Lunar South Polar Water Cycle and Water Resources: Diurnal and Spatial Variations in Surficial Hydration From Repeated Moon Mineralogy Mapper Observations

The diurnal variation and distribution of lunar surficial hydration (OH/H2O) is of great significance for understanding the solar wind implantation and water cycle on the Moon. Lunar south pole is an ideal place to study the diurnal variation of surficial hydration due to the large number of repeat observations of the same region, which is very limited in mid‐ or low‐latitudes. Here we showed clear 0.5‐hr interval diurnal variation of surficial hydration at lunar south pole. The variation of hydration band depth with local time is exactly the opposite to the variation of temperature, indicating that lunar surficial hydration changes sufficiently with temperature. This relationship indicates that both the diurnal variation and hydration content are latitude dependent. Our observations support the hypothesis that the diurnal variation of hydration on the Moon is due to the formation of metastable hydroxyl.


Introduction
Lunar surficial hydration (OH/H 2 O) not only records important information about the accretion and evolution of the Moon but also is one of the core considerations for site selections of future lunar bases.A number of recent observations and laboratory measurements have revealed that hydration presented on the lunar surface comes from endogenous and exogenous sources, including magmatic water, impacts from small bodies, and solar wind implantation (see reviews by Lucey et al., 2022).
The definitive discovery of surficial hydration came from the near-infrared (NIR) reflectance spectra acquired by three independent missions in 2009 (Clark, 2009;Pieters et al., 2009;Sunshine et al., 2009).These NIR reflectance spectra all exhibit OH/H 2 O absorption features near a wavelength of 3 μm, which was further confirmed by the recent Chandrayaan-2 mission (Chauhan et al., 2021).Observations of the Moon at 6 μm first prove that molecular water (H 2 O) is also present on the lunar dayside (Honniball et al., 2021).China's recent Chang'E 5 mission reveals that although Chang'E 5 samples have a dry lunar mantle reservoir (Hu et al., 2021), solar wind induced water is abundant in lunar minerals and impact glasses (He et al., 2023;Lin et al., 2022;Liu et al., 2022;Y. C. Xu et al., 2022;Zhou et al., 2022), and the latter could be the potential reservoirs (He et al., 2023).Although hydration has been confirmed on the lunar surface, its distribution and variation have elicited ambiguity and conflicting views due to different data sets and thermal correction methods.For example, hydration content in the morning and evening was observed to be higher than that at local noon by various authors (Hendrix et al., 2019;Honniball et al., 2020;Laferriere et al., 2022;Li & Milliken, 2017;Pieters et al., 2009;W ö hler et al., 2017;Wohlfarth et al., 2023), but these diurnal variations are basically discontinuous due to lack of sufficient repeat observations of same area at the low-or mid-latitudes.Stronger hydration absorptions were observed to occur at higher latitudes of the Moon (Clark, 2009;Honniball et al., 2020;Li & Milliken, 2017;McCord et al., 2011;Pieters et al., 2009;Sunshine et al., 2009;W ö hler et al., 2017;Wohlfarth et al., 2023), while Bandfield et al. (2018) demonstrated that prominent 3 μm spectral features can be observed across a range of latitudes, local times, and surface types.Li and Milliken (2017) suggested that surficial hydration is not significantly related to the mineralogy composition at a global scale, but rather to regolith maturity, while several observations showed that the felsic highland terrains retained hydration more efficiently than did the mafic mare terrains (Honniball et al., 2020;Laferriere et al., 2022;McCord et al., 2011;Pieters et al., 2009;Sunshine et al., 2009;W ö hler et al., 2017).A recent study by Wohlfarth et al. (2023) revealed that highlands exhibit stronger absorption bands than mare regions during lunar midday, whereas the reverse is observed during lunar morning and evening.In addition, reports regarding whether lunar surficial hydration will decrease when the Moon moves into the Earth's magnetotail are conflicting.Although some studies reported that the Earth's magnetotail has no influence on the absorption of surficial hydration by analyzing the Lyman Alpha Mapping Project data (Hendrix et al., 2019), Moon Mineralogy Mapper (M 3 ) data (Li et al., 2023;Wang et al., 2021) and Deep Impact data (Laferriere et al., 2022), Cho et al. (2018) showed that lunar surficial hydration content decreased when the Moon was inside the Earth's magnetotail based on M 3 data at low and mid-latitudes.
Benefiting from the extensive coverage of M 3 data, lunar south pole region is an ideal place to study the variation of surficial hydration.In this study, we proposed a coarse-to-fine method to process M 3 data and performed a detailed analysis of surficial hydration at the lunar south pole to study the diurnal variation, spatial distribution of lunar surficial hydration, and further discuss the water cycle process.

M 3 Data
M 3 collects visible and near-infrared data in 85 continuous bands, covering wavelengths between ∼0.46 and 3 μm which contains highly diagnostic absorptions (∼2.9 μm) caused by fundamental OH and H 2 O stretching.The Chandrayaan-1 worked in a circular polar orbit so that M 3 could provide the most complete spatial and temporal NIR coverage of the lunar south polar region.These two advantages-namely, spatial and temporal coveragerender M 3 data the most comprehensive data set currently available for this study.
The M 3 data were acquired in five optical periods (OP1A, OP1B, OP2A, OP2B, and OP2C), during which the detector temperature varied, and M 3 images were classified into "cold" and "hot" groups (Green et al., 2011).To obtain reliable hydration absorptions, only the images acquired when the detector is cold are used to study the variation of surficial hydration.In addition, images acquired during OP2C, although under hot conditions, provide the most complete coverage of the lunar south pole, and are used to study the relative spatial distribution of surficial hydration.
The reflectance of band 81 (2,816 nm) and band 84 (2,936 nm) of the M 3 data are obviously lower than adjacent bands, which might be considered as the absorption of hydration.However, regions of different latitudes of the Moon all exhibit the similar characteristics, indicating that it might be due to the systematic artifacts of the detector rather than hydration absorption (Figure S1 in Supporting Information S1).So, these two bands are not considered in this paper.
In this study, the 2 days before and after the full moon are considered to be affected by the Earth's magnetotail.Among the 150 orbits of M 3 data collected when the detector is cold, data from 7 February 2009 to 11 February 2009 (OP1B) were acquired when the Moon was in the magnetotail.Additionally, data from 16 April 2009 to 21 April 2009 (OP2A) covered the same location as the February In-Magnetotail data but were acquired when the Moon was outside the magnetotail (Table S1 in Supporting Information S1).

Processing of M 3 Data
The signal-to-noise ratio (SNR) of M 3 data at high latitudes is downgraded because of high phase angles and shadows.The noise (especially the strip-like system noise) can distort the shape of, or even produce falsepositive absorptions in the ∼2.9 μm wavelength region.In addition, thermal emission contributions at wavelengths longer than ∼2 μm severely affect the spectra obtained by M 3 and would mute the OH fundamental stretching absorption near 2.9 μm.All these factors would preclude accurate mapping of surficial hydration at the lunar south pole.Thus, we proposed a coarse-to-fine processing pipeline, which can minimize the influence of known spectral artifacts (e.g., low SNRs) and thermal emission components in M 3 data.The specific steps are as follows: Step 1: A total of 207 orbits of M 3 level 1B radiance data which cover 80°S-90°S region are downloaded from the NASA Planetary Data System, and are resized to the south polar region (80°S-90°S).Histogram equalization method proposed by Tan et al. (2005) is used to remove the stripes in all orbits (Figure S2 in Supporting Information S1).The derived radiance data are then transferred into reflectance factor (I/F) based on the solar spectrum.
Step 2: The semi-empirical thermal correction model proposed by Li and Milliken (2016) is used in this study to remove the thermal emission contributions.We use the same method as the M 3 team to do topographic correction, and the photometric correction is based on our newly developed photometric model (T.Y. Xu et al., 2022).
Step 3: The SNR index (SNRI) is calculated for all orbits: where r′ i and r i are the reflectance values from the smoothed and measured spectra at band i, respectively (Li & Milliken, 2017).Areas with SNRI higher than 0.025 are considered as low signal and are all masked.The finally derived reflectance data are map-projected and then mosaiced accordingly.
Step 4: Band depth near 2.9 μm is calculated to reflect the hydration abundance.It is defined as 1 (R b /R c ), where R b is an average of reflectance at 2,856 and 2,896 nm and R c is an average of reflectance at 2,657 and 2,697 nm.
The above process is implemented for all orbits of M 3 data used in this study.In addition, to contribute to the study of the temporal variations, we use the SPICE Toolkit package (Acton, 1996) to calculate the local time (lunar time of day) of M 3 data with the observation time and longitude.

Diurnal Variation of Surficial Hydration at the Lunar South Pole
Figure 1a shows the locations of all the orbits which cover the lunar south polar region.As can be seen, most orbits cover the area of 88.5°S-90°S, providing a great opportunity to study the hydration absorption of the same place at different observation time, that is, local time.The region around the Connecting Ridge of the Artemis III candidate landing sites, located at a latitude of 88.9°S-89.3°Sand a longitude of 212°E 242°E, boasts the most extensive coverage of M 3 data within the lunar south pole (Figure 1b).We collect band depths per 5 degrees of longitude (222°E 237°E) and 0.01 degrees of latitude for each image covering this area.The band depths and incidence angles at different latitudes (88.9°S-89.3°S)but the same longitude (e.g., 222°E) are averaged since they have the same local time, for example, t local .The average band depth is considered as the hydration absorption depth at local time t local .Figure 1c shows the variations of band depth with local time at this region.Despite some fluctuations, the plot clearly exhibits a parabolic trend.The band depth decreases gradually toward the noon, but then recovers to the morning level by evening.Fitting the averaged values yields the following equation: average band depth = 0.0007 × t 2 0.0175 × t + 0.2107 where t is the local time, and the R 2 is 0.912.The plot and equation indicate that the variation of band depth with local time is generally symmetric, with a center around 12.3798.

Spatial Distribution of Surficial Hydration at the Lunar South Pole
Using the equation established above, we corrected the band depth of all orbits to 12 o'clock local time.Figure 2 shows the overview map of surficial hydration in the lunar south polar region.Hydration is generally widespread at the lunar south pole, consistent with the water equivalent hydrogen abundance map derived from the Lunar Exploration Neutron Detector data (Sanin et al., 2017).Note that the band depth in the South Pole-Aitken basin (SPA) is clearly lower compared to other regions.Compared with mineralogy abundance and OMAT maps (Lemelin et al., 2022), we found that the plagioclase abundance in SPA is significantly lower than in other regions (Wang et al., 2024), while the OMAT is significantly larger.

Discussion
Observation geometry can have a significant influence on the band depth.Changes in incidence angle change the way the surface material is sampled: the larger the incidence angle, the shallower the sampling depth.If there is a gradient in OH/H 2 O, for example, more near the surface, there will appear to be more of it when observed at nearer grazing angle then at nearer vertical angle.Figure 1 shows that the band depth is, indeed, well-correlated with the incidence angle.However, it should also be noted that the incidence angle affects both temperature and sensing depth at the same time.Since there is no published gradient in OH/H 2 O, we tried to investigate the influence of the observation geometry in two ways: (a) assuming that OH/H 2 O gradient is correlated with temperature gradient: the higher the temperature, the lower the OH/H 2 O content.The sensing depth (L) of M 3 spectrometer is about 1-2 mm   (Pieters et al., 2009), and all the incidence angles (i) within our study area exceed 60°.Assuming the actual sensing depth (d): d = L × cos i, so the maximum sensing depth in our study area is 1 mm.Based on the thermophysical model and parameters outlined in Hayne et al. (2017), we simulated the temperature at varying incidence angles and depths at 75°latitude (Figure S4 in Supporting Information S1).This latitude was determined because the incidence angle in our study area is approximately 75°at local noon (Figure 1d).The simulated temperature is also largely in agreement with the temperature derived by Diviner (Figure S5 in Supporting Information S1).The results indicate that the difference between the temperature at 1 mm depth and at the surface is less than 8 K (Figure S4 in Supporting Information S1).This temperature difference is an order of magnitude smaller than that between local morning/evening and noon (>100 K).Therefore, we believe that such a small temperature difference could not have an obvious influence on the absorption band depth.In other words, the band depth at different sensing depth remains almost unchanged, and the diurnal variation established in this study is not affected by the observation geometry.Additionally, temperatures in our study area are below 300 K (Figures S4 and S5 in Supporting Information S1), indicating that the diurnal variation established in this study is also not affected by the thermal correction method.(b) assuming that the gradient of hydration abundance within the sensing depth is homogeneous across our study area (88.9°S-89.3°S,212°E 242°E) and that the diurnal variation we observed is due to the variation in sensing depth.Figure S6 in Supporting Information S1 demonstrates that even at similar incidence (74 ± 0.5°) and observation (13 ± 0.5°) angles, that is, at similar sensing depth, the hydration abundance still varies with local time.Although the incidence angles of these pixels are similar, their temperatures can vary due to transverse heat transfer, indicating the influence of temperature.Both assumptions suggest that the diurnal variation established in this study is correlated with temperature and is likely unaffected by observation geometry.However, we recognize that these assumptions have not yet been confirmed and we can't really rule out the possibility that the diurnal variation of hydration we observed is affected by the observation geometry.Further studies are required to test these hypotheses.
As the same area located at the lunar farside is being repeatedly observed, we excluded the effects of latitude, composition, maturity, and lunar phase (Li et al., 2023), so that the variations of hydration absorption band depth are only affected by local time.The continuous variation of band depth over local time is consistent with the telescopic observations reported by Honniball et al. (2020) but different from the far ultraviolet observations (Hendrix et al., 2019), which show a sudden drop near local noon.This is probably because that the diurnal variation in Hendrix et al. (2019) was not established based on repeat observations of same area, and there might be variations within their study area.In addition, the variation trend of band depth is generally consistent with that of incidence angle (Figure 1d), and is opposite to that of temperature (Figures S4 and S5 in Supporting Information S1), indicating that lunar surficial hydration is directly affected by the instantaneous temperature (Sunshine et al., 2009).Due to the absence of the solar wind implantation at night, the band depth might remain stable during nighttime and would suddenly increase to the morning level at sunrise (Tucker et al., 2019).
The negative correlation between hydration band depth and temperature indicates that the strength of the diurnal variation in hydration band depth is temperature and thus latitude dependent.Lower latitudes have larger diurnal variation of temperature and hydration band depth.In other words, the equatorial latitudes have the largest diurnal variation in hydration band depth while the polar regions have the lowest.This is generally consistent with observations reported by Honniball et al. (2020) and Wohlfarth et al. (2023), which showed that the diurnal variations are the smallest at the highest latitudes (Figure S7 in Supporting Information S1).However, it is in contrast to Li and Milliken (2017), which reported that mid-latitudes have the largest diurnal variations in hydration while equatorial latitudes have the smallest.This relationship could also be applied to other areas of the Moon to eliminate the effects of local time based on the correlation between Diviner temperature and local time (Williams et al., 2017).
The negative correlation also indicates that the hydration content is latitude dependent.At the same local time, higher latitudes have lower temperatures and thus higher hydration content.This latitude effect is most significant at local noon and weakest at morning and evening.This is, again, consistent with previous observations (Figures 8a and 9 in Honniball et al., 2020;Figure 9 in Wohlfarth et al., 2023).Note that these conjectures were speculated based solely on the local time, without considering the effects of mineralogy, maturity, and other factors.The addition of these factors would definitely make the hydration content much more complex, which might explain the little difference between this work and previous studies.
The hydration band depth changes efficiently with local time, suggesting that OH/H 2 O is continuously removed and replenished.There are two hypotheses that could explain the variation in hydration band depth with temperature: (a) Lunar surficial hydration is migrating along temperature gradients, for example, migrating to colder higher latitudes and/or colder regions with earlier or later local times (Hendrix et al., 2019;Laferriere et al., 2022;Sunshine et al., 2009).(b) The surficial hydration is under the dynamic equilibrium processes between solar wind implantation and diffusion (Y.C. Xu et al., 2022).The diffusion time of solar wind implanted hydrogen is temperature dependent, varying as exp(U/T) with U as the activation energy and T as the surface temperature (Farrell et al., 2015(Farrell et al., , 2017;;Starukhina, 2001Starukhina, , 2006;;Tucker et al., 2019).
Solar wind has been implicated as a primary source of water on the Moon (Pieters et al., 2009;Sunshine et al., 2009), and hydration content should decrease when the Moon moves into Earth's magnetotail because it can significantly reduce the flux of solar wind hydrogen (Li et al., 2023).However, comparison of repeat In-Magnetotail and Out-Magnetotail mosaics showed that there is no obvious hydration content variation between the Moon is in and outside the magnetotail.This observation seems to support the migration mechanism (Hendrix et al., 2019;Laferriere et al., 2022).However, Wang et al. (2021) argued that Earth wind could be considered as an alternative source of hydration when the Moon is in the magnetotail.Li et al. (2023) proposed that irradiation by the high-energy electrons in the plasma sheet leads to the formation of OH/H 2 O. Theoretical simulations showed that low-latitude dayside hydroxyl is decreased in the tail compared to out but the difference is too small to be detected by current infrared observations (Tucker et al., 2021).In addition, lunar surficial hydration is observed to be much lower at magnetic anomalies than surrounding areas (Kramer et al., 2011;Li & Garrick-Bethell, 2019;Li & Milliken, 2017), indicating that the hydration formation is directly influenced by the solar wind.This also might invalidate the migration hypothesis as hydration migration shall not be affected by the magnetic field.Recent ground-based observations also showed that metastable temperature-dependent hydroxyl is more consistent with the exospheric constraints than migrating H 2 O (Honniball et al., 2020), and the migration mechanism would result in a surface exospheric density 7 or 8 orders of magnitude higher than the Lunar Atmosphere and Dust Environment Explorer constraint (Flom et al., 2023).In summary, the diurnal variations of hydration band depth we observed are consistent with the theoretical simulations (Tucker et al., 2019), supporting the metastable hydroxyl hypothesis.
SPA is prominent on the lunar farside and exhibits multiple features similar to lunar maria, including elevated FeO and Th abundances, higher pyroxene and lower plagioclase abundance compared to lunar highlands.Specifically, the OMAT of SPA is also comparatively higher (Figure 2; Lemelin et al., 2022).SPA exhibits a lower hydration band depth than surrounding highland areas, consistent with previous observations that highland areas typically contain more hydration than maria (Honniball et al., 2020;Laferriere et al., 2022;McCord et al., 2011;Pieters et al., 2009;W ö hler et al., 2017).It is currently unclear and under debate which factor, mineral abundance or OMAT, dominates the hydration content.Li and Milliken (2017) demonstrated that some crystalline plagioclase exposures exhibit enhanced hydration.In addition, the terrestrial H + implantation experiments also showed that plagioclase can capture more H + than other silicate phases to form the OH/H 2 O (Tang et al., 2021).This might suggest that hydration content is probably more correlated with plagioclase abundance than OMAT.

Summary
Based on multiple repeat observations of the same area at lunar south pole by M 3 , we show clear 0.5-hr interval diurnal variation in lunar surficial hydration.The variation trend is exactly the opposite to that of surface temperature, indicating lunar surficial hydration changes sufficiently with instantaneous temperature.This correlation further reveals that both hydration content and diurnal variations are temperature and thus latitude dependent.In addition, hydration content seems to be more correlated with plagioclase abundance than soil maturity, which explains the difference in hydration content between the highlands and the maria.There is little change in hydration content before and after the Moon enters the Earth's magnetotail, suggesting the possibility of additional OH/H 2 O formation mechanisms beyond solar wind implantation.
respectively.The LROC WAC data can be accessed from the Arizona State University at https://wms.lroc.asu.edu/lroc/view_rdr/WAC_ROI_SOUTH_SUMMER.All the original data generated in this study have been archived at Lu (2024).
• 0.5-hr interval diurnal variation of lunar surficial hydration was revealed at lunar south pole for the first time • Lunar surficial hydration changes sufficiently with instantaneous temperature • Lunar surficial hydration did not change when the Moon enters the Earth's magnetotail Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a) Locations of all the M 3 orbits which cover the lunar south pole region (80°S-90°S).The black dashed circle marks the location of (b).(b) 88°S-90°S of lunar south pole.The background image is LROC WAC South Pole Summer mosaic (Speyerer et al., 2020).Red dashed boundaries show the areas used to study the diurnal variation of the hydration.(c) The diurnal variation of surficial hydration at the lunar south pole region.Points with different colors represent the band depth of different longitudes.Black open circles indicate the average band depth and local time for every 0.5 hr.The black dashed curve indicates the best fitting of these circles.(d) Variation of average incidence angle with local time.Points with different colors represent the incidence angles of different longitudes.

Figure 3
Figure 3 depicts a comparison of the band depth measurements taken when the Moon is situated inside and outside the Earth's magnetotail.The average band depth of the overlapping area is 0.0821 (n = 111,334) and 0.0808 (n = 95,270) for In-Magnetotail and Out-Magnetotail mosaics, respectively.The average difference (out-in) is 0.0017 (n = 90,792).To exclude the possible effects of different optical periods of M 3 data, we also compared the band depth of overlapping OP1B and OP2A data, all of which are collected when the Moon is outside the magnetotail (FigureS3in Supporting Information S1).The average difference (OP2A-OP1B) is 0.0029 (n = 57,624), comparable to the difference between Out-Magnetotail and In-Magnetotail images.

Figure 2 .
Figure 2. The distribution of surficial hydration at 12 o'clock local time in the south polar region derived from the OP2C mosaic.(a) Hydration absorption band depth overlying on WAC mosaic.Red dashed curve marks the location of the best-fit topographic ellipse of SPA (Garrick-Bethell & Zuber, 2009).(b, c) Distribution of OMAT and plagioclase abundance(Lemelin et al., 2022).Note that red color in (b) indicates small OMAT while blue color indicates large OMAT.

Figure 3 .
Figure 3. Hydration absorption band depth when the Moon is inside the magnetotail (a) and outside the magnetotail (b).Red colors in (b) mark the areas where (a, b) overlap.(c) Difference between overlapping areas in (b) and (a).Plot on the right indicates the statistics of the difference.