 to 10 mg/L, and the a_g(443) values were set to 0.01, 0.05, 0.1 and 0.5 m⁻¹ (

Table 1. Parameters of the AOS in PCOART model for the RT simulations.

	Variable	Constrainer
Ocean	Chla	0.01–1 mg/m3
	NAP	0.1–10 mg/L
	ag(443)	0.01, 0.05, 0.1, 0.5 m−1
Atmosphere	AOTs	0.02–0.7
	Aerosols	M90, U50
	hm	1–5 km
Angular	Solar zenith angles	0–60°
	Viewing zenith angle	0–90°
	Sensor azimuth angle	0–180°
Others	Bands (nm)	412, 443, 490, 510, 555, 660, 745, 865

).

We performed RT simulations using the TOA solar irradiance model of Thuillier et al. [47] across eight standard ocean-color wavelengths (412, 443, 490, 555, 660, 745, and 865 nm), matching the standard spectral bands of the GOCI satellite. The simulations covered solar zenith angles (SZA) from 0° to 60° (10° intervals) and viewing zenith angles (VZA) from 0° to 90° (2.8° intervals). Moreover, the sensor azimuth angle (SAA, φ_v) varied over a range of 0° to 180°, in steps of 15°. Notably, balloon-based platform calibration was conducted in the Qinghai Province, China [31]. The flight altitude of the scientific balloon was 30 km (Figure 1a). Hence, two RT simulations were conducted, aimed at quantifying the contribution from upwelling radiance above the near-space platform to the L_t at the TOA: one for the condition with 26 atmosphere layers along the vertical direction (total atmospheric height = 30 km) and the other with 32 atmosphere layers (total atmospheric height = 100 km) and a nonblack ocean, including pure seawater and oceanic constitutions (Figure 1b). The upwelling radiance above the near-space platform (ΔL= L_t − L_30km) and L_t at the TOA were subsequently obtained, and the equivalent contributions (L_R) were calculated as follows:

$$L_R={\displaystyle \frac{L_t-L_{30\mathrm{km}}}{L_t}}={\displaystyle \frac{\Delta L}{L_t}}$$

(13)

2.2. MLP Neural Network for Vicarious Calibration

Deep learning models are crucial for radiometric calibration in ocean color remote sensing research and applications [48,49]. In this study, we developed a multilayer perceptron neural network (MLP) with an input layer consisting of radiance and spectral features. The MLP, which is inspired by biological nervous systems, comprises multiple neurons organized into input, output, and hidden layers. In the MLP, each neuron within a layer is interconnected with all the neurons in the preceding layer. Each input to a neuron is assigned an independent weight, summed with a bias term, and processed through a logistic or other nonlinear activation function. These interneuronal connections fundamentally define the functionality of the network. The resulting output is subsequently transmitted to all the neurons in the following layer.

The MLP model was then constructed with an input layer containing six features. Experiments were conducted with two and three hidden layers, respectively, where for each hidden layer, the number of neurons was attempted as 128, 64, 32, 16, and 8, respectively, and the activation functions were attempted as “ReLU” and “Sigmoid” respectively. For the output layer, the better-performing activation function was selected between “ReLU” and “Linear”. The learning rate was trained from 0.001 to 0.005, increasing by 0.001 each time. The dataset contained 98,280 samples, which are divided into a training set, a validation set, and a test set in an 8:1:1 ratio. Importantly, the upwelling radiance, measured at the near-space platform, was contaminated with approximately 0.5% Gaussian-like noise, according to the radiometric calibration accuracy of the near-space platform instruments [25]. Training encompassed up to 1000 epochs, with an early stopping criterion in place to halt training if the mean absolute percentage difference (MAPD) between the validation set output features and predictions remained below 0.5% for 20 consecutive epochs. Pre-experiments showed that additional training for 100 epochs only improved the MAPD by 0.007%, so 0.5% was selected as the threshold to prevent unnecessary prolongation of training. Finally, the test data was reserved for subsequent evaluation. Through the above process, the optimal model structure was obtained. It consists of two hidden layers with 32 and 16 neurons, respectively, both employing the ReLU activation function, an output layer with a Linear activation function (Figure 1c). In this architecture, information propagates through sequential transformations governed by mathematical operations at each layer.

2.3. Statistical Assessment

Model accuracy in the radiance conversion from near-space to TOA was evaluated by calculating the Mean Absolute Percent Difference (MAPD) and Root Mean Square Error (RMSE). These metrics are defined as:

$$MAPD={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{L_M-L_i}{L_i}\right|}\times 100\%$$

(14)

$$RMSE=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _{i=1}^n{(L_M-L_i)}^2}}$$

(15)

where n is the number of samples, L_i is the simulated data, L_M is MLP neural network outputs.

3. Results

3.1. Water Optical Properties Parameters

3.1.1. Variability of L_R with Observation Geometry

Given that the near-space altitude experiment for satellite radiometric calibration operated at 30 km [27], the magnitude and spectral characteristics of atmospheric contributions (L_R) along the observation geometries between the platform and satellite sensors were determined. Using a Chla concentration of 0.01 mg/m³ and an AOT of 0.5 as representative inputs, Figure 2a shows the angular distributions of L_R at special scene at eight visible wavelengths. It was found that the significant directional variations in L_R are evidently covarying with the illumination-observation geometric conditions, with the maximum value (exceeding 30%) around azimuth approximated to 180° (Figure 2a). This is mainly due to the strong contribution of specular reflection, indicating that the atmospheric scattering has a strong directionality. Notably, an azimuth angle of 0° indicates coincidence with the solar principal plane, also known as the anti-specular plane. As a result, the influence range of sun glint formed a circular area within 15° around the specular reflection point, progressively weakening as it deviated from this point (Figure 2a). The impact of solar glare enhanced with increasing wavelength, primarily due to the gradual reduction in atmospheric molecular scattering as wavelength increasing. To avoid sun glint when the solar zenith angle is small (<19°), the sensor must be tilted forward [4]. Similarly, the RT simulations indicated that the near-space calibration measurements also need to avoid solar glint, with observational geometries located beyond a ∼30° radius from the specular reflection direction being recommended, with L_R showing minimal variation for azimuth angle of 0–120°, and then this observation angular span is ideal for radiometric calibration conducted from near-space platforms.

Figure 2b also shows that the L_R values exhibited a baseline increase with sensor zenith angle for solar zenith angle lower than 60° for the contribution of atmospheric diffuse scattered light. And the L_R increased for sensor zenith angle larger than 75° due to the longer atmosphere path radiance [50]. It demonstrated that the L_R value exceeded 2% across the different wavelengths for a sensor azimuth angle of 0° and 90° (

Table 2. Spectral distribution characteristics of the contribution percentage (L_R, %) of near-space upwelling radiance to the total radiance at the TOA, under 30° sensor zenith angle and varying SZAs from 0° to 60° at 10° intervals.

SAA	SZA	412 nm	443 nm	490 nm	510 nm	555 nm	660 nm	745 nm	865 nm
0°	0°	2.86	3.06	3.44	3.65	4.15	5.54	6.49	7.49
	10°	2.45	2.43	2.41	2.43	2.48	2.75	2.88	2.99
	20°	2.49	2.46	2.43	2.44	2.48	2.75	2.90	3.00
	30°	2.60	2.57	2.55	2.57	2.64	2.99	3.24	3.41
	40°	2.71	2.71	2.77	2.82	2.98	3.59	4.03	4.45
	50°	2.74	2.72	2.77	2.82	2.98	3.59	4.04	4.53
	60°	2.80	2.69	2.62	2.62	2.66	2.92	3.12	3.35
90°	0°	2.86	3.06	3.44	3.65	4.15	5.54	6.49	7.49
	10°	2.67	2.78	3.00	3.12	3.44	4.36	4.97	5.61
	20°	2.43	2.43	2.46	2.50	2.59	2.93	3.13	3.32
	30°	2.28	2.24	2.18	2.18	2.19	2.30	2.35	2.38
	40°	2.17	2.06	1.90	1.84	1.72	1.47	1.23	0.92
	50°	2.17	2.03	1.82	1.74	1.56	1.16	0.79	0.31
	60°	2.32	2.18	2.01	1.96	1.86	1.71	1.57	1.40

). Taking the L_R at 490 nm as an example, the L_R typically exceeded 2.41% (1.82%) for azimuth angle of 0° (90°), respectively. Figure 2b shows the variations in L_R with respect to the SZA and VZA. And the maximum L_R value at lower VZA decreased as the SZA increased, while the distinctiveness of the spectral variations in L_R decreased when the SZA exceeded 30°, likely because of enhanced atmospheric multiple scattering and path radiation [51]. Similarly, the L_R for sensor zenith angle of 30–60° showed minimal variations, and the contributions above upwelling radiance above the near-space platform for those observations of angularity might be a preferable choice for radiometric calibration conducted from near-space platforms. The statistical analysis of L_R vs. L_30km, and ΔL across geometries and environmental conditions were also discussed. As the sensor zenith angle increased from 0°to 90°, the L_30km exhibited high values and strong discreteness at small observation angles, then decreased rapidly with increasing sensor zenith angles and eventually stabilized (Figure 2c,d), and the L_30km varied from 0.12 to 2.63 with the unit of mw/(cm²·nm·sr). Moreover, the ΔL showed a “gentle fluctuation to rapid rise” pattern as the sensor zenith angle increased (Figure 2d). Within the 0–75° range, the ΔL remained at a medium-low level of 4.0–10 mw/(cm²·nm·sr) with slight fluctuations, and as the sensor zenith angles ranged from 75° to 90°, it climbed rapidly, approaching a high value close to 12 mw/(cm²·nm·sr). Additionally, at small sensor zenith angles, L_30km was high while ΔL was low, and at large sensor zenith angles, L_30km became low while ΔL turned high (Figure 2c). Consequently, the L_R was collectively determined by L_30km and ΔL. Although the L_R exhibits significant angular distribution characteristics, and the variation patterns across different wavelengths are determined by solar and observation geometry, the influence of upwelling radiance above the near-space platform remains relatively stable within a certain range of observation angles. This makes them a preferable choice for radiometric calibration based on near-space platforms, and the specific angle recommendations are provided in

Table 3. Selection of observational geometry angles for radiometric calibration based on near-space platforms.

Name	Variable	Constrainer
SZA	θs	≥19°
SAA	φv	0–120°
VZA	θv	30–60°

.

3.1.2. Variability of LR with Spectral

Taking the sensor azimuth angles of 0° and 90° as an example, Figure 3 shows the spectral variations in L_R of different sensor zenith angles, with Chla concentrations of 0.01 mg/m³, 0.1 mg/m³, and 1 mg/m³. The RT simulations showed that the L_R increased with wavelengths under the various solar zenith angles because of the weakened atmosphere scattering as the wavelengths increased from blue to near-infrared (NIR) band and then significantly reduced the L_t. On the contrary, the influence of atmosphere scattering on the L_30km was weaker than L_t [50]. However, for a sensor azimuth angle of 90°, the L_R slightly decreased at specific solar zenith angles, such as 50° and 60° (Table 3).

Specifically, only the L_R values at the 745 and 865 nm near-infrared wavelengths fell below 2% with solar zenith angles of 60° for the weak atmospheric radiance contributions (Figure 3a–c). Moreover, the spectral variations in L_R were determined by the solar zenith angles (

Table 4. Contribution of L_R (%) in the vertically downward direction at differing solar zenith angles (SAA is 90°, Chla is 0.01 mg/m³, the AOT at 865 nm is 0.5).

Band (nm)	0°	10°	20°	30°	40°	50°	60°
412	20.29	15.68	6.97	3.04	2.39	2.25	2.35
443	25.47	20.02	8.85	3.28	2.38	2.18	2.23
490	32.21	26.01	11.88	3.75	2.40	2.12	2.12
510	34.72	28.32	13.21	3.99	2.43	2.11	2.09
555	39.29	32.63	15.95	4.49	2.49	2.10	2.05
660	46.16	39.35	20.96	5.57	2.63	2.12	2.00
745	49.48	42.58	23.69	6.23	2.70	2.14	1.98
865	52.59	45.53	26.27	6.91	2.78	2.16	1.97

). This is mainly due to the differences in backscattering characteristics of atmospheric molecules and aerosol particles for different observation geometries [52,53]. Overall, the L_R values remained above 1% for all the visible and NIR bands. Franz et al. (2007) have proposed that 1% radiance calibration could lead to ~10% uncertainties in atmospheric correction [5], so it is essential to account for atmospheric RT processes and the contributions above near-space for all spectral bands during the radiometric calibrations of near-space platforms.

3.2. Impact of Oceanic Constituents on L_R

The optically active constituents determine the L_w observed by satellite sensors, which is the partial component of L_R and L_t. These biogeochemical components primarily influence L_w by being associated with the total absorption and backscattering coefficients [5]. To quantify the influence of oceanic constituents on L_R, we systematically performed RT simulations across varied water component scenarios. As shown in Figure 4, the variations in L_R for different oceanic constituents, including Chla, CDOM (a_g(443)), and NAP, were compared, where the Chla concentrations were 0.01, 0.1, and 1 mg/m³, the NAP concentrations were 0.1, 0.5, 1, 5, and 10 mg/L, and the a_g(443) values were 0.01, 0.05, 0.1 and 0.5 m⁻¹, and the AOTs were 0.125, 0.25, and 0.5. The results showed that the L_R exhibited less sensitivity to the variations in the Chla concentrations and a_g(443) (Figure 4a–c). Obviously, the L_R increased with increasing sensor zenith angle for differing oceanic constituents, and the variations gradually weakened as the sensor angle increased for strong diffuse scattering effect [54]. The impact of NAP concentrations on L_R was more pronounced than that of Chla and a_g(443). Specifically, the L_R decreased from 2.86% to 2.31% as NAP concentrations increased, under a sensor zenith angle of 4.5° and a sensor azimuth angle of 0° (Figure 4d–f). The RT simulations showed that both the L_t and the L_30km increased with the NAP concentrations increasing, while the increase in L_30km was slightly smaller than that in L_t. With 412 nm as example, the increase in L_30km was only 11.92%, whereas its increase was 12.01% when compared with L_t, and this difference ultimately led to a decrease in L_R. Moreover, the L_R slightly increased as a_g(443) increased for the decrease in L_t [53].

Overall, in clear waters with NAP concentrations below 5 mg/L, the impact of oceanic constituents on L_R is minimal yet consistently discernible across all viewing azimuths and spectral bands. Therefore, radiometric calibration based on near-space platforms offers greater flexibility and significant advantages in selecting calibration sites, whereas vicarious calibration typically requires more homogeneous ocean conditions with low variations in constituents and IOPs.

3.3. Effect of Aerosols Optical Properties on L_R

The optical properties of aerosols, including the AOTs and vertical distribution characteristics, play a pivotal role in modulating atmospheric RT processes. Among these, the AOT governs atmospheric light absorption and scattering magnitudes, thereby critically modulating atmospheric path radiation intensity [33]. Commonly, the vertical distribution characteristics of aerosols govern their concentration gradients and spatial configurations across different altitude layers [35]. Diverse vertical distribution patterns of aerosol optical properties mechanistically alter RT pathways and efficiencies through their modulation of atmospheric photon transport processes, and then the upwelling radiance above the near-space platform and Lt at the TOA [39]. These two parameters exhibit coupled interactions through aerosol radiation feedback mechanisms, collectively determining the multidimensional response of aerosol effects on L_R via nonlinear optical coupling processes.

3.3.1. Overall Impact of AOTs on L_R

The impacts of the AOTs on the angular-dependent distributions of the L_R were first discussed as shown in Figure 5. It was found that the angular variations in L_R at 412 nm exhibited similar patterns across the different solar zenith angles and AOTs, albeit with varying magnitudes. As the AOTs increased, the maximum L_R value gradually decreased for the regions affected by sun glint (Table 3). In these observational regions, the maximum value typically exceeded 30% due to the sun glint. The increase in AOTs resulted in the L_t gradually decreasing, while the distribution of atmospheric aerosols is primarily concentrated in the lower atmosphere, hence the increase in L_30km and L_t is inconsistent [35]. Additionally, the geometry of the sun glint regions shifted as the SZA increased. The spatial extent significantly affected by sun glint diminished with AOTs increasing, often exceeding an observation zenith angle of 20°. The atmospheric diffuse scattering intensified with increasing AOTs, whereas the contributions of specularly reflected glint at the TOA conversely diminished due to intense diffuse scattering. Typically, the accuracy of L_t at the TOA must remain within an error margin of less than 1% [3]. To minimize the impact of sun glint, in situ observation deployments are often strategically planned. However, even in regions outside glint-contaminated areas, the L_R could also exceed 2%. Under these conditions, the atmospheric path radiance above scientific balloons, as determined by RT simulations, cannot be neglected.

Figure 6 shows the variations in L_R with respect to VZA at 412 nm and 490 nm for a SZA of 20° and a sensor azimuth angle of 90° under varying AOTs. The influence of AOTs on L_R was significant for VZA below 20° due to sun glint, and the L_R decreased from 41.96% to 20.23% for the zenith observation (Table 4). A substantial decline in L_R was observed as AOTs increased. For example, at an AOT of 0.125, the L_R value was twice as high as that at an AOT of 0.5 for lower sensor zenith angles (

Table 5. Contribution of the upwelling radiance above the near-space platform to the total radiance at the TOA (L_R, %) with the vertically downward direction toward 412 nm and 490 nm under differing sensor zenith angles.

Bands (nm)	AOTs	0°	10°	20°	30°	40°	50°	60°
412	0.125	41.96	26.38	8.58	2.88	2.41	2.36	2.44
	0.25	33.05	20.12	6.78	2.76	2.46	2.35	2.42
	0.5	20.29	12.05	4.65	2.65	2.55	2.32	2.41
490	0.125	61.85	45.08	16.75	3.70	2.42	2.29	2.29
	0.25	50.24	34.51	12.29	3.30	2.47	2.26	2.24
	0.5	32.21	20.29	7.23	2.87	2.55	2.20	2.19

). When avoiding solar glint, the L_R distributions were relatively uniform across different azimuth angles. Similarly, the L_R value exhibited a baseline increase with sensor zenith angle increasing, typically exceeding 2% (>2.3%) (Table 5). In practice, the sensor zenith angle was usually small during near-space platform deployment, and the L_R value remained relatively stable across most observation areas. Consequently, the atmospheric influence on radiation above the near-space platform remained relatively consistent. Additionally, the near-space platform offered greater flexibility in angle settings, which could be aligned with the observation angles of in-orbit ocean color sensors. Simultaneously, the angular differences between the sensors of the two platforms can be corrected via the observation and space-time matching algorithm [15]. Therefore, the timing and angular settings for radiometric calibration of the near-space platform can be closely coordinated with those of satellite radiometry.

3.3.2. Sensitivity of the L_R to Aerosol Vertical Distribution

The balloon-based platform calibration was conducted in the Qinghai Area [31]. And the aerosol model usually entails the absorption of aerosols for the calibration experiments, such as dust aerosols. The vertical distributions of absorbing aerosols significantly impact AC algorithms [39]. This influence can alter L_t by up to 8% for dust aerosols and 10% for fine-particle-dominated absorbing aerosols [55], leading to errors of L_w retrieval up to ~12–15% and ~30–40% [16,39]. And vertical distributions also affect the atmospheric RT above the near-space platform [56,57]. Current AC algorithms typically represent aerosols in one of two ways; either as a layer below the molecular layer, simplifying the atmosphere into a two-layer model, or by assuming an exponential decrease in aerosol concentration with altitude [16]. It showed that the vertical distributions of absorbing aerosols are suitable for employing a Gaussian function from CALIPSO observations [35]. The influence of the aerosol vertical distribution on L_R was further discussed with h_m ranging from 1 to 5 km for the U50 aerosol model.

The variations in L_R with increasing mean heights of the AOT profiles at 412 nm, 443 nm, and 490 nm were discussed under different sensor zenith angles (Figure 7). The solar zenith angles were 0°, 10°, and 20°. It demonstrated that the influence of hm on L_R was significant for sensor zenith angles lower than 20° and sensor zenith angles greater than 60°, and the L_R increased from 2.34% to 2.81% as the h_m ranged from 1 km to 5 km (

Table 6. Comparisons of the L_t of the homogeneous distribution to the Gaussian-like distributions with different mean heights of the aerosol optical thickness profile in the vertically downward direction under differing solar zenith angles.

LR (%)	1 km	2 km	3 km	4 km	5 km
0°	2.34	2.09	2.10	2.35	2.81
10°	2.46	2.17	2.15	2.36	2.81
20°	2.59	2.31	2.29	2.46	2.87
30°	2.58	2.33	2.33	2.54	2.99
40°	2.40	2.19	2.24	2.53	3.09
50°	2.06	1.89	2.06	2.54	3.46
60°	1.52	1.53	2.06	3.23	4.54

). The value of L_R could reach 15% for vertically downward-facing sensors under different mean heights of the aerosol optical thickness profile due to sun glint (Figure 7a). As h_m increased, the L_R slightly increased (Figure 7). This phenomenon was expected, as the scattering effect in the upper atmosphere intensifies with increasing aerosol altitude, leading to a corresponding increase in the radiative contributions. Similarly, the maximum value of L_R for different aerosol vertical distributions showed high variability with solar zenith angle. Overall, the L_R values associated with absorbing aerosols exceeded those of the maritime aerosol models. Consequently, when conducting radiometric calibrations using the near-space platform as a reference, it is crucial to account for the RT contributions above the near-space platform due to aerosol vertical distributions, particularly for the absorbing aerosols.

A comparative analysis of L_R values between atmospheres with homogeneous and vertically heterogeneous aerosol distributions was further discussed (Figure 8). The results indicated that the atmospheric inhomogeneity significantly influenced the L_30km and L_t, and then to the spatial distribution of L_R values. As shown in Figure 8a–f, the L_R value for different mean heights of the AOTs profile was slightly higher than that for the homogeneous case. The vertical distribution of atmospheric aerosols impacted the intensity of radiation received by sensors at the TOA. Moreover, Figure 8g–l shows the angular distribution of L_t at the TOA for a Chla concentration of 0.1 mg/m³ with varying hm and a homogeneous distribution. While the angular distributions of the L_t remained largely consistent, slight differences in the radiation intensity were observed by ocean color sensors.

Furthermore, the comparisons of the L_t between homogeneous and Gaussian-like distributions are shown in Figure 9. It showed that the differences could exceed 5%. For sensor zenith angles between 15° and 60°, the L_t for Gaussian-like aerosol distributions was greater than that for homogeneous distributions. The difference gradually weekend as the hm increased for these observation geometries. An increase in the hm essentially shifts the “center of gravity” for scattering and absorption to higher altitudes. It causes more solar radiation to be scattered back into space near the TOA or absorbed by high-altitude aerosols and not be transmitted downward [50]. This process then directly leads to a decrease in L_t. By taking considering of the comparisons of the vertically downward direction as an example, the differences were found to gradually increase as the hm increased under different solar zenith angles (Table 4). The L_t for the Gaussian-like aerosol distributions was lower than that for the homogeneous aerosol distribution along the vertically downward direction. A simple assumption of uniform aerosol distribution in the atmosphere could lead to significant errors in radiometric calibration (>0.5%). Therefore, it was essential to consider the vertical distribution of aerosols for the near-space radiometric calibrations.

3.4. The Transformability from Near-Space Radiance to TOA Radiance

The contribution of atmospheric path radiance above near-space is non-negligible based on the RT simulations. And then, the impact of L_30km on the radiometric calibration accuracy of spaceborne sensors was further investigated, aiming to analyze the transformability from near-space radiance to L_t at the TOA. The L_t was retrieved using the MLP on the basis of the upwelling radiance above near-space. As shown in Figure 10, the retrieved L_t at the TOA and the RT simulated data were compared. Importantly, the retrieved L_t exhibited strong agreement with the RT simulations, with MAPDs of 0.416% (412 nm), 0.349% (443 nm), 0.432% (490 nm), 0.218% (510 nm), 0.480% (555 nm), 0.479% (660 nm), 0.495% (745 nm), and 0.497% (865 nm). The tight error distributions between MLP retrievals and the RT simulations data demonstrated that the MLP model enabled high-fidelity conversion from L_30km to L_t, with the correlation coefficient (R²) and slope approaching 1 for different wavelengths and AOTs. Moreover, the RMSEs of the retrieved L_t were 0.089 (412 nm), 0.089 (443 nm), 0.076 (490 nm), 0.066 (510 nm), 0.058 (555 nm), 0.040 (660 nm), 0.031 (745 nm), and 0.022 (865 nm) with a unit (mW/(cm²·μm·sr)). The slightly poor performance of the L_t at 745 nm and 865 nm might be due to the low radiance values. The MAPD values for all the wavelengths were lower than 0.5% (Figure 11). Therefore, the radiometric calibration based on the platform for satellite ocean color instruments is highly advantageous for high calibrations accuracy under various observation geometries.

When RT models were used to estimate the L_t, radiometric calibration based on a near-space platform can suppress the interference of the nonuniform lower atmosphere, particularly the impact of aerosols. In contrast, when L_w for in situ observations are employed for ocean color vicarious calibrations, the interference from the lower atmosphere can introduce significant errors when characterizing the atmospheric path radiation due to imperfect AC and variable atmospheric conditions, thereby affecting the estimation of the L_t and impacting the accuracy of radiation calibration [5]. The calibration method using the near-space platform leverages simplified atmospheric modeling to enable high-fidelity transformation of near-space radiance to radiance at the TOA, effectively eliminating interference effects from low-altitude complex atmospheric conditions.

With respect to the angular distributions of the performance of the MLP model in retrieving the L_t using the upwelling radiance above near-space (Figure 11), the MAPDs were significantly lower than 0.5% across the visible and NIR bands. Significant directional variations in the MAPD were observed as the sensor azimuth angle varied from 0° to 180°. The MLP model performed best at 510 nm, with an overall MAPD of approximately 2.2%. Within the 412–510 nm wavelength range, the MAPDs gradually decreased as the wavelength increased. The MAPDs then gradually increased as the wavelength continued to range from 550 nm to 865 nm. The MAPD at 865 nm approached 0.5%; however, the 865 nm band is frequently neglected in current satellite radiance calibration practices [5]. In contrast, the radiometric calibration using the near-space platform can cover the entire spectral range and offer a more stable reference standard for radiometric calibration. Additionally, the radiometric calibration, based on a near-space platform, establishes a robust foundation for high-precision quantification of satellite ocean color sensors. It is crucial to comprehensively account for the bidirectional characteristics of the upwelling radiation measured on near-space platforms, taking the temporal-spatial matching of observations into consideration. Consequently, the transformability from near-space radiance to L_t at the TOA enables high-precision calibration for ocean color sensors through angular correction modeling.

4. Discussion

The radiometric calibration uncertainty of ocean color satellites must remain below 3%, as higher uncertainty would severely limit their capability for accurate ocean color observation. As an emerging approach for satellite radiometric calibration, cross-calibration based on near-space platforms offers strong resilience against atmospheric disturbances and thus holds potential for oceanic radiometric calibration. However, the radiative transfer mechanisms between near-space platforms and satellite observation systems remain unclear. In this study, we employed RT simulations to investigate the radiometric signal differences between near-space platforms and satellite observation systems, as well as their key influencing factors. The results revealed that the contributions of the upwelling radiance above scientific balloon platforms to the L_t at the TOA for most geometric regions outside glint contamination was greater than 2%, indicating that we should not neglect the atmospheric path radiance above scientific balloons on the basis of RT simulations (Figure 2). The L_R value was relatively stable for most of the observation areas and variable IOP conditions (Figure 4), particularly for the NAP concentrations below 5 mg/L. Moreover, the L_R showed high sensitivity to the AOTs as well as vertical distribution of atmospheric aerosols. The maximum L_R gradually decreased as the AOT increased (Table 3) for sensor zenith angles lower than 20° due to the glint contamination (Figure 5). Furthermore, comparisons of the L_R values between atmospheres with homogeneous and vertically heterogeneous distributions revealed that the L_R can reach 15% for vertically downward observations under varying mean heights of aerosol optical thickness profiles (Figure 8), as the L_t at the TOA showed a difference of more than 5% between the homogeneous and Gaussian-like distributions (Figure 7). Lastly, the transformability from near-space radiance to TOA radiance was achieved using an MLP model, with MAPDs not exceeding 0.5% (Figure 10).

Currently, many radiometric calibration methods, including the lunar calibration [58], on-board calibration [59], vicarious calibration [60,61], and cross-calibration [61,62], are used to improve the quality of radiance data at the TOA. The moon, by contrast, covers the entire optical path from entrance optics to detector, yet it does not fully fill the field of view (FOV) of push-broom instruments, which is a limitation that may introduce problems related to spatial heterogeneity [63]. In the absence of onboard calibrators, vicarious calibration and cross-calibration can be used alternatively and complementarily. While the two calibrations methods exhibit independence from both satellite sensors and target data sources, it is inherently specific to a given AC algorithm [5]. In addition, the two calibration methods could not fully eliminate the systematic biases introduced by AC or the residual errors remaining from on-orbit calibration. Moreover, the vicarious calibration is performed over open-ocean sites characterized by typical maritime aerosols. As a result, they are not expected to compensate for algorithmic deficiencies across the full spectrum of oceanic and AC, particularly in coastal regions and inland waters. Furthermore, the cross-calibration must be constructed to exclude the bad-quality pixels based on the data quality control criteria to minimize influence from meteorological and illumination-observation conditions [4]. It also needs to account for the impact of spectral band differences between satellites.

Compared to vicarious calibration, near-space radiometric calibration platforms offer greater flexibility in observation and site selections. On the one hand, the influence of upwelling radiance above the near-space platform remains relatively stable within a certain range of observation angles, which makes them a preferable choice for radiometric calibration based on near-space platforms. While vicarious calibration typically relies on stable, homogeneous sites such as MOBY [11] and requires strict pixel filtering (e.g., >50% valid pixels after excluding those with CV > 5% [64]), near-space calibration boasts two key advantages: low sensitivity to changes in inherent optical properties and applicability beyond optically uniform ocean regions, making it more adaptable, especially in waters with low Chla or dominated by non-algal particles (Figure 5).

Another critical aspect is that the atmospheric contribution above near-space platforms is relatively reduced under high AOT conditions (Table 3), consequently yielding smaller error propagation from the platform to the TOA. Moreover, due to the exceptional atmospheric purity at high altitudes, the calibration error during radiative transmission from near-space to the TOA is significantly smaller (<0.5%) compared to the vicarious calibration methods using in situ measurements. And then, radiometric calibration using near-space platforms exhibits greater tolerance to variations in lower atmospheric optical properties, thereby relaxing the requirements for near-space radiometric calibration. Additionally, current atmospheric correction and vicarious calibration approaches largely neglect aerosol vertical distributions, inducing ~0.5% uncertainty in ocean color calibration [35,65]. And the vertically heterogeneous aerosols will cause ~15% L_R deviation compared with homogeneous distributions and >5% TOA L_t difference under Gaussian-like profiles (Figure 7). As aerosol mean altitude rises, the enhanced light scattering in upper layers (>30 km) amplifies atmospheric path radiance above near-space platforms. Theoretically, the molecular scattering contribution from the clean atmosphere above 30 km is indeed relatively stable, varying smoothly mainly with the observational geometry, which forms a stable baseline for ΔL. However, the RT simulations indicate that L_30km itself is not an independent variable. It is significantly modulated by the scattering and absorption of the lower atmosphere beneath it, particularly the aerosol layer with non-uniform vertical distribution. The relationship L_R = L_30km/L_t essentially reflects the complex ratio between the near-space signal already modulated by aerosols and the total TOA signal further influenced by the same aerosol layer. This coupling is not a simple univariate function but rather a nonlinear response driven by hidden variables such as aerosol optical properties and their vertical distribution parameters. Therefore, incorporating vertical profiling into calibration protocols is necessary for accuracy when performing near-space radiometric calibration.

High-altitude near-space platforms offer significant advantages for radiometric calibration and stability monitoring of satellite ocean color sensors, due to their sustained stability, large payload capacity, and rapid-response capabilities [31]. This study, however, has two main limitations regarding aerosol representation. Although RT simulations incorporated both homogeneous and Gaussian-like vertically inhomogeneous aerosol distribution using M90 and U50 aerosol models, strongly absorbing aerosols were not considered. Thus, integrating auxiliary data from weather balloons or spaceborne lidars (e.g., CALIPSO/CATS) is recommended to improve atmospheric vertical profiling in future near-space calibration experiments. Another area for improvement involves noise characterization in the MLP. Here, radiance noise estimations rely on laboratory-derived data; these should be replaced with noise levels specific to actual near-space instruments to better evaluate (1) band-dependent influences of ground-platform noise on satellite radiometric calibration, and (2) combined effects of instrument noise and MLP uncertainties on overall calibration accuracy. For reference, the MAPD of L_t increased from 0.71% to 1.02% as L_30km noise rose from 1% to 3%. Hence, high-altitude balloon missions might be an important alternative to satellite deployment or the establishment of ground stations for radiometric calibrations. Conducting radiometric calibration using field-measured data and comparing results with vicarious calibration and cross-calibration will constitute key future research efforts.

5. Conclusions

Radiometric calibration conducted in near-space effectively mitigates atmospheric interference in radiative transfer, thereby enhancing calibration accuracy and reliability. Its versatility allows it to be conducted at various altitudes and under diverse environmental conditions, yielding substantial observation data that facilitate the study of atmospheric radiative transfer characteristics. This, in turn, aids in refining AC models and elevating the overall quality of ocean color remote sensing products. The use of a near-space platform to conduct radiometric calibrations for ocean color sensors is a promising method for refining the calibration precision. However, the impact of the upwelling radiance above the near-space platform on the total radiance at the TOA should be addressed proactively.

In this study, we examined the contribution of the upwelling radiance above near-space s to L_t at the TOA using RT simulations and investigated the impacts of observation geometry, spectral characteristics, oceanic constituents, and aerosol optical properties on L_R. The RT simulations revealed that the angular distributions of the contribution of the upwelling radiance above the near-space to the total radiance at the TOA (L_R) surpassed 2% with changes in observation angles. The maximum L_R typically exceeded 30% in those geometric regions affected by the sunlight reflected from the sea surface. The angular variations in L_R showed similar patterns for each solar zenith angle and AOT. As the AOT increased, the maximum L_R gradually decreased, particularly for those sun-glint geometric regions.

Moreover, the sensitivity of the aerosol vertical distribution to L_R was discussed. The influence of hm on L_R was significant for sensor zenith angles lower than 20° and sensor zenith angles greater than 60°. The value of L_R could reach 15% for the vertically downward direction when the mean height of the AOT profile was different. As h_m increased, L_R slightly increased. Furthermore, the impact of the AOT on L_R was analyzed, and the maximum L_R gradually decreased as the AOT increased. The influence of AOTs on L_R was significant for sensor zenith angles lower than 20°. Overall, the atmospheric path radiance above scientific balloons (near-space platforms) derived from radiative transfer simulations cannot be neglected for the conversion between near-space and spaceborne sensor observations. Additionally, the total radiance at the TOA retrieved by the established MLP model provides effective support for the conversion of observation data between near-space and space-borne platforms, its results are able to adapt to the output characteristics of RT simulations, showing good consistency across the visible bands, which lays a foundation for the flexible conversion between the two observation modes. Within the wavelengths ranging from 412 nm to 865 nm, the model results exhibit stable adaptability, which further confirms its practical value in the conversion between near-space and spaceborne sensors observations.

The radiometric calibration utilizing near-space platforms exhibit superior simplicity in capturing radiative transfer from the platform to the atmosphere summit, differing from the more complex ground-based alternative calibration methods. Notably, the complexity of the lower atmospheric environment exacerbated the impact of radiometric calibration when ground-level in situ observational data were employed, thereby introducing considerable errors. Moreover, near-space radiometric calibration can be integrated with various calibration techniques (such as satellite-based and ground-based calibration) to form a comprehensive calibration system, further enhancing the accuracy and efficiency of the radiometric calibration process. In summary, radiometric calibration utilizing near-space represents a significant innovation method for satellite-borne ocean color sensors.