SAI beats no SAI for temperature almost everywhere
Every SAI strategy is closer to the temperature target than SSP2-4.5 in 457 of 460 region–run pairs. The three exceptions are CESM2 runs over Greenland/Iceland and Northern Europe.
Interactive guide by Cindy Wang · Earth's Future, October 2026
Stratospheric aerosol injection meets its temperature target but does not restore the climate
Wang and colleagues use a distance-to-target metric, D, to measure how closely stratospheric aerosol injection (SAI) restores the 2050–2069 climate to an early-century target, using four SAI experiments in four Earth system models. At each location, D compares the average seasonal cycle, month by month, with the target's and divides the difference by natural year-to-year variability. This puts temperature, precipitation and extremes on one scale: the lower D, the closer to the target. D can be further decomposed into three parts: an offset in the annual mean, a difference in the size of the seasonal swing, and a shift in the timing or shape of the seasons. SAI removes most of the warming, but what remains is largely a change in the timing and shape of the seasonal cycle. SAI does much less for rainfall: the seasonal cycle of precipitation ends up almost as far from the target as with no SAI at all, and many of the remaining differences are too small to tell apart from natural year-to-year variability.
Wang, C., Visioni, D., Lee, W. R., Duffey, A., Wentland, C. R., Wheeler, L., Wagman, B., Turbeville, S., Watanabe, S., & Henry, M. (2026). Quantifying the effectiveness of multiple SAI strategies across different dimensions. Earth's Future, 14(10), e2026EF008696. https://doi.org/10.1029/2026EF008696. Open access under CC BY 4.0.
The setup
Three SAI strategies, four models
Recent generations of SAI experiments are designed to stabilize global-mean surface air temperature (GMSAT) at a reference climate: here 1.5 °C above pre-industrial, the 2020–2039 SSP2-4.5 climate in most runs (1.0 °C in one run). All SAI runs here follow SSP2-4.5, with SAI starting in 2035, and are evaluated over 2050–2069 against the same model's early-century SSP2-4.5 climate. The three strategies differ in where, when and how high they inject sulfur dioxide, and in which temperatures they control.
Strategy
- Injection site
- Sites of the other strategies
- Tropopause (schematic)
- Aerosol layer (schematic)
The metric
One dimensionless distance for every variable
To start, at each grid cell, average 20 years of output into a monthly climatology: twelve values, one per calendar month. Do this for the scenario and for the target. The distance to target, D, is the root-mean-square difference between the two sets of twelve values, divided by the target period's year-to-year variability.
D = RMSE / σbase, where
RMSE2 = mean over the 12 months of (xscenario − xtarget)2
Dividing by variability puts different variables and metrics (for example temperature, precipitation and extremes) on one scale. D = 1 means the typical monthly error equals one year-to-year standard deviation of the annual mean. D is computed on each model's native grid and then averaged over regions, so no regridding is needed.
Three parts of the error
Following Murphy (1988), the squared error splits exactly into three terms. μ and σ are the mean and standard deviation over the twelve months, and r is the correlation between the scenario and target seasonal cycles.
RMSE2=
(μs − μr)2Mean offset
+
(σs − σr)2Amplitude
+
2σsσr(1 − r)Phase / pattern
A mean offset means the whole year is too warm or too cold; more or less cooling could in principle remove it. An amplitude error means summer and winter are too far apart or too close together. A phase/pattern error means the seasons arrive at a different time or with a different shape.
D is very sensitive to timing. Where the seasonal swing is large compared with year-to-year variability, as for temperature over most extratropical land, a shift of a few days is enough to give D = 1.
Ideally, a perfect restoration would give D = 0. In practice it does not, because the climatologies themselves contain natural variability, as the next section shows.
Seasonal-cycle playground
An illustration at one grid cell, not data from the paper. Values are in units of σbase, the baseline's year-to-year standard deviation of the annual mean.
- Target climatology
- Scenario climatology
- Monthly error
Presets
Distance to target
D = 0.00
The noise floor
A perfect restoration still scores above zero
Each climatology averages only a few ensemble members over 20 years, so it contains sampling noise. Two climatologies drawn from the same climate still differ, and D counts that difference. This noise floor is higher for noisy variables and lower for larger ensembles.
Wang et al. (2026) estimate the floor for every model, experiment and variable. They resample years from the baseline ensemble to build a pseudo-target and a pseudo-scenario of the same sizes as the real ones, compute D, and repeat this 1000 times. A scenario's distance-to-target is statistically significant only if its D exceeds the 97.5th percentile of these values.
The toy simulator shows three things. A five-day timing shift is easy to detect when the seasonal cycle is strong (temperature-like) and hard to detect when it is weak (precipitation-like). Larger ensembles lower the floor. And pure noise lands mostly in the phase/pattern term, so a phase-dominated D is meaningful only when D is above the floor.
Noise-floor simulator
Variable
Target members
Scenario members
- Same climate, resampled (null)
- With a forced change
- 97.5th percentile of the null
Where pure noise lands in D2
Each of 1000 draws builds a target from (members × 20) synthetic years, compares it with each scenario member's 20-year climatology, and averages D over members, as in the paper. The noise here is synthetic. The paper resamples each model's own baseline years and averages D over many grid cells, which narrows its null distributions.
Result
SAI brings temperature closer to the baseline, but brings precipitation only a little closer
Each line in the chart is one run in 2050–2069. The gray dot is the distance-to-target for a future without SAI (SSP2-4.5), the colored dot is the distance-to-target for the same future with SAI, and the number on the right is the percent change. For temperature and temperature-related extremes, SAI shrinks the distance-to-target by about a third to four-fifths relative to a future without SAI. For precipitation, wet days and dry days, SAI shrinks it by only 0–20%.
- Temperature: 53–78% smaller globally (47–76% over land). In 10 of 11 runs, both globally and over land, the SAI distance-to-target is above its noise floor, so the remaining temperature difference is statistically significant.
- Warm and cold days: 51–77% smaller for warm days and 29–83% for cold days globally (39–72% and 34–71% over land). Most runs stay above the noise floor.
- Precipitation: 0–20% smaller globally (1–20% over land). The SAI distance-to-target is within the noise floor in 7 of 11 runs globally and 6 of 11 over land.
- Wet and dry days: 0–14% smaller globally. Over land, up to 15% smaller, and 1% larger in one run (CESM2 G6-1.5K-HiLLA). About half the runs are within the noise floor.
Within the noise floor means that the precipitation difference between the SAI run and the target is no larger than the difference between two samples of the same climate, given these ensemble sizes and 20-year windows. It does not mean that precipitation is restored: the runs are too short and too few to tell.
Domain
Variable
Distance to target with and without SAI
- SSP2-4.5, no SAI
- ARISE-SAI-1.5
- ARISE-SAI-1.0
- G6-1.5K-HiLLA
- G6-1.5K-SAI
- Within the noise floor
Result
Seasonal timing makes up most of the remaining temperature distance-to-target
The decomposition shows what kind of error makes up the remaining distance-to-target. For temperature over land, the SSP2-4.5 distance-to-target is almost entirely a mean offset: the climate is simply warmer. SAI removes most of that offset, and in most runs the phase/pattern term becomes the largest part.
For temperature, the timing errors that make up most of the remaining distance-to-target (the phase/pattern term) are likely due to changes in circulation and in the seasonal pattern of cooling. Sulfate aerosol cools most where and when sunlight is strongest, and it heats the lower stratosphere, which changes the atmospheric circulation. Earlier studies found that SAI can reduce the seasonal temperature cycle at high latitudes, with warmer winters and cooler summers (Jiang et al., 2019), strengthen the winter westerlies and warm Eurasian winters (Banerjee et al., 2021), and shift regional and monsoon precipitation (Simpson et al., 2019). Timing matters for seasonal risks, such as heat extremes arriving during the growing season.
Variable
- Mean offset
- Amplitude
- Phase / pattern
- Faded: within the noise floor
Land only, 2050–2069. Shares of D2 computed from the model output with the method of the paper's Fig. 4 (each grid cell's shares, averaged over members and land). D for the SAI runs from Fig. 3. The SSP2-4.5 bar uses the same target as G6-1.5K-HiLLA, as in the paper.
Regions
The SAI strategy closest to the target varies by region and climate model
Wang et al. (2026) average D over each of the 46 IPCC AR6 land regions (their Figs. 5–7, with MIROC-ES2H and E3SMv3 in the Supporting Information). This shows where SAI restores the target climate well, where it falls short, and whether one SAI strategy is best for certain regions.
Model
Variable
Map
Distance by region
Three patterns hold in all four models. First, SAI brings temperature closer to the target than SSP2-4.5 almost everywhere: every SAI strategy beats SSP2-4.5 in 457 of 460 region–run pairs, and the median regional temperature distance-to-target falls by 50–74%. Second, the remaining temperature distance-to-target is statistically significant (above the noise floor) in 288 of the 460 region–run pairs (63%). Third, the largest remaining temperature distances-to-target are over Northern Hemisphere land. The latitude band with the largest typical SAI distance-to-target is north of 50°N in CESM2 and MIROC-ES2H and 25–50°N in UKESM1 and E3SMv3. In UKESM1, MIROC-ES2H and E3SMv3, the tropics come closest to the target.
G6-1.5K-HiLLA injects at 60°N and 60°S in spring to concentrate the cooling at high latitudes, an approach studied as a way to preserve Arctic sea ice (Lee et al., 2021, 2023). Because its forcing is focused near the poles, it cools high latitudes more strongly than injection in the tropics and subtropics (Lee et al., 2023; Duffey et al., 2026), and it can overcool them relative to the target. Consistent with this, HiLLA is farther from the temperature target than G6-1.5K-SAI in 6 to 9 of the 10 regions north of 50°N in every model.
With SAI, regions also end up more similar to each other in how far they are from the target. The spread (interquartile range) of regional temperature distance-to-target across the 46 regions is 0.51–0.79 under SSP2-4.5 and only 0.15–0.40 with SAI. Without SAI, the mean offset is the largest error term in every region. With SAI, the phase/pattern term becomes the largest in 10 to 37 of the 46 regions, depending on model and strategy (CESM2, MIROC-ES2H and E3SMv3).
For temperature, the closest strategy changes from model to model. In CESM2, ARISE-SAI-1.5 is closest in 41 of 46 regions. In UKESM1 the three strategies share the regions (HiLLA 19, ARISE-SAI-1.5 17, G6-1.5K-SAI 10): ARISE-SAI-1.5 is closest in 8 of the 10 regions north of 50°N, HiLLA in 9 of the 18 tropical regions. E3SMv3 favors G6-1.5K-SAI (33 regions) and MIROC-ES2H favors HiLLA (28), although in MIROC-ES2H the two strategies differ by a median of only 0.03. Under the paper's robust-winner test (the map above), one scenario is robustly closest for temperature in 25 regions in CESM2, 21 in E3SMv3, 16 in UKESM1 and only 7 in MIROC-ES2H.
For precipitation, ARISE-SAI-1.5 is most often closest in CESM2 and UKESM1, but the differences between strategies are small: one scenario is robustly closest in only 5 to 13 of the 46 regions per model. 362 of the 460 regional SAI precipitation distances-to-target (79%) are within their noise floor, compared with 87 of 184 (47%) for SSP2-4.5. SSP2-4.5 is closest in one to three regions per model, and these are different regions in each model.
Northern land stays farthest from the temperature target
In every model, the latitude band with the largest typical SAI distance-to-target is north of 25°N. Greenland/Iceland and East Central Asia are each among the ten regions with the largest distance-to-target in three of the four models.
The polar strategy misses most at high latitudes
North of 50°N, HiLLA is farther from the temperature target than G6-1.5K-SAI in most regions in every model, which may partly reflect polar overcooling. In CESM2, HiLLA is also the farthest strategy in all 18 tropical regions.
ARISE-SAI-1.5 is closest almost everywhere
It has the lowest temperature distance-to-target in 41 of 46 regions and the most uniform regional distances of any run (interquartile range 0.15). Its two extra temperature targets, the interhemispheric gradient (T1) and the equator-to-pole gradient (T2), may help (Richter et al., 2022).
A latitude split between strategies
ARISE-SAI-1.5 is closest in 8 of 10 regions north of 50°N, HiLLA in half of the tropical regions. UKESM1's ARISE run is measured from a different target period (2014–2033) than its G6 runs (2020–2039), so compare them with care.
West Africa is the hardest region to restore
West Africa has the largest SAI precipitation distance-to-target in all four models, always above the noise floor. In 7 of 10 runs, including HiLLA in every model, its precipitation seasonal cycle ends up farther from the target than without SAI.
Implications
What the results mean for SAI research
The paper judges SAI by how much of the earlier climate it restores, across variables, seasons and regions, not only by whether it meets a global temperature target. Seen this way, the results carry several lessons for how SAI strategies are designed, compared and communicated.
Judge SAI by more than the global mean
Every run holds global-mean temperature near its target, yet land temperature is still detectably off target in 10 of 11 runs and in 63% of region–run pairs. Judging strategies by global-mean temperature alone overstates how much of the earlier climate they bring back. Evaluations should also report seasonally resolved, regional measures such as D.
More or less aerosol cannot fix what remains
With SAI, changes in seasonal timing and shape make up 40–65% of the land temperature D2, the largest share in 8 of 10 runs. Most of the rest is a local mean offset: some places end up too warm and others too cold. Changing the injection rate shifts the annual mean everywhere at once, so it does little for either error. Reducing them would likely require changing where and when aerosol is injected, or controlling regional and seasonal quantities directly.
Controlling more than the global mean pays off regionally
In CESM2, ARISE-SAI-1.5, which also holds the interhemispheric and equator-to-pole gradients, is closest in 41 of 46 regions and has the most even regional distances. Extra control targets appear to spread the benefit across regions, although ARISE also differs from G6 in injection sites and ensemble size.
Regional precipitation needs larger ensembles
SAI reduces precipitation distances by only 0–20% globally and by 2–14% in the median region, and 79% of regional SAI precipitation distances are within the noise floor. With 3–10 members and 20 years, these runs mostly cannot tell whether SAI restores, worsens or leaves regional precipitation seasonality unchanged. Regional precipitation conclusions, positive or negative, need larger ensembles or longer windows.
Some regions need targeted study
Where precipitation differences are detectable, they are not always improvements. In West Africa, the largest precipitation residual in every model, SAI moves the seasonal cycle farther from target than no SAI in 7 of 10 runs. Monsoon regions, where rainfall timing governs farming and water supply, deserve focused analysis in future SAI assessments.
Do not choose a strategy from one model
The closest strategy changes from model to model, and the four models agree on whether G6-1.5K-SAI or HiLLA is closer in only 5 of 46 regions for temperature. Comparing strategies requires coordinated multi-model experiments such as the GeoMIP G6 runs used here, and conclusions should be reported with the spread across models.
None of this says that SAI leaves the climate worse off than no SAI: for temperature, it is closer to the target than SSP2-4.5 in almost every region of every model. Instead, this study shows that a strategy designed to meet its GMSAT target still leaves a climate with a different seasonal cycle, and that with current ensemble sizes we cannot yet characterize how far precipitation is from the target in most regions. Nonetheless, the distance-to-target metric D provides a way to measure this gap and to compare SAI strategies across variables, seasons, regions and models.