A Model for Estimating the Earth’s Outgoing Radiative Flux from A Moon-Based Radiometer
Abstract
:1. Introduction
2. Model and Methodology
2.1. Observation Geometry
2.2. Radiation Transfer Function
2.3. The Earth’s Outgoing Radiative Flux Estimating Model
- (1)
- The input parameter: We build the temporal system and spatial coordinate system transformation by using the Planetary and Lunar Ephemerides DE430 and Earth orientation parameters (EOP) [35,36]. The time system is the Coordinated Universal Time (UTC) in this work and a linear transformation can be conducted between different systems. The unification of the spatial coordinate system involves five basic coordinate systems, and the transformation of coordinate systems is completed by a series of matrix operations. The more detailed coordinate transformation can be found in Refs. [20,37]. The start time, end time, and time step are used to determine the exact spatial geometry. Based on the observation geometry, the precise position relationship can be gained, which is the key step in ascertaining the radiometer-viewed region and sunlit area. Here, by calculating the zenith angle of the Moon and the Sun for each global observation grid, we mark all grids where the zenith angle is larger than zero degrees as “1” and the rest as “0” to map out these regions. Then, based on the grid visibility, the established model is used to obtain the Earth’s outward radiative heat flow.
- (2)
- The simulated EPIs of the MWFVR: Based on the radiation transfer model, the ERBE ADMs, and the CERES flux datasets [38,39], the MWFVR’s EPI can be obtained. Due to the actual MWFVR not being placed on the lunar surface, the actual measurements have not been obtained. Therefore, the simulated EPI time series is used as the substitute for the true measurements of the MWFVR and then the simulated EPI time series is utilized as the reference input value for validating the feasibility and correctness of the estimating model. It is worth noting that the CERES SYN1deg data with a time resolution of one hour are used in the calculation of irradiance, which is a dataset directly observed by satellite-based instruments. However, the CERES data (private communication) used in Table 2 and Table 3 are the fusion data (see Section 3.2.3) specially generated by the team to verify the NISTAR and EPIC data, so they are used as the comparison data for the model verification in this work.
- (3)
- The model core mainly includes three parts, the coordinate system transformation, Moon-based Observation geometry, and the determination of the Earth’s outgoing radiative flux. The calculation process of Earth’s outgoing radiative flux and the method is presented in this Section 2.3. In this process, the distance and area correction factors need to be confirmed by the geometry built in Section 2.1. In the MWFVR-viewed sunlit region, the Sun and the Moon are both visible. However, the positions of the Sun and the Moon in the unified coordinate system are variable, and when the angle between the Sun vector and the Moon vector is larger than 5°, the calculated SW daytime outgoing radiative flux from the MWFVR will have a larger error. In actual work, based on the radiometer measurement data, the ADMs, and the spatial geometric relationship at the time of data acquisition, the Earth’s outgoing radiative flux can be obtained. Because radiometer measurements do not currently exist, simulated values are used instead. At the same time, the simulated value of the model is compared with the heat flux data obtained by the NISTAR instrument to verify the correctness of the model. In addition, the site 0°E0°N is selected as the position of the MWFVR and the established model can also be extended to other lunar positions.
July | August | September | |
---|---|---|---|
FS | 194.4 | 193.0 | 198.7 |
FN | 220.5 | 219.2 | 222.3 |
FM | 197.5 | 194.3 | 199.8 |
RMS (FS, FM) | 2.04 | ||
RMS (FS, FN) | 25.33 | ||
RMS (FN, FM) | 23.49 |
July | August | September | |
---|---|---|---|
FS | 251.5 | 248.9 | 245.5 |
FN | 261.4 | 258.6 | 261.1 |
FM | 260.3 | 263.1 | 262.5 |
RMS (FS, FM) | 13.76 | ||
RMS (FS, FN) | 12.04 | ||
RMS (FN, FM) | 2.79 |
3. Results and Discussions
3.1. The Analysis of Correction Factor KSW/LW
3.1.1. The Platform Height
3.1.2. The Radiometer-Viewed Region
3.1.3. The SW Invisible Night Portion (Ad)
3.2. The Analysis of Earth’s Outgoing Radiative Flux
3.2.1. The SW and LW GMAFs
3.2.2. The Outgoing Radiative Flux without the Correction Factor K
3.2.3. The Earth’s Outgoing Radiative Flux
3.3. Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Scene Bin | Scene | Cloud Fraction Range | Angle Bin | Viewing Zenith Angle Range |
---|---|---|---|---|
1 | Clear Ocean | 0.00–0.05 | 1 | 0~15 |
2 | Clear Land | 0.00–0.05 | 2 | 15~27 |
3 | Clear Snow | 0.00–0.05 | 3 | 27~39 |
4 | Clear Desert | 0.00–0.05 | 4 | 39~51 |
5 | Clear Land–Ocean Mix (Coastal) | 0.00–0.05 | 5 | 51~63 |
6 | Partly Cloudy Over Ocean | 0.05–0.50 | 6 | 63~75 |
7 | Partly Cloudy Over Land or Desert | 0.05–0.50 | 7 | 75~90 |
8 | Partly Cloudy Over Land–Ocean Mix | 0.05–0.50 | ||
9 | Mostly Cloudy Over Ocean | 0.50–0.95 | ||
10 | Mostly Cloudy Over Land or Desert | 0.50–0.95 | ||
11 | Mostly Cloudy Over Land–Ocean Mix | 0.50–0.95 | ||
12 | Overcast | 0.95–1.00 |
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Zhang, Y.; Dewitte, S.; Bi, S. A Model for Estimating the Earth’s Outgoing Radiative Flux from A Moon-Based Radiometer. Remote Sens. 2023, 15, 3773. https://doi.org/10.3390/rs15153773
Zhang Y, Dewitte S, Bi S. A Model for Estimating the Earth’s Outgoing Radiative Flux from A Moon-Based Radiometer. Remote Sensing. 2023; 15(15):3773. https://doi.org/10.3390/rs15153773
Chicago/Turabian StyleZhang, Yuan, Steven Dewitte, and Shengshan Bi. 2023. "A Model for Estimating the Earth’s Outgoing Radiative Flux from A Moon-Based Radiometer" Remote Sensing 15, no. 15: 3773. https://doi.org/10.3390/rs15153773