Introduction

Ship emissions are the largest source of anthropogenic SO2 over the ocean, and they accounted for more than 10% of total anthropogenic SO2 emissions during the 2010s1. Ship emissions increase the total burden of aerosol particles and thus cloud droplet number concentration (Nd) in marine clouds. Increased Nd can modify cloud properties such as cloud brightness2, amount, and precipitation3, which leads to changes in Earth’s energy balance and creates a climate forcing. One of the clearest manifestations of these aerosol-cloud interactions is ship-tracks4, quasi-linear features embedded in marine low clouds that often appear brighter than background, unaffected clouds because ship-emitted aerosols increase Nd. They are excellent natural experiments to study aerosol-cloud interactions5,6,7.

However, it is challenging to estimate the magnitude of the total aerosol indirect forcing due to ship emissions (AIF-ship), and large uncertainty remains in its estimates. For example, Capaldo et al.8 estimates AIF-ship to be −0.11 Wm−2 with a global chemical transport model. Lauer et al.9 uses a global climate model to simulate the radiative forcing of ship emissions and estimates it to be between −0.6 and −0.19 Wm−2, depending on the emissions database used. Peters et al.10 estimates the radiative forcing to be −0.45 to −0.08 Wm−2 using a global model. Observational studies, however, generally show much lower estimates. An observational study aggregating manually detected ship-tracks from the “bottom-up" determines the AIF-ship to be  −0.4 to −0.6 × 10−3Wm−211. Peters et al.12 also fails to detect the effect of ship emissions from the “top-down" on large-scale satellite observed cloud properties upstream and downstream of several busy shipping corridors where characteristic low-level winds blow perpendicular to the corridors.

Estimates of global AIF-ship, therefore, differ more than 1000 times (−0.6 VS −0.4 × 10−3Wm−2). The large discrepancy has important implications for estimates of total AIF and climate engineering techniques such as marine cloud brightening (MCB)13,14,15. One important question is whether and how results from ship-tracks can be scaled up to estimate global AIF and AIF-ship. Moreover, ship-tracks are widely considered as analogues for MCB (ref. 16). Were AIF-ship much weaker than what is estimated in modeling results and instead agreed with what observational studies have shown, it would suggest MCB may not be viable given the small impact from large ship emissions. It is imperative to improve our understanding of this large discrepancy, which can help reduce the uncertainty of AIF in general and benefit MCB studies.

Recent advances offer tools to do so. Automated ship-track detection using deep learning techniques detects more samples than those using manual methods11,17 by orders of magnitude18,19. Global model results could bias towards higher AIF-ship values because they often simulate stronger increases of cloud liquid water path in response to added aerosols than observations (e.g.,15,17,20,21), which may help explain part of the discrepancy.

At the same time, top-down statistical analyses of climatological satellite retrievals provide novel observational estimates on the AIF-ship for the southeast Atlantic (SEA) region22, where low-level winds blow parallel to a major shipping corridor and keep pollution relatively spatially constrained, with results suggesting a strong regional forcing in line with that produced by climate models9.

Shipping fuel regulations from the International Maritime Organization that took effect in 2020 (IMO2020) have already resulted in a decrease in ship-track formation18 and detectable microphysical signatures in the SEA shipping corridor23. Combining estimated Nd changes from a chemical transport and machine learning models with meteorology-dependent cloud fraction and liquid water path adjustments from ship-tracks21, Yuan et al.15 estimate the AIF-ship due to IMO2020 to be +0.2 Wm−2, which is in better agreement with studies that use global models8,9. This new progress provides the opportunity to understand the disparity in previous estimates of AIF-ship. An accurate estimation of AIF-ship could also contribute to reducing the significant uncertainty surrounding total AIF24.

Here we combine recent advances in both bottom-up and top-down approaches to study the magnitude of AIF-ship in the SEA region. The goal is to elucidate the sources of discrepancy in the literature and provide approaches that could scale up insights from small-scale experiments. Section “Closure between bottom-up and top-down estimates” presents the data and method used. Section “Decomposition of forcing components” shows our results. Discussions and conclusions are presented in Section “Discussion and conclusions”.

Closure between bottom-up and top-down estimates

Method

More detailed description of our methods and data can be found in the Method and Data section. Here we briefly outline them. We derive Nd perturbations introduced by ship-emissions by multiplying the frequency of ship-track density and mean ΔNd in a ship-track in a bottom-up (BU) estimate. ΔNd from the top-down (TD) method is derived from geospatial krigging while it is modled in a chemical transport model by differentiating runs with and without ship emissions. AIF-Ship in BU is estimated by combining cloud adjustments with estimated ΔNd’s while in a TD method, it is also estimated by krigging. BU methods are differentiated by their sources of ΔNd that include TD, ship-track density, and modeled. We examine the closure of AIF-ship between BU and TD methods.

Results

Figure 1A shows the MODIS derived Nd map for the southeast Atlantic region during the September, October and November (SON) season when the impact of ship emission is most prominent22. The counterfactual Nd climatology map from TD (see Methods) without the influence of ship emissions is shown in Fig. 1B, and the difference between the observed and counterfactual values, interpreted as the causal effect of shipping, is shown in Fig. 1C. The core shipping lane, following the definition in Diamond et al.23, is highlighted as the area covered by white dots. The southern tip of this core lane, south of 15S, is less well defined in terms of Nd, possibly because the control Nd is even higher to the east of the core lane.

Fig. 1: ΔNd estimated using BU and TD methods.
Fig. 1: ΔNd estimated using BU and TD methods.The alternative text for this image may have been generated using AI.
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Spatial maps of A climatology of Nd with the shipping lane visible as a line of elevated Nd; B Counterfactual Nd from TD without the impact of ship emissions; C ΔNd from TD, i.e., Nd from A minus Nd from B; D ship-track frequency as a percentage of total observations; E ΔNd derived by multiplying ship-track frequency and Nd perturbation from each ship-track (BU-ST Nd).

Figure 1D shows the frequency of visible ship-track pixels as a percentage of all MODIS observations, fST. The peak frequency is around 2% for this region, more than 20 times higher than what is reported in ref. 11. fST shows a well-defined shipping lane and its distribution aligns well with the core shipping lane in Fig. 1A. These two distributions are independently derived.

Comparing the distributions of Nclim (Fig. 1A) and fST, we note that fST becomes near zero at around 9oS while the elevated Nclim values reaches further north at around 5oS, possibly due to unfavorable cloud types for detection at these tropical regions18.

Figure 1E shows ΔNd using BU-ST, which also features a well-defined shipping lane shape and aligns well with the Diamond et al.23 definition, albeit showing a broader lane. Its centerline shifts around 1o to the downwind (west) side at several latitudes. ΔNd from BU-ST peaks at 0.5–1 cm−3, an order of magnitude smaller than the TD ΔNd whose peak is around 10 cm−3. BU-ST likely underestimates the ΔNd because ship-emitted aerosols do not always form detectable ship-tracks. In addition, the “background" used (see Methods) is a mixture of actual background values and clouds affected by ship emissions that do not form visible ship-tracks. Both factors make the BU-ST density likely to severely underestimate ΔNd.

Next we compare estimates of AIF-ship in the SEA during SON season using the manually-logged tracks of Schreier et al.11, our BU-ST method (with ML-detected tracks), and our TD method as well as a hybrid approach taking the ΔNd values from TD and cloud adjustments from the ML-detected ship-tracks21. For the hybrid BU-TD approach, we use two functional forms of LWP and Cf adjustments: Adj;= f(Nd, Cf) or Adj = f(Nd), because Cf adjustment is more sensitive to the choice of these parameters and the two forms usually represent the upper and lower bounds15,21.

The results are shown in Fig. 2. Our BU-ST estimate is about an order of magnitude larger than the previous estimate from Schreier et al.11, but more than an order of magnitude smaller than that from TD (and thus also BU-TD), regardless of which adjustment functional form we choose. The order of magnitude difference between BU-ST and TD is in line with the estimated ΔNd difference between BU-ST and TD in Fig. 1. The order of magnitude difference between BU-ST and previous BU estimate is also consistent with the fST difference between BU-ST and11. TD and BU-TD estimate AIF-ship to be around –2 Wm−2 in the SEA during SON, with much of the uncertainty coming from cloud adjustments. Our results show that visible ship-tracks only represent  ~5% the total indirect forcing from ship emissions. They represent only tips of the iceberg.

Fig. 2: Climatological AIF-ship estimates from BU-ST, BU-TD-Hybrid, and TD during the SON season, as well as one year of ship-track detections using manual labels from ref. 11.
Fig. 2: Climatological AIF-ship estimates from BU-ST, BU-TD-Hybrid, and TD during the SON season, as well as one year of ship-track detections using manual labels from ref. 11.The alternative text for this image may have been generated using AI.
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The x-axis uses log-scale. Uncertainty for the BU methods is represented by the spread in the triangle markers, each representing a different set of background meteorology variables used to calculate the adjustments. Uncertainty for the TD method is quantified as the 95% confidence interval of simulated counterfactual fields for the Twomey effect only (dark red violin plot) and for AIF-ship including adjustments (light red violin); the black line and white circle represent the interquartile range and mean, respectively.

Decomposition of forcing components

In Fig. 3, we show maps of total AIF-ship and its components, i.e., the Twomey effect, the LWP adjustment, and the cloud fraction adjustment, using the BU-ST, BU-TD hybrid, and TD methods. BU-ST again estimates the lowest AIF-ship because of the ΔNd underestimation since not all emissions lead to detectable ship-tracks. Mean AIF-ship averaged over the shipping lane from BU-TD and TD are closer to each other at approximately  −2.5 Wm−2 and  −1.5 Wm−2, respectively, over the core corridor (C) but there are clear differences in their breakdowns and spatial distributions. The BU and hybrid results show uniformly positive cloud fraction adjustments (negative forcing) and negative liquid water path adjustments (positive forcing), whereas the TD results show a clear and strong north-south contrast featuring positive cloud fraction adjustments in the north (N) and negative LWP adjustments in the south (S). The net result is much stronger cooling in the northern region (10o–14oS) and much weaker cooling in the southern region (14o–18o) than that of BU-TD.

Fig. 3: Estimated AIF-ship maps.
Fig. 3: Estimated AIF-ship maps.The alternative text for this image may have been generated using AI.
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BU-ST is shown in the top row, BU-TD in the middle row, and TD in the bottom row. The Twomey effect, liquid water path and cloud fraction adjustments, and their net effective forcing are shown as the columns from left to right. Insets in the bottom row show the TD results broken down by averaging over the core corridor (C), 10o–14o S (N), or 14o–18o (S) (see Fig. S2 for more details).

In Fig. 4, we show estimates of forcing due to the IMO2020, i.e., AIF-IMO2020 during the SON season. For BU-ST, we calculate ΔNd due to IMO2020 by first calculating changes in fST between the climatological mean and 2020 and then multiplying it with ΔNd using equation 3 (see Method). For the hybrid BU-GEOS method, we use the modeled IMO2020-induced ΔNd from Yuan et al.15. In 2020, detectable ship-tracks strongly decreased in this region Yuan et al.21. Yet, BU-ST estimates total AIF-IMO2020 to be around  +0.11 Wm−2 within the shipping lane. That is again almost an order of magnitude smaller than the BU-GEOS and TD estimates of just under  +1 Wm−2. TD again displays a seemingly dipole pattern in the AIF-IMO2020, albeit with a substantial degree of noise from the limited temporal sampling22. BU-GEOS also has a slight and gradual north-south change in both the LWP and the Cf adjustments, but its magnitude is much more muted compared to the contrast in TD. Whereas the TD magnitude is dominated by the Twomey effect due to near-perfect cancellation between the liquid water path and cloud fraction adjustments, in BU-GEOS, the cloud fraction adjustment contributes substantially to the effective forcing. It is worth noting that in the broader SEA region, there are multiple shipping lanes and BU-GEOS estimates significant AIF-IMO2020 from them other than the one discussed in above figures. Their contributions put the overall AIF-IMO2020 in the broader SEA region stronger than only considering the central shipping lane Yuan et al.15.

Fig. 4: As in Fig. 3, but for the estimated AIF-ship map due to IMO2020 regulations.
Fig. 4: As in Fig. 3, but for the estimated AIF-ship map due to IMO2020 regulations.The alternative text for this image may have been generated using AI.
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Insets in the bottom row here represent core corridor values from the pre- and post-2020 periods and their difference (IMO effect; see Fig. s3 for more details on the inset.).

The decomposition and its spatial distributions still have important differences between BU and TD methods that need to be resolved.

Discussion and conclusions

Our results show that the forcing estimate based on explicitly detectable ship-tracks represent less than 5% of the total AIF-ship based on either top-down or hybrid methods with top-down or model-based microphysics and bottom-up macrophysical cloud adjustment estimates. Our closure study thus reveals that visible ship-tracks represent only the tips of the iceberg that is the total aerosol effective radiative forcing through ACI. Several factors can prevent ship emissions from forming detectable ship-tracks such as unfavorable cloud conditions18, weak emission rates that do not affect clouds enough to be visible, or background clouds that are already not aerosol-limited18,25. Heterogeneous background cloud fields, especially in deeper boundary layers, provide a particular challenge for detecting aerosol perturbations without prior knowledge of where the plume has spread26 and once-compact plumes spread into the “background" over time27.

Instead, it appears that ship emissions realize their forcing primarily through increasing Nd in terms of diffused and undetected plumes. Given the level of agreement between the TD and BU-GEOS methods regarding AIF-IMO2020, both the global AIF-Ship and its reduction post-2020 should be on the order of  −0.1 Wm−2, which agrees with global model estimates. This is also crucial for designing the deployment and assessing the impact of MCB; detecting and attributing the impact of an MCB experiment will need to consider the total effect instead of visible tracks. Virtual ship-tracks have been used to address the impact of undetected ship-tracks25. However, this approach has important assumptions and errors that affect the derived cloud adjustments28,29.

The consistent forcing estimates of AIF-IMO2020 from BU-GEOS and TD are encouraging because they are completely independent. The BU-GEOS and TD approaches thus also provide an independent check and validation for each other. Both approaches provide valuable estimates of AIF and the potential efficacy of MCB, at least in stratocumulus clouds.

It is also important to investigate and resolve the clear differences in geographic distributions of cloud adjustments between the two methods. In particular, LWP and Cf adjustments show major disagreements between the two approaches in terms of their geographic distribution and the very large uncertainties on the TD results complicate their physical interpretation. Several factors could contribute to this difference such as uncertainties in cloud retrievals, uncertainties and assumptions in the TD geospatial kriging algorithm, and uncertainty of scaling cloud adjustments at ship-track scale to larger scales. Cloud retrievals in this area can also be strongly affected by the presence of absorbing aerosols above low level clouds30, which could affect the pattern of cloud adjustment estimates from kriging if there is a systematic difference in above-cloud absorbing optical depth between the north and south of the domain. We leave further investigations into such factors to follow-up studies.

The BU and TD approaches analyzed here thus have complementary strengths and weaknesses. The overall strength of the ΔNd perturbation is not recoverable from the BU approach alone while the TD values and modeling results are based on observations and modeling of processes. However, the TD adjustment values are very poorly constrained compared to the relationships derived BU from visible ship-tracks. A combined TD-BU approach may thus offer the best path for quantifying AIF-ship in this region, if it can be shown that the adjustment relationships derived using visible ship-tracks generalize to undetected perturbations. Indeed, if it can be shown that cloud adjustments and their dependence on background cloud and environmental conditions based on large number of ship-tracks under diverse conditions21 offer good approximation of cloud adjustments at larger scales, hybrid methods combining cloud microphysical estimates with parameterized adjustments could prove useful not just for the IMO2020 problem15, but also historical aerosol indirect forcing more broadly.

To summarize, we conduct a closure study that compares bottom-up approaches with a top-down approach in estimating AIF-ship in the SEA. We show that visible ship-tracks represent only a small fraction, around 5%, of the total forcing. On the other hand, analyses of visible ship-tracks are valuable because they provide functions of cloud LWP and Cf adjustments to Nd. Our results resolve the outstanding large disparity in the literature between observation-based and modeling estimates of AIF-ship in the SE Atlantic, which should apply over other regions. The strong underestimate by previous studies is mostly due to two factors. First, detection of ship tracks is an order of magnitude lower than the current state of the art; second, the assumption that visible ship-tracks represent the majority of the impact is incorrect. Most of the forcing appears to come from diffusion of aerosols that do not form readily detectable ship-tracks.

Method and data

Bottom up methods

We study the impact of emissions in the SEA shipping lane using two sets of opportunities and estimate AIF-ship. The two opportunities are changes induced by IMO2020 and the long-term climatology. We compare estimates of AIF-ship from bottom-up approaches, a top-down approach, and hybrid approaches that combines bottom-up cloud adjustments with microphysical perturbations from the top-down method or a chemistry-climate model, to better constrain AIF-ship and understand the discrepancy in the literature. The top-down approach uses geospatial krigging to create counterfactual distributions of cloud properties with and without the influence of ship emissions (refs. 22,23), referred to as the TD method in the following. The difference between the observed and the counterfactual is taken as the impact of ship emissions on clouds.

In both the bottom-up and hybrid approaches, we combine cloud adjustments in liquid water path (LWP) and cloud fraction (Cf) derived from Yuan et al.21 with estimated perturbations in Nd, i.e., ΔNd, to estimate AIF-ship (refs. 15,17,21. Briefly, the scene albedo sensitivity to Nd can be determined by:

$${S}^{* }= \frac{dA}{d{N}_{d}}=\frac{d\left({A}_{ac}{Cf}_{total}+{A}_{s}\left(1-{Cf}_{total}\right)\right)}{d{N}_{d}}\\ \approx \, Cf\times S+\left(1-{Cf}_{high}\right)\times \frac{dCf}{d{N}_{d}}\times \left({A}_{ac}-{A}_{s}\right)$$
(1)

where A, Aac, Cftotal, As, Cf, and Cfhigh are the scene albedo, cloud albedo, total cloud fraction, surface albedo, low cloud fraction, and high cloud fraction, respectively. S is cloud albedo sensitivity to Nd:

$$S=\frac{d{A}_{c}}{d{N}_{d}}=\frac{{A}_{c}(1-{A}_{c})}{3{N}_{d}}\times \left(1+\frac{5}{2}\frac{dln\,LWP}{dln\,{N}_{d}}\right).$$
(2)

\(\frac{dln\,LWP}{dln\,{N}_{d}}\) and \(\frac{dCf}{d{N}_{d}}\) are derived from ship-track analysis Yuan et al.21. Together with observations of clouds, surface, and ΔNd, we can calculate AIF-ship. For more details, please refer to these two refs. 15,21.

The bottom-up and hybrid approaches differ in the sources of ΔNd. In the BU-ST, we use the frequency of visible ship-tracks and cloud properties of background and ship-track pixels to calculate ΔNd due to ship emissions. The derived ΔNd is then used to calculate the AIF-ship in the shipping lane. ΔNd can be estimated as

$$\Delta {N}_{d}={f}_{ST}(\overline{{N}_{ST}}-\overline{{N}_{BG}}),$$
(3)

where \(\overline{{N}_{ST}}\) and \(\overline{{N}_{BG}}\) are average Nd’s for ST and background pixels, respectively, and fST is fraction of pixels that are visible ship-tracks. Following a similar procedure, we can derive the difference between shipping lane and background in other variables. This BU-ST approach assumes the AIF-ship mostly comes from visible ship-tracks.

In the BU hybrid approach, we couple cloud adjustments to Nd perturbations from alternative sources including ΔNd from TD, dubbed BU-TD, and ΔNd simulated by NASA’s Global Earth Observing System (GEOS) with the Goddard Chemistry Aerosol Radiation and Transport (GOCART) aerosol module, using two separate neural-network models to convert modeled aerosol optical depth to cloud condensation nuclei (CCN) and CCN to Nd for IMO202015, dubbed BU-GEOS. In the case of the climatology, we use the same ΔNd derived from TD to calculate AIF-ship. It assumes that the cloud adjustments derived from ship-tracks can be applied to large-scale AIF calculations and that AIF-ship results from all impacts of ship emissions on Nd, including both those that form ship-tracks and those that do not7,18.

The uncertainty and assumptions of the BU methods can be found in previous studies Toll et al.17, Yuan et al.15, Yuan et al.21. To quantify uncertainty in this study, we calculate the LWP and Cf adjustments separately for a case based on binning the ship tracks by background Nd only and a case using 2D binning by background Nd and Cf. These binning choices produced the largest spread in estimates in previous work Yuan et al.15, Yuan et al.21.

Top-down method

The top-down method of universal kriging for the southeast Atlantic shipping corridor was introduced in Diamond et al.22 and refined in Diamond et al.23. Kriging is a classic geostatistical method31 in which values at unknown locations are estimated based on the spatial relationship between known values of a given variable. In universal kriging, a mean function is fit on the spatial location (here, latitude, longitude, their squares, and their product) and other co-variates (here, the cloud controlling factors of sea surface temperature, estimated inversion strength, and surface wind speed) and then errors are assumed to be spatially correlated based only on their distance from nearby values, as quantified via an empirical semivariogram. Grid boxes surrounding the SEA shipping corridor are treated as unknown and their neighbors, assumed to be unaffected by shipping, are used to fit the kriging algorithm that predicts a counterfactual field of what values would have looked like in the absence of shipping. Uncertainty is quantified via simulation of 5000 counterfactual kriged fields consistent with the fitted parameters. Because the creation of the counterfactual relies on interpolation from the background and errors are related to spatial variability of the background, relatively smooth background fields are needed for the counterfactual to be well constrained. Constraints are generally weak when only a few years of data are available. For further details and the uncertainties of the method, readers are referred to Diamond et al.22 and Diamond et al.23.

Data

We use cloud retrievals from the MODerate resolution Imaging Spectrometer (MODIS) instrument on board Aqua that include droplet effective radius (Reff), cloud optical depth (τ), Cftotal, Cf, and Cfhigh, We derive Nd and LWP using Reff and τ32,33. Both Level2 instantaneous and L3 month mean data are used here. Radiative fluxes, solar incoming fluxes, and cloud and surface albedo from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) version 4.1 are obtained to calculate AIF-ship34. Cloud fraction for the TD method is from the CERES/Aqua Single-Scanner Footprint monthly regional product34. visible ship-tracks from Aqua MODIS is used to calculate fST and cloud properties of polluted cloud pixels and background clouds19,21.

In BU-ST, we use visible ship-track masks and corresponding MODIS pixel level Nd to obtain ΔNd for the period between 2003 and 2019 with equation 3. ΔNd introduced by IMO2020 is taken as the difference in simulated Nd by a global chemical transport model between with and without IMO2020 fuel regulation’s impact on emissions15. Together they are used to calculate forcing using the cloud adjustment approach.