Introduction

Knowledge of the impactor flux onto the Moon is significant for dating the lunar surface and understanding its geological evolution1,2. It can also provide critical insights into the populations of main belt asteroids and the dynamics of the inner solar system3,4. Impact craters preserve key records of the bombardment history5, serving as the most direct means of estimating the impactor flux. By linking the radiometric ages of the Apollo, Luna and Chang’E (CE) samples with the crater size-frequency distributions (CSFDs)6, the lunar chronology function was established1,7, which supports a relatively constant cratering rate over the past 3 Ga. However, due to multiple erosion processes (for example, micrometeorite bombardment, ejecta burial, and seismic shaking)8,9,10, impact craters undergo a gradual increase in diameter and decrease in depth since their formation11,12, only surviving for a limited time on the lunar surface13. Particularly, smaller impact craters degrade faster than larger ones11, with craters below 20–50 m in diameter surviving for <∼50−125 Myr13. Craters smaller than a few hundred meters across have typically reached an equilibrium abundance in the lunar mare14. The scale-dependent nature of crater degradation can lead to a considerable bias between the observed size-frequency distribution of small craters and their true production11. Therefore, previous estimates of the small impactor flux based on crater populations may be inaccurate, as supported by multiple lines of evidence15,16,17. For example, recent observations from the Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) temporal image pairs revealed that the lunar crater production rate at decameter scales is 1.33 times higher than the widely accepted Neukum production function (NPF)15. The 40Ar/39Ar dating of impact glass beads in the Apollo 12, 14, 16, and 17 samples showed that their formation ages are primarily concentrated into the most recent ∼400 Ma16,17, which may indicate a higher small impactor flux.

Impact products offer another unique perspective for estimating the impactor flux18,19. Almost the entire lunar surface is covered with a fragmental regolith layer with thickness ranging from a few meters to tens of meters20, which is primarily generated by the impact cratering process21. Shortly after the emplacement of basaltic mare lava flows, little to no regolith is present22. Meteorite bombardment by both small and large impactors can shatter the coherent protolith and produce new regolith22. The cratering rate on the lunar surface directly controls the regolith growth rate, referred to as the impact flux trend23. As regolith thickens, small impactors overturn the existing regolith layer24, while larger impactors capable of penetrating the pre-existing regolith can fracture the underlying substrate25. As a result, regolith growth rate decreases over time and becomes lower in older units, a phenomenon known as the buffering trend or self-limiting process22,23. Considering the formation mechanism, lunar regolith is generally expected to be thicker in older surfaces, which has long been presumed in previous studies18,22,26,27,28,29,30. Observations from radar31, microwave radiometer32, and crater morphology20 collectively suggest that regolith thickness across lunar maria is statistically correlated with age (Supplementary Text 1 and Supplementary Figs. 1–5), though the correlation is not particularly strong due to several factors (measurement uncertainty, target property, randomness of large impacts, and the buffering effect; Supplementary Text 2). Besides, the growth of lunar regolith is dominated by and sensitive to craters at sub-hectometer scales25, making regolith thickness particularly suitable for deciphering the small impactor flux. Recent advances in crater shape models, cratering mechanisms, and topographic degradation have facilitated the development of a 3-D regolith evolution model25,33 that can well characterize the self-limiting growth process of lunar regolith resulting from continuous bombardment. By comparing the observed and modeled regolith thicknesses, new constraints on the small lunar impactor flux can be provided.

To achieve this, a geologically young, isotopically dated lunar landing area with homogeneous target properties representative of typical mare basalts is required. First, high-resolution optical imagery of the landing area enables a reliable estimate of regolith thickness. The precise radiometric age avoids the large dating uncertainty associated with crater statistics. Second, the impact flux inferred from a representative mare unit can serve as a benchmark for comparison with the standard production function (for example, the NPF1), which was established across broader mare regions. Third, the lunar regolith developed in such a unit is formed mainly by small, local impacts with less influence from exotic materials or other geological processes. Most large source craters that contributed to regolith formation are only slightly degraded and thus remain clearly identifiable. Finally, the growth of a relatively thin regolith layer is less affected by the buffering effect, enhancing the ability to detect variations in impact flux from regolith thickness. To date, a number of lunar samples with isotopic ages ranging broadly from >3.9 Ga to 25 Ma (Cone crater) have been acquired6. However, most of them are older than 3 Ga, and the corresponding geological units have undergone complex evolution processes, making it difficult to reconstruct the growth history of regional regolith. Some samples collected by the Apollo missions are inferred to source from the Copernican-aged young impact craters2,6 (for example, Copernicus and Tycho). However, their impact melt sheets show non-uniform geological features (for example, cracks and knobs; Supplementary Fig. 6), which could affect the regolith growth process.

China’s CE-5 landing site (43.058°N, 51.916°W) is located on the youngest isotopically dated mare basalt unit (P58/EM4) in the northern Oceanus Procellarum, with a precise radiometric age of 2.03 ± 0.004 Ga34. Spectroscopic observations show that the landing region exhibits uniform target characteristics several tens of kilometers across35 (Supplementary Fig. 7). Statistical analysis of rocky crater populations across 15 different mare units in Oceanus Procellarum, Mare Imbrium, Mare Nubium, Mare Tranquillitatis, Mare Humorum, and Mare Serenitatis reveals that the P58 unit exhibits no anomalous target mechanical properties36. Also, the rock abundance of the P58 unit aligns well with the temporal trend observed across 291 mare units on the Moon, indicating that the P58 unit is representative of typical mare basalts37 (Methods and Supplementary Fig. 8). Besides, high-resolution descent camera data covering the landing area, as well as the thorough investigation of source craters for the CE-5 samples38, facilitate an accurate identification of crater morphology and systematic modeling of regolith evolution. Therefore, the CE-5 landing region presents a unique opportunity to unravel the small impactor flux during the past 2 Ga.

In this study, we provide evidence for an increased flux of lunar impactors less than tens of meters, by comparing the regolith thickness in the CE-5 region estimated using fresh crater morphology with that from regolith growth modeling.

Results and discussion

Regolith thickness from crater morphology

Photographs from Ranger and Lunar Orbiter (LO) showed that the small fresh craters on the lunar surface exhibit four typical morphological types39: normal, central mound, flat-bottomed, and concentric. Extensive impact experiments revealed that the formation of these craters with different morphologies depends on the ratio of crater size to local regolith thickness40 (see Methods). Compared with in situ seismic experiments41,42 and radar remote sensing techniques43, the morphology and size-frequency distribution of small fresh craters can be used to derive the distribution of regolith thickness over a large area, independent of the geophysical model. Therefore, this approach has been widely used for regolith thickness estimation in different regions across the Moon12,18,20,27.

High-resolution imagery with appropriate solar incidence angle is key to ensuring the reliability of this method, as it determines the accuracy of crater morphology identification. Existing studies35,44,45 on the regolith thickness in the CE-5 region were conducted based on optical images with a low resolution of 1.5 m, which could lead to misidentifications of crater morphology (see Supplementary Fig. 9 for an example) or biased crater samples toward the large diameter ranges. If a central mound, flat-bottomed, or concentric crater is misidentified as a bowl-shaped normal one, then the area fraction with thick regolith deposits increases and thus the regional regolith thickness would be overestimated (see Methods for detail). Their results indicated a regolith thickness of 5 m35 or 4–6 m44,45 in the CE-5 region, which is generally thicker than that in the older Apollo landing sites (3.7−4.4 m41,42 from seismic experiments and 3.1–5.0 m46 from crater morphology; Supplementary Table 1). Considering the statistical correlation between regolith thickness and surface age, this may again suggest an overestimated thickness.

Here, we select a flat region across the CE-5 landing site with homogeneous spectral characteristics for crater morphology identification (17.3 km2; Supplementary Fig. 10), where the descent camera images are available. An obvious secondary crater field is excluded because secondary craters tend to be normal ones and may affect the statistics. The FeO/TiO2 content, optical maturity, and crater density of the study area all fall within one standard deviation of the mean value of those in the P58/EM4 unit (34,797 km2; Supplementary Fig. 11), indicating that the selected CE-5 landing region can well represent the whole basalt unit in terms of target properties and impact history. The CE-5 descent camera images (<0.5 m/pixel), the generated digital orthophoto map (DOM) and digital terrain model (DTM) (0.5 m/pixel), as well as four LROC NAC images (0.8−0.9 m/pixel; Supplementary Table 2) are used for crater measurements (see Methods). To ensure the accurate identification of crater diameter and morphology, only craters with diameters larger than 10 pixels were considered47. In total, 361 fresh impact craters with diameter ranging from 5 to 120 m were counted (Fig. 1a), including 174 normal, 118 central mound and flat-bottomed, and 69 concentric ones. Based on the fractions of these counted craters using high-resolution imagery (Supplementary Fig. 12), the regional regolith thickness is estimated to vary from ∼1 to 8 m, with a median of 3.6 ± 0.3 m (1σ uncertainty; Fig. 1b). This is in line with the observation from the CE-5 Lunar Regolith Penetrating Radar48 (>2.0−2.5 m), and generally lower than the regolith thickness in the older Apollo landing regions (Supplementary Table 1). Using a radiometric age of 2.03±0.004 Ga, the mean regolith growth rate in the CE-5 region is calculated to be 1.8±0.15 m/Gyr, which is larger than those in the Apollo landing regions (for example, 1–1.4 m/Gyr in the Apollo 11, 12, 15, and 17 regions; Supplementary Table 1). This could result from the self-limiting formation nature of lunar regolith22, which leads to a progressively decreasing growth rate as regolith thickens over time, or reflect an elevated small impactor flux recently. Systematic simulations on regolith evolution in the CE-5 region will provide further insights into the underlying mechanisms.

Fig. 1: The counted fresh craters and estimated cumulative distribution of regolith thickness arcoss the CE-5 landing region.
Fig. 1: The counted fresh craters and estimated cumulative distribution of regolith thickness arcoss the CE-5 landing region.
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a Spatial distribution of 361 fresh craters with four morphological types: normal (red), central mound and flat-bottomed (green), and concentric (blue). The red star represents the CE-5 landing site (43.058°N, 51.916°W). The yellow region shows a secondary crater field, which is excluded from crater counting. The basemap is the CE-5 DOM generated from descent camera images superposed on a LROC NAC image (ID: M1437763435L). b Cumulative percentage of area with regolith thickness < \(T\) as estimated from the normal (red) and concentric (blue) craters. The shaded regions show the 1σ uncertainty range calculated from the SFDs of normal and concentric craters67, respectively.

Regolith growth modeling

The production, distribution, and transportation of lunar regolith are closely linked to the impact cratering process21,22. We have developed a Lunar Topography and Regolith Evolution Model (LTREM) to simulate the formation and growth of lunar regolith resulting from continuous bombardment and topographic degradation25,33. When each individual impact crater forms, we consider the fragmentation of bedrock during the excavation stage, the formation of a breccia lens during the modification stage, and the secondary cratering during the ejecta deposition process49 (Methods). LTREM can quantitatively simulate regolith growth process by accounting for various components, including contributions from impact craters of various sizes and origins (i.e., primary and secondary), crater morphologies, the buffering effect of the existing regolith layer, and topographic degradation. This enables a systematic evaluation of the key factors that govern the present-day regolith thickness observed on the lunar surface. The uncertainty in the simulated regolith thickness arises from three main sources: the populations of primary and secondary craters, the production of regolith by individual craters, and the topographic degradation rate (see Methods).

In this study, we utilize an observation-constrained LTREM with consideration of global-scale impact events to investigate the regolith evolution over a 2 × 2 km area around the CE-5 landing site from 2.03 Ga to the present. The minimum crater diameter is set to be 2 m (twice the pixel resolution). Smaller craters are generally unable to penetrate the pre-impact regolith layer to produce new regolith (Supplementary Fig. 13), thus hardly affecting the results. Specifically, the input crater populations include three parts: the global source craters of the CE-5 regolith, invisible eroded craters at the local scale, and secondary craters formed by primaries (Methods). Based on our previous investigations38,50, there are eight major source craters outside the P58/EM4 unit (Supplementary Table 3 and Fig. 2a), and 2171 craters inside P58/EM4 (Fig. 2b). In particular, all the visible craters within a 2 × 2 km study area across the CE-5 landing site were counted (Fig. 2c). There are 1223 in total with diameters ranging from ∼4 to 408 m. Their size-frequency distribution aligns with the NPF at hectometer scales but falls below the NPF at diameter smaller than 85 m (Fig. 2d). This indicates a large number of small, invisible craters that once existed on the lunar surface but have been erased by erosion processes10. The populations of these invisible craters can be accounted for by using a crater production function (for example, the NPF). As will be shown later, they contribute significantly to lunar regolith growth and therefore their actual production can be well constrained through regolith thickness. The formation ages of the most important contributors among the CE-5 source craters are estimated based on the degradation states or the size-frequency distributions of superposed small craters (Supplementary Table 3; Methods), which are incorporated in our simulation. To ensure statistical significance, all the subsequent modeling results for each parameter set are averaged over at least 100 realizations, as further realizations yield negligible changes in the outcomes (Methods).

Fig. 2: Distribution of the CE-5 source impact craters at global, regional and local scales.
Fig. 2: Distribution of the CE-5 source impact craters at global, regional and local scales.
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a Eight major source craters of the CE-5 samples with ages < 2 Ga outside the P58/EM4 unit. b 2171 source craters inside P58/EM4 unit. c 1223 visible craters within the CE-5 landing region of 2 km across. The two most important contributors are labeled in yellow: Xu Guangqi (C1) and C2. The red star represents the CE-5 landing site. d Size-frequency distribution of 1223 visible craters shown in (c) (red dots). The blue line and shaded region represent the CSFD constructed from the empirical density function (EDF)67 and its 1σ uncertainty, respectively. The 2.03 Ga isochron calculated from the NPF (black line) is shown for comparison (extrapolated to 2 m, shown as the dashed line). The population of small craters with \(D\) < 85 m fall below this isochron, indicative of a large number of erased craters.

We first present the results by taking the NPF as the crater production function. As shown in Fig. 3, while new craters continue to form in the simulation area, older craters degrade progressively, and some fade away eventually. Large primary craters such as Philolaus (72.22°N, 32.88°W; 71.4 km) outside the area also contributed to the development of local regolith through their distal ejecta and secondary craters. The regolith layer thickens over time and is continuously reworked, as indicated by infilling within crater interiors and the redistribution of ejecta deposits. The populations of primary and secondary craters produced in the simulation area over 2 billion years are shown in Supplementary Fig. 14. Since the formation of regolith thickness is most sensitive to small craters ranging from several meters to 10 s of meters (Supplementary Fig. 13)25, the presence of over 4 × 106 craters with D > 2 m ensures the statistical significance required to infer the impactor flux. As shown in Fig. 4a, the spatial distribution of regolith thickness is highly correlated with impact craters, ranging from nearly zero on the steep crater walls to more than ten meters in the crater interior (breccia lenses) and exterior (ejecta blankets) regions. The median regolith thickness across the simulation area is 2.90 ± 0.14 m when both the breccia lenses and ejecta are considered as regolith (1σ uncertainty; see Methods), and 1.27 ± 0.06 m if only the ejecta blankets are incorporated. The ejecta-only case represents the thickness of the fine-grained part within the regolith layer, which is significantly lower than that derived from crater morphology (3.6 ± 0.3 m). Therefore, we follow previous research22,29, considering both breccia lenses and ejecta as lunar regolith in the subsequent analysis, which can be regarded as, to some extent, an upper-bound estimate.

Fig. 3: An example model realization showing the evolution of topography and regolith thickness across the CE-5 landing region.
Fig. 3: An example model realization showing the evolution of topography and regolith thickness across the CE-5 landing region.
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a–c The surface elevation at model run times of 80, 90, and 1500 Myr (1950, 1940 and 530 Ma). d–f Topographic cross sections of the two-layered target across the blue lines in (a–c). The difference between 80 and 90 Myr primarily reflects the influence of distal ejecta and secondaries of Philolaus crater (72.22°N, 32.88°W; 71.4 km), which is outside the simulation area. The red arrows in (a–c) highlight a crater in different degradation states (see Supplementary Fig. 27 for a close-up view), while those in (d–f) indicate regolith infilling in the crater interiors and the redistribution of ejecta deposits in our model.

Fig. 4: Distribution and evolution of regolith thickness within the CE-5 landing region modeled using LTREM.
Fig. 4: Distribution and evolution of regolith thickness within the CE-5 landing region modeled using LTREM.
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a Spatial distribution of regolith thickness at the present from one typical model realization. The topographic cross section along the dashed black line is shown on the right, where the red and black lines represent the surface and bottom elevations, and the gray region represents the lunar regolith. b Cumulative contribution to regolith thickness as a function of distance from source impact craters to the CE-5 landing site. The surges correspond to the major source craters such as Xu Guangqi and C2. The shaded region shows the 1σ uncertainty range from 200 simulations (same as below). c Temporal evolution of regolith thickness from 2.03 Ga to the present, as characterized by the 25% quartile (blue line), median (black line), and 75% quartile (red line) across the study area. d Regolith growth rate versus time. The black, red, and blue lines represent the regolith produced by the observed, invisible, and secondary craters, respectively. The surges in regolith growth created by secondary craters correspond to the formation of large craters outside P58/EM4.

From a perspective of source craters, we find that 90.9 ± 0.1% of the regolith is generated by primary craters, with 50.2% from the observed craters and 40.7% from eroded primary craters. The remaining 9.1% of lunar regolith is produced by secondary craters. The simulations also show that the majority of the regolith at the CE-5 landing site originated within a 1 km radius (∼93.5%), with only 5.2 ± 1.8% of material being distal ejecta from large impact craters outside the P58/EM4 unit (Fig. 4b). For the first time, we incorporate the contribution from eroded craters to the regolith thickness and provide a more accurate estimate for the fraction of exotic materials in the CE-5 samples, which is consistent with laboratory analyses (∼5% exotic materials)51,52. In terms of the growth dynamics, the median and quartiles of regolith thickness grow smoothly with time in general, with several leaps associated with the formation of Xu Guangqi and three large impact craters outside the P58/EM4 unit (labeled in Fig. 4c). The invisible craters play a dominant role in regolith accumulation during the initial stage (the red line in Fig. 4d) while their contribution decreases gradually as regolith thickens, reflecting the regolith buffering trend. The contributions of observed craters show a similar, though less pronounced, decreasing trend at first, but begin to increase at about 600 Ma (the black line in Fig. 4d). This may imply a higher recent impact flux, but further evidence is required because the number of craters with age information (listed in Supplementary Table 3) is insufficient to ensure statistical significance. The overall effect of secondary craters on the regolith growth rate is quite weak (typically accounting for 1%; the blue line in Fig. 4d), except during periods when large impact craters formed and deposited ejecta into the landing region (for example, Philolaus, Harpalus, Sharp B, and Copernicus). This is primarily due to the substantially shallower excavation depths of secondary craters compared with primaries53. As a result, secondary craters play a dominant role in mixing the surficial regolith24 but contribute little to the formation of new regolith.

Evidence for an increased impactor flux

Through a large number of simulations with varying parameter sets, including the transient crater depth, secondary crater population, and topographic diffusivity (see Methods), the model prediction (2.90 ± 0.14 m) when using the NPF as the production function is always found to be lower than the observation (3.6 ± 0.3 m). Such a difference is statistically significant at the 2σ level (>95% confidence; Methods), indicating that it cannot be attributed to the variation of other factors but likely results from an underestimated production of small, primary craters. We further test three different crater production function hypotheses other than the NPF (PF 1). These include, a 1.33 times higher impactor flux than the NPF as supported by observations from the LROC NAC temporal image pairs (PF 2)15, an increase of impact flux at 400 Ma with a factor of 3.7 as inferred from the age of impact spherules (PF 3)17, and an increase of impact flux at 290 Ma with a factor of 2.6 as revealed by the ages of rocky craters (PF 4)54 (Supplementary Fig. 15). The probability distributions of regolith thickness across the study area modeled using these PFs are shown in Fig. 5a. The median regolith thicknesses are 3.45 ± 0.17 m (PF 2), 3.66 ± 0.18 m (PF 3), and 3.22 ± 0.15 m (PF 4), respectively (the dashed lines in Fig. 5a), all of which align with the observation within the 1σ uncertainty range. This indicates that the small crater production and the corresponding impactor flux (<10 s of meters) is most probably higher than that predicted by the NPF.

Fig. 5: Comparison of the modeled and observed regolith thickness.
Fig. 5: Comparison of the modeled and observed regolith thickness.
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a Probability density of regolith thickness modeled from LTREM using different impact flux models, including the NPF and those taken from Speyerer et al.15 (PF 2), Culler et al.17 (PF 3), and Mazrouei et al54. (PF 4). Both the ejecta and breccia lenses are regarded as regolith except for the results modeled using the NPF, where the case for ejecta only is also considered. The dashed lines represent the modeled median regolith thicknesses. The black line and gray region represent the median thickness and the 1σ uncertainty estimated from small crater morphology, which is 3.6 ± 0.3 m. b The median regolith thickness obtained from observation (the red line) and modeled from LTREM (the black and colored dots) using different impact flux assumptions. The shaded region and error bars represent the 1σ uncertainty range.

Such an underestimation of the small impactor flux could probably result from the scale-dependent nature of crater degradation, which is more pronounced for small impact craters10,11. Previous studies showed that the lifetimes of impact craters with diameters smaller than 20−50 m are no more than 50−125 Ma12,13. This implies that the record of very small impact craters is still incomplete even on young geological units such as craters Aristarchus (164 ± 1.4 Ma)54, Tycho (109 ± 4 Ma)6, and North Ray (50.3 ± 0.8 Ma)6, where crater counting was conducted to extend the diameter range of the NPF down to 10 m1,55. In contrast, the lifetimes of craters larger than several hundred meters are estimated to be several billion years9,13, whose populations are therefore not significantly influenced by degradation in the mare units. Consequently, the lunar chronology function, which was recently recalibrated through the radiometric age of the CE-5 samples and size-frequency distributions of craters with diameters >200 m in the CE-5 region, is minimally affected by the small impactor flux.

We further conduct a series of simulations by considering different cratering rates varying from 1 to 2 times relative to the NPF over the past 2 Ga. Within the 1σ uncertainty, the modeled regolith thickness aligns with that observed when the relative cratering rate ranges between 1.2 and 1.6 (the black line in Fig. 5b). The optimal match occurs at a relative cratering rate of 1.45, which could be the most probable flux of small lunar impactors. The aforementioned PFs 2–4 correspond to equivalent cratering rates of 1.33, 1.53, and 1.23 times the NPF during 2 Ga, respectively (the colored dots in Fig. 5b), all falling within this range. Such an elevated small impactor flux is significant for dating very young craters and volcanic units (for example, irregular mare patches56) and also implies higher regolith overturn and boulder breakdown rates, which can provide critical insights into the geological evolution of the Moon.

Information from the CE-5 regolith thickness alone can only provide evidence for an overall increased impact flux over 2 billion years, without the ability to further determine the timing when it started to increase nor whether the increase factor varied across different crater size ranges. As a preliminary investigation, we explore several possibilities regarding these two aspects. Based on the estimated ages of major source craters around the CE-5 landing site through their degradation states in this study (for example, C1–C12; Supplementary Table 3), the timing of this increase is estimated to be ∼600 Ma (the black line in Fig. 4d). Several independent studies also support an increase in recent impact flux within a similar time interval. For example, the topographic diffusivity, which reflects the flux of micrometeorite bombardment, was estimated to be higher over the recent 700 Ma than during earlier periods9. The ages of impact glass beads in the CE-5 samples were found to be concentrated in the latest ∼600 Ma57. Moreover, seismic observations of impacts on Mars detected by NASA’s InSight also revealed a higher production rate of small craters (∼1.1–3.0 times) at scales of meters to tens of meters at present58,59. If this is the case, then it indicates recent catastrophic asteroid disruption events in the source regions of lunar and martian impactors, for example the breakups of the parent bodies of L chondrites (470 Ma60,61) and the asteroid Baptistina (160 Ma62) in the main belt.

Alternatively, the elevated impact flux may have persisted during the past 2 Ga, with the increase being more pronounced for smaller impactor sizes. This aligns with recent observations that the power-law slope of the crater size-frequency distribution at tens of meters is steeper than that of the NPF (Supplementary Fig. 16). We performed additional simulations assuming two plausible steeper production functions (PFs 5 and 6; Supplementary Text 3 and Supplementary Figs. 17 and 18) and found that the simulated regolith thicknesses under both scenarios can match the observation. This suggests that the elevated impact flux could be skewed towards smaller impactor sizes, which is consistent with current understanding of the source and delivery mechanism of Earth-Moon impactors. That is, the kilometer-sized and smaller Earth-Moon impactors, which are sourced directly from near-Earth objects (NEOs), were fundamentally resupplied from the main belt primarily via the Yarkovsky and YORP (Yarkovsky–-O’Keefe–Radzievskii–Paddack) effects and orbital resonance from ∼3.8 Ga to the present63,64. Unlike collisions and gravitational perturbations, the Yarkovsky and YORP effects change the orbits of asteroids through thermal thrust in the long term, and are more pronounced for smaller asteroids64. The preferential delivery of smaller asteroids to the inner Solar System would result in more abundant small impactors in the NEO populations than those in the main belt3, thus leading to a steeper power-law slope for smaller impactor populations.

Nevertheless, even though the CE-5 region represents the most suitable study area currently available, the increased small impactor flux inferred from the regolith thickness at an individual site may still be affected by local stochastic variability. The broader applicability of our conclusions to the entire Moon remains to be validated in the future, for instance through seismic impact detections by the CE-7 seismometer65 and observations of lunar impact flashes during forthcoming missions66. As the accuracy of regolith thickness estimates improves and the understanding of target property diversity deepens, the framework developed in this study can be applied to a wider range of geologically representative regions, allowing for a more comprehensive assessment of the magnitude and temporal evolution of the small impactor flux on the Moon.

Methods

Regolith thickness estimation from small crater morphology

Optical imagery showed that small impact craters (D < 250 m) on the lunar surface exhibit four different morphological types: normal (bowl-shaped), central mound, flat-bottomed, and concentric39. Follow-up laboratory impact experiments and numerical simulations revealed that the strength discontinuity between the surface porous layer (for example, the lunar regolith) and coherent substrate is the primary factor controlling the crater morphology40. Specifically, a normal crater forms when the ratio of crater diameter (D) to regolith thickness (T) <4 ± 0.1 (1σ uncertainty); a concentric crater forms when D/T > 9 ± 0.6 (1σ uncertainty); a central mound or flat-bottomed crater forms when 4 ± 0.1 < D/T < 9 ± 0.640. Therefore, the size-frequency distributions of small, fresh craters with different morphologies can be used to estimate the distribution of regolith thickness in an area.

The morphological types of impact craters can be determined based on their shadow patterns in optical images27. The CE-5 digital orthophoto map (DOM; 0.5 m/pixel) generated from the descent images and four LROC NAC images (0.8−0.9 m/pixel) with different solar incidence and azimuth angles covering the study area (Supplementary Table 2) are primarily used for crater morphology identification. To enhance reliability, high-resolution descent camera images (<0.5 m/pixel) and the generated CE-5 DTM (0.5 m/pixel) are also utilized to assist in crater morphology determination. Impact craters less than ten pixels in diameter are excluded in the statistics because of their indiscernible internal structures and large relative errors in diameter measurements47. Due to topographic degradation, crater morphology may change over time (for example, from concentric to normal), and crater diameter also increases progressively12. Therefore, only fresh craters are considered in this study. They typically exhibit sharp rims, bright halos, and/or ray patterns, with very few superposed smaller craters. Impact craters formed on slopes (for example, superposed on the walls of larger craters) are also excluded because they are susceptible to the mass wasting process and tend to exhibit asymmetrical features.

We used the kernel density estimator and bootstrap method67 to estimate the size-frequency distributions (SFDs) of craters with different morphologies and the confidence intervals (Supplementary Fig. 12). The percentages of normal and concentric craters within each diameter range represent the area fractions of regolith thickness larger than D/(4 ± 0.1) and less than D/(9 ± 0.6), respectively. From all the measured craters of different sizes and morphological types, the distribution of regolith thickness in the study area can be obtained27. The 1σ uncertainty of regolith thickness was calculated by considering both the variation in range of the crater formation condition (D/T) and the SFD error. In principle, the cumulative distribution of regolith thickness can be estimated through both the normal and concentric craters and their results are generally consistent (the red and blue lines in Fig. 1b). However, because of the limited number of fresh craters at large diameters, the distribution exhibits noticeable fluctuations, particularly for concentric craters. Here, we adopt the result calculated from normal craters as the best estimate of median regolith thickness due to its smaller uncertainty.

For this approach, if a concentric, flat-bottomed, or central mound crater is misclassified as a normal crater (due to crater degradation or low-resolution imagery), the proportion of normal craters in a given diameter interval would increase. Because the proportion of normal impact craters indicates regions where the regolith thickness exceeds \(D/(4 \pm 0.1)\), this could lead to a higher median thickness (for example, 5 m35). In another approach for regolith thickness estimation through the inner and outer diameters of concentric craters44, the inner structures of small concentric craters cannot be recognized when low-resolution imagery is used. This would lead to biased crater samples that include only large concentric craters, resulting in an overestimate of the regolith thickness (e.g., 4–6 m45).

Lunar topography and regolith evolution model (LTREM)

LTREM simulates the formation and evolution of lunar regolith driven by continuous bombardment over geological timescales. It considers the impact fragmentation, ejecta deposition, secondary cratering, and topographic degradation process25,33. In LTREM, the lunar target is characterized as a two-layer structure, with a progressively growing fine-grained regolith layer atop the underlying coherent substrate (mare basalt in this study). Although complex internal layering within the regolith has been revealed by the Apollo drilling cores22, such microscale structure does not influence the overall regolith thickness. The two-layer simplification adopted by LTREM is based on the widely recognized impact experiments39,40 and simulations68, which have been demonstrated to be valid for regolith thickness estimation. For each impact crater, LTREM simulates the formation of its ejecta blanket and breccia lens during the excavation and modification stages, respectively. During this process, the existing regolith is redistributed, and new regolith may be produced if the transient cavity can shatter the underlying basalt. Generally, LTREM consists of three steps that are repeated for each time interval during the simulation: (1) crater production determination; (2) regolith generation and migration; (3) topographic degradation. Through LTREM, one can obtain the time-varying growth rate and spatial distribution of regolith thickness in an area of interest.

In this study, we employ an observation-constrained LTREM by considering both the global and regional scale impact events that affected the regolith evolution in a 2 × 2 km area across the CE-5 sampling site. Specifically, the crater populations consist of three parts: the observed source craters delivering materials to the CE-5 region (Fig. 2), invisible craters due to degradation, and secondary craters formed by primaries. Generally, we regard the observed source craters as primary craters because their SFD at the hectometer-scale aligns well with the NPF (Fig. 2d). Taking a minimum ejecta thickness of 0.1 mm as the screening threshold, a total of 956 source craters outside the simulation area38 are considered in the simulation. Within the study area, all the 1223 visible impact craters are counted and taken as model inputs (Fig. 2c). These observed source craters have known locations and diameters, but most have no age information except for the 28 major contributors listed in Supplementary Table 3. The undated craters would form at random times during a geological period from 2 Ga to the present. The populations of invisible craters are determined according to the crater production model extrapolated down to a minimum diameter of 2 m (Supplementary Text 4 and Supplementary Figs. 14b and 19). We note that the slope of the production function for craters <10 m may be steeper than that of the extrapolated NPF69,70. However, craters in this size range mostly garden rather than producing new regolith, and thus have a negligible effect on the simulated median regolith thickness. They would form at random times from 2 Ga to the present following the probability distribution of the selected impact flux model. Secondary craters were modeled based on the mass-frequency distribution of ejecta fragments and the scaling law of crater size49 (see Supplementary Text 5 for details), with key parameters validated through secondaries produced by the Orientale basin and several other primary craters49. This approach is more refined than using a generic global secondary crater flux (for example, ref. 71), as it accounts for the specific source craters that contributed ejecta to the CE-5 landing region. The key parameter is the power-law slope of the secondary crater SFDs, which is typically −4 as supported by multiple observations72. We also tested other potential values provided by different studies (−4.1415 and −3.573), which will be discussed later in the parameter sensitivity analysis section. Overall, the population of secondary craters used in this study is comparable with that in ref. 74.

Each impact crater is assigned a size-dependent topographic profile (for example, the decreasing depth/diameter ratio versus crater diameter) before being added to the lunar surface. The primary crater profiles are taken from the newly developed shape models of small fresh lunar craters ranging from 36 m to ∼1 km12,75, which include various morphological types and could capture any potential compression during the impact cratering process (Supplementary Text 6 and Supplementary Figs. 20 and 21). The shape models for sub-hectometer craters exhibit a volume-neutral characteristic (Fig. 6 in Zhang et al.25), and therefore small craters incapable of penetrating the existing regolith layer neither increase nor reduce the regolith. Secondary craters are assumed to be parabolic in shape with lower depth/diameter ratios than primaries due to their lower impact velocities (<2.4 km/s), which can be determined according to the distance from their parent primary craters (Supplementary Text 5). When an impact crater forms, we first simulate the opening of the transient crater during the excavation stage and then the collapse during the modification stage. The fragmentation and uplift of bedrock, redistribution of pre-existing regolith, and deposition of impact ejecta are implemented by updating the elevation of two-layer target according to the crater geometry. The crater addition with consideration of the complex pre-impact topographic relief is treated according to cratering dynamics, where hypervelocity impacts essentially erase the original terrain within the crater, whereas the lower-energy ejecta deposition allows the pre-impact surface beyond the rim to be partially preserved (“Crater formation on a two-layer target” in Zhang et al.33). The results of crater superposition using this method have been validated against observations based on LROC NAC DTM data (Fig. 2 in ref. 33).

During the crater formation process, breccia lenses and ejecta blankets on the crater interior and exterior regions are major sources of lunar regolith22, whose thicknesses can be constrained by the topographic profiles of transient and final craters. Since the shape models of final craters were established from high-resolution topographic data (NAC DTMs and SLDEMs), the main uncertainty arises from the shape of the transient crater. Previous laboratory experiments and impact modeling showed that the transient crater can be characterized as a parabolic cavity with a depth/diameter ratio of ∼1/321, which is adopted in our simulation. Different potential depth/diameter ratios are also tested to modify the transient crater shape and will be analyzed later.

The topographic degradation process is simulated using a diffusion model9, expressed as:

$$\frac{\partial h}{\partial t}=\kappa {\nabla }^{2}h\,,$$
(1)

where \(h\) is the surface elevation, \(t\) is time, and \(\kappa\) is the scale-dependent diffusivity, linked via:

$$\kappa \propto {D}^{\varphi },$$
(2)

where \(D\) is the fresh crater diameter and \(\varphi\) is the scaling factor11, which is typically 0.9. In LTREM, an equivalent diffusivity for the entire simulation area is employed because craters of different diameters are superimposed on each other. However, each location should really have its own diffusivity. According to the median crater size in this study (∼2.5 m), the diffusivity is selected to be 0.031 m2/Myr as determined from the scaling relationship of Eq. (2). We note that applying a uniform equivalent diffusivity across the entire simulation area could lead to an underestimation of the degradation rate for large craters and slightly alter the spatial distribution pattern of regolith thickness. However, different diffusivities tested show that this parameter has a negligible influence on the median regolith thickness (see Parameter Sensitivity Analysis in Methods), as the degradation process primarily redistributes rather than produces lunar regolith.

Model convergence

In our simulation, most of the craters are random in size, location, and/or formation age following the production function. However, although the modeled regolith thickness at a single pixel exhibits strong fluctuations across different realizations, the median thickness across the entire simulation area remains highly stable (Supplementary Fig. 22). This is because the diameters, locations, and ages of major source craters are already known and have been incorporated in our model. For example, Fig. 2 shows 2171 craters with known size and location, among which the 28 major source craters further have age information (Supplementary Table 3). Our observation-constrained Monte Carlo model effectively mitigates the randomness introduced by a large number of impact craters, resulting in outputs that converge within a narrow range. The simulation results show that the median regolith thickness across the study area stabilizes rapidly varying less than 0.01 m after ∼20 realizations (Supplementary Fig. 23a). The relative change induced by each new realization drops to less than 0.1% after ∼30 realizations (Supplementary Fig. 23b). Based on 100,000 bootstrapping samples, the standard error of the median regolith thickness averaged over 100 realizations was estimated to be 0.003 m, and the 95% confidence interval was 2.902–2.912 m (Supplementary Fig. 24). This uncertainty is negligible compared with the error introduced by model parameters (see Parameter Sensitivity Analysis). Other statistical parameters, such as the quartiles, also converge within a narrow range after several tens of realizations. To ensure the statistical significance, all the results provided in this study are the average of at least 100 realizations.

Parameter sensitivity analysis

LTREM includes a series of parameters describing the grid settings, impact flux, crater morphology, and topographic features. Essentially, lunar regolith is produced by repeated impact events, so the regolith thickness is primarily affected by the crater population and regolith production through individual impact craters. The former includes both the primary and secondary crater populations, where the primary impact flux is the parameter to be constrained in this study, and the secondary impact flux is governed mainly by the power-law slope of the secondary populations. The lunar regolith generated by an individual impact can be constrained by the topographic profiles of the transient and final craters. Since the shapes of final craters were directly extracted from the elevation data of fresh craters12,75, the transient crater depth is the main factor influencing regolith production. Topographic diffusivity controls the rate of lateral transport of lunar regolith and hence its spatial distribution, and therefore could also make a difference to the median regolith thickness. In summary, the SFD slope of secondary craters, transient crater depth, and topographic diffusivity are the three main factors influencing the simulated regolith thickness.

We note that target properties (for example, bulk density and strength) can also affect the size of each impact crater and thus the volume of regolith produced (that is, the volume of shattered bedrock, see ref. 25 for detail). Previous studies showed that the rocky crater populations and rock abundance can act as probes for the mechanical properties of the protolith36,37. Both indicate that the P58 unit does not exhibit any anomalies in target mechanical properties. Specifically, the frequency of rocky craters in P58 unit (3.6 × 10−3 km−2) is close to the median value (4.0 × 10−3 km−2) and falls within the interquartile range (3.2 × 10−3–4.8 × 10−3 km−2) among 15 different mare units across Oceanus Procellarum, Mare Imbrium, Mare Nubium, Mare Tranquillitatis, Mare Humorum, and Mare Serenitatis36. From our analysis, the median rock abundance of the P58 unit (0.34%) also aligns well with the temporal trend derived from 291 mare units across the Moon (0.33 ± 0.08%; Supplementary Fig. 8). Moreover, the size-frequency distributions of craters are directly taken as model inputs in this study and they are not derived from impactor populations and target properties using the scaling law76. Given that the crater populations (D > 200 m) in the CE-5 region and the radiometric age of the CE-5 samples align well with the lunar chronology function7, the target properties of the P58/EM4 unit are expected to be broadly consistent with those of other mare basalts, for example, the Apollo and Luna landing regions.

We first allow a single parameter to vary within its potential range while fixing other parameters to analyze its influence on the regolith thickness. As shown in Supplementary Table 4, a steeper (−4.1415) secondary SFD slope can increase the regolith thickness by 1.0%, and a shallower slope reduces the regolith thickness by 2.2%. When the transient crater depth/diameter ratio ranges from 3/8 to 3/1021, the median regolith thickness varies by up to 8.8%. The effect of topographic diffusivity is relatively minor, as setting it to zero or increasing it by a factor of 10 only leads to a variation of no more than 1.1% in the median regolith thickness.

We further estimate the overall uncertainty of the LTREM using the Monte Carlo method by simultaneously allowing the three parameters to take random values throughout the potential parameter space. The median regolith thicknesses from 1000 simulations are shown in Supplementary Fig. 25 with a minimum of 2.56 m and a maximum of 3.20 m, respectively. However, most results are concentrated within a narrow range with one standard deviation of 0.14 m, corresponding to a relative model uncertainty of 4.8%.

Statistical significance of the difference between observation and simulation

The observed and modeled regolith thicknesses are 3.6 ± 0.3 m and 2.9 ± 0.14 m (1σ uncertainty), respectively. Here, we employed the effect size and bootstrap method to evaluate the statistical significance of the difference. Effect size is a quantitative measure of the magnitude of the difference between two independent groups, which is defined as:

$$d=\frac{\left|\bar{{x}_{1}}-\bar{{x}_{2}}\right|}{\sqrt{{\sigma }_{1}^{2}+{\sigma }_{2}^{2}}},$$
(3)

where \(\bar{{x}_{1}}\) and \(\bar{{x}_{2}}\), and \({\sigma }_{1}\) and \({\sigma }_{2}\) are the means and standard deviations of two independent groups. According to commonly used guidelines for interpretation77, an effect size greater than 0.2, 0.5, and 0.8 is considered small, medium, and large, and values above 2 are regarded as huge. Based on Eq. (3), the effect size of the difference between the observed and modeled regolith thicknesses is 2.11, exceeding the uncertainties by more than two standard deviations. Besides, from 100,000 bootstrapping samples, the 95% confidence interval (2σ level) of the difference between the observation and simulation is estimated to be 0.06–1.35 m (Supplementary Fig. 26), which is completely above zero. In conclusion, the difference between the observed and modeled regolith thicknesses is statistically significant at 2σ level.

Dating of individual impact craters

For craters larger than 1 km in diameter, their ages are taken from previous studies45 through CSFD measurements on the ejecta blanket regions. For impact craters smaller than several hundred meters, their ages were estimated based on the degradation states. According to the morphological prominence (for example, the sharpness of the crater rim, depth/diameter ratio, inner wall slope), craters with different degradation states can be classified into three major types13: A (fresh), B (moderately degraded), and C (heavily degraded), and two transitional types: AB and BC. The ages of craters with different degradation states can be estimated according to their types: A and AB (<3% of lifetime), B (3−20% of lifetime), BC (20−50% of lifetime), and C (>50% of lifetime). The lifetime (\({t}_{{{\rm{life}}}}\), in Myr) of a crater refers to its survival time on the lunar surface (from formation to erasure), which can be calculated as13:

$${t}_{{\mathrm{life}}}=\left\{\begin{array}{l}2.5D\ \left(D < 160\,{{\rm{m}}}\right) \hfill \\ 8D-900\ \left(160\,{{\rm{m}}} < D < 1-2\,{{\mathrm{km}}}\right)\end{array}\right.,$$
(4)

where D is the crater diameter in meters.

For validation, we conducted a detailed degradation modeling for the 13 small impact craters listed in Supplementary Table 3 (C1−C12 and the unnamed crater). The topographic evolution of each crater is simulated based on the diffusion model (Eq. 1) using a scale-dependent diffusivity (Eq. 2). The optimal estimate of the crater age can be obtained when the modeled depth/diameter ratio matches the observed value extracted from the NAC DTM. We tested a wide range of potential initial diameters ranging from 0.625D to 1D, with both the initial crater topographic profiles of Yang et al.12 and Cai and Fa75 considered. As shown in Supplementary Table 5, the ages derived from modeling are generally consistent with those estimated through the degradation states.